Lucie Galand
email: lucie.galand@dauphine.fr

Thibaut Lust
email: thibaut.lust@lip6.fr

Multiagent Fair Optimization with Lorenz Dominance (Extended Abstract)

Keywords: F.2 [Theory of computation]: Analysis of algorithms and problem complexity, J.4 [Social and Behavioral Sciences]: Economics, G.1.6 [Numerical Analysis]: Optimization-Integer programming Algorithms, Economics Multiagent optimization, Fairness, Lorenz dominance

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INTRODUCTION

In multiagent decision problems, where one wants to make a decision with respect to the preferences of several agents, the concept of fairness turns out to be a crucial concern. This occurs for example when several agents (e.g. countries, companies) share the exploitation of an earth observation satellite in order to reduce their cost [START_REF] Lemaître | Exploiting a common property resource under a fairness constraint: A case study[END_REF]. When the preferences are cardinal, the agents express their preferences over the alternatives through utility functions, each agent having his/her own utility function to maximize. Therefore a decision is evaluated by a vector of utilities where a component represents the utility of an agent for this decision. Since there is generally not a solution that is the most preferred for all the agents, one has to determine compromise solutions that fairly satisfy all the agents. Pareto efficiency (P -efficiency) enables to define a partial preorder over the solutions based on the unanimity principle: if all the agents prefer a solution x to a solution y, then solution y is considered as dominated by solution x. However some very unfair solutions can be P -efficient. The Lorenz dominance has been proposed in economics to refine the Pareto dominance by taking into account satisfaction inequality among the agents. Roughly speaking, the Lorenz dominance enables to select all the P -efficient solutions that realized wellbalanced compromises between the utilities of the agents. Endriss et al. [START_REF] Endriss | Negotiating socially optimal allocations of resources[END_REF] have proposed conditions under which negotiation in a multiagent system will converge to an allocation that is Lorenz efficient (L-efficient). Nevertheless, a few works deals with the determination of the L-efficient solutions (see [START_REF] Baatar | Advancing equitability in multiobjective programming[END_REF][START_REF] Endriss | Reduction of economic inequality in combinatorial domains[END_REF][START_REF] Perny | A decision-theoretic approach to robust optimization in multivalued graphs[END_REF]), which is generally a difficult problem (NP-complete and intractable [START_REF] Endriss | Reduction of economic inequality in combinatorial domains[END_REF][START_REF] Perny | A decision-theoretic approach to robust optimization in multivalued graphs[END_REF]). The aim of this work is to study the problem of multiagent fair optimization, where one looks for the L-efficient solutions in a combinatorial optimization problem.

MULTIAGENT FAIR OPTIMIZATION

Lorenz dominance

We consider in this work that p utility functions have to be maximized. The Lorenz dominance can be defined through the construction of particular vectors, called generalized Lorenz vectors.

Definition 1. For all y ∈ R p , the generalized Lorenz vector of y is the vector L(y) defined by: L(y) = (y (1) , y (1) + y (2) , . . . , y (1) + y (2) + . . . + y (p) ) where y (1) ≤ y (2) ≤ . . . ≤ y (p) represent the components of y sorted by non-decreasing order. Definition 2. The Lorenz dominance relation (L-dominance for short) is defined for all y 1 , y 2 ∈ R p by: y 1 L y 2 ⇐⇒ [L(y 1 ) P L(y 2 )], where P denotes the Pareto dominance relation (y

1 P y 2 ⇐⇒ [∀k ∈ {1, . . . , p}, y 1 k ≥ y 2 k and y 1 = y 2 ]).
The space in which the generalized Lorenz vectors of a solution are represented is called the Lorenz space. Within a feasible set X , any element x 1 is said to be L-efficient (resp. P -efficient) when there is no x 2 in X such that u(x 2 ) L u(x 1 ) (resp. u(x 2 ) P u(x 1 )).

New methods

As L-efficient solutions are also P -efficient, one could resort to an approach that would consist in generating all the P -efficient solutions and then keeping only the L-efficient solutions. One of the most famous methods in multiobjective optimization is the two-phase method that enables to efficiently generate the P -efficient solutions to a biobjective problem (see e.g. [START_REF] Ulungu | The two-phases method: An efficient procedure to solve biobjective combinatorial optimization problems[END_REF]). It consists in generating first the subset of P -efficient solutions that optimize a weighted sum (i.e. supported P -efficient solutions), and second the other P -efficient solutions. However, the number of L-efficient solutions can be very small compared to the number of P -efficient solutions. Furthermore, the generation of Pefficient solutions is generally hard (see e.g. [START_REF] Aziz | Pareto optimality in coalition formation[END_REF][START_REF] Ehrgott | Multicriteria Optimization[END_REF]). For these reasons, we propose new methods that directly determine the L-efficient solutions. More precisely we study the adaptation of the two-phase method proposed in biobjective optimization to the fair optimization framework when two agents are involved.

Straight adaptation of the two-phase method. The adaptation of the two-phase method to generate only the L-efficient solutions thoroughly follows the original method, but in the Lorenz space. In the first phase, all the supported L-efficient solutions are generated. Actually, this amounts to optimizing Ordered Weighted Averages (OWA) [START_REF] Yager | On ordered weighted averaging aggregation operators in multicriteria decision making[END_REF], with decreasing positive weights, in the utility space. In the second phase, all other L-efficient solutions are determined, by exploring the search space defined by two consecutive Lefficient solutions in the Lorenz space.

Supported P -efficient solutions based method. Even if the straight adaptation of the two-phase method is theoretically interesting, the main drawback is in the first phase: the OWA functions that have to be optimized are non-linear and therefore even generating only the supported L-efficient solutions will be computationally expensive. We propose thus another method where the optimization of OWA functions is avoided. One can show that one can identify in the utility space the subset of supported P -efficient solutions that are L-efficient. It enables us to generate those Lefficient solutions by linear optimizations in the first phase. In the second phase, all other L-efficient solutions are determined, by exploring the search space defined by the Lefficient solutions previously determined.

EXPERIMENTAL RESULTS

We have applied the method based on the supported Pefficient solutions to the bi-agent knapsack problem. We used the instances developed by Bazgan et al. [START_REF] Bazgan | Solving efficiently the 0-1 multi-objective knapsack problem[END_REF] to solve the multiobjective knapsack problem. The results are given for random (no relation between the utilities) instances (Type A, 100 items) and for instances with positive correlations (Type B, 600 items) in Tables 1 and2. The experiments have been run on a Intel(R) Core(TM) i7-3820 CPU at 3.60GHz. We compare the running times of the method based on the supported P -efficient solutions (called SP) with the running times of the method of Perny et al. [START_REF] Perny | A decision-theoretic approach to robust optimization in multivalued graphs[END_REF] (called Rkg). We report the number of the instance (from 0 to 9), the number of P -efficient solutions (#P ) and L-efficient solutions (#L) and the CPU times in seconds. We see that the L-efficient solutions represent only a small part of the P -efficient solutions. A sign "/" means that the method was not able to solve the instance within 20 minutes. We can observe that the method SP is faster.

Table 1 :

 1 Type A

				CPU(s)				CPU(s)
	# #P #L	Rkg	SP	# #P #L Rkg	SP
	0	125	6	1.98	1.40	0	66	22	/	4.56
	1	184	8	22.43	2.63	1	71	17	/	2.13
	2	171	6	5.76	1.43	2	111	26	/	7.76
	3	198	18	/	2.49	3	88	21	/	12.32
	4	112	6	0.92	0.45	4	49	20	/	8.16
	5	136	5	0.17	0.16	5	82	24	/	7.05
	6	135	12	117.28	0.78	6	56	25	/	15.71
	7	155	49	/	979.5	7	74	23	/	69.56
	8	163	4	0.34	0.24	8	97	2	3.52	0.70
	9	98	7	6.70	0.44	9	49	20	/	3.13

Table 2 :

 2 Type B

Acknowledgments

This research was supported by the ANR project CoCoRICo-CoDec (14-CE24-0007-01).


Felix Friemann
email: ffriemann@ethz.ch

Manuel Rippel
email: mrippel@ethz.ch

Paul Schönsleben
email: pschoensleben@ethz.ch

Warehouse capacities in the pharmaceutical industry -Plan or outsource?

Keywords: Supply Chain Management, Pharmaceutical Industry, Long-Range Warehouse Capacity, Strategic Planning, Outsourcing

The pharmaceutical industry is undergoing a change. Different future developments such as the increasing amount of biopharmaceutical products and even stricter regulations increase the need for a reliable long range warehouse capacity planning. Results from a literature analysis indicate that managing these operations will mainly remain the responsibility of the pharmaceutical company itself and may not be outsourced. Hence, the capabilities must be built up within the pharmaceutical companies itself, too. However, none of the models identified in the literature can fulfill all requirements of a reliable and detailed long-range planning process in the pharmaceutical industry. Providing suggestions for further research areas, the paper contributes to the further development of more reliable planning processes.

Introduction

Global medicines spendings will increase from $965Bn in 2012 to $1Tn in 2014 and exceed $1.17Tn by 2017 according to IMS Health showing the size of the pharmaceutical industry [START_REF]The Global Use of Medicines: Outlook through 2017[END_REF]. The industry can be divided into the market segments of ethical (prescription) and "over-the-counter" products [START_REF] Savage | A Holistic Analysis of Pharmaceutical Manufacturing and Distribution: Are Conventional Supply Chain Techniques Appropriate?[END_REF]. This paper focuses on researching pharmaceutical companies (RPC) which are making most of their revenue from ethical products. Due to various future trends, supply chain managers in this industry will increasingly face challenges: The market of biologics (complex macromolecules with some form of polymer structure) will grow above average and amount to approx. 19-20% of the overall pharmaceutical market in 2017 [START_REF]The Global Use of Medicines: Outlook through 2017[END_REF]. These products are generally more sensitive to environmental changes (e.g. temperature) on transports and in the warehouse than traditional solid products (e.g. tablets). With the BRIC markets (Brazil, Russia, India, China) being key growth drivers, these capacities are needed at different locations than before, in sometimes challenging settings [START_REF] Altmann | Die Entwicklung des internationalen Pharmamarktes[END_REF]. All this has to be done under the umbrella of the highly regulated pharmaceutical industry where most process changes require new approvals of different authorities and warehouse security (anti-counterfeiting) is becoming more and more important [START_REF] Efrati | Lilly Drugs Stolen in Warehouse Heist[END_REF]. The new European "Guidelines of 7 March 2013 on Good Distribution Practice of Medicinal Products for Human Use (2013/C 68/01)" further increase the requirements for qualification, temperature control and traceability in the distribution [START_REF] Sponheimer | Supply-Chain-Trends und Regularien in der Pharmalogistik[END_REF].

Increasing supply chain transparency by better monitoring warehouse capacities and their development in the long-term seems one answer to better cope with these challenges. Expert interviews indicated that several pharmaceutical companies lack this capability. To exploit the reasons of this discrepancy, this paper firstly analyzes whether there can be a trend identified that capacities are outsourced and, consequently, warehouse planning will not be an issue anymore in the future. This is reviewed in a semi-structured interview series within 11 out of the 2012 TOP20 pharmaceutical companies (according to revenue) [START_REF] Health | IMS Health, IMS MIDAS, Top 20 global corporations[END_REF]. Secondly, the paper summarizes the findings of a literature analysis identifying relevant planning processes and models in academic publications.

Methodology

Originating from a case study with supply chain experts of a leading pharmaceutical company, different alternatives to increase transparency for warehouse capacities were evaluated. A basic question that arose was whether the company should estimate capacities on its own or whether the general trend is to outsource it in the industry.

The derived hypothesis was that companies outsourcing this task to logistics providers face less limitations with regards to warehouse capacities. To answer this, a semistructured interview series with supply chain managers from 11 out of the 2012 TOP20 researching pharmaceutical companies was used [START_REF] Health | IMS Health, IMS MIDAS, Top 20 global corporations[END_REF]. The interview guideline used contained both qualitative and quantitative questions. The interviews were conducted between 04'13 -05'13. All interviewees were senior managers in a Supply Chain Management position. For reasons of validation, the survey results were sent to all participants with the request of approval. All results were approved. If a company differentiates between business units (animal health, generics branch, etc.), our study focused on the research-oriented pharmaceutical branch whenever possible to ensure comparability of the answers.

Secondly, to answer the question whether good models and practices exist to plan warehouse capacities in the pharmaceutical industry, the state-of-the-art is evaluated by a literature analysis. Scopus (www.scopus.com) was used as the main database. The findings of this literature search were further analyzed using scientometrics ( [START_REF]Science of Science (Sci2) Tool[END_REF], see [START_REF] Gram | Equipment efficiency metrics in production systems. A literature review and survey[END_REF] for an application example).

Pharmaceutical Supply Chains

The American Production and Inventory Control Society (APICS) define supply chain management as the design, planning, execution, control, and monitoring of supply chain activities with the objective of creating net value, building a competitive infrastructure, leveraging world-wide logistics, synchronizing supply with demand, and measuring performance globally [START_REF]APICS -The Association for Operations Management[END_REF]. Drug development can take around 15 years before it comes to the market. These phases can be divided into discovery-phase, clinical (exploratory) and registration (full development) phase ( [START_REF] Savage | A Holistic Analysis of Pharmaceutical Manufacturing and Distribution: Are Conventional Supply Chain Techniques Appropriate?[END_REF]). The earlier the stage in the drug development process, the bigger the uncertainty for a supply chain manager on whether to consider this product in the corresponding long-range capacities (i.e. how probable it is that it passes on to the next stage) and which logistics requirements this drug will actually have (i.e. temperature range, volume, special characteristics).

Within the product life cycle of a drug, the development phase is followed by an introductory, growth, maturity and decline stage. Production / capacity planning and inventory management becomes especially important in the growth and maturity stage [START_REF] Laínez | Challenges and opportunities in enterprise-wide optimization in the pharmaceutical industry[END_REF] as products at these stages consume most of the warehouse capacities.

The general pharmaceutical manufacturing supply chain (Fig. 1) consists of the stages primary manufacturing where the active pharmaceutical ingredient (API) is produced, secondary manufacturing formulating the drug (e.g. producing a tablet), 3) packaging and 4) finished product distribution [START_REF] Friemann | Best Practices for Supply Chain Management Techniques and Concepts across Industries[END_REF]. These stages are globally distributed.

Outsourcing at research-focused pharmaceutical companies

Interviews with experts of one case study company in a TOP5 researching pharmaceutical company ( [START_REF] Health | IMS Health, IMS MIDAS, Top 20 global corporations[END_REF]) indicated that no high-level process is in place to monitor global warehouse capacities. Limitations happened in the past and are expected to increase in future due to previously mentioned developments. One argument not to spend resources on capacity planning might be that the operations tend to be further outsourced in future. Outsourcing means that parts of the value-added chain are turned over to other companies [START_REF] Schönsleben | [END_REF]. As one can notice, nowadays especially distribution centers are mostly outsourced (79% on average). Here the trend is to outsource even more. At the other stages of the supply chain, the level of outsourcing is generally lower. Outsourcing in general is expected to increase throughout all stages of the Supply Chain. One hypothesis to check was especially whether companies with higher percentages of outsourced operations encountered less warehouse capacity limitations in the past. The underlying reason is that logistics providers with greater process knowledge and multiple customers are able to better balance warehouse utilization and therefore encounter fewer limitations. But, as the interview results show, most limitations (e.g. not enough capacity available when needed) occur at the distribution centers. Hence, the hypothesis cannot be confirmed. The explanation can be manifold. One reason might be that there are different characteristics in the pharmaceutical industry (long lead times, high equipment costs and corresponding high utilization) that make planning difficult downstream the supply chain.

The degree of outsourcing within the packaging stage seems to be the lowest. Reasons for this might be the complexity e.g. with regards to product variety or counterfeiting risks at this stage. Anti-counterfeiting is still a very important topic in the industry.

As outsourcing reasons, the most common answers were 1) strategic decision -decide based on strategic importance of the product, 2) not core competence -outsource when the operation is not a core competence, 3) risk mitigation -outsource production and distribution to ensure supply and increase flexibility, 4) external know-howoutsource when internal competence is not available.

Overall, it can be stated that even though outsourcing seems to generally increase, it will still be on a comparably low level at the production facilities from drug substance production until packaging making it necessary for pharmaceutical companies to establish a reliable process in order to estimate the required warehouse capacities and therefore ensure supply chain reliability. At a next step, the literature is analyzed for corresponding processes and models to help the pharmaceutical industry in this matter.

Warehouse capacity planning in the pharmaceutical industry

To identify streams and applicable literature in the field of warehouse capacity planning, keyword combinations 1) "supply chain", 2) "supply chain" AND "capacity", 3) "supply chain" AND "planning" and 4) "warehouse" AND "planning" were used in the Scopus database. Whether or not pharmaceutical supply chains should be treated with different tools than other industries is discussed in a controversial manner. Nevertheless, one can acknowledge that the pharmaceutical supply chain is more regulated than any other industrial sector and decisions can become ethical if a failure of the supply chain may have a severe impact on patients' lives, especially when dealing with ethical (prescribed) medicines like in this paper [START_REF] Savage | A Holistic Analysis of Pharmaceutical Manufacturing and Distribution: Are Conventional Supply Chain Techniques Appropriate?[END_REF]. This imposes specific requirements on pharmaceutical supply chain planning. To identify the documents mentioning pharmaceutical issues, the keyword "pharmaceutical" was added to the previous keyword combinations. The number of results and especially the relation between general and pharmaceutical-specific literature is illustrated in Fig. 3. The primary y-axis (n=1 to 6000) with the corresponding dotted lines show the results of a generic keyword search. The secondary y-axis (n=1 to 90) with the corresponding continuous lines show the same keyword search limited to papers mentioning the pharmaceutical industry.

A first interesting finding is that the relation between general literature and literature mentioning pharmaceutical keywords is more or less continuously around 1.5 % (1.6%, 1.3%, 1.5% resp. 0.9% for the keyword searches mentioned before) over the given timeframe. Some literature is stating that many papers concentrate on a handful of industry sectors, automobile being among them [START_REF] Burgess | Supply chain management: a structured literature review and implications for future research[END_REF]. So repeating the keyword search for the automotive sector, using "automotive" instead of "pharmaceutical" as a keyword, doubles the overall number of papers found (factor 2.0 -2.5 for all keyword combinations compared to the previous search). It leaves the conclusion, that pharmaceutical supply chain planning tends indeed to be underrepresented compared to other industries. The reasons for this were not further analyzed and might be a good area for further research.

When analyzing collaboration of authors in the pharmaceutical field using the scientometrics method ( [START_REF]Science of Science (Sci2) Tool[END_REF]), the area seems rather fragmented. Two groups identified are L. Patrono, Mainetti, De Blasi et al. publishing about RFID-tracking in the pharma-ceutical supply chain or Westenberger, Buhse et al. dealing with quality monitoring throughout the supply chain ( [START_REF] Keire | Characterization of currently marketed heparin products: key tests for quality assurance[END_REF], [START_REF] Kauffman | Pharmaceutical surveillance with rapid spectroscopic screening technologies[END_REF]). From the above streams, exemplary papers can be highlighted that deal with capacity planning in the context of supply chain managament. Gu et al. provide an extensive literature analysis with regards to warehouse operation planning whereas they do not discuss the global context within supply chain planning [START_REF] Gu | Research on warehouse operation: A comprehensive review[END_REF]. Heragu et al. discuss intra-warehouse improvements of the functional areas and propose an algorithm [START_REF] Heragu | Mathematical model for warehouse design and product allocation[END_REF]. Susarla et al. or Levis et al. discuss integrated planning for a globally operating pharmaceutical companies, not considering warehouse requirements specifically though [START_REF] Susarla | Integrated supply chain planning for multinational pharmaceutical enterprises[END_REF], [START_REF] Levis | A hierarchical solution approach for multi-site capacity planning under uncertainty in the pharmaceutical industry[END_REF]. Chen et al. discuss a simulation-optimization of the clinical trial supply chain [START_REF] Chen | Simulation-optimization approach to clinical trial supply chain management with demand scenario forecast[END_REF]. Aghezzaf generally discusses strategic capacity and warehouse location planning including uncertainty and proposes a model [START_REF] Aghezzaf | Capacity planning and warehouse location in supply chains with uncertain demands[END_REF]. For production capacity planning, several models exist. A profound general overview is provided by Mula et al. [START_REF] Mula | Models for production planning under uncertainty: A review[END_REF]. However, literature dealing with warehouse capacity planning in the context of a global supply chain and specifically fulfilling the requirements of pharmaceutical capacity planning (e.g. pallet spaces within different temperature zones) could not be identified by the literature research. "supply chain" AND "planning" (n=7027) warehouse AND planning (n=1520) "supply chain" AND pharmaceutical (n=705) "supply chain" AND "capacity" AND pharmaceutical (n=34) "supply chain" AND "planning" AND pharmaceutical (n=108) warehouse AND planning AND pharmaceutical (n=13)

Discussion and Conclusion

This paper has introduced the reasons why warehouse capacity planning in the pharmaceutical industry will gain relevance in the future. The main production steps are still performed in-house at the interviewed pharmaceutical companies and this will stay mainly in-house in the future. Different developments will make it more difficult for supply chain managers to correctly plan the warehouse capacities in the longrange in order to get the right products to the right place in the right condition. With emerging markets getting more and more important in future, warehouse capacities will get even more difficult to correctly estimate. Analyzing the current literature, this paper states that specific, highly automatable, readily applicable models for long-term warehouse capacity planning in the pharmaceutical industry could not be identified.

Further research has to be done in specifying requirements of such a model in the pharmaceutical industry, analyzing in greater detail how warehouse capacity planning is done in other industries and whether this can be leveraged for the pharmaceutical industry.

Fig. 1 .

 1 Fig. 1. General pharmaceutical supply chain structure (material flow)

Fig. 2

 2 illustrates the results of a semi-structured interview series with 11 out of the TOP20 pharmaceutical companies. It shows the mentioned level of outsourced activities (in percent and in terms of volume) throughout the supply chain indicated by the also expresses whether this percentage is expected to change in future (absolute value indicated by the black arrows).

Fig. 2 .

 2 Fig. 2. Percentage of outsourced operations in the various stages of the Supply Chain and future change in percentage points (in terms of volume)

Fig. 3 .

 3 Fig. 3. Keyword search, timeframe 1990 -2013 (shown: 1996-2013). Source scopus.com/. Updated: 04/2014.

  " (n=44459) "supply chain" AND "capacity" (n=2625) supply chain AND "planning" (n=7027)warehouse AND planning (n=1520)"supply chain" AND pharmaceutical (n=705) "supply chain" AND "capacity" AND "pharmaceutical" (n=34) "supply chain" AND "planning" AND pharmaceutical (n=108) warehouse AND planning AND pharmaceutical (n=13) " (n=44459) "supply chain" AND "capacity" (n=2625) supply chain AND "planning" (n=7027)warehouse AND planning (n=1520) "supply chain" AND pharmaceutical (n=705) "supply chain" AND "capacity" AND "pharmaceutical" (n=34) "supply chain" AND "planning" AND pharmaceutical (n=108) warehouse AND planning AND pharmaceutical (n=13) " (n=44459) "supply chain" AND "capacity" (n=2625) supply chain AND "planning" (n=7027)warehouse AND planning (n=1520)"supply chain" AND pharmaceutical (n=705) "supply chain" AND "capacity" AND "pharmaceutical" (n=34) "supply chain" AND "planning" AND pharmaceutical (n=108) warehouse AND planning AND pharmaceutical (n=13) " (n=44459) "supply chain" AND "capacity" (n=2625) supply chain AND "planning" (n=7027) warehouse AND planning (n=1520)"supply chain" AND pharmaceutical (n=705) "supply chain" AND "capacity" AND "pharmaceut "supply chain" AND "planning" AND pharmaceutical (n=108) warehouse AND planning AND pharmaceutical (n Solid lines (pharmaceutical-specific): Dotted lines (general): " (n=44459) "supply chain" AND "capacity" (n=2625)"supply chain" AND "planning" (n=7027) warehouse AND planning (n=1520) "supply chain" AND pharmaceutical (n=705) "supply chain" AND "capacity" AND pharmaceutical (n=34) "supply chain" AND "planning" AND pharmaceutical (n=108) warehouse AND planning AND pharmaceutical (n=13) " (n=44459) "supply chain" AND "capacity" (n=2625) "supply chain" AND "planning" (n=7027)warehouse AND planning (n=1520) "supply chain" AND pharmaceutical (n=705) "supply chain" AND "capacity" AND pharmaceutical (n=34) "supply chain" AND "planning" AND pharmaceutical (n=108) warehouse AND planning AND pharmaceutical (n=13) " (n=44459) "supply chain" AND "capacity" (n=2625)


Aya Ishigaki
email: ishigaki@rs.noda.tus.ac.jp

Hironori Hibino
email: hibino@rs.tus.ac.jp

OPTIMAL STORAGE ASSIGNMENT FOR AN AUTOMATED WAREHOUSE SYSTEM WITH MIXED LOADING

Keywords: Automated warehouse, storage assignment policy, mixed loading. 1

In this study, an automated warehouse system with mixed loading is considered. The majority of previous studies considered assumptions that were similar to those for a single-shuttle system with single loading. Due to the increased number of items in recent years, storage assignment strategies with single loading are not feasible because of the shortage of storage racks. This study adopts a storage policy with mixed loading for an automated warehouse system, which enables the use of one warehouse. Additional movement and transshipment operations, which involve mixed loading, are considered in this paper.

Introduction

In this study, an automated storage and retrieval system (AS/RS) for multiple items is considered. The basic components of an AS/RS are the input/output (I/O) locations, storage racks, and automated stacker cranes (Fig. 1). An important measure of system performance is the cycle time of a stacker crane, which is the sum of the expected travel time and pickup/deposit time. The expected travel time is dependent on the storage assignment strategy. A low expected travel time is critical in the selection of the storage assignment strategy for an AS/RS.

In the past 30 years, studies of AS/RSs have addressed storage policies to reduce the travel time of a stacker crane. Hausman et al. [START_REF] Hausman | Optimal storage assignment in automatic warehousing systems[END_REF] analyzed the cycle time of a stacker crane in a single-shuttle system in an AS/RS using a mathematical model. They analyzed different storage assignment strategies (dedicated storage policy and randomized storage policy) and demonstrated that full turnover-based dedicated storage was a suitable assignment policy. Hackman and Rosenblatt [START_REF] Hackman | Allocating items to an automated storage and retrieval system[END_REF] considered the allocation of items to an AS/RS when it has insufficient space to store all of them. Using a dedicated storage policy, a set of storage locations is reserved for each product for the duration of the planning horizon. While the literature deals mostly with dedicated storage policies. Francis et al. [START_REF] Francis | Facility layout and location: an analytical approach[END_REF] discussed about the four storage policies. They are: dedicated storage policy, randomized storage policy, class-based dedicated storage policy, and shared storage policy. A shared storage policy, allows units of different products to successively occupy the same location, and can provide substantial benefits when precise information is available concerning the timing of storages and retrievals.

Maximal benefits of this type of system are dependent upon the optimal system design. Eynan and Rosenblatt [START_REF] Eynan | Establishing zones in single-command class-based rectangular AS/RS[END_REF] and Wen et al. [START_REF] Wen | The impact of acceleration/deceleration on traveltime models in class-based automated S/R systems[END_REF] demonstrated the influence of the system design (e.g., the length and height of the storage racks and the horizontal and vertical speeds of the stacker crane) on the optimal storage assignment policy. They clearly showed that the system design does not influence an optimal storage assignment policy.

The manufacturing industry is converting to multi-item small-sized production. Thus, a dedicated storage policy requires numerous storage racks because of the increased number of items. In addition, a dedicated storage policy may lack a storage rack. However, the replenishment factor for a storage rack is decreasing. In recent years, many companies load two or more items together to prevent shortage of storage racks. The influence of mixed loading on the optimal storage assignment strategy remains ambiguous.

In this study, an AS/RS with mixed loading is designed. High-performing storage assignment strategies are analyzed using a simulation technique.

2

The Model

Model

The assumptions of Hausman et al. [START_REF] Hausman | Optimal storage assignment in automatic warehousing systems[END_REF] are employed throughout the paper:  The analyzed single-shuttle system consists of a single stacker crane serving as a single one-sided aisle.  A "First In First Out (FI-FO)" storage strategy was implemented in this system.

 The length and height of the storage rack and the S/R machine velocities in the horizontal v x and vertical v z directions (v x > v z ) are known. The acceleration and deceleration of the S/R machine are not considered.  The pickup and deposit times are assumed constant and equivalent to the forking time.  The location number is set to in the order of early arrival from an I/O point (

K t t t ≤ ≤ ≤  2 1
).

The following assumptions are added to consider mixed loading:  One pallet is deposited by a storage location. The replenishment factor of the storage location per item is less than 50%.  If two or more items are deposited on the same pallet, these items will be mixed to create one pallet. If an item is picked up from the mixed loading pallet, the pallet will be divided into two pallets.

CYCLE TIME OF A STACKER CRANE WITH MIXED LOADING

Fig. 2 shows the movement of a stacker crane with single loading. When depositing a pallet with single loading, a stacker crane receives the item at the I/O point and carries it to a previously determined storage location (t k ). After depositing the pallet in a storage location (t f ), the stacker crane returns to the I/O point (t k ). In the case of a pallet with single loading, the required time for depositing and picking up for movement to location k is

f k k t t + × = 2 ω . ( 1
)
Fig. 3 shows the movement of a stacker crane with mixed loading. When depositing a pallet of mixed loading, it is necessary to pick up a pallet with single storage rack stacker crane I/O location loading from the storage location ( k ω ) and to mix these items at an I/O point (t p ). A stacker crane receives the pallet at the I/O point, carries it to a storage location, and returns to the I/O point ( k ω ). Thus, the movement of the stacker crane with mixed loading consists of the movement of the pallets with single and mixed loading. In the case of the pallet with mixed loading, the required time for depositing and picking up for movement to the location k is ) (

p k k t + + ω ω . ( 2
( ) [ ]           × + + × = ∑ ∑ = = K k k p k K k k k t N CT 1 1 1 µ ω λ ω . ( 3
) ∑ = = K k k N 1 λ . (4)
Here, if k 1 is smaller than k 2 ,

1 k ω is smaller than 2 k ω because the relation of 2 1 k k t t ≤
is consistent with the assumption. As the first terms of Eq. ( 3) decrease, the turnover of the location near an I/O point increases for the condition of Eq. ( 4). Hausman et al. [START_REF] Hausman | Optimal storage assignment in automatic warehousing systems[END_REF] proposed full turnover-based dedicated storage using an item's turnover. That is, the first term of Eq. ( 3) can be minimized by assigning items with larger turnover to the order near the I/O point. The results of a numerical experiment indicate that a full turnover-based dedicated storage policy was an acceptable assignment policy compared with a randomized policy. Items with a large turnover are combined and assigned near the I/O point to effectively minimize the first terms.

The second terms of Eq. ( 3) decrease when the movement of a mixed loading pallet does not occur. However, if items with a large turnover are combined, the number of movements for a mixed loading pallet will also increase.

GENERAL MODEL FORMULATION

In the study by Housman et al. [START_REF] Hausman | Optimal storage assignment in automatic warehousing systems[END_REF], the discrete function t k was approximated by a continuous function, and the turnover at the storage location k λ was estimated using the mathematical method. They considered warehouse system configurations, such as square-in-time (SIT), and estimated the S/R machine travel time using the following equation:

j j t = ) ( , ( 1 0 ≤ < j ). (5)
Here, j is the index of a pallet in a rescaled rack and ] 1 , 0 ( ∈ j . However, when considering mixed loading, the travel time to the storage location k needs to be considered a discrete function. We can then estimate the S/R machine travel time using the following equation:

2 2 k k k y x t + = , ( K k , , 2 , 1  = ). ( 6
)
and calculate the turnover of the storage rack k ( k λ and k µ ) using a simulation technique.

The results for the different policies for different s-parameter values of the ABC curve are shown in Fig. 3. The ABC curve is formulated by

s i i G = ) ( , ( 1 0 ≤ < s ). ( 7
)
Assuming that the total demand = 1, a demand of item i is shown by the following equation:

1 ) ( - = s si i D , ( 1 0 ≤ < i ). ( 8
)
We created eight demand patterns using different values of s (1.000, 0.748, 0.569, 0.431, 0.317, 0.222, 0.139 and 0.065). If s increases, the demand for every item will be equivalent. In contrast, as s decreases, the demand differs significantly.

Comparison with the storage policy with mixed loading

In this section, the performance of the full turnover-based dedicated storage policy is compared with the performance of the randomized storage policy. The formulas for the full turnover-based dedicated and randomized storage policies are derived from Hausman et al. [START_REF] Hausman | Optimal storage assignment in automatic warehousing systems[END_REF].

In a randomized policy, every item can be deposited to the vacant rack of the nearest neighborhood from an I/O point. If a shortage of empty racks occurs, a pallet will be loaded with various items together and deposit the rack near an I/O point. In a full turnover-based dedicated storage policy, the storage location of all items is determined in advance. Thus, even when the empty rack remains, it loads various items together at the previously determined location.

In Fig. 4, the average cycle time is plotted along the vertical axis, and the pattern number of demand is plotted along the horizontal axis. The pattern number of demand p was set to the descending order of s. Fig. 4 shows the results for three different values of t p (0.0, 1.0, and 2.0) for each policy. In this study, t p was set to 0 for simplification. The number of order N was set to 50,000.

In the case of single loading, the full turnover-based dedicated storage policy is optimal [START_REF] Hausman | Optimal storage assignment in automatic warehousing systems[END_REF]. However, in the case of mixed loading, the randomized storage policy is optimal when the demand of items are similar (s is small). Fig. 5 and 6 display the average travel time and the number of mixed loading movements when t p = 0.0 and 2.0. If a full turnover-based dedicated storage policy is used, the average travel time decreases and the number of mixed loading movements increases when p is large. However, if the randomized storage policy is used, the average travel time and the number of mixed loading movements have a slight influence on the variation of p. Furthermore, the number of mixed loading movements is small in the case of the randomized storage policy, and the randomized storage policy becomes effective when t p is large. Fig. 7 shows the comparison results for single and mixed loading using a full turnover-based dedicated storage policy. The mixed loading is effective when p is small. If p is small, many empty racks occur near the I/O point. Therefore, despite permitted mixed loading, the movements by single loading and the distance have decreased. This finding shows that a mixed loading of items is effective not only when a shortage of a storage location occurs but also when the demand of items is similar.

pattern number of demand pattern number of demand

Conclusions

An AS/RS with mixed loading is designed and analyzed. In the case of single loading, the average cycle time was reduced using a full turnover-based dedicated policy. However, our experiments show that a randomized storage policy is effective for mixed loading. In this research, the testing is done on hypothetical data. The future issues include a real-life implementation and improvement in storage policy. The method for determining the combination of items in a shared storage policy is critical for future operations.

Fig. 1 .

 1 Fig. 1. Configuration of an AS/RS.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Movement of a stacker crane with single loading

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. Average cycle time for different values of demand (D: full turnover-based dedicated storage policy; R: randomized storage policy) pattern number of demand

Fig. 7 .

 7 Fig. 7. Comparison results for single and mixed loading.


Cyrille Pach

Yves Sallez

Thierry Berger

Thérèse Bonte

Damien Trentesaux

Benoit Montreuil
email: benoit.montreuil@cirrelt.ca

Routing Management in Physical Internet Crossdocking Hubs: Study of Grouping Strategies for Truck Loading

Keywords: Crossdocking hubs, Routing, Physical Internet, Interconnected Logistics, Supply chain

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Montreuil [START_REF] Montreuil | Towards a Physical Internet: Meeting the Global Logistics Sustainability Grand challenge[END_REF] points out that current logistic systems are unsustainable economically, environmentally and socially. The aim of the innovative Physical Internet (PI or π) paradigm-shifting initiative is to reverse this situation from three points of view:  The economic goal is reducing by an order of magnitude the global costs induced by logistics and unlocking significant business opportunities;  The environmental goal is reducing by an order of magnitude the logistics induced global energy consumption, greenhouse gas emission and pollution;  The societal goal is enhancing the quality of life of the different actors (e.g. truckers, logistic workers…) implied in the logistic systems, and of society at large through better goods accessibility and mobility. The PI concept is based on a metaphor of the Digital Internet. By analogy with data packets, the goods are encapsulated in modular, reusable and smart containers, called π-containers. The π-containers range in modular dimensions from large to small. The ubiquitous usage of π-containers will make it possible for any company to handle and store any company's products because they will not be handling and storing products per se. The efficient management of PI crossdocking hubs is a key enabler of quick and synchronized transfer of π-containers through interconnected logistics networks. It has been shown in a previous study [START_REF] Pach | Proposition of a potential fields approach to solve routing in a rail-road π-hub[END_REF] that truck loading activities in PI crossdocking hubs are crucial activities that should be studied in depth. The aim of this paper is to focus on this issue and to propose an approach and strategies for preloading grouping of π-containers to reduce the overall loading time.

The paper is structured as follows. The management issues of PI crossdocking hubs are introduced section 2. Section 3 focuses on the grouping approach and introduces alternative strategies. The simulation platform, protocol and results are then detailed in section 4. Finally a conclusion and some prospects are offered in section 5.

Physical Internet context

The specificities of the Physical Internet crossdocking hubs (denoted π-hubs hereafter) are introduced in the following sections.

From the classical crossdock to π-hub

In a usual crossdocking approach, supply and demand chains are coupled and synchronized, replacing or greatly minimizing inventory buffers [START_REF] Kulwiec | Crossdocking as a Supply Chain Strategy[END_REF]. However usual crossdocking hubs are not designed for supporting the Physical Internet. Several points differentiate a π-hub from a usual crossdocking hub. The main difference is based on the foundation principles of the PI: usual crossdocking hubs are restricted to some suppliers and/or clients of a company, while the PI proposes an open meshed approach. The π-hubs are conceived by default to be open to any π-certified users and to handle multiple dynamically selected sources and destinations.

From a technical point of view, several other differences can also be noticed:  First, existing crossdocking hubs handle all kinds of freight (e.g. cartons, shrink-wrapped pallets) while π-hubs are specifically designed to deal with modular and standard π-containers.  In usual hubs, depending of the type of freight, the transportation is executed manually (e.g. by workers using forklifts for palletized freight) or based on dedicated automated systems [START_REF] Van Belle | Crossdocking: State of the art[END_REF]. As a π-hub handles only smart, standardized modular π-containers, it opens the way for high automation and high reactiveness. An automated π-hub can be mainly composed of a flexible network of πconveyors, allowing decomposition, sorting and re-composition of the πcontainers. The π-conveyors allow moving π-containers in the four directions (front, back, left and right) as depicted in Figure 1.  In a π-hub, a π-container must not be considered as only a standardized container with a cargo as in usual crossdocks. It has informational, communicational and decisional capacities and can play an "active" role in the crossdocking process.

Illustration of a road-rail π-hub

Different π-hub combinations may exist: road-road, road-rail, etc. In order to make clear the nature of π-hubs, Figure 1 presents an illustrative example of a railroad π-hub, inspired from the works of [START_REF] Ballot | Functional Design of Physical Internet Facilities: A Road-Rail Hub[END_REF]. This railroad π-hub aims to realize smooth interconnections between trains and trucks in shortest time. It allows the unloading of five wagons simultaneously and is composed of a sorting area and a manoeuvring area.

Fig. 1. Example of a railroad π-hub (inspired from [5])

The sorting area is used to sort the inbound π-containers and to route them toward the manoeuvring area. The sorting area is composed of a grid of π-conveyors as depicted in Figure 1. The manoeuvring area allows returning the π-containers and moving them towards the different gates, where trucks are located. Note that this railroad π-hub can be extended into a bilateral rail-road π-hub by adding to the right a roadrail π-hub section.

Current issues in π-hub management

In the recent PI research field, the management of π-hubs constitutes an important issue [START_REF] Ballot | Functional Design of Physical Internet Facilities: A Road-Rail Hub[END_REF]. The quick and flexible transfer of π-containers from one transporter to another is the core activity of a π-hub. Different modal transfers (e.g., road to rail, road to road, ship to rail) are currently distinguished in PI networks and several problems must then be considered in the crossdocking process:  Transporter scheduling in short term horizon: the π-hub gates are considered as resources (used by the trucks by example) that have to be scheduled. This problem requires deciding on the succession of inbound and outbound transporters (trucks, ships, etc.) at the gates of a π-hub.  Allocation of π-containers to transporters: this problem consists in choosing the most appropriate loading of trucks with the π-containers unloaded from inbound train or trucks.  Routing of π-containers across the π-hub: Once the π-containers have been unloaded from their inbound transporter, they are engaged in a preparation process that will get them composed appropriately with other π-containers and brought in time to be loaded in their outbound transporter.

The management of a π-hub as studied in this paper must concurrently deal with two types of perturbations:

 The external perturbations, taking into account the following degrees of variability and uncertainty: o The flow of π-containers to be treated can vary through time, both in terms of quantity, size mix and destination mix. o The incoming flow will normally be known to arrive a few hours ahead of time. Considering a train coming from a preceding π-hub, the information relative to its load is forwarded upon its departure. However in a railroad hub, if a train is delayed, another train may enter the π-hub while the trucks are already positioned for the delayed train. Thus the control system should reactively solve a problem that was unknown until that moment.  The internal perturbations concern mainly the network of π-conveyors: A part of the flexible conveying network can be out of order due to breakdowns or curative maintenance operations.

The next part presents a literature review in the field of π-hub control.

Short survey of π-hub control

In the recent PI field, a few studies have been already done on π-hub control. In [START_REF] Ballot | Functional Design of Physical Internet Facilities: A Road-Rail Hub[END_REF] and [START_REF] Montreuil | Functional Design of Physical Internet Facilities: A Unimodal Road-Based Crossdocking Hub[END_REF], the authors propose respectively a specific design of a railroad π-hub and of a road-based π-hub. The primary goal of these studies was to produce a functional design that performed at an acceptable level in terms of user key performance indicators and to explore its robustness with various flows. A simulation study has allowed to model and to validate the normal functioning of a π-hub. However, no perturbation on the conveying system or on the loading/unloading processes has been taken into account.

Moreover, at this point of development of the PI, very few research works have also addressed the routing problems in a π-hub [START_REF] Ballot | Functional Design of Physical Internet Facilities: A Road-Rail Hub[END_REF][START_REF] Meller | Functional Design of Physical Internet Facilities: A Road-Based Transit Center, Progress in Material Handling Research[END_REF]. Recent works [START_REF] Gue | GridStore: A Puzzle-Based Storage System with Decentralized Control[END_REF][START_REF] Mayer | Deadlock prevention in a completely decentralized controlled materials flow systems[END_REF] have proposed decentralized control to prevent deadlocks on a grid of π-conveyors. However these previous works deal with only small-size goods located on a unique conveying module and do not take into account different sizes of containers.

In [START_REF] Pach | Proposition of a potential fields approach to solve routing in a rail-road π-hub[END_REF], the authors study the routing of π-containers in a road-rail π-hub inspired from [START_REF] Ballot | Functional Design of Physical Internet Facilities: A Road-Rail Hub[END_REF][START_REF] Ballot | OPENFRET : contribution à la conceptualisation et à la réalisation d'un hub rail-route de l'Internet Physique[END_REF]. They aimed to find the parameters that have a significant impact on the π-hub effectiveness. The parameters studied were the π-containers' size, their number of movements in the system, the numbers of conflicts between π-containers and the loading time of π-containers in trucks. The works presented in the next section are in the continuity of [START_REF] Pach | Proposition of a potential fields approach to solve routing in a rail-road π-hub[END_REF] and focus more precisely on the grouping of π-containers. Only the routing problem is treated in this paper. Interested readers can refer to [START_REF] Walha | A rail-road PI-hub allocation problems: model and heuristic[END_REF] for a study of the allocation problem and a proposition of a formal model for the π-hub.

Grouping approach and strategies

Simulations presented in [START_REF] Pach | Proposition of a potential fields approach to solve routing in a rail-road π-hub[END_REF] have shown that the loading of trucks is the bottleneck activity of the π-hub. Thus to optimize the transfer of π-containers, an interesting solution is to assemble several small π-containers in front of the truck prior to loading and to load them as a single composed π-container. This section proposes a grouping approach using active π-containers.

Several approaches can be adopted (i.e. distributed or centralised) to solve the truck loading problem in a railroad π-hub. In this paper, the concept of active product [START_REF] Sallez | The Life Cycle of Active and Intelligent Products: The Augmentation concept[END_REF] is chosen for reactivity and adaptability reasons to face uncertainties and perturbations. Usually, distributed approaches can suffer from myopic behaviors [START_REF] Zambrano | The control of myopic behavior in semi-heterarchical production systems: A holonic framework[END_REF].

In this case study, myopic behaviors cannot occur because each π-container already knows its destination truck. Moreover, for each truck a sole initiator can exist at a given time. In the retained approach, communicational and decisional capabilities are embedded in π-containers. These play an active role by creating groups of πcontainers before being loaded onto a truck to reduce the loading queue.

The grouping approach, aiming at loading several π-containers while respecting a determined grouping size, is detailed below and depicted in figure 2 for a threecontainer group (initiator and two other containers).

Fig. 2. Example of container grouping approach

(1) Proposal: The first π-container (the initiator) that arrives in front of its destination truck sends a "grouping proposal" to know the π-containers that could be grouped and loaded with it.

(2) Answer: The concerned π-containers answer to it by giving their arrival time.

(3) Decision: The initiator chooses the π-containers based on two parameters:

-the grouping size limit (defined by the strategy chosen), that provides the maximum number of π-containers in the group, -the arrival times sent by the other π-containers. The initiator container chooses the π-containers with the earliest arrival times to form the group until the size limit. (4) Choice diffusion: The initiator container sends to the chosen π-containers their specific location in the group formed at its right. It also sends a refusal to the unselected π-containers.

Using this approach, three strategies can be used to determine the grouping size limit (used in step 3 of Figure 2). First, all the containers going to the same truck are grouped and loaded at once (i.e. infinite limit). Second, the number of containers in each group is limited statically to avoid disturbing the loading of the neighbor trucks. And third, the number of containers in each group is limited dynamically by extend-ing them if the gates on the right are not used (no truck allocated to the neighbor gates). Figure 3 presents a view of the simulator during this grouping approach and the location of containers within the π-hub.

To validate our approach, the next section presents the simulation environment, protocol and the results for each one of these strategies.

Simulation protocol and results

The grouping approach is evaluated through a simulation experiment by using the Netlogo multi-agent environment. This environment is well adapted for rapid prototyping of reactive multi-agent systems and provides user-friendly interfaces. The behaviors of the active π-containers are represented by agents with processing, communicational and decisional capabilities. Figure 3 presents a screenshot of the simulator during the grouping process presented in Figure 2. Fig. 3. View of the simulator describing a three-container grouping Four series of simulations were performed: the first one presents a basic truck loading without grouping and the three others respectively concern the three grouping strategies presented above. Each simulation experiment contains 2000 runs of the simulator with a random positioning of trucks and π-containers. The train is assumed loaded with only small unitary π-containers that constitute the more interesting case study as highlighted in [START_REF] Pach | Proposition of a potential fields approach to solve routing in a rail-road π-hub[END_REF]. The different simulation experiments are as follows:

Sim. #1: π-containers route themselves into the π-hub and are loaded without grouping (i.e. grouping size limit = 1). Sim. #2: the first π-container that reaches a truck waits for all the containers that go to the same truck to be loaded at once (i.e. grouping size limit = remaining space in the truck). Sim. #3: the groups of π-containers are limited to three containers to avoid disturbing neighbor loading gates (i.e. grouping size limit = space between two gates = 3). Sim. #4: the grouping size limit is now dynamic and can be extended if the neighbor loading gate is not used (i.e. 3 ≤ grouping size limit ≤ remaining space in the truck). The performance indicator is the evacuation time that represents the time between unloading the first π-container from the train and loading the last π-container onto its truck. Table 1 summarizes the different simulation results.

Table 1. Simulations results

First these simulations show that the grouping of containers is efficient. The evacuation time for simulation experiment #2 is around 30% lower than the one for the first baseline scenario (without grouping). The grouping of containers greatly reduces the evacuation time with several containers going in the same truck. Thus the maximum value is divided by two, which implies a lower standard deviation for the simulation experiment.

However, the simulations in experiment #2 exhibit some blocking situations where some truck loading is delayed because the place in front of the truck is occupied by the π-container grouping of the truck on the left. In simulation experiment #3, these blocking situations were avoided because the group size limit was set to 3. The extension of the grouping size limit in simulation experiment #4 does not impact most of the simulations. But in some cases, the evacuation time was lowered by 120 seconds (i.e. one loading time). Indeed, with this modification six containers can be loaded at once (if the gate on the right is not used) instead of two times three containers.

If the scenario includes a lot of π-containers going to the same truck, the strategies tested in experiments #3 or #4 have to be chosen. If there are some gates that are not used in the scenario, the strategy simulated in experiment #4 should be used to provide better results. So the strategies proposed consider an increasing number of specific cases without impacting the overall results. Indeed, the enhanced strategies respectively lower the evacuation time of simulation experiment #2 by 1% to 2% in average over 2000 runs, while taking into account the specific scenarios.

Conclusion

This paper presented a study of routing inside a π-hub and focused more particularly on the loading of π-containers onto trucks. The aim of this paper was to show the impact of different grouping strategies using the concept of π-container activeness.

The simulations proposed showed that the grouping of containers has significant value. It lowers the evacuation time of the system by 30%. The grouping of containers could be made using different parameters like the number of containers grouped or the time waited by containers before loading. This paper illustrated this with some grouping strategies dedicated to specific scenarios.

Next studies should first consider other performance indicators like the departure time of each truck or π-container. It could make easier the evaluation of specific scenarios and of the corresponding strategies. Another perspective is to include internal perturbations to prove the robustness of the routing mechanism in a disrupted environment. Finally, the routing approach could be extended for example by taking into account future states of the system in the decisional and grouping mechanism.


Prof. Dr Adrian E Specker
email: adrian.specker@fhnw.ch

Dieter Fischer
email: dieter.fischer@fhnw.ch

Toni Waefler
email: toni.waefler@fhnw.ch

Multi Layer Modeling of Socio-Technical Production Planning and Control Systems

Keywords: socio-technical systems, modeling, production planning and control, manufacturing

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

During a project in several manufacturing companies which has been supported by the Swiss Confederation (KTI), the need for suitable representations and a model method emerged in order to support our analysis and conceptual tasks. The project has been about decision support and the optimization of production planning and control tasks and related decisions. During our project work it became (once more) clear, that in an interdisciplinary project regarding production planning and control, unfortunately, one has to develop inevitably "ad hoc" and individually favored representations and modeling technologies. Surprisingly up to the present day no standardized, uniform, comprehensive and "complete" system modeling method exists as an established standard. It is not clear at all with which methods one has to document socio-technical production systems in an integrated way, and how these systems are to be modeled or to be explained. That is, no real methodical certainty exists when a project has to deal with many system aspects. Rather originate within the scope of such projects -in the absence of alternatives and of necessity -more or less new situation-related visualizations. This shows an attempt to do justice to the complexity and diversity of the systems to be described. Meanwhile most representation and modeling methods lack an integrating frame, which is why one has to use different and quite separate representations -which lack a clear and recognizable relation between different aspects of the system. The mental integration of different and especially separate representations can therefore not succeed in an optimal way. Modeling methods, like CIMOSA [START_REF]CIM -Open System Architecture[END_REF], ARIS [START_REF] Scheer | ARIS: Modellierungsmethoden, Metamodelle, Anwendungen[END_REF], SCOR [START_REF] Schnetzler | Das Supply Chain Operations Reference (SCOR)-Modell zur Beschreibung der Wertschöpfungskette Holz[END_REF], Viable system model -VSM [START_REF] Beer | Kybernetik und Management[END_REF], UML [START_REF] Burkhard | UML -Unified Modeling Language: Objektorientierte Modellierung für die Praxis[END_REF], Value Stream Method -VSM [START_REF] Hines | The seven value stream mapping tools[END_REF] etc. lay their focus mainly on the technical or organizational side. Especially social and cognitive aspect models are not an integrated part of those methods, like e.g. MTO-Analysis [START_REF] Strohm | Ganzheitliche Betriebsanalyse unter Berücksichtigung von Mensch, Technik und Organisation. Vorgehen und Methoden einer Mehr-Ebenen-Analyse[END_REF], Rasmussen [START_REF] Rasmussen | Information Processing and Human-Machine Interaction[END_REF], Hierarchical Task Model [START_REF] Stammers | Task Analysis. in: Evaluation of Human Work: A practical Ergonomics Methodology[END_REF], or Knowledge Networks [START_REF] Stanton | Distributed situation awareness in dynamic systems: theoretical development and application of an ergonomics methodology[END_REF].

Problem Statement

The deficit we face in projects concerning the investigation of "production planning and control systems" depends in fact on our view, to sum it up, that there is no general accepted method to model socio-technical systems which is broad enough to deal with all social, cognitive and technical aspects in an adequate way -or that the methods in use rather negate important social and cognitive aspects. However, the success of projects in such a field depends on the fact, how well the project partners succeed in grasping all those aspects of the production system in order to form a comprehensive conceptual model. Today every successful project like e.g. in construction engineering would be totally inconceivable without high quality, comprehensive construction blueprints. Models and representations of a socio-technical manufacturing system are not only a topic in the project area. Adequate models would also be valuable for employees who are active in the daily business -as with adequate models they could better understand their enterprise. To eliminate a misunderstanding in advance: Business processes are in many ways mapped or modeled in ERP systems and furthermore there exist quality manuals. However, on the other hand, we found that central factors about the work system are not well documented neither in ERP systems nor in quality manuals (s. below).

Goals and Requirements

On account of the problem formulation described above and the ascertained deficits, from our point of view the need of a method which documents socio-technical manufacturing systems has arisen. The method should permit therefore in particular taking into account the most different aspects (aspect systems) and integrate them without losing the internal relations to the overall system. The goals are:

 a model of the system hierarchy and its respective levels (system / subsystem)  an integrated framework for various subsystem and aspect systems  suitable to model technical and social aspect systems and their interrelations  expansible to new aspects according to the user's needs  easy navigation between different aspects and views of the system

Multilayer Modeling Approach

One purpose of the project consisted in creating an integrating representation meta frame in which different aspect systems at alternatively different system levels can be arranged, without the respective mutual relation gets lost. The system to be visualized must be integrated in a stable frame. As a base of the system representation and in analogy to an architect's plans or construction blueprint a so called "floor plan of the enterprise" served us here. This "floor plan" shows the overall system with his accompanying subsystems. Here, the possibility exists, to illustrate already several layers of the system. In support of the black box representation, known from the system engineering approach quite an easy representation with rectangles was chosen [START_REF] Züst | Einstieg ins Systems Engineering, kurz und bündig[END_REF].

System hierarchy: Systems and Subsystems

The uppermost representation level shows the overall system, which is called "S(0)". On the level "S(-1)" the system is shown with its subsystems (Fig. 2). In the example (Fig. 1) the system shows an overall system S(0) of our project partner. Eight departments, like painting, prototypes, logistics, etc., illustrate the according subsystems.

With the change of the level S(0) to the level S(-1) the level of detail increases -this step is called "Drill-Down". The requirement of the Drill-Down has been realized in our software tools with the help of hyperlinks as the software tool we used did not support the generation of a hierarchy. In this feature is a major weakness of most graphic tools. Our prototype was provided in Microsoft Visio.

Aspect Systems -Aspect Layers

The system to be visualized has to be modeled -in order to understand its complexity -with its aspect systems or aspect layers (s. Fig. 3). These aspect layers should be integrated into the pre-existing floor plan as described above. During our project we have been able to derive a first set of these so called aspect layers. They emerged from our different perspectives of the planning and logistics system. There is no sequence in these layers, it is just a set which can vary according to the needs.

Formal Organization

The formal organization is a mapping of the hierarchical leading structures of the company ("floor plan").

Planning and Control Operations & Policies

Describes the planning and control system, especially relations between different elements (push, pull).

Knowledge Network

Describes implicit and explicit knowledge elements in relation with a concrete task or decision.

Social Network

Describes the frequency of formal and informal contacts between different people. The frequency and importance is analyzed by ratings of the interviewed person.

Object Layer

The object layer describes system elements like raw material, products.

Process Layer Describes the relevant business or work processes

The number of the aspect layers which can be illustrated is arbitrarily extendable, at least in principle (Tab 1.). Essential is not primary which symbols or which form a single representation uses -here personal preferences may rule. It is much more vital that different aspects in any combination can be faded in and out. This helps the understanding of the system and the successive mental integration of different system aspects and views.

Of course one has to determine well understandable symbols for the representation of these aspect layers. Besides, we tried hard not to invent new symbols or new methods but to use wherever possible already well known symbolic libraries like these from e.g. "Value Stream Modeling" [START_REF] Hines | The seven value stream mapping tools[END_REF]. This simplifies the general intelligibility of the system representation.

Examples of Realized Aspect Layers

In the following section exemplarily some of the aspect representations realized in the project are described in a more detailed way. An entire documentation of all used representations is not possible, because countless combinations of levels and aspects are possible what leads to a very high number of visualizations of the system [START_REF] Specker | Modellierung von Informationssystemen: Ein methodischer Ansatz zur Projektabwicklung[END_REF]. It matters for us to illustrate the basic and fundamental principles of the provided representation method. That is to focus on the internal relation between the different aspect models with the underlying "floor plan".

Aspect of Planning and Control

An essential aspect of the analysis of the production system concerns the analysis of "work order relations" between different shop floors and departments. Work orders can be generated either from of a central planning and control department or as an alternative they can be initialized in a co-operative way (s. Fig. 4). In order to understand the planning and control philosophy one has to analyze the order relations between different systems. In particular we tried also to differentiate so called "push" and "pull" relations. As a "push relation" (straight arrows) we defined in our project relations, where the order-taking department has only a minimal autonomy concerning the timing of the order sequence as a central planning department releases these orders. On the other hand in "pull" relations (circle within the arrow) the order taking place is autonomous. The example below shows the differentiation between several places and departments. According to our notation it becomes evident that some workshops plan with push relations while others maintain only pull relations. We have defined different types of relationships concerning the work orders and have been relating these relations on the preexisting "floor plan". Every line could be augmented by some attributes in order to describe the exact type and purpose. This has been one starting point to document our analysis results. It shows how we have been able to relate our findings into the pre-existing floor plan.

Aspect of the Knowledge Network

As an example of the analysis of a social aspect system, we will illustrate how the so called "knowledge network" [START_REF] Stanton | Distributed situation awareness in dynamic systems: theoretical development and application of an ergonomics methodology[END_REF] could have been integrated into the same "floor plan" as other elements without loosing the representation of the overall system. This analysis concerns the description of existing "knowledge items", that is, which relevant knowledge elements are "instantiated" at the same time for a very specific task.

The result is illustrated in Fig. 5. The clouds show "knowledge elements" whereas the lines determine which person uses a certain concept or knowledge element.

In our specific project, the analysis of a "knowledge network" representation has been conducted for several selected specific tasks -in Fig. 5. the task of dealing with a "machine breakdown" is described. This analysis has been carried out by the work psychologists of our group. The results concerning the crucial knowledge and data items could be key to the design of the new ERP-system. This example indicates clearly how one can succeed in inserting a preexisting representation method -the one of the "knowledge network" -into a preexisting "floor plan", without the relation would have gone lost to the overall systems.

Aspect of the Social Network

In the area of planning & control of work orders almost always a so called "secondary network" can be identified [START_REF] Wäfler | Planning and Scheduling in Secondary Work Systems[END_REF]. This secondary network is established in order to fulfill the task of coordination of work order as e.g. the optimal timing of work orders. This network maps e.g. the distribution of decision-making competencies or the flow of certain information throughout the company (s. Fig. 6). It can be analyzed by interviews, e.g., by analyzing the frequency and the importance of bilateral relations.

Experiences of Practice

The first experience concerns the software-technical implementation. The second category concerns the aspects of the shown content. The technical category can be characterized by the fact that the chosen software tool used had limited capabilities and supported certain demands only with considerable expenditure -the possibility of a hierarchical and comfortable drill-down was not supported adequately. The chosen software tool (Microsoft Visio) permitted it rather well, to select different aspects layers and to fade them in and out. However, a bigger problem consisted in the fact that new information could be integrated only with quite an effort into the pre-existing "floor plan". The "experience of practice" showed many positive aspects as we have been able to integrate results of work psychologists and industrial engineers.

Conclusion

The need for an integrated representation method which makes modeling of different aspects of a socio technical system on different layers possible could be fulfilled. It could have been shown that many -otherwise rather disjointed representations and models -can be integrated in an overall meta frame. Late changes of the floor plan can cause an effort in order to maintain the picture.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Example of a Level S(-1) system

Fig. 3 .

 3 Fig. 3. Aspect Layers of the Socio-Technical System

Fig. 4 .

 4 Fig. 4. Relations concerning planning and control -Push-und Pull-relations

Fig. 5 .

 5 Fig. 5. Knowledge Network in Connection with the Organization and the "Floor Plan"

Fig. 6 .

 6 Fig. 6. Social Network

Table 1 .

 1 Aspect Layers

	Layer	Description


Rodolfo De Oliveira

Jorge ¹ Muniz
email: jorgemuniz@feg.unesp.br

Fernando S Marins
email: fmarins@feg.unesp.br

Rodolfo Alves De Oliveira

Fernando A S Marins¹

Analysis of Factors for Implementing TPM: A Study in Welded Tube Manufacturers

Keywords: Total Productive Maintenance. Critical factors. Continuous improvement projects. Welded tube industries. adfa, p. 8, 2014

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Companies seek solutions to increase their profitability through eliminating losses, reducing time spent in models and tools exchange, setting standards of speed to productive machines and improving the final quality of products [START_REF] Cakmakci | Set-up time reduction process and integrated predetermined time system MTM-UAS: A study of application in a large size company of automobile industry[END_REF][START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF]. With a view of improving operational performance, continuous improvement programs have been run

with control and production management tools.

It is discussed the influence of contextual factors as size, age of the plant, and the influence of the workmen union of the sector in successful TPM's implementation, and other good production practices [START_REF] Shah | Lean manufacturing: context, practice bundles, and performance[END_REF][START_REF] Muniz | Lean Management Practice: Toyota Brazilian Plants Case[END_REF].

This study aims to identify and assess critical factors influencing on the implementation of continuous improvement projects, specifically the TPM. This research is a quali-quanti study and collects data with managers who lead TPM implementation in the shop floor.

Autonomous maintenance aims to increase operational uptime of equipment through training and involvement of operational staff, but this goal can be hindered if there is an inadequate implementation of the program, blurring in planning, coupled with a lack of top management support and commitment of the staff.

Searching for better results, for the solution of recurring problems and due to fierce competition, the industrial sector has been striving to carry out improvement projects, targeting gains through the implementation of appropriate tools, among which the TPM stands out, but it is necessary to monitor, track and identify the critical success factors involving the entire staff.

In this perspective, the present work can contribute to production managers with an assessment of the critical factors that will assist in decision-making processes for implementing improvement projects and troubleshooting methods, more specifically based on the TPM and Autonomous Maintenance.

The present work is structured into sections. Section 2 presents a theoretical exploratory review that discusses continuous improvement, TPM and Critical Success Factors. In Section 3, it is presented the used research method. Section 4 discusses the case study on the metallurgical industry and the Critical Success Factor for the improvement project are consolidated. Section 5 presents the final considerations, followed by references.

Theoretical Basis

Critical factors for a successful implementation of TPM are need for training, allocation of necessary resources, definition of workload and an autonomous working group focused on the TPM [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF]. It was registered gains of 83% increase in productivity, and a reduction in the rate of 517 machine stops for 89 times [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF].

The literature analysed indicates a methodology that uses computational resources through a system developed to compare the losses of different machines and equipment by the OEE and identify the hidden times that saddled the process [START_REF] Joeng | Operational efficiency and effectiveness measurement[END_REF].

There are applications of Single Minute exchange of dies (SMED) methodology added to Method Time Measurements (MTM) to preserve the best arrangement through standardization to be incorporated by the TPM [START_REF] Cakmakci | Set-up time reduction process and integrated predetermined time system MTM-UAS: A study of application in a large size company of automobile industry[END_REF].

It is also explores the use of the SMED and its relevance in studying tools exchange, particularly the reduced-time ones [START_REF] Cakmakci | Process improvement: performance analysis of the setup time reduction-SMED in the automobile industry[END_REF]. The present study did not use the SMED, but notes the importance of attention in quick exchanges. Next, it is going to be demonstrated significant gains revaluating and redefining operation routines, but the author goes further and emphasizes that it must be applied during the development and design of equipment. Table 1 presents the definitions for the Critical Success Factors adopted in this paper.

Project Financing

Financial contribution that must be measured and invested in the program for fulfilling all steps necessary to achieve the expected results [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF].

Responsibilities Definition

Definition of the ones who are directly responsible for the project, with autonomy and authority to assign responsibilities to the staff [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF], [START_REF] Shah | Lean manufacturing: context, practice bundles, and performance[END_REF].

Adopted Methodology and Scope

Tools and methods defined for the project implementation, the way in which it was sectioned a more comprehensive program in relation to the initially defined scope [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF].

Steps Planning

Fulfillment of the previously established steps, respecting necessary time and sequence for the project success [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF].

Leadership

The needed profile of the Leader for conducting teamwork, with influence and motivation to seek results, assumptions which are fundamental for the project success.

Training

Personnel training, knowledge dissemination, and information level equalization among all those involved [START_REF] Cakmakci | Process improvement: performance analysis of the setup time reduction-SMED in the automobile industry[END_REF][START_REF] Cakmakci | Set-up time reduction process and integrated predetermined time system MTM-UAS: A study of application in a large size company of automobile industry[END_REF][START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF].

Supporting areas

Support and assistance that should be given by the support areas that are not directly involved in the project.

Management Dedication

Attention that must be devoted by a part of the Managers in the actions defined by the group that are not associated to routine activities, giving them due importance and providing necessary resources [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF].

10. Workload Definition of the activities and an association of routine with the dedication needed by the whole staff in relation to the project [START_REF] Cakmakci | Set-up time reduction process and integrated predetermined time system MTM-UAS: A study of application in a large size company of automobile industry[END_REF].

Goals and Indicators

Definition of indicators that are aligned and have an interaction with business objectives. Bold targets, but compatible with projects underway [START_REF] Cakmakci | Process improvement: performance analysis of the setup time reduction-SMED in the automobile industry[END_REF]34,[START_REF] Joeng | Operational efficiency and effectiveness measurement[END_REF] .

Staff Motivation

Recognition of the achieved work and applicability of developed projects in order to contribute to the growth of the company and generate gains for the staff [START_REF] Chan | Implementation of total productive maintenance: A case study[END_REF].

Staff Commitment

Commitment of each staff member with a continuous improvement [START_REF] Shah | Lean manufacturing: context, practice bundles, and performance[END_REF].

Research Method

This study was developed in two metallurgical industries of São Paulo, the most industrialized State in Brazil, which are manufacturers of carbon steel products for the industrial, oil and gas sectors for the national and international markets (Table 2). Respondents were asked to indicate the most important factor with the number 1, and so on until the number 13, the least important, in the column called "Rating" on the Survey Form of the Critical Success Factors. The closed questionnaire was conducted with 12 leaders with 83% return of responses.

Both companies launched their programs with embryonic projects. As midsize companies, they invested in continuous and manufacturing processes improvement within possible. The need to establish a position on the market and modernize the plant significantly reduced investment aid in modern management tools that require more extensive programs. However, the quest for better results has led these companies to adopt some programs of continuous improvement in a fragmentary form. In this study, it was adopted the Autonomous Maintenance that represents only one of the pillars of the TPM.

Data management and ordering Critical Success Factors aims to highlight those that were considered of utmost importance. Table 3 presents the weightiness assigned to each of the 13 factors. It is noted that the most important critical factors presented by Leaders of company E1 demonstrate its structural and sizing needs, i.e. it is not clear what resources are available and the adopted standardization through measurements and tar-gets for achieving project success, pointing also to financial aid, staff motivation and leadership profile, basic factors that must be previously defined.

Table 3. Importance Indication and assigned weight for indication

The result of the assessments made by Leaders of company E2 show needs for planning, organization and defining responsibilities for the project to succeed.

By comparing the results of assessments carried out by Leaders of companies E1 and E2, it is possible to observe that company E1 lacks basic structural definitions, while leaders of company E2 direct their actions towards activities organization and project participant assignments.

Note that in a joint evaluation of the results obtained between E1 and E2 companies, as shown in Figure 8, the ratings of Critical Success Factors changes again.

Figure 1 presents the ratings of factors with a joint assessment. Top Management Commitment (CSF 1) is indicated as the most important factor to both companies.

Some results of the TPM implementation were identified along the survey, as Table 4.

In these projects, even though it has been an attempt of partial implementation and despite the flaws in program structure, it was found that the analyzed companies had significant gains.

Conclusion

This study aimed to identify the determining factors for the success of implementing the TPM from managers' perspective. Top Management Commitment, Leadership, Management Dedication, Indicators and Targets, and Steps Planning were identified and assessed.

Furthermore, this study is also proposed to present positive results, but warns that savings could have been greater if the program had been restructured, even if abiding by a prior decision to be implemented just under the pillar of Autonomous Maintenance, being reoriented by factors herein indicated, though.

There is coherence among the results and the literature by presenting similar factors. This indicates that the factors analyzed are similar independent the sector researched.

This paper presented coherence between the analyzed companies in relation to the Critical Success Factor of greatest importance, both pointing to the lack of commitment by Top Management as being determinant for success.

It is noteworthy that positive and proven results that are routinely divulged in several specialized communication media induce companies' managers to adopt, even without preparation or pre-planned improvement programs, however, often by ignorance and/or being poorly advised, a partial implementation of a complete and extensive program as the TPM, as it was highlighted in this work into which two companies had adopted only the Autonomous Maintenance which is just one of the TPM pillars, without following the steps and adequately predicting necessary investments.

There are no impediments to adopting partial programs, regardless of the reasons for the decision, even if it were a strategic definition, steps must assessed and sized. It is crucial to define and present clear objectives in order not to generate expectations on the team, and avoid losses and disrepute if the program is extended or resumed in the future.

This work showed that the competitive differential between capital goods companies that act with commodities, which are goods with prices (pre)defined by the market, lies in continuous improvement, and that programs which are properly implemented with support from Top management could mean the survival of the business.

Staff participation and contact with the culture of continuous improvement, necessary to introduce the concepts of Autonomous Maintenance, brought changes in behaviour for all those involved in both companies, in the form of seeing and participating in results in a more active way, in the perception that it actually adds value to product, and even in their attitude towards safety.

As

  The open questionnaire was comprised of questions as follows. It sent by email to 5 leaders who held leadership positions in the company's structure. a) In your opinion, what does it take for an implementation project of Autonomous Maintenance to succeed? Why? b) Given the assessment made on question (a), answer: what was missing and/or undermined the implementation of Autonomous Maintenance and TPM in the unit? Why? c) What do you expect from the TPM implementation in the unit? Which results? Why?The respondents are Project Leaders of implementation. They are professionals with technical training dedicated to shop floor management, all with years of experience in the metallurgical industry. Open interview responses were obtained with professionals in the following profiles: 4 Improvement project Leaders in company 1 (E1) and 1 improvement project leader in company 2 (E2). The open interview was analyzed according to the method of Content Analysis defined[START_REF] Bardin | Content Analysis (Análise de Conteúdo)[END_REF].A closed questionnaire was elaborated in order to obtain the opinion of each of the respondents on the order of importance of each of the 13 Critical Success Factors obtained in the open interview.

  respondents and companies can be found in the Appendix. According to Leaders of company E1, the CSF1 (Top Management Commitment) was appointed as being the most important factor, which was also appointed by Leaders of company E2. Another coincidence was the CSF11 (Indicators and Targets) were ranked as the fourth most important factor in both companies. However, other rated factors follow their own characteristics. CSF9 (Management Dedication) appears in second, CSF5 (Steps Planning) in third, and CSF3 (Definition of Responsibilities) was ranked as the fifth most important factor.

  The reduction in time of tool exchange generated gains of R$42,835.06/year to company E1 and R$10,162.60/year to company E2. The improvement work in productivity involved other actions focused on machines performance that go beyond the work conducted on non-detailed Machines Stops. However, reducing time span and considering the productivity achieved after the improvements indicated a potential annual savings of R$723,644.23 to company E1 and R$333,959.81 to company E2.

Figure 1 .

 1 Figure 1. Assessment of Critical Factors

Table 1 .

 1 Definition of the Identified Critical Success Factors

	Critical Success Factor (CF)	Description
	1. Top Management	Full support by Top managers of the company in following, participating and
	Commitment	monitoring actions for the result.

Table 2 .

 2 Companies Description

		Company 1 (E1)	Company 2 (E2)
	Employees	350	450
	Annual Turnover	R$ 60 and 110 million / year	R$ 40 and 90 million / year
	Productivity	110 thousand ton / year	70 thousand ton / year
	Time in operation	Over 50 years	Over 50 years
	The sectors defined for carrying out these projects were conformation and
	welding, involving a group of professionals of different levels and areas of expertise.

Table 4 .

 4 Gains (2007Gains ( -2009) )

	900
	800
	700
		425
	600
	500
			136
	400
				261	112
	300		350		335
	200	450	375			78
					310	161
	100		127	211	127	176	72	87 78	62 14	47 23	14 56	29 38
	0
		Item			Before	After		Gain		Company

Indic Weight Indic Weight Indic Weight Indic Weight Indic Weight Indic Weight Indic Weight Indic Weight Indic Weight Indic Weight

  proposal for further work, it is suggested the use of decision making methods with multiple criteria, such as the Analytic Hierarchy Process (AHP) for assigning weights that were arbitrarily set, aiming to highlight the 5 most important critical factors, as shown in item 3.2.2. It is also recommended the use of statistical methods and software for evaluating results. The AHP can give more accuracy in the weights set for each factor.It would be interesting to deepen in performance results, extending to sales lead and measuring profit, not only comprising savings that reflect in production costs, as presented in this study, but going beyond the definition of the Critical Factors and introducing boundary conditions and delimitations in order to effectively restructure the adopted program, and make a comparison between a complete program and a partially implemented one.

												CRITICAL SUCCESS FACTORS
		CSF1		CSF2		CSF3		CSF4		CSF5		CSF6		CSF7		CSF8		CSF9		CSF10	CSF11		CSF12		CSF13	Interviewee /
																					Indic	Weight Indic	Weight	Indic Weight	Company
	1	100	1	100	6	1	6	1	4	25	1	100	9	1	4	25	3	50	8	1	1	100	4	25	6	1	Leader 1	E1
	2	75	2	75	5	10	9	1	2	75	2	75	4	25	9	1	4	25	7	1	2	75	3	50	5	10	Leader 2	E1
	1	100	3	50	5	10	3	50	7	1	4	25	9	1	5	10	6	1	9	1	4	25	4	25	4	25	Leader 3	E1
	2	75	5	10	3	50	5	10	8	1	2	75	6	1	7	1	3	50	5	10	5	10	2	75	8	1	Leader 4	E1
	1	100	2	75	7	1	4	25	4	25	1	100	8	1	5	10	8	1	10	1	6	1	6	1	4	25	Leader 5	E1
	E1	450		310		72		87		127		375		29		47		127		14		211		176		62
	1	100	6	1	5	10	6	1	1	100	3	50	5	10	8	1	2	75	6	1	2	75	4	25	12	1	Leader 6	E2
	1	100	7	1	6	1	6	1	5	10	4	25	4	25	5	10	1	100	5	10	5	10	3	50	9	1	Leader 7	E2
	3	50	5	10	2	75	9	1	3	50	7	1	7	1	5	10	4	25	5	10	6	1	7	1	5	10	Leader 8	E2
	2	75	3	50	3	50	3	50	2	75	5	10	8	1	7	1	2	75	4	25	1	100	9	1	13	1	Leader 9	E2
	1	100	3	50	4	25	4	25	1	100	3	50	6	1	9	1	2	75	5	10	2	75	9	1	8	1	Leader 10 E2
	E2	425		112		161		78		335		136		38		23		350		56		261		78		14
	(E1+E2)	875		422		233		165		462		511		67		70		477		70		472		254		76