Erlend Alfnes

Hans-Henrik Hvolby

APS Feasibility in an Engineer to Order Environment

Keywords: Engineer to Order (ETO), One-of-a-kind production (OKP), Advanced Planning and Scheduling (APS), Enterprise Resource Planning (ERP)

This paper discus the feasibility of using advanced planning and scheduling (APS) in an engineer to order manufacturing company. The starting point is a company producing customised variants of standard products involving engineering, machining, sub-assembly, and final assembly operations. There is limited degree of parts commonality as the product variety is high with respect to material and size. APS is normally used in repetitive manufacturing companies but we argue that some ETO companies with a somewhat fixed planning setup could benefit of implementing an APS engine on top of their ERP system. One of the critical elements is, however, whether the company is able to formalise their tacit knowledge in the complicated planning processes to rules and options in an APS environment.

1

Introduction.

In this paper, we investigate the feasibility of using Advanced Planning and Scheduling (APS) in an engineer to order (ETO) company. APS is mainly used in repetitive manufacturing companies and has become the state-of-the-art within planning and control adding features such as comparing different planning scenarios before plan release. Manufacturing planning and control systems have gradually developed from simple materials requirements planning towards handling a large variety of core elements in a manufacturing company such as capacity planning, finance, human resources and payrolls [START_REF] Jacobs | Enterprise resource planning (ERP) -A brief history[END_REF][START_REF] Hsu | Development of a Cloud-based Advanced Planning and Scheduling System[END_REF]. Enterprise Resource Planning (ERP) and Advanced Planning and Scheduling (APS) systems have improved the integration of materials and capacity planning. While MRP systems merely calculated the materials and capacity requirements, APS systems have the ability to create a feasible plan way faster and better than previous systems which involved a number of iterations with manual adjustments [START_REF] Jacobs | Enterprise resource planning (ERP) -A brief history[END_REF][START_REF] Hsu | Development of a Cloud-based Advanced Planning and Scheduling System[END_REF][START_REF] Slack | Operations Management[END_REF]. APS require good input in terms of data quality and this is more difficult in an ETO company compared to a repetitive manufacturing environment [START_REF] Kjellsdotter | Problems in the onward and upward phase of APSsystem implementation: Why do they occur?[END_REF]. Further, APS systems are very expensive and for many small and midsize companies, it is a question as to whether a high investment in an APS system pays off [START_REF] Slack | Operations Management[END_REF].

Engineer-to-order products are engineered to the specific requirements of the customer order [START_REF] Haug | From engineer-to-order to mass customization[END_REF]. Each customer order results in a unique set of part numbers, bills of material, and routings for manufacturing. The engineer-to-order strategy is suitable for highly customised, capital intensive, one-of-a-kind products [START_REF] Adrodegari | Engineer-toorder (ETO) production planning and control: An empirical framework for machinery-building companies[END_REF]. An engineer-to-order strategy implies that engineering is involved in order fulfilment. The level of engineering adaption to customer requirements can range from new product development to minor modifications to an existing product [START_REF] Hendry | Competitive advantage, customisation and a new taxonomy for non make-to-stock companies[END_REF]. Engineering and manufacturing activities are often performed concurrently, and engineering changes can happen in all phases of the order fulfilment process, including manufacturing [START_REF] Wikner | Integrating production and engineering perspectives on the customer order decoupling point[END_REF]. The engineer-to-order strategy means a high level of uncertainty in terms of product specifications, demand composition, supply and delivery times, and processing times [START_REF] Grabenstetter | Developing due dates in an engineer-to-order engineering environment[END_REF].

The engineering process is an iterative process that aims to find the best solution together with customers and suppliers. Since the design of an ETO product is not realised until after the engineering process have been completed, the information available for planning is limited [START_REF] Seunghoon | SCP-Matrix based shipyard APS design[END_REF]. The final product structure, routings, and processing requirements are not known before detailed engineering is complete. Manufacturing will basically make a new product for each order, and the uncertainty and variations in processing times can be high.

2

Industry Case.

This study takes a starting point in a capital intensive Engineer to Order (ETO) case company producing large products with a low to medium engineering complexity. The product structure is deep and includes several sub-assemblies and parts. Manufacturing involves machining, sub-assembly, and final assembly operations. A typical product consists of more than 500 parts, where less than 20 pct. of the parts are engineered to order. There is limited degree of parts commonality as the product variety is high with respect to material and size leading to high inventory levels. The non-customised products stems mainly from one generic unit. Customer orders typically starts with a tender several months ahead. However, it is common that orders are changed in terms of delivery dates and engineering specification adjustments both before and during manufacturing. The design uncertainty is therefore fairly high through the whole order fulfilment process.

Most ETO products are constructed from a mix of parts with different level of customization. There might be cases where the entire product is engineered-to-order. Usually, a large share of the elements has standard design and are made-to-stock or made-to-order. Standard parts and assemblies that are required in low volumes are often made-to-order (or assembled-to-order) while standard parts required in higher volumes are made-to-stock.

To level production and to comply with short lead times, some production orders are initiated before the customer order has been fully specified. Forecasts of expected new orders are used to initialize purchasing to deal with long lead times, as well as production of standard items. High volume spare parts are produced to stock whilst low volume and customised parts are produced as rush orders due to the criticality of deliveries.

The company has developed a configurator to generate customer order specification including manufacturing and purchase order input. This involves selection of process flow and estimation of processing times. This enables the company to use an ERP backbone for planning instead of a project management application which some OKP companies favour. Compared to a repetitive manufacturing company this limits to some degree the quality of the detailed planning process due to the uncertainty of the processing times. The main planning processes are described in table 1.

Process

Sales and operations planning

Master production planning

Shop floor control

Time horizon 6-18 months before delivery 3-18 months before delivery 0-3 months before delivery Main objective Set delivery week for tenders, and balance mix to ensure sufficient capacity Set sequence in order to compress product throughput times.

Balance the flow during manufacturing and handle interruptions

Description

Supply planning of internal capacity (feasible mix pr. week) and deliveries from suppliers.

Rough-cut capacity planning on critical resources to find feasible product sequence pr. week.

Monitoring and control of the flow from fabrication throughout assembly.

ERPsupport

Estimate material and capacity requirements, and to issue long lead-time purchase orders.

Calculate material and capacity requirements, and to issue short leadtime purchase orders

Keep track of job status and inventory status.

Available data

Customer design and delivery preferences, ERP templates for similar parts in terms of BOMs, routings and processing times.

Final specifications in terms of BOMs, routings, and more accurate processing times.

Inventory status

Job status for some workstations (started, completed).

Manual decision making

Delivery due date setting. Capacity balancing. Expedite and postpone manufacturing due dates. Find alternative resources when overload. Make-or-buy analysis. Supplier selection.

Detailed capacity balancing on critical resources. Sequencing of order specific parts. Decide which MTS parts and service parts to produce to fill up slack capacity Handle delays in detailed design and purchased parts.

Resequencing of machining and assembly orders to reduce number of open orders and delays. Take countermeasures (e.g. overtime, reallocation of operators, re-allocation of parts between projects) to increase capacity or material availability.

Table 1: Main planning processes in the case company Sales and operations planning (S&OP) is performed to estimate delivery dates for bids and aftermarket requests. This is a collaborative process that involves other disciplines such as sales and engineering. Only an overall product specification and design exists at the bidding stage, so the material and capacity requirements will not be accurate. The planning involves a high level of human judgement and is mainly performed on standalone tools for rough-cut planning. A small but profitable share of the sales comes from the aftermarket, and these products often need to be delivered on a shorter notice than ordinary products. A main task for the planner is, therefore, to revise the plan in order to include aftermarket orders and still keep customer deadlines for all products.

With regards to master production planning and shop floor control, the main task for the planner is to find a mix of products per week that ensures sufficient capacity on bottleneck resources and, if needed, to add extra capacity in terms of overtime or outsourcing. There are large variations in work content from product to product, so the likelihood of capacity shortage on some critical work stations or machines is high.

A more accurate material requirement planning is performed after the complete and detailed BOM is handed over from engineering. Work orders are generated by the ERP system and released before start of production. The detailed BOM enables the planner to check the real capacity utilization for each critical resource and to make counter measures if required.

When production has started the progress is monitored by the planner to check that all fabricated and purchased parts are available in time for assembly operations. As the assembly stations receives a broad range of manufactured and purchased parts, the risk of delay is substantial. Identified challenges includes rush orders, engineering change orders, supplier delays, defects on incoming parts, lack of pre-fabricated materials, lack of personnel, set-up problems, lack of correct jigs or variations and uncertainty in processing times for customised parts. Further, shop floor operators may request changed sequences to increase efficiency on machine cells. The main task for the planner is to cope with all variations and create a flow of parts that reduces delays in assembly.

Summary of planning challenges

The high degree of customisation, the many engineering changes and the long lead times from suppliers forms a complicated planning environment. On top of this comes the challenges of after sales (rush) orders and a desire to level the production and assembly resources. The challenges are divided in a) short range planning and scheduling and b) long range sales and operations planning: a) Short range: Most importantly the plan must secure an assembly of products according to customer delivery dates ensuring a balanced capacity load. Different mix configurations generate large variations in work content and shifting bottlenecks. Rescheduling is initiated by customer changes, supplier changes, and shop floor challenges b) Long range: Most importantly the plan must include rough cut capacity considerations and supplier availability based on accepted orders and tenders. The final product structure, routings, and processing requirements are not known before detailed engineering is complete. At this stage, product data, processing times and lead times are estimates from a sales configurator which leads to some uncertainty regarding the capacity and supplier constraints. This includes forecasting on materials and capacity needs are somewhat difficult in a OKP environment due to the uncertainty not only on quantities and models but also actual configuration

3

APS feasibility in an engineer to order company.

Advanced planning systems utilize complex mathematical algorithms to forecast demand, to plan and schedule production within specified constraints, and to derive optimal sourcing and product-mix solutions. APS seeks to find feasible, near optimal plans while potential bottlenecks are considered explicitly. Unlike ERP, Materials and capacity issues are considered simultaneously and thereby avoiding ERP planning process with multiple recalculations to obtain the feasible plan both materials-and capacity wise. APS-systems aim at reducing costs of goods sold and to increase customer satisfaction by initiating production at the best time, using an optimal combination of manufacturing resources. This enables the generation of a far more realistic and reliable production plans than ERP systems [START_REF] Jacobs | Enterprise resource planning (ERP) -A brief history[END_REF]. When multiple objectives exist in a manufacturing environment, and most of these are in conflict with each another, an approach is needed for modelling and evaluating the trade-off among the conflicting objectives. Here two options exist, constraintbased planning and optimization.

Constrained based planning is based on hard and soft (or goal) constraints. Its distinguished feature is that the objectives can be stated as minimising deviations from pre-specified goals. Hard constraints are not overruled, whereas soft constraints are overruled, if necessary. As no plan optimisation objectives or criteria are considered, this option produces a feasible but not necessarily an optimal plan although a hidden plan objective function minimizing the plan costs is used to drive the planning and trade-off among the soft constraints.

Optimised plans are generated based on plan objectives, penalty factors, and constraints besides the hard and soft constraints. The constraint-based rules are exchanged with decision variables and penalty factors. As in the constraint based plan, hard constraints are not overruled, where soft constraints might be overruled if this reduces the total costs. As an example, overtime work will be preferred in order to avoid late delivery if the penalty for late demand is higher than the penalty for exceeding resource capacity. Industry studies show that optimised plans are rarely used in industry as it is difficult to convert all business decisions into a cost perspective (e.g. late delivery versus overtime work of reduced inventory turns) [START_REF] Kjellsdotter | Problems in the onward and upward phase of APSsystem implementation: Why do they occur?[END_REF].

As APS is an add-on to ERP, most APS implementations and case studies have been conducted in repetitive manufacturing or process industry (automobile, dairy, oil, steel industry, etc). We have only identified one study on APS in an ETO environment dealing with possible improvements in a shipyard by adding an APS module to the current ERP system [START_REF] Seunghoon | SCP-Matrix based shipyard APS design[END_REF]. As little help on this issue is found in litterature we have chosen to evaluate the pros and cons according to the challenges identified in the previous section

Planning challenges APS support

Multiple ERP-run's to adjust the manufacturing plan according to capacity (machines, manpower, and jigs), sequence, materials supply, assembly capacity and customer order lead times One single APS-run that satisfies all hard constraints and, if possible, soft constrains. The critical issue is the ability to model all the constraints which the planner takes into consideration, not least the estimated process times for new variants.

Due-day setting of tenders and new orders, based on rough cut capacity considerations and supplier availability. Product data and processing times are estimates from a sales configurator. Forecasting of materials in spite of uncertainties regarding final specifications.

Parts of this decision process are well supported by APS but the uncertainties in the engineering phase, as well as the complexity of the sales configurator, makes the value of APS support more doubtful.

The most valuable functionality is probably fast what-if scenarios.

Table 2: Short and long range planning challenges and possible APS support

The modelling and implementation aspects are discussed in the following section 4 Discussion and conclusion.

The paper has presented an in-depth single case study in an ETO company with the purpose of identifying the feasibility of implementing an APS module on top of their ERP system. APS functionality in terms of short and long term planning has been discussed both theoretically and in practice. However, an important factor for successful implementation of APS is a correct and consistent model [START_REF] Zoryk-Schalla | Modeling the planning process in advanced planning systems[END_REF]. The modelling aspects will, therefore, be briefly discussed in the following.

A supply chain or a manufacturing system can be simple, complicated, or complex [START_REF] Pathak | Complexity and adaptivity in supply networks: Building supply network theory using a complex adaptive systems perspective[END_REF]. Simple systems have a small number of well-understood components. Complicated systems have many components that interact through predefined coordination. Linear relationships between components that make the behaviour of the overall system predictable, and hence possible to model. Complex systems on the other hand, typically have many components that can autonomously interact through emergent, non-linear rules. This non-linearity makes it impossible to fully predict the overall systems behaviour by knowing its structure and components and hence makes them challenging to model [START_REF] Weichhart | Challenges and current developments for sensing, smart and sustainable enterprise systems[END_REF]. Inspired by [START_REF] Pathak | Complexity and adaptivity in supply networks: Building supply network theory using a complex adaptive systems perspective[END_REF][START_REF] Weichhart | Challenges and current developments for sensing, smart and sustainable enterprise systems[END_REF][START_REF] Zoryk-Schalla | Modeling the planning process in advanced planning systems[END_REF][START_REF] Ivert | When should advanced planning and scheduling systems be used in sales and operations planning?[END_REF] defining condensed data and decision variables [START_REF] Zoryk-Schalla | Modeling the planning process in advanced planning systems[END_REF]. An aggregated model will be less complicated and require less data but provide less detailed answers. 4. Data availability and quality. APS systems rely on a significant amount of detailed and accurate data. Basic data such as item data, bill-of material data, routing data and work centre data, as well as operational data such as inventory status, delivery date requirements and resource utilisation. These data has to be available and have sufficient quality in order to make a feasible plan. 5. Uncertainty and variations. APS systems are well-suited for complicated tasks where the demand and supply are uncertain and fluctuating [START_REF] Ivert | When should advanced planning and scheduling systems be used in sales and operations planning?[END_REF]. However, determining production targets and detailed schedules can be significantly influenced by interruptions such as defects, varying processing times, material changes, engineering changes, sequence-rules that are not followed, maintenance stops, rush orders, prototype work, etc. Such factors reduce the planning correctness, as well as frequent updates of the APS plan can create planning nervousness. Based on the analysis, the pros and cons of APS in an ETO environment and the 5 factors described above, it has been decided to develop tree demonstrators in terms of constraint-based models of 1) Sales and Operations Planning (due-date settings) and 2) Master Production Scheduling (assembly order sequencing) and 3) Shop Floor Control (machine cell job allocation). The outcome of this work will be used in the final decision making as to whether an APS system is likely to improve the current planning setup. The difficult parts of this work is to enrich the current machine data with alternative routes and process times as well as the tacit knowledge of planners and foremen on e.g. machine and operator capabilities which is currently not formalised in the ERPsystem but has a great impact of the useability of the plan. Based on the outcome of the demonstrator a final assessment of the feasibility of implementing APS in the case company will be conducted. In case of a fruitful outcome of the demonstrator, the critical elements of the model development will be used as requirements in the selection phase of the best-fit APS system.

Table 3 :

 3 the following table[START_REF] Slack | Operations Management[END_REF] have been constructed: Evaluation of APS support in the case company where (↑) indicates high degree of support etc. Inspired by[START_REF] Pathak | Complexity and adaptivity in supply networks: Building supply network theory using a complex adaptive systems perspective[END_REF][START_REF] Weichhart | Challenges and current developments for sensing, smart and sustainable enterprise systems[END_REF][START_REF] Zoryk-Schalla | Modeling the planning process in advanced planning systems[END_REF][START_REF] Ivert | When should advanced planning and scheduling systems be used in sales and operations planning?[END_REF] The planner's value of an APS model is briefly evaluated on 5 factors from table3above:1. Decision complicatedness. Complicated planning problems can be hard to solve because they include many objectives and elements, but they are addressable with rules and recipes and can be modelled. 2. Decision complexity. Complex planning problems involve many unknown and interrelated factors that must be modelled in terms of rules and processes in a model. A valuable APS model must capture sufficient aspects of the planning problem to provide correct decisions support. 3. Level of aggregation. Aggregation is a process for simplifying a problem by

	Factors	Sales and oper-	Master produc-	Shop floor
		ations planning	tion planning	control
	Decisions complicatedness	Medium (↑)	High (↑)	High (↑)
	Decisions complexity	Medium (-)	Medium (-)	High (↓)
	Data availability and quality	Low (↓)	Medium (-)	Medium (-)
	Uncertainty, disruptions, variations	High (↑)	High (↑)	High (↑)

Acknowledgements.

We would like to express our gratitude to the Research Council of Norway (MAROFF) for financial support as well as the engaged contribution from the case company representatives involved in this research.


Daryl Powell
email: daryl.john.powell@km.kongsberg.com

Eivind Reke
email: eivind.reke@losnorge.no

No Lean Without Learning: Rethinking Lean Production as a Learning System

Keywords: Lean Production, Toyota Production System, Total Quality Management

It's one of the most popular and most misunderstood business concepts of our time. Since the term Lean Production was first popularized in 1990, lean has come to mean very different things to different people. In this paper, we go back to the origins of Lean Production -an alternative business approach pioneered by Toyota Motor Corporation -and present insights into how Toyota actually developed a learning system to gain competitive advantage through the continuous development of people, rather than simply designing and optimizing an efficient production system. We draw on our observations from Toyota plants around the world and our discussions with various Toyota sensei, and present a framework for understanding lean as a learning system, not a production system.

Introduction

Lean Production has a research history spanning over 30 years. Yet, it is still a puzzle why some companies and CEOs who adopt Lean Productions tools and principles experience extraordinary business results, while others experience little or no improvement, at best exhibiting only marginal gains in operational performance.

In the Machine that changed the World [START_REF] Womack | The machine that changed the world[END_REF] the authors present Lean Production as a complete business system, consisting of five parts: Dealing with the customer, Designing the car, Running the factory, Coordinating the supply chain, and Managing the (lean) enterprise. Yet, Lean Production is still mostly associated with efficient production and operational excellence. Because the systematic learning practices of Toyota consist of tools and principles, it becomes easy for companies and CEOs who operate in the business paradigm of design-execute-optimize to turn these tools and principles into one-time improvements to their production system by interpreting Lean Production simply as a set of best practices that can be implemented to achieve operational excellence.

There are many different paths to new value creation, to realize products and services that will create value for both the customer and the producer. For example, one can introduce a product or service that is radically different to what has ever been offered before, and then optimize the delivery process for that particular product or service until defunct. On the other hand, it is possible to incrementally change an existing product to deliver more functionality at lower cost. Often, Lean is thought of as simply a method for optimizing flow in the design, manufacturing and delivery process, and has even been critiqued as a hinderance of innovation [2].

In this paper we present Lean as a different paradigm, based on the assumption that Toyota asked themselves a different question from the outset. Instead of asking; "how do we optimize the design, manufacture and delivery of our products?", they asked themselves; "how can we create, manufacture and deliver ever better products by learning and evolving from one change to another, always looking for the next step?" [3] This paper identifies four separate learning systems that each serve a different purpose. The basic questions underpinning these systems are: How to create a constantly evolving product line? What to keep and what to change when developing new products? How to constantly and consistently look for the next step? And how to make the managerial organization change its response as the company evolves?

Literature Review

After over 40 years of research into the operational and managerial practice of Toyota and 30 years of research on Lean Production there is an abundance of literature that presents these practices [cf. 3], the adoption of such practices into different companies or different industries [START_REF] Andersen | Lean construction practices and its Effects : A case study at St Olav ' s integrated Hospital , Norway[END_REF][START_REF] Andersen | Lost in translation: A case-study of the travel of lean thinking in a hospital[END_REF], how to implement these practices [START_REF] Achanga | Critical success factors for lean implementation within SMEs[END_REF][START_REF] Netland | Critical Success Factors for Implementing Lean Production : The Effect of Contingencies[END_REF][START_REF] Bhasin | Prominent obstacles to lean[END_REF], what to expect from adopting them [START_REF] Netland | What to Expect From a Corporate Lean Program[END_REF][START_REF] Karlsson | Assessing changes towards lean production[END_REF], and how these practices influence worker conditions [START_REF] Huxley | Three Decades of Lean Production: Practice, Ideology, and Resistance[END_REF][START_REF] Hasle | Lean and the working environment: a review of the literature[END_REF].

The research that has studied Lean Production and learning simultaneously has usually focused on the evolving understanding of Lean Production. For example, [START_REF] Hines | Learning to evolve -A review of contemporary lean thinking[END_REF] describes the evolution of the understanding of Lean Production, concluding that a separation of the strategic and operational aspects of lean is needed. Another example is [START_REF] Holweg | The genealogy of lean production Matthias[END_REF] which discusses the history of the International Motor Vehicle Program (IMVP) that gave rise to the term Lean Production, highlighting the key events of the development of car production and the major publications that chronicled them.

There is also a body of research on organisational learning in general [cf. 16]. Some of this research was based on case studies of Japanese companies in the quality management tradition [17]. However, this body of research has not explicitly looked at the practices of Toyota as a system of organisational learning per se.

Fujimoto, one of the first researchers who studied lean as a learning system [START_REF] Fujimoto | The Evolution of a Manufacturing System at Toyota[END_REF] described the evolutionary learning capabilities of the Toyota Production System, and how they built on the practices of American automakers and from their experiences with producing automatic looms. Toyota further developed a system that enhanced the learning capabilities of its people through smaller lot sizes, and the experimentation needed to develop in-house design and production capabilities [START_REF] Cusumano | Manufacturing Innovation: Lessons From The Japanese Auto Industry[END_REF].

By looking at Lean as a learning paradigm, the tools and techniques can be seen as accelerators for learning rather than as a means for achieving operational excellence, showing where and what we need to improve [START_REF] Ballé | The Lean Leap: Lean as a Learning Accelerator[END_REF]. The improvements are realized by the people working in the system, not by the tools themselves. In fact, Some Toyota veterans refer to TPS as the Thinking People System -a system for continuously developing people through problem solving [START_REF] Balle | The Thinking production system[END_REF] placing greater emphasis on the suggestion that "Toyota makes people before they make products" [22].

Toyota's practices are both "hard", allowing the company to constantly develop its technical know-how in design and manufacturing, and "soft"; an organisation open for criticism, where there is enthusiasm for improvements and a focus on developing employees [START_REF] Osono | The contradictions that drive toyota ' s success[END_REF]. These practices create a learning environment for self-testing and adoption [START_REF] Van Driel | Path dependence, initial conditions, and routines in organizations -The Toyota production system re-examined[END_REF] where the emphasis is not on process efficiency, but instead on developing the technical and creative skillsets of the company's workers and managers -skillsets that are critical for sustained innovation [START_REF] Ballé | Why Learning Is Central to Sustained Innovation[END_REF]. The emphasis on learning is what drives innovation in both design, engineering and manufacturing, and what allows Toyota to align the organisation by engaging "all the people, all the time, everywhere" [START_REF] Morgan | Designing the Future, 1st ed[END_REF].

Research Design

This is a conceptual paper based on an exploratory investigation of Toyota Motor Corporation (TMC), drawing new insights from the observations of the authors during site visits, from the available literature that describes Toyota's business practices, and from semi-structured interviews with current and former company employees from various functions in the organization -including product planning, product development, production and quality management. In addition, we draw on our practical experience with lean implementations in various industries and companies worldwide.

Lean as a Learning System with Four Distinct Sub-systems

Through our research (as a process of discovery), we have gradually come to recognize lean as a learning system. In this process of discovery, four distinct sub-systems emerged, each serving a different purpose:

• Product Planning (PP) system -how can we learn what products to improve or introduce next to make each customer a life-time customer? • Toyota Product Development System (TPDS) -how do we keep in touch with customers evolving needs and better understand what to keep and what to develop or discard in each product? • Toyota Production System (TPS) -How can we continuously look for the next step?

• Total Quality Management (TQM) -How do we develop the management and back-office practices that are needed to support the other three learning systems?

The Lean Product Planning system has more recently been exemplified by Apple, a company that, as if by clockwork, introduces new products each year in September. Some products will go through a full update of specifications and features, while others will have smaller, sometimes cosmetic changes made to them. Ever since Toyota and the other Japanese car companies decided to compete in all segments, as opposed to dividing the different market segments between them, Toyota has constantly sought to learn how to make a first-time customer a life-time customer; whereas other companies have sought to be efficient in their use of capital and assets by constantly looking to shed older products and / or move away from unprofitable market segments. Toyota has constantly evolved its range of products, while efficiency of capital and assets are driven by Value Analysis and Value Engineering (VAVE), a fundamental part of the Target Cost planning system [27]. The core learning challenge for the Product Planning system is how to constantly evolve the product line-up such as to never lose a customer.

When Toyota set out to design and develop its own automobiles, they did not start by licensing American or European models. Instead, they set out to learn how to design automobiles from scratch. Exemplified by the 12 generations of Corollas designed and manufactured for almost 60 years, the Toyota Product Development System (TPDS) builds on generations of acquired engineering know-how that is recorded and kept in the form of A3 reports and concrete technological learning curves [START_REF] Morgan | Designing the Future, 1st ed[END_REF]. Instead of creating a production system from scratch, Toyota set out to create a revolutionary learning production system that built on the industrial engineering breakthroughs of Ford, GM [START_REF] Fujimoto | The Evolution of a Manufacturing System at Toyota[END_REF], and German aircraft manufacturers [START_REF] Holweg | The genealogy of lean production Matthias[END_REF]. However, instead of just adopting best practices, we believe that Toyota developed its production system practices by continuously looking for the next step. First, by mechanically connecting each process with its direct customer through Just-in-time and the Kanban system in order to foster continuous improvement through respect for people and full worker participation [28]. Second, by reducing changeover time in order to reduce batch sizes and reduce the lead-time between order and delivery on each internal Kanban; and third, by creating a system of visual control (Andon) to stop and fix defects at the point of discovery [START_REF] Ohno | Toyota Production System: Beyond Large-Scale Production[END_REF]. Indeed, from our discussions with current and previous Toyota employees, we understand the core learning challenge of this system is satisfying the conditions of basic stability, just-in-time, jidoka, and employee satisfaction by encouraging the constant search for the next step of lead-time reduction, flexibility-enhancement, cost-reduction and quality-improvement, made possible by the continuous development of all employees, at all levels. This will lead to higher customer satisfaction.

Finally, after discovering that the rate of quality improvement did not keep up with the rate of productivity improvements, Toyota accepted the challenge from Ishikawa and Deming to build quality into the product at the design stage, by creating a system of quality assurance, rather than inspecting poor quality out of the system after production [START_REF] Ishikawa | What is Total Quality Control?: The Japanese Way[END_REF]. This Total Quality Management (TQM) system evolved from the early 1960s into "The Toyota Way" [3] and represents the fourth learning system. The core learning challenge of this system is how to support the development of zero defect thinking amongst managers and back office staff -in addition to front line associates.

Conclusions

Based on the findings, we are able to reframe Lean Production as a learning system, consisting of four distinct sub-systems (see Fig. 1). The sub-systems are by no means discrete but are profoundly integrated and intertwined throughout the organization as an organic entity. The learning sub-systems described herein consist of both principles and tools that aim to deepen thinking and experimentation. Understanding and adopting both is critical to the success of the lean enterprise. Ignoring the principles and simply copying the tools and adopting them as best practices often leads to unsatisfactory results and discontinued lean implementations, yielding little learning and at best offering only point optimization. The learning system as presented in this paper represents the findings from looking at Toyota's principles and practices together from the lens of a learning paradigm. With the continuous development of people at its core,

Product Planning System Toyota Production System

Toyota Product Development System

Total Quality Management System

Lean Learning System such a learning system promises to build improved organizational capabilities through a resolute process of continuous experimentation and learning.

We suggest that this article has implications for both theory and practice. Firstly, with regard to theory, we reframe Lean Production as a learning system, by drawing on insights from Toyota Motor Co. as the de facto exemplar of the Lean Learning System. This promises to help academic researchers to understand the real reasons for the success of Toyota -a company that exhibits the sales volumes of Volkswagen combined with the 'boutique' profitability of BMW.

Secondly, for practice, we suggest that by rethinking Lean Production as a learning system to continuously develop people (throughout the entire enterprise not just factory floor operations) through promoting structured problem solving and improvement using deep thinking, reflection and experimentation, organizations may be better prepared to realize the true potential of a successful lean transformation, reducing the otherwise high rate of failure reported for so-called "lean implementations". This is achieved in practice by actively discovering what one needs to learn to solve the next problem, rather than simply planning to implement the next best practice from the lean toolbox.

Understanding that lean is not a production system but rather a system for continuous improvement and learning is essential for business success in the future. After all, improvement without learning is not lean thinking [START_REF] Netland | The Routledge Companion to Lean Management[END_REF].

  The core learning challenge for this system is to discover what to keep and what to change (Approx. 70% of an existing product remains untouched in the next version [27]).

Figure 1 :

 1 Figure 1: Lean Learning System: Four Distinct Sub-systems


David Görzig

Susann Kärcher

Thomas Bauernhansl

Capability-based Implementation of Digital Service Innovation in SMEs

Keywords: Service Development, Innovation, Capability-based, Digitalization

In order to be successful in the market in the long term, enterprises must not only continuously optimize their operations but also constantly innovate. It is necessary to develop radically new digital services which disrupt their existing business model. For small and medium-sized enterprises (SMEs), it is a major challenge to put the generated solutions into practice. They have to cope with digitalization while having limited resources. The presented paper starts by examining the challenges for SMEs in the context of digitalization. Thus, an analysis of the approaches used in practice for implementing digital services in 36 SMEs is carried out. Essential differences between start-ups and established SMEs are identified. On this basis, a capability-based, agile methodology is presented which supports enterprises in advancing newly developed, digital services from prototype status to the customer's environment. Finally, the methodology is put into practical application within an innovation project in an SME.

Introduction

In the context of digitalization, new service-based business models are developed that confront established market actors with major challenges [START_REF] Bauernhansl | Geschäftsmodell-Innovation durch Industrie 4.0. Chancen und Risiken für den Maschinenund Anlagenbau[END_REF]. Physical products are transformed into digital services that adapt to the customer's individual context. In order to remain competitive, established enterprises must succeed in digitally transform their product portfolio and transfer the resulting changes into an operational business. This includes the deep integration of people and technology as well as high customer involvement. [START_REF] Lusch | Service innovation. A service-dominant logic perspective[END_REF] Most challenges usually arise during the transition from the first demonstrators to the operating service system at the customer's site. [START_REF] Ward | Success and Failure in Transformation. Lessons from 13 Case Studies[END_REF] Small and medium-sized enterprises (SMEs) have to face these challenges with a lack of financial resources and competencies. For this reason, they have to be particularly efficient in the application of their resources. [START_REF] Görzig | Approaches for the Development of Digital Products in Small and Medium-sized Enterprises[END_REF] The objective of this paper is to present a methodology for advancing digital services of SMEs from prototype status to the live production environment. As a research methodology a design science approach is applied. First, the problem is formulated in chapter two. Then, a capability-based methodology is invented and finally applied and reflected in a first use case. This paper describes just the first iteration. The methodology will be continuously developed in future projects. [START_REF] Recker | Scientific Research in Information Systems[END_REF] 2

Digital Service Innovation in SMEs

In order to be able to examine the processes of the implementation of digital service innovation in SMEs more closely, the necessary terminology must be defined first. A service is a process in which resources (e.g. goods, knowledge and skills) are applied for the benefit of others or oneself. Thus, the focus is no longer on the physical product, but on the benefit achieved. [START_REF] Lusch | Service innovation. A service-dominant logic perspective[END_REF] Innovation is a phase of technical ontogenesis. It starts with cognition, the scientific investigation of unknown natural phenomena. If the inventions based on this are technically implemented and brought onto the market, the term "innovation" can be used. [START_REF] Ropohl | Allgemeine Technologie. Eine Systemtheorie der Technik[END_REF] The term 'digital' covers gathering, storing, processing, providing and using information electronically with the help of information technology (IT). [START_REF] Lusch | Service innovation. A service-dominant logic perspective[END_REF] Important methodologies for the implementation of digital service innovations are for example agile approaches like Scrum. [START_REF] Schwaber | Agile Software Development With Scrum[END_REF] In this paper, the implementation of the innovation is examined in particular. Technical aspects, as well as the requirements of employees and customers, are considered. The process of invention and the actual market launch are not taken into account.

Analysis of Digital Service Innovation in SMEs

The approach presented in this paper focuses on SMEs which act as digital service providers. SMEs can be characterized as enterprises with fewer than 250 employees and a turnover of less than 50 million euros [START_REF]European Union: User guide to the SME Definition[END_REF]. They have considerably fewer resources to implement service innovations. SMEs lack investment capital, which leads to increased pressure to succeed in innovation projects. Besides, they frequently do not have the competencies required for the realization of digitalization projects. [START_REF] Görzig | Approaches for the Development of Digital Products in Small and Medium-sized Enterprises[END_REF] For a more in-depth analysis, it is necessary to examine the current methodology of SMEs. Therefore, the following section analyzes how SMEs are currently dealing with the challenges in the implementation and introduction of digital services. It is based on an analysis of the funding measure "Industrie 4.0 Testbeds for SMEs", which offers the opportunity to advance existing inventions towards market maturity with the help of shortterm testing and development activities in research institutes. In 2018, a total of 36 SMEs who participated in the funding measure were interviewed in a semi-structured manner about their processes in service innovation. The SMEs belong to the information and communication sector (13), the manufacturing sector [START_REF] Homann | A business-oriented foundation for service orientation[END_REF], the scientific and technical services [START_REF]European Union: User guide to the SME Definition[END_REF] and other sectors [START_REF] Recker | Scientific Research in Information Systems[END_REF]. The main differences in the implementation and introduction procedures can be observed between start-ups and enterprises that have been established on the market for a long time. In the following, these differences are further detailed. The results are summarized in Table 1.

Start-ups. 14 out of the 36 analyzed enterprises can be characterized by the fact that they are operating on the market for less than five years. All of them are very focused on the development and operation of just a single service innovation. The implementation is very methodical. Based on an elaborated business model, agile approaches (e.g. scrum) are used in eleven of the start-ups for operational implementation of user stories. If there are existing contacts, lead customers are strongly involved in the development activities in ten of the enterprises. However, most start-ups are technology-driven. The know-how required for implementation is systematically built up. Development and operations of the product are supervised by the same people, which makes an internal product launch unnecessary.

Established SMEs. The SMEs of this group have been on the market for an average of 23 years. They have already well-established physical products and services. Only six of the analyzed enterprises are developing a completely new range of services. 16 of the 22 enterprises are trying to further develop their existing range of products to digital services. The implementation of the strategy and the development process in all enterprises are strongly driven by the managing director and are not explicitly planned. Mostly, a rough and technology-based vision was formulated, which addresses a clearly defined customer need. Based on this, a first prototype is developed. Customer feedback only takes place at the end of development. (Waterfall model) Generally, only little methodical support was applied in the investigated enterprises of this group. The execution is mostly carried out by the R&D department. The projects are realized in groups of two or three employees. Only five projects involve employees from operations. Often, the necessary competencies for development are only available at partners like research institutes or software companies.

Requirements for a Methodology to Implement Digital Services

In summary, there is a clear difference between established enterprises and start-ups. Start-ups follow agile approaches to identify customer needs and develop digital service innovation. In this way, they are continuously approaching customer needs. Established companies have deficits in their methodology. However, through their experience and deep inside to customer processes, they are able to identify highly relevant customer issues. What they need is an approach that supports them in formulating their digital service innovations clearly understandable and adaptable to the fast-changing customer requirements. To support such an agile approach, a central communication element is necessary, which meets the requirements of both, operations and development. Therefore, it has to be understandable without background knowledge, but also offer space for detailed considerations. Capability-based approaches can meet these requirements. Since they are not technology-oriented, but based on specific goals and benefits, capabilities link strategy, development and operations holistically. Thus, a capability-based solution approach will be pursued in the following.

Capability-Based Implementation of Digital Innovations

In this section, initially, the term capability is defined shortly. A detailed discussion can be found in [START_REF] Sandkuhl | Capability Management in Digital Enterprises[END_REF]. Afterwards, a methodology for the development of digital service innovation in four steps is presented.

Capability Definition

Business capabilities are abilities or capacities that a business may possess or exchange to achieve a specific purpose or outcome [START_REF] Homann | A business-oriented foundation for service orientation[END_REF]. Ability refers to the level of available resources like people, hardware and software needed for the performance of a process [START_REF] Homann | A business-oriented foundation for service orientation[END_REF][START_REF] Aldea | Capability-Based Planning WP. The Link between Strategy and Enterprise Architecture[END_REF]. The capacity of a capability describes the scale of the outcome. [START_REF] Bērziša | Capability Driven Development[END_REF]. In order to model capabilities based on this definition, they are regarded as a system in the following. This results in an inner and an outer view to describe capabilities.

The outer view describes the relationships among the capabilities of the value creation system. This includes the capabilities of the own enterprise, but also those of partners and customers. In this black-box description, it can be distinguished between input, output and context. The input describes the form and the type of the required variables for generating the capability. (e.g. information, materials). The output describes reliability, accuracy, scale and form of the results of a capability. (e.g. the regular provision of specific information via a defined interface) The context describes the boundary conditions under which the capability is realized. This might include a specific customer environment, a defined time frame or the available financial resources. In summary, the outer view defines the required capability performance. This definition can be made by describing specific scenarios or by a collection in a table.

Moreover, capabilities have an inner structure. This can be described on the one hand by decomposing capabilities into sub-capabilities. On the other hand, they are characterized by a process which is enabled by resources. Basically, a distinction can be made between the resources people, software and hardware. Each of them is linked to the process. Figure 1 summarizes the elements of capabilities. Further capability-based approaches can be found in the information systems literature. [START_REF] Sandkuhl | Capability Management in Digital Enterprises[END_REF] Another approach can be found in military research. [13] A major hurdle in both approaches is their large scope. This makes it difficult to implement them in SMEs.

Implementation of Capabilities

The presented approach is based on existing agile procedures which enable a rapid response to changes in the environment such as new customer or employee requirements [START_REF] Uebernickel | Design Thinking -Das Handbuch[END_REF]. It consists of four steps, which are performed iteratively. First, the required capabilities are derived from the aspired service innovation and collected in a backlog. This is followed by the steps 'finding ideas', 'prototyping' and 'testing'. Fig. 2 gives an overview of the approach. The individual steps are described in detail in the following.

Fig. 2. Approach for capability-based service innovation

Backlog. The aim of this step is to identify the individual capabilities and their objectives. As described above, this paper starts after the invention of a new digital service. Ideally, the idea is detailed in a business model and translated into the required business capabilities. A comparison with the capabilities already available in the company follows to identify capability gaps. Missing capabilities and their requirements are documented, for example in a table. It is crucial that the outer view is first elaborated for each capability. This forms the boundary conditions under which the capability can later be used operatively. Moreover, the objectives, as well as the reliability and accuracy with which the capability must be performed, are defined. Furthermore, the timeframe of the capability deployment and the required capacity of each capability are defined. This includes a description of the extent to which the capability must later be implemented and what financial resources are available for it. The results for each capability are stored in the backlog.

Finding Ideas. The aim of this step is to generate and select implementation alternatives for capabilities. Therefore, the capabilities are taken from the backlog. First, it must be analyzed whether it is sufficient to adapt to existing capabilities. If this is not possible, new capabilities have to be developed. Therefore specific resource combinations are stored. Creativity techniques such as brainstorming are used. A capability can be generated in different ways. For example, a different degree of automation can be set. The generated capability alternatives are compared using a cost-utility-analysis, which enables a joint consideration of costs and benefits. A suitable capability alternative is selected. The other proposals are documented for later iterations.

Prototyping. The aim of this step is to quickly create capability prototypes by implementing the resources. These prototypes are developed in several iterations of finding ideas, prototyping and testing. In the first iterations, this can be done for example by simple storytelling or mock-ups. Requirements for people, hardware, software and interfaces can be further detailed. In later iterations, the prototypes are implemented with simple hardware, such as Arduinos or Raspberry PIs, to carry out the tests quickly at low costs. In the last step, the capability is converted into practicable hard-and software. At the same time, the competencies of the employees are gradually being developed. Therefore, education activities are systematically planned based on the required business capabilities.

Testing. The aim of this step is to test the previously generated capability prototypes with the intention to quickly generate feedback. Thus, the prototypes are immediately tested by employees and customers. Holistic feedback must be requested and all those people who are affected by the capability must be involved. Tests can be executed in different ways. One possibility is the use of test beds which is a realistic environment at a research institute. Another possibility is to test the solution together with a lead customer. The aim is to move forward step by step towards the operative application of the capability. For this purpose, the capability can be used initially for certain customers or smaller operational scenarios.

Validation

In the following, the approach presented above is applied to a service innovation project. Innovation provider is a consulting company that wants to offer an innovative consulting service, based on the exact recording of processes and times in the manual assembly of large-volume products. The objective is to create transparency and to identify optimization potentials in assembly, data-based. A comprehensive description of the technical development can be found in Kärcher et al. [START_REF] Kärcher | Sensor-driven Analysis of Manual Assembly Systems[END_REF].

First, the target capabilities are identified, by analyzing the aspired business model. The capabilities 'data acquisition', 'data processing' and 'information provision' are defined. For each capability, requirements are deposited. For example, the data acquisition for large components must take place with an accuracy of 0.5 seconds and an accuracy of 99%. The data acquisition must be possible within a period of 7 days without interruption. The aim of the capability is to generate total process times. For this purpose, the start or end of an assembly process must be detected. The capability requirements are collected in a table which is used as a Now ideas for the implementation of the capabilities are generated. The consulting company already has the capability to record times paper-based. However, since it is not possible to sufficiently develop this capability further, the development of a new capability is aimed at. There are different possibilities. The recording is possible with the help of an app which makes the data immediately available in real time. With a higher level of automation, data can be captured with the aid of sensors (e.g. RFID, camera, sensors on components). Based on the cost-benefit analysis, the company decides to implement sensors on the components. In order to get the first feedback quickly, storytelling is used for first prototypes. For this, the procedure of the capability is presented to several stakeholders from the assembly in a workshop. In the second step, the implementation of prototypes takes place with the help of simple sensors. Only in the last step, own sensors are developed.

Testing is first carried out in a test environment at a research institute where a demonstrator is set up. At the same time, competence requirements for employees were recorded. It was determined that the consultants on site needed additional knowledge in configuration and bug fixing in order to implement the capability. Appropriate training material is created and tested with the first version of the system. In the second step, the solution is introduced into the customer's assembly in small projects.

Discussion. The advantage of the approach presented in this paper is that customers and employees from the operations are involved in the development process at an early stage. By using capabilities, the development is less technology-driven and strongly geared to the benefit. This led to numerous new ideas in the presented project. In addition, the components of the service innovation were developed independently of each other. As a result, these can be reused in further service innovation projects. An important hurdle was the application of the concept of capabilities, as this was often misunderstood. Thus, a training concept should be developed.

Summary and Outlook

This paper presents a capability-based approach to implementing digital services in SMEs. The challenges of SMEs were first examined in the context of a literature search and a short study. This showed that especially established SMEs have great difficulties in implementing solutions in operations. Based on this, an agile, capability-based approach was examined in more detail and applied on a practical innovation project. A major advantage of the approach was the detachment from specific technologies. It shows how SMEs can gradually implement solutions. Through the use of capabilities, they remain focused and receive a holistic overview of the necessary adjustments. In addition, capabilities can be used to holistically map a situation and the customer benefit generated by the service. The application has shown that while the method is very simple to use, it is limited to smaller projects. Very complex digital service innovations, as they occur in large enterprises, can only be mapped roughly without creating too much complexity. Further work is to apply this approach to a larger group of companies. In addition, elements of change management should be integrated. For example, the approach could be broadened by the strategic planning of change.

Fig. 1 .

 1 Fig. 1. Structure of capabilities

Table 1 .

 1 Comparison of development approaches for digital service innovation.

	Criteria	Start-up	Established SME
	Product range	Focus on a single service	Wide product range in operations ties development capacities
	Strategy	Difficulties to find customer	Based on a rough vision, more
	Implementation	needs, based on a business model	focused on technology
	Methodology	Agile approach	Waterfall model
	Operations Involvement	Same people in development and operations	To limited extent
	Customer Involvement	Early involvement aimed at	Involvement in tests after development phase
	Knowledge Building Built up systematically	Mostly covered by partners

Acknowledgments

The authors gratefully acknowledge the support from The German Federal Ministry of Education and Research (BMBF) through the I4KMU project (Grant No. 01IS16020).


Kaan Kalkanci

Christoph Roser
email: christoph.roser@hochschule-karlsruhe.de

Options for Maintaining Weak FIFO in Parallel Queues

Keywords: FIFO, pull production, storage, lean manufacturing

Maintaining a FIFO sequence is a common aspect of manufacturing, especially in lean manufacturing. This can easily be realized by having FIFO lanes, where items are added at one end and removed at the other end. This maintains their FIFO sequence. In industry, however, there is often the situation that the required quantity of items would result in a very long single FIFO lane. This creates subsequent problems with available floor space. Hence, a practical solution is often to have multiple parallel FIFO lanes. However, a separate system is now needed to maintain the FIFO sequence across multiple parallel FIFO lanes. Ideally this would not require much additional managerial overhead and high investment costs. This paper investigates different options on how to manage parallel FIFO lanes, and measures their sequencing performance.

Introduction

The sequence of material flow in manufacturing and other processing systems is relevant for overall performance. About the most common method used is FIFO (First In, First Out). The oldest material is always used first. The primary advantage of FIFO is that it reduces the fluctuations of the lead time for individual items. All items will have a similar lead time in a FIFO lane. In contrast, a LIFO (Last In, First out) will create vastly different lead times for different items. The first item in will have the longest lead time, and the last item added will have the shortest lead time. LIFO is generally not advisable, but may sometimes be used due to the nature of storage. Both principles are shown in the following Figure 1. FIFO is most of all a buffer inventory to decouple fluctuations between the arrival and departure processes. By limiting the maximum inventory, it also prevents excess build up of material. FIFO also has other advantages, as it allows better traceability. If there is a systematic product quality issue, or if there is a design change, it is much easier to track the items that have to be changed. It is also much easier to use up the items of the "old" design before switching over to the "new" design [START_REF] Günthner | Schlanke Logistikprozesse: Handbuch für den Planer[END_REF]. Furthermore, FIFO represents a transparent material storage, because the information flow is ensured through the materials in the FIFO lanes.

Problem Statement

This paper is based on a master thesis [START_REF] Kalkanci | Entwicklung und Simulation von Ein-und Auslagerungsstrategien zur Sicherstellung des FIFO-Prinzips bei dezentralen parallelen Materiallagerungen[END_REF]. In this paper, we will discuss possibilities for managing parallel FIFO lanes. In theory, it is often assumed to have a single FIFO lane in a certain length that is needed. There are different academic methods to determine the FIFO size (for example [START_REF] Lutz | Determination of buffer location and size in production lines using tabu search[END_REF], [START_REF] Altiparmak | Optimization of Buffer Sizes in Assembly Systems Using Intelligent Techniques[END_REF], [START_REF] Bulgak | Integrating a modified simulated annealing algorithm with the simulation of a manufacturing system to optimize buffer sizes in automatic assembly systems[END_REF], [START_REF] Roser | Buffer Allocation Model Based on a Single Simulation[END_REF], [START_REF] Roser | Single Simulation Buffer Optimization[END_REF]). These can be used to design capacities of FIFO lanes and production areas. In practice, however, limitations on the floor space and storage system often make it difficult or impossible to place all required items into one FIFO lane. One option is to have random-access storage and track the FIFO sequence using an overarching ERP system. Another option commonly seen in industry is to use multiple parallel FIFO lanes, what is being investigated in this article.

An example of multiple parallel FIFO lanes is shown in Figure 2. The items arrive in sequence. An adding logic decides in which of the multiple parallel FIFO lanes an item is stored. Naturally, this has to be a FIFO lane that is not yet completely full. In addition, there is also customer demand, where the customer requests items periodically. A removing logic decides from which of the multiple parallel FIFO lanes an item will be removed. Similar to the adding logic, this has to be a FIFO lane that is not yet completely empty. If all FIFO lanes would be full, no more items could be added. The system is blocked. Otherwise, if all FIFO lanes are empty, no more items could be removed. The system is starved. Hence through the adding and removing logic, it is possible to maintain FIFO [START_REF] Atz | Integrierte Lagersystemplanung[END_REF].

Here we have to distinguish between two definitions. First, a strict FIFO where the items leave the system in exactly the sequence they arrived. Second, a weak FIFO sequence where the items leave the system approximately in the sequence they arrived [START_REF] Atz | Integrierte Lagersystemplanung[END_REF]. While within this paper we analyze weak FIFO sequences in particular, we would first briefly introduce the approach for a strict FIFO sequence.

Strict FIFO Sequence Approach

There are three basic approaches in multiple parallel FIFO lanes that are able to maintain a strict FIFO sequence. The first is to create a digital or physical timestamp of the time when the item was added into the parallel FIFO system. Alternatively, a number could be used to indicate the sequence. If an item is needed, the item with the oldest timestamp is used. The disadvantage of this method is the effort in creating a timestamp and the effort in searching for the oldest item during removal. Nevertheless, this approach is used, in particular in combination with a digital MES (manufacturing execution system) or ERP (enterprise resource planning) system.

A second approach is to fill the parallel FIFO lanes sequentially (i.e. fill the first FIFO lane, then the second FIFO lane, etc.).This is followed by the removal of parts by emptying the first FIFO lane, then the second FIFO lane, etc. The major caveat of this approach is that the filling process must not overtake the emptying process. This is visualized in Figure 3, where for your understanding the parts are numbered in the sequence of arrival. On the left image the filling process is about to fill a lane before the lane assigned for emptying. In the right image this lane is now full, and the filling process switches to the next lane. This, however, breaks the sequence. This breaking of the sequence not only breaks the strict FIFO sequence, but due to the nature of the break we now no longer even have a weak FIFO sequence. Depending on the subsequent arrivals and departures, the items in the other FIFO lanes may remain in the buffer for a very long time while filling and emptying use only one FIFO lane.

This problem can be avoided by blocking the filling of the FIFO lane that is currently emptied. In this case, however, the usable buffer space is less than the total buffer space, and the buffer capacity fluctuates. On the shop floor it would also require very stringent enforcement of standards to prevent, for example, a forklift driver from dropping a part in the only available space just because something indicates he should not place it there.

Another option is to have a signal (red sign, dummy part, etc.) in between the two non-sequential parts. This would be, for example, parts 28 and 44 in Figure 3. The challenge here is to know when to add this signal, which may not be obvious to the person adding the items. This does have potential for mistakes.

A third option is to always fill the next part into the next FIFO lane adjacent to the previous adding. For removal, the part from the next FIFO lane is removed adjacent to the previous removal. This is also modeled below in the Add Cyclic & Take Cyclic combination.

Overall, it is possible to maintain a strict FIFO in parallel systems without the use of timestamps. However, this may require some effort. For example, it can be imagined that a forklift driver would have to get off his forklift to move a signal -and we all know that forklift drivers usually prefer not to get off their vehicle. Furthermore, this may not use the entire available space. Additionally, if a mistake is made, the items can potentially be very badly out of sequence. Especially the second approach above is hence not very robust, and small mistakes may have significant consequences.

In many situations, however, a weak FIFO sequence is sufficient (e.g., if the surrounding system does not include traceability, or in general the advantages of a strict FIFO are not utilized). In this case it may be better to maintain only a weak FIFO with less effort. In the following we compare possibilities for a weak FIFO sequence that are

• more robust against mistakes;

• do not require complex signals within the FIFO; and

• use all of the available space in the FIFO.

Methods for Adding and Removing

We will consider five different strategies for adding and removing items from multiple parallel FIFO lanes, which are presented below.

Adding Methods

One method for adding items is Add Random. In this case, the items arriving are randomly assigned to one of the empty FIFO lanes. The assignment is equally distributed, with only non-full FIFO lanes being used as addition possibilities.

Another method is Add Max, where the item is added to the FIFO lane with the largest non-full inventory. If more than one FIFO lane has the largest non-full inventory, the method prefers the FIFO lane that was used for the last addition. If this no longer has the largest non-full inventory, sequentially the next FIFO lane from these equally largest non-full inventories will selected for the addition process.

A further method represents Add Min, where the item is added to the FIFO lane with the smallest inventory. If more than one FIFO lane has the smallest inventory, the method prefers the FIFO lane that was used for the last addition. If this no longer has the smallest inventory, sequentially the next FIFO lane from these equally smallest inventories is selected.

The fourth method is Add Repeat, where items are repeatedly added in the same FIFO lane until it is full. After this FIFO lane is full, the next non-full FIFO lane is selected. Items are added into this new FIFO lane until it is also full. Then the process is repeated. Please note that if this method includes a signal in case of an overlap, then this Add Repeat and corresponding Take Repeat would maintain a strict FIFO as presented in section 3.

Finally, Add Cyclic is used as the fifth method, where each item is added to the next non-full FIFO lane from the previous one. Doing this, the first item is added to FIFO lane 1, the second to FIFO lane 2, and the third to FIFO lane 3, etc. This will continue until an item has been added to the last FIFO lane, after which the cycle begins again with FIFO lane 1. If during this procedure a FIFO lane is full, it is skipped.

Removing (Taking) Methods

Similar methods are used for removing items. One of these is the Take Random method, which takes an item randomly from one of the non-empty FIFO lanes. The random removal is with equal probability from the non-empty FIFO lanes.

The Take Max method removes the item from the FIFO lane with the largest inventory. If more than one FIFO lane has the largest inventory, the method prefers the FIFO lane that was used for the last removal. If this no longer has the largest inventory, sequentially the next FIFO lane from these equally largest inventories will be selected for the addition process.

The Take Min method removes an item from the FIFO lane, which contains the smallest non-zero inventory. If more than one FIFO lane has the smallest non-zero inventory, the method prefers the FIFO lane that was used for the last removal. If this no longer has the smallest non-zero inventory, sequentially the next FIFO lane from these equally smallest inventories.

The Take Repeat method removes items repeatedly from the same FIFO lane until it is empty. After this FIFO lane is empty, the next non-empty FIFO lane is selected, and items are removed from this FIFO lane until it is also empty. Then the process is repeated. The sequence of the FIFO lanes for the removal is identical for the sequence of the FIFO lanes for adding if the adding method has a sequence (Add Repeat, Add Cyclic).

The fifth method is Take Cyclic, where each item is removed from the next nonempty FIFO lane from the previous one. In this case, the first item is removed from FIFO lane 1, the second from FIFO lane 2, and the third from FIFO lane 3, etc. By analogy to Add Cyclic, this will continue until an item has been removed from the last FIFO lane. After this the cycle begins again with FIFO lane 1. If during this procedure a FIFO lane is empty, it is skipped. The sequence of the FIFO lanes for the removal is identical for the sequence of the FIFO lanes for adding if the adding method has a sequence (Add Repeat, Add Cyclic). Please note that the combination of Add Cyclic and Take Cyclic would give a strict FIFO sequence.

There would also be another method, Take Oldest, where the oldest item in the parallel FIFO lanes is removed. This would ensure a strict FIFO, where the removal of the items is exactly in the sequence they are added. This is regardless of the method in which they were added to the FIFO lanes. However, this would require a data system or a comparison of the first item in all parallel FIFO lanes to find the oldest one. While best for the sequence, it is not always practical due to the effort in determining the oldest item and the amount of investment costs incurred.

Combination Adding and Removing (Taking) Methods

Within the scope of selecting FIFO lanes, we have five methods for adding items and five for removing items (excluding Take Oldest). Hence, we have a total of 25 combinations of adding and removing methods as shown in Figure 4. Please note again that combination 25 gives a strict FIFO sequence.

Simulation Approach

We simulated all 25, adding and removing combinations for a system with 10 parallel FIFO lanes with a capacity of 10 each. The inter-arrival and inter-departure times were exponentially distributed. The system was tested under three different load conditions. A low load had an on average 0.5% less items arriving than demanded (i.e., the customer frequently had to wait and the inventory was frequently empty). A high load had on average 0.5% more items arriving than needed, resulting in a mostly full inventory. Finally, a medium load had on average as many items arriving as consumed. We measured the sequencing quality as the root mean square error (RMSE) of the difference between the position in the arrival sequence and the position in the departure sequence. For each simulation this was calculated as shown in equation ( 1), where i is the i th item in the arrival sequence out of n items in total, and Ti is the position of the item i in the departure sequence.

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = � 1 𝑛𝑛 �(𝑖𝑖 -𝑇𝑇 𝑖𝑖 ) 2 𝑛𝑛 𝑖𝑖=1 (1)
Each simulation processed 10,000 items. Furthermore, each simulation was repeated 52 times for statistical accuracy. This resulted in almost 4,000 simulations to determine the mean RMSE and its confidence interval.

Simulation Results

Below are exemplary of the results of all 25 combinations for inter-arrival and interdeparture times with same parameters, including its 2.5% confidence interval. The results in the following Figure 5 are sorted by the removing methods. Full results can be found in [START_REF] Kalkanci | Entwicklung und Simulation von Ein-und Auslagerungsstrategien zur Sicherstellung des FIFO-Prinzips bei dezentralen parallelen Materiallagerungen[END_REF]. The differences between the removing methods indicates that the removal method has a significant effect on the sequence quality. Removing items using the Take Min approach results in the worst sequencing quality, having an average RMSE across all five adding strategies of 180. The Take Repeat and Take Max approaches are only marginally better with an average RMSE of 131 and 115. Removing items randomly using Take Random is actually a pretty good strategy with an average RMSE of 13. However, the best sequence quality was achieved by using Take Cyclic, with an average RMSE of only 5.6 across all five adding strategies. Comparable results were achieved with the low-and high-load conditions. A strict FIFO can be maintained by the combination of Add Cyclic-Take Cyclic strategy with a RMSE of 0. This combination brought overall the highest quality FIFO sequence. If a weak FIFO is sufficient, a Take Cyclic approach gives the smallest RSME regardless of the adding sequence, saving the additional effort of Add Cyclic. appropriate solution for practical applications. Overall this gives a good trade-off between effort and FIFO quality if a strict FIFO sequence with parallel FIFO lanes would lead to high effort or additional investment costs.

Figure 1 :

 1 Figure 1: Simplified illustration of FIFO and LIFO

Figure 2 :

 2 Figure 2: Example of four parallel FIFO lanes each with a capacity of five items

Figure 3 :

 3 Figure 3: Problem of filling overtaking the emptying process

Figure 4 :

 4 Figure 4: 25 combinations of adding and removing strategies, with #25 having a strict FIFO sequence

Figure 5 :

 5 Figure 5: RMSE and confidence intervals of all 25 combinations for medium load

Summary

Overall, a strict FIFO maintaining the correct sequence is of course the best approach. However, for parallel FIFO lanes that are not managed digitally, the effort of maintaining strict FIFO may exceed the benefit. In these cases, a weak FIFO can be achieved simply by using the Take Cyclic approach, where every item is taken from the next FIFO lane. This approach maintains an adequate FIFO sequence with acceptable additional effort, regardless of the logic used for adding items into the FIFO. It is also a robust approach. While this does not maintain a strict FIFO sequence, it is often the


Christoph Roser
email: chris-toph.roser@hochschule-karlsruhe.de

Daniel Nold

Practical Boundary Case Approach for Kanban Calculation on the Shop Floor Subject to Variation

Keywords: kanban formula, pull production, random variation, replenishment time, lean manufacturing

Determining the number of kanban in a pull production is essential for a good system performance. While this is simple in a static case, it becomes much more challenging if the system is subject to variations, as all practical systems are. The paper presents a novel boundary case approach to determining the number of kanban subject to a desired delivery performance. The approach is compared with the well-known Toyota formula. An extensive simulation-based approach verification for different coefficients of variations for the replenishment time and the customer takt was used to verify this boundary case approach also in comparison with the Toyota formula. The presented approach handles variation much better and determines a much more suitable number of kanban. This approach can also be adapted to practical everyday use in industry with little additional effort and with only a limited understanding of the underlying randomness of the key variables.

Introduction

Lean production is one of the best approaches for promoting business excellence through continuous improvement [START_REF] Kurilova-Palisaitiene | Challenges and Opportunities of Lean Remanufacturing[END_REF]. One of the key concepts is pull production. The idea of pull production is based on limiting the maximum number of products or jobs processed in the system at the same time. The most common approach to implement pull production is through kanban, especially for high-volume low-mix products. In setting up a kanban system, the number of kanban cards has to be determined. There exist a variety of different kanban formulas. All of them are based on the relation between the replenishment time and the customer takt as shown in [START_REF] Kurilova-Palisaitiene | Challenges and Opportunities of Lean Remanufacturing[END_REF], where RT is the replenishment time, TT is the customer takt, NPK are the number of parts per kanban, and K is the number of kanban.

𝐾𝐾 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 � 𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅•𝑁𝑁𝑁𝑁𝑁𝑁 � (1)
As we will see below, this equation works well for a static system, but presents a challenge for dynamic systems that include random variations. Unfortunately, all real-world systems are dynamic, and these random variations cannot be ignored. This paper will look at the relation between replenishment time, customer takt, and the number of kanban using both theoretical and experimental approaches.

Theoretical Approach

Static Situation

In the first part we assume a static situation with no random fluctuations. This of course is a widely optimistic and unrealistic assumption for practical use. However, it is useful to understand the theoretical foundations. A key variable here is the customer takt. It represents the average demand of the customer during a time period. To calculate it, you divide the available working time by the customer demand during that time, as shown in equation ( 2) [START_REF] Badiru | Handbook of Industrial Engineering Equations, Formulas, and Calculations[END_REF], where TT is the customer takt, AT is the available work time, and CD is the customer demand during that time:

TT = AT CD (2)

Customer Takt slower than or equal to replenishment time

If the customer takt is larger than the replenishment time, one Kanban card will suffice for production. If the customer wants a product, he receives the single piece in stock, and then we reproduce it to increase stock again to one piece. Hence, the behavior of the inventory over time may look like Figure 1. As the RT is faster than the TT, the product is always completed before the customer requests the next one. This concurs with equation (1) above.

Figure 1: Theoretical behavior if customer takt is slower than the replenishment time

Customer Takt faster than replenishment time

If the customer takt is larger than the replenishment time, we would need multiple Kanban cards as calculated in equation ( 1). An example is shown in Figure 2, where the replenishment time is almost three times as long as the customer takt. Hence, we would need three kanban to have one part ready before the customer demands it.

Dynamic Situation

In reality both the replenishment time and the customer takt have random variations.

The distribution of customer takts can often be approximated using exponential or lognormal distributions. For replenishment times we also often find log-normal distributions, Weibull, Gamma, or Pearson type 5 distributions. Overall, the equation ( 1) would now consist not of discrete numbers but random variables. Hence, equation (1) would change to equation [START_REF] Curtiss | On the Distribution of the Quotient of Two Chance Variables[END_REF].

𝐾𝐾 = 𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅•𝑁𝑁𝑁𝑁𝑁𝑁 (3)
There are methods available to calculate the division of probability functions. The general ratio distribution is shown in equation ( 4), where p K (k) is the probability density function of the number of kanban needed [START_REF] Curtiss | On the Distribution of the Quotient of Two Chance Variables[END_REF].

𝑅𝑅 𝑁𝑁 (𝑘𝑘) = ∫ |𝑇𝑇𝑇𝑇| ∞ 0 𝑅𝑅 𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅 (𝑘𝑘 • 𝑡𝑡𝑡𝑡, 𝑡𝑡𝑡𝑡)𝑅𝑅𝑡𝑡𝑡𝑡 (4)
However, this requires independence of the variables, which is not given in our case.

The replenishment time depends on the customer takt, as more orders increase the replenishment time. Furthermore, the replenishment time also depends on itself, as, for example, a part with a long replenishment time is usually followed by another part with a long replenishment time. Finally, the option of buffering parts in a supermarket is not included in this simplified model. Hence, the theoretical approach has unrealistic assumptions and cannot be used. Therefore the problem in determining the number of kanbans is how to deal with these uncertainties.

Simulation Approach

We have also analyzed manufacturing systems using a simulation-based approach. In this simulation, a single process is controlled using a kanban system in order to supply parts to a customer.The customer demand is modeled using a lognormal distribution. The processing time is modeled using a Pearson Type V distribution.Due to the large number of possible variables, an exhaustive search is prohibitive. Nevertheless, we simulated a wide range of different systems, varying three primary variables: Additionally, the number of kanban cards was varied exhaustively between 1 and 50, with additional simulations having up to 1000 kanban cards to also test for systems with extremely large number of kanban cards. Each simulation was repeated 30 times for statistical validity and to allow the calculation of confidence intervals. Two primary results were measured:

• Work in process inventory: how many parts were in the system • Delivery performance: what percentage of the customer request were fulfilled immediately. Not immediately fulfilled request were fulfilled when the next part became available. The full details of the simulation experiment can be found in [START_REF] Nold | Simulationsbasierte Analyse der Liefererfüllung und des Umlaufbestands verbrauchsgesteuerter Produktionssysteme in Abhängigkeit von der Anzahl verwendeter Kanban-Karten[END_REF]. Figure 3 shows the location of the kanban cards in the system for different number of kanban cards for both the customer takt and the cycle time having a coefficient of variation of 1, with a mean customer takt of 12 and a mean cycle time of 10. Showing all results from [START_REF] Nold | Simulationsbasierte Analyse der Liefererfüllung und des Umlaufbestands verbrauchsgesteuerter Produktionssysteme in Abhängigkeit von der Anzahl verwendeter Kanban-Karten[END_REF] would exceed the scope and space available within this paper.

Figure 3:Location of the kanban cards for a system with the customer takt and the cycle time having a coefficient of variation of 1, a mean customer takt of 12 and a mean cycle time of 10. The system was simulated for all kanbans up to 50, and then for selected kanbans up to 1000.

4

The Toyota Formula

The formula used by Toyota to calculate the number of kanban is called the Toyota Formula, and is widely used in literature, e.g. [START_REF] Berkley | A review of the kanban production control research literature[END_REF] [6] [START_REF] Chan | Effect of kanban size on just-in-time manufacturing systems[END_REF]. This approach calculates the number of kanban based on the average daily demand DD, the replenishment time (called lead time, but includes the times for collecting kanban), the container capacity (i.e., the number of parts per kanban NPK), and a safety factor α as shown in equation [START_REF] Berkley | A review of the kanban production control research literature[END_REF].

𝐾𝐾 = 𝐷𝐷𝐷𝐷•𝑅𝑅𝑅𝑅 𝑁𝑁𝑁𝑁𝑁𝑁 • (1 + 𝛼𝛼) (5)
As the daily demand DD is merely the inverse of the customer takt TT, equation ( 5) translates into equation ( 3) with an additional safety margin. The safety factor α is to account for uncertainties, and is generally recommended to be no more than 10%. We verified this Toyota formula using the simulation and the resulting data from [START_REF] Nold | Simulationsbasierte Analyse der Liefererfüllung und des Umlaufbestands verbrauchsgesteuerter Produktionssysteme in Abhängigkeit von der Anzahl verwendeter Kanban-Karten[END_REF]. For full details on the simulation data please refer to [START_REF] Nold | Simulationsbasierte Analyse der Liefererfüllung und des Umlaufbestands verbrauchsgesteuerter Produktionssysteme in Abhängigkeit von der Anzahl verwendeter Kanban-Karten[END_REF]. The average for the simulated systems was a delivery performance of 71.3%, which is still far from acceptable for a functioning production system.

A practical Boundary Case Kanban Approach

Description of the Boundary Case Kanban Approach

The boundary case approach for calculating the number of kanban is based on equation (1). However, instead of using the mean value for the replenishment time and the customer takt, we now use boundary cases. This is not the extreme case, as customer takts and process times are time-based and hence have boundaries of [0,∞], which would give us an infinite number of Kanban in the worst case. More practically, we will be using the values for selected percentiles of the distribution. For the replenishment time we want to cover all but the slowest replenishment times. Similar is true for the customer takt, but now we want to cover all but the fastest customer takt. The selected percentile depends on the desired reliability and delivery performance of the kanban system.

Simulation Verification of the Boundary Case Kanban Approach

Using the same simulation data as from the verification of the Toyota formula, we now verified the boundary case approach. We selected to verify this approach for 80% percentiles, 90% percentiles, and 95% percentiles on both all but the slowest replenishment time and all but the fastest customer takts. Table 1, Table 2, and Table 3 show the resulting number of kanban for a coverage of 80%, 90%, and 95% respectively for the customer takt and the replenishment time for different coefficients of variation. The resulting delivery performance is shown in Table 4, Table 5, and Table 6. Overall, the performance is much more satisfactory. If both the customer takt and the replenishment time is set to cover 80% of the slowest and fastest times respectively as shown in Table 4 the average delivery performance across all tested situations is 87,8%. Similarly, for a coverage of 90% as shown in Table 5, the average delivery performance is 93.3%. Finally, for a coverage of 95% as shown in Table 6, the average delivery performance is 95.4%. Overall, the calculated number of kanban is much more suitable for the needs of the industry. Delivery performances of 87%, 93%, or 95% for the different percentile boundaries are much more acceptable than an average delivery performance of 71% using the Toyota formula. The level of coverage can also be influenced by the percentile of the boundary case. Covering 95% of the fastest and slowest cases for the replenishment time and customer takt respectively will give a higher number of kanban and hence an overall better delivery performance than a coverage of only 90%, which in turn will again be better than a coverage of 80%.

Practical Application of the Boundary Case Kanban Approach

The boundary case approach to determine the number of kanban works very well as verified using extensive simulation data. For a practical application, however, these 80%, 90%, or 95% percentiles are difficult to determine. While the mean customer takt or mean cycle time are usually well known on the shop floor, the shape of the distribution of this random variable is usually unknown. Hence, there is usually insufficient data to determine an 80%, 90%, or 95% percentile. However, there is usually either historic data or -more commonly -personal experience of "bad days," where either the customer demand or the replenishment time was exceptionally difficult, meaning very fast or very slow respectively. Therefore, while sacrificing some accuracy, we propose for practical purposes to select the worst case that has to be covered either from data or from the experience of the personnel. In personal experience, shop floor supervisors seek safety in numbers and may want to cover worse situations but change their opinion once they see the resulting number of kanban and hence potential inventory. Therefore, we also propose that this selection of the boundary cases to be covered is not done in independence, but should involve a back and forth of selecting boundary cases and determining the number of kanban until a suitable compromise of boundary case coverage and number of kanban is achieved. Thus we achieve a suitable tradeoff between a high delivery performance (lots of kanban) and low inventory (fewer kanban).

Summary

The presented boundary case approach uses the well-known relation of the replenishment time to the customer takt as in equation ( 1) to determine the number of kanban. However, rather than mean values, this approach uses boundary cases (i.e., the largest replenishment time and the smallest customer takt that the system has to cover). This can be either expressed as a percentile of the distribution function if the function is known, or more practically based on the boundary cases known from experience or historic data that the system has to cover. The approach is intuitive, and requires little knowledge of statistics, hence making it suitable for everyday shop-floor use. Nevertheless, the approach has been extensively verified based on simulations, and returns much better delivery performances with much less outliers than the conventional Toyota formula. This information can be used to aid with the implementation of the Kanban system, regardless if it is a paper Kanban, a digital Kanban (where the time for the information flow is usually significantly less), or any other form of Kanban.

Figure 2 :

 2 Figure 2: Theoretical behavior if customer takt is faster than the replenishment time

5 •

 5 The relation of the customer takt to the process cycle time, which effectively changes the utilization of the process • The standard deviation of the customer takt • The standard deviation of the process cycle time.

Table 1 :

 1 Number of kanban for different coefficient of variations, covering 80% of the customer takt and replenishment time

					Customer Takt
			CV	0% 25% 50% 75% 100%
	Production	Process	0% 25% 50% 75%	1 2 3 5	2 2 4 6	3 4 6 9	7 8 11 15	14 16 20 23
			100%	6	8	13	19	31

Table 2 :

 2 Number of kanban for different coefficient of variations, covering 90% of the customer takt and replenishment time

Table 3 :

 3 Number of kanban for different coefficient of variations, covering 95% of the customer takt and replenishment time

Table 4 :

 4 Delivery performance for different coefficient of variations using the boundary case approach covering 80% of the customer takt and replenishment time

Table 5 :

 5 Delivery performance for different coefficient of variations using the boundary case approach covering 90% of the customer takt and replenishment time

								Customer Takt
						CV	0% 25% 50% 75% 100%
			Production	Process	0% 25% 50% 75%	1 2 3 5	2 3 5 8	4 6 9 12	9 11 16 23	19 23 31 38
						100%	8	11	19	30	51
								Customer Takt
						CV	0% 25% 50% 75% 100%
			Production	Process	0% 25% 50% 75%	1 2 4 6	2 3 6 9	5 7 11 17	12 15 22 33	26 33 44 56
						100%	9	14	25	43	78
								Customer Takt
					CV		0%	25%	50%	75% 100%
	Production	Process		0% 100,0% 96,9% 82,4% 89,4% 92,9% 25% 96,2% 84,1% 86,3% 90,2% 94,1% 50% 82,2% 85,8% 86,1% 90,2% 95,3% 75% 78,3% 81,4% 85,8% 89,0% 92,0%
				100% 71,6% 80,0% 85,2% 87,9% 92,4%
								Customer Takt
					CV		0%	25%	50%	75% 100%
	Production	Process	0% 100,0% 96,9% 92,2% 93,7% 96,9% 25% 96,2% 96,0% 95,9% 95,8% 98,2% 50% 82,2% 91,2% 95,4% 96,8% 99,1% 75% 78,3% 89,1% 91,3% 96,5% 98,6%
			100% 78,2% 87,0% 93,1% 95,4% 97,6%

Table 6 :

 6 Delivery performance for different coefficient of variations using the boundary case approach covering 95% of the customer takt and replenishment time