Asma Rakiz
email: asma.rakiz@emines.um6p.ma

Pierre Fenies
email: pierre.fenies@emines.um6p.ma

Production-storage and transport integrated planning for a multi-site mining industry

Keywords: Intergated lot sizing, Transportation, Linear optimisation, Mining industry

Assuming that local planning usually leads to sub-optimal solutions, this work aims to solve an integrated production, storage and distribution problem as part of a global supply chain system. The problem we address combines a lot sizing and distribution problem in a multilevel, multi-product, multi-period production network. To solve it, we propose a MILP (Mix Integer Linear Program) taking into consideration the local constraints of the different subsystems, but also the global ones that express the interactions between subsystems. This model proposes simultaneously a production, storage and transport plan that satisfies a known demand while minimizing total production, storage and distribution costs. Finally, the solutions found within this approach have the advantage of considering the system's overall decisional cohesion as well as the constraints propagation in the various links of the chain. The originality of the work comes from the fact that we have addressed a multi-level lot-sizing problem, combined with a single rail transport problem. This integrated problem, to the best of our knowledge, has not been previously addressed. The model is tested and validated on a real mining industry, it proposes an integrated solution for simultaneous production, storage and distribution planning.

Introduction

This work takes place at OCP group, one of the world's leading companies in the phosphate market. OCP has a complex supply chain structure that starts with the mining phosphate deposits and reaches customers all over the world. The present study concerns Youssoufia site, located in the central axis, one of the three independent parallel axes of OCP's supply chain. This site produces three products (P1, P2, P3) delivered for two types of customers: local customers who refer to chemical transformation sites where acids and fertilizers are produced, and international ones from around the world. Youssoufia site is composed of three plants (laundry, calcining, and drying plant) that are interconnected by conveyors and separated by stocks upstream and downstream of each transformation process. This research focuses on supply chain planning problems as a whole. It considers an integrated planning approach where production, inventory, and transportation decisions are integrated. It adopts a global approach aiming to achieve an integrated flow planning that considers all the supply chain components including their respective constraints and specifications. The aim is to propose a single optimisation model taking into consideration (i) the characteristics of each subsystem composing the global production system, but also (ii) the different interactions that interconnect these subsystems in order to guarantee their synergy in the global logistics system. Classical models address supply chain planning problems sequentially or independently. The most classical approach starts with production and storage planning decisions, and establishes later transport decisions in an independent way. Though, it is now demonstrated that production and distribution decisions are mutually related problems and need to be dealt with simultaneously in an integrated manner [START_REF] Fahimnia | A review and critique on integrated production-distribution planning models and techniques[END_REF]. According to [START_REF] Adulyasak | Formulations and branch-and-cut algorithms for multivehicle production and inventory routing problems[END_REF], integrating these decisions lead definitely to a considerable increase in efficiency and effectiveness.

In addition, this paper addresses a real industrial problem posed by OCP. The studied system is a complex mining industrial system consisting of a multilevel, multi-product supply chain. This supply chain is composed by a multi-site production system, several storage sites and a train transport system within a single railway. This railway is used sequentially for passengers transport and for finite products transport, which imposes fixed time windows for finite products transport. This said, this paper addresses a capacitated lot sizing problem, combined with a hybrid transport problem using conveyors (for inter-site transport) and a single rail with time windows (for finished product delivery). All the production, storage and transport resources are limited by finite capacities. The remainder of this paper is organized as follows: section 2 presents a literature review of the main themes addressed by this work. The proposed MILP to answer the problem is detailed in section 3 before illustrating it with a practical case study in section 4. Finally, some conclusions are addressed in section 5.

Literature review

Many researchers have been interested in production and stock planning using the lot sizing problem which has led to a literature proposing diverse and varied models to solve this kind of problems. The main objective of these models is determining the quantities of products to be manufactured in order to meet the demand while minimizing production, set up and storage costs [START_REF] Brahimi | Single item lot sizing problems[END_REF]. Other costs may be added such as stock shortage cost. One of the reasons for interest in these models is their wide scope. Indeed, these models can be applied for the uncapacitated lot sizing [START_REF] Bahl | Or practice-determining lot sizes and resource requirements: A review[END_REF], scheduling and lot sizing (small bucket) [START_REF] Graves | A review of production scheduling[END_REF], and flow control [START_REF] Kuik | Batching decisions: structure and models[END_REF]. They can also be associated with other supply chain planning problems [START_REF] Adulyasak | Optimization-based adaptive large neighborhood search for the production routing problem[END_REF] such as distribution problems to form the Integrated lot sizing with direct shipment models class, or to routing problems to form the class of models called Inventory Routing Problem (IRP), or even include all supply chain planning problems (production, storage, distribution, and routing) to cre-ate the Production Routing Problem (PRP) class. The extension of lot sizing models to multi-level supply chain structure is called multi-level lot sizing problem (MLLSP). The basic multi-level model, called the Multi-Level Capacitated Lot Sizing Problem (MLCLSP), was proposed by [START_REF] Billington | Heuristics for multilevel lot-sizing with a bottleneck[END_REF]. Its purpose is to link the end-products demand with the needs for internal components using the Gozinto matrix. This matrix is composed of the coefficients a i,j which represent the number of products i necessary to produce a product j, where i is the immediate predecessor of j in the product bill of material.

Based on the research that we analyzed, we could not find a paper that combines the problem of multi-level lot sizing with that of transport using a single railway track with time windows. To the best of our knowledge, little attention has been given to the problem of variable transport capacity and minimum quantity to be transported. Moreover [START_REF] Jans | Modeling industrial lot sizing problems: a review[END_REF] indicate that the most of industrial lot sizing literature is interested on discrete production problems, which makes production planning in the process industry a promising area for new research. All of these and other differences were synthesized in Table 1 containing the comparison between our MILP model and the reviewed ones that are dealing with a multi-level modeling.

[6] [1] [3] [4] [10] [7] MILP Parameters Production capacity X X X X X X X X X X Dynamic stock capacity X Variable transport capacity X X Transport capacity X X X X X X Minimum quantity to be trans- ported X Product structure X X X X X X X Inter-site travel time X X X Set up time X X X X Maximum number of trains per period X Holding stock cost X X X X X X X X X X X Variable production cost X X X X X X X X X X X Set up cost X X X X X X X X X Transport cost X X X X X X X Decision variables hline Multi-level production X X X X X X X X X Storage X X X X X X X X X X X X X X Train transport X
3 Multi-level integrated planning model

The considered production network Fig. 1 is inspired by a real case industrial problem, it is composed of several manufacturing plants producing N products intended to meet two types of demand: an independent final demand known for a finite horizon, and an intermediate one of a product being a component of another downstream product in the supply chain. Shortages are not allowed and manufactured product have general type structure. The planning horizon is discrete and is composed by T periods. One product can be manufactured in several plants. Each plant is limited by a maximum production capacity and has a downstream stock in which the manufactured products can be stored. Each stock is limited by a maximum stock capacity. The different plants are interconnected by conveyors characterized by z u,u : which refer to time required for a product to be transferred from plant u to plant u , u being a downstream plant of the plant u in the supply chain All finished products are transported via a single railway track to two different destinations: the port from which products are exported to international customers, and the local customers (chemical manufacturing sites). Products can be stored at the train unloading stations. Each train can ship only one product at a time and requires time to travel between production sites and destination sites. There are fixed time windows (train paths) in which the transport of finished products is possible; outside these hours, the railway is reserved for passenger transport. The delivery of the finished products must therefore respect these train paths. In order to solve this problem, we propose a multi-level multi-product linear model where the shipment of end-products to the final stocks is provided by trains respecting the transport time windows. The objective of the model is to identify the periods in which production takes place as well as the production quantities, the amount that has to be stored and the quantity to be transported by train and the time windows to exploit. The production of each product gen-erates a variable production cost, a set up cost and a set up time are incurred whenever a production batch starts. A holding cost is incurred per unit held in inventory per period. In addition, transport by train of a product generates a train transport cost. The considered notations of the mathematical model are detailed in Table 2. The formulation of the mathematical model is as follows: Set of final stocks Di,t

Final demand for product i in period t X max u Maximum production capacity at the plant u ai,j,u The quantity of i needed to produce a unit of j at the plantu. ai,j,u = 0 if j < i (j predecessor of i) dbi,t,u Hourly production rate of product i in the plant u at the period t Imax,u Maximum storage capacity at the site u Qmax Maximum train transport capacity Qmin Minimum train transport capacity λt Binary parameter equals to 1 if train transport is possible at period t, 0 otherwise z u,u Time required for a product to be shipped from the plant u to the plant u tsi Set up time of the product i βi,u

Binary parameter equals to 1 if the productican be produced at the plant u, 0 otherwise hi Unit holding cost of product i pi Unit production cost of product i si Set up cost of product i tu Train transport cost from the plant u M Large number R Maximum number of trains allowed per day Xi,t,u Quantity of product i, to be produced at plant u in period t Ii,t,u Inventory level of product i at the end of period t for plant u Qi,t,u Quantity of product i delivered by train from site u to final stocks, at the end of period t γi,t,u Binary set-up variable equal to 1 if and only if Xi,t,u > 0 ωi,t,u Binary transport variable equal to 1 if and only if Qi,t,u > 0 Minimize

t u i (p i .X i,t,u + s i .γ i,t,u + h i .I i,t,u + t u .ω i,t,u ) (1)
Subject to:

I i,t-1,u + X i,t,u -Q i,t,u - j a i,j .X j,t+z u;u ;u -I i,t,u = 0 (∀i, t, u ∈ S p , u ∈ S f ) (2)
I i,t,u = I i,t-1,u -D i,t (∀i, t < z u ;u , u ∈ S f ) (3)
I i,t,u = I i,t-1,u + u Q i,t-z i,u ;u ,u -D i,t (∀i, t ≥ z i,u ;u , u ∈ S f ) (4) ts i .γ i,t,u .db i,t,u + X i,t,u ≤ X max u (∀i, t, u) (5)
i

I i,t,u ≤ I max u (∀t, u) (6)
X i,t,u < β i,u .X max u (∀i, t, u) (7)
I i,t,u < β i,u .I max u (∀i, t, u) (8)
Q i,t,u ≤ Q max .λ t (∀i, t, u) (9)
Q i,t,u ≥ Q min .ω i,t,u (∀i, t, u) (10)
t∈H

ω i,t+((j-1).H),u ≤ R (∀i, j ∈ J, u) (11)
X i,t,u -M.γ i,t,u ≤ 0 (∀i, t, u) (12)
Q i,t,u -Mω i,t,u ≤ 0 (∀i, t, u) (13)
I i,t,u .X i,t,u ≥ 0 (∀i, t, u) (14)
γ i,t,u , ω i,t,u ∈ 0, 1 (∀i, t, u) (15)
Objective function (1) minimizes total costs. Constraint ( 2) is stock balance equation of stocks downstream the production plants. Constraints ( 3) and ( 4) are stock balance equations of final stocks. Constraints ( 5) and ( 6) ensure the respect respectively of the maximum production and inventory capacity. Constraints [START_REF] Brahimi | Multi-item production routing problem with backordering: a milp approach[END_REF] and ( 8) assign the products respectively to the plant / stocks in which they are produced / stored. Constraints ( 9) and ( 10) ensure maximum and minimum quantity limitations for transport by train. Constraint (11) limits the maximum number of trains per day. Constraints ( 12) and ( 13) bind binary variables to corresponding decision variables. Constraints ( 14) and ( 15) define the domain of the decision variables.

Case study

In what follows, we illustrate the model previously described by a numerical example. The model is solved on a one week horizon with a temporal mesh of one hour (168 periods). The daily demand has been converted to hourly demand by assuming it is evenly distributed during the day. The program has been solved in few minutes using Xpress solver. The model has calculated an integrated plan of all components of the overall production system. These plans have enabled a demand satisfaction rate of 100%. For each period, product and site, the model proposes: (i) A production plan defined by the quantity to be produced per period and per product in each site where the fact that product P2 can be manufactured in two different sites has been considered. (ii) An inventory plan for the whole stock of the productive system. (iii) A transport plan, which identifies the quantity to be transported from the production sites to the final stocks. This plans respects travel time required to transport products to final stocks which is 2 hours. The results of the products P1, P2 are respectively presented in table 3, 4. These plans have enabled a demand satisfaction rate of 100%. We have found a global solution applicable in a global supply chain context.

Conclusion

In this paper, we propose a MILP to perform simultaneous planning of production, storage and transport over a finite horizon composed of discrete periods. This planning takes place in the context of a multi-level, multi-period, multi-product supply chain structure, while taking into account all the different capacities. Also, the transport of the finished products is ensured by a single railway track, with fixed time windows. This model has been tested on a mining system in order to achieve an overall flow optimization, that takes into account the characteristics of the different subsystems, their interactions and the propagation of constraints all along this chain.

Fig. 1 .

 1 Fig. 1. Multi-level, multi product supply chain structure

Table 1 .

 1 Comparison of the proposed MILP and reviewed models

	[20] [16] [17] [14] [19] [11] [18]

Table 2 .

 2 Parameters and variables

	N	Number of products (i = 1..N)
	T	Number of periods in the planning horizon (t = 1..T)
	J H S p	Number of days (j = 1..J) composing the planning horizon Number of hours considered per days Set of production sites
	S f

Table 3 .

 3 Production, storage and transport plans for product P1

Table 4 .

 4 Production, storage and transport plans for product P2


Tanja Todorovic
email: ttodorovic@uns.ac.rs

Bojan Lalic
email: blalic@uns.ac.rs

Nemanja Tasic
email: nemanja.tasic@uns.ac.rs

General readiness assessment of Industry 4.0: Evidence from Serbian manufacturing industry

Keywords: Industry 4.0, manufacturing industry, readiness assessment 1

The implementation of Industry 4.0 concepts has significant implications for the manufacturing landscape. The aim of this study is to assess the level of general readiness for Industry 4.0 in the emerging economy of Serbia. The obtained results indicate that the majority of Serbian manufacturing sector has not yet embarked on the path towards transformation and implementation of advanced technologies.

Introduction

The prospects of Industry 4.0 indicate a substantial change in the manufacturing value chain. The introduction of highly flexible and highly productive factories of the future is gaining momentum in industries of developed regions [START_REF] Lichtblau | IMPULS-Industrie 4.0-Readiness[END_REF]. In order to adapt to the new manufacturing paradigm, emerging markets should analyze their readiness for the implementation of Industry 4.0 concept. The aim of this paper is to evaluate the extent of usage of advanced digital technologies in manufacturing companies in the context of developing countries, i.e. Serbia.

Literature review

Although there is a lack of consensus regarding the Industry 4.0 definition [START_REF] Castelo-Branco | Assessing Industry 4.0 readiness in manufacturing: Evidence for the European Union[END_REF], the prevailing terminology of Industry 4.0 concept entails the implementation of digital advanced manufacturing technologies into the manufacturing landscape [START_REF] Kagermann | Recommendations for implementing the strategic initiative INDUSTRIE 4.0: Securing the future of German manufacturing industry[END_REF], along with other non-technological enabling factors [START_REF] Camisón | Organizational innovation as an enabler of technological innovation capabilities and firm performance[END_REF], [START_REF] Schumacher | A Maturity Model for Assessing Industry 4.0 Readiness and Maturity of Manufacturing Enterprises[END_REF]. Research in this field is primarily focused on companies from developed countries, whilst companies from developing countries are facing different obstacles regarding their technological and organiza-tional capabilities to implement novel concepts [START_REF] Lalic | Open innovation in developing regions: An empirical analysis across manufacturing companies[END_REF] [7] [START_REF] Delić | Assessment of key LEAN dimensions implementation in organisations from developing region[END_REF]. Although emerging economies are lagging behind when it comes to implementation of advanced technologies, they have slowly begun to pave a way for inclusion of Industry 4.0 elements [9] [10].

The application of various readiness models [5] [11] [12] in order to assess the specific industry's status regarding advanced technologies implementation could indicate the industries with the highest level of Industry 4.0 penetration [13] [14]. Since Industry 4.0 is driven by advanced technologies [START_REF] Smit | Industry4.0 a Study for the European Parliament[END_REF] [16] as core enablers of its implementation, this paper examines the utilization of advanced manufacturing technologies as a first step in analyzing the readiness for Industry 4.0 [START_REF] Lalic | Big Data Analysis as a Digital Service: Evidence Form Manufacturing Firms[END_REF].

To assess the general readiness to digitalize, it is of particular interest whether companies use and combine several technologies at the same time or in which technological fields companies are increasingly active. Regarding the nature of Industry 4.0 enabling technologies, the authors have differing points of view [START_REF] Pacchini | The degree of readiness for the implementation of Industry 4.0[END_REF]. The Fraunhofer Institute for Systems and Innovation Research ISI developed an I4.0 general readiness assessment methodology [START_REF] Lerch | Wie digital ist Deutschlands Industrie wirklich?[END_REF] that combines the number of digital technologies used with three technological fields and thus provides information on the digitalization readiness of individual companies. The model applied in this study follows the readiness assessment methodology of the Fraunhofer ISI and aims to assess the current situation in terms of implementation of digital advanced manufacturing technologies in the manufacturing sector in Serbia. Based on this assessment, the future steps in further digitalization of economy could be planned and executed both on governmental and individual company's level.

Research questions

Against this background, we investigated how intensively Serbian manufacturing companies are currently implementing Industry 4.0 relevant technologies. Based on the literature review, the following research questions were proposed:

 RQ1: What is the level of general readiness for Industry 4.0 in Serbian manufacturing industry?  RQ2: Which industries in Serbia have the highest level of general readiness for Industry 4.0?

Data and Methodology

Our analysis used the Serbian dataset from the European Manufacturing Survey (EMS) conducted in 2018. EMS investigates technological and non-technological innovation in the European manufacturing sector. It represents the most detailed and widest survey on industrial value-added processes and modernization strategies of companies in the manufacturing industry and is coordinated by Fraunhofer ISI. The survey is carried out on a triennial basis and targets a random sample of manufacturing companies with more than 20 employees (NACE Rev 2 codes from 10 to 33). The Serbian dataset includes 240 companies. Concerning descriptive statistics, the sampled companies report, on average, a company size of 124 employees (SD = 207). In total, 110 companies are small firms (fewer than 50 employees), 103 companies are medium-sized (between 50 and 249 employees), and 27 companies are large enterprises (more than 250 employees). To be able to assess the general willingness to digitalize, it is of particular interest whether companies use and combine several technologies at the same time or in which technological fields companies are increasingly active. For this purpose, the Fraunhofer ISI developed an I4.0 general readiness assessment methodology that combines the number of digital technologies used with three technological fields and thus provides information on the digitalization readiness of individual companies. The Fraunhofer I4.0 Readiness assessment approach is exclusively focused on technology and is based on seven digital technologies: • Software system for production, planning and control;

• Digital visualization at the work place of the workers; • Digital data exchange with customers/suppliers; • Techniques for automation and control of internal logistics; • Real-time production control system; • Mobile devices for programming and operation of plants and machines; and • Product Life Cycle Management Systems. These are combined into the following technology fields: 1. Digital Management Systems: The first field of technology consists of "Software system for production planning and control" and "Product Lifecycle Management Systems". 2. Wireless human-machine communication: In the second field of technology the "Digital Visualization" is combined with the "Mobile Devices". 3. Cyber-Physical Production System (CPS) related processes: The third field of technology is the "Real-time production control system", the "Automation of internal logistics" and "Digital data exchange with customers and suppliers" together.

While the first two technology fields tend to cover basic digital technologies and still have a clear distance from I4.0, the third technology field already contains the first approaches of digitally networked production. Using this grouping, therefore, those companies that are closer to I4.0 are those who use and combine digital technologies in all three technology fields and use several of the CPS-related processes on the one hand. By contrast, companies that only apply digital technologies in one or two technology fields are less willing to work for digitally networked production in the sense of Industry 4.0 There are six different levels which are summarized graphically on Figure 1:

Results

The following Table 2 gives a distribution of general readiness of Serbian manufacturing firms by level of readiness. For RQ1 (What is the level of general readiness for Industry 4.0 in Serbian manufacturing industry?), we conducted descriptive statistics presented in Table 2 and Figure 2. From the results, we could say that majority (41.67%) of manufacturing companies are still at Level 0 and just a few (6.25%) at the Level 5 of general readiness for Industry 4.0. Furthermore, for RQ2 (Which industries in Serbia have the highest level of general readiness for Industry 4.0?), the most prepared manufacturing industry in Serbia for Industry 4.0 is Manufacture of rubber and plastic products (NACE 22), followed by Manufacture of food products (NACE 10), and Manufacture of wearing apparel (NACE 14), as presented in Table 3. As for the specific industries, manufacture of rubber and plastic products sector (NACE 22) has four companies at the Level 5, manufacture of food products sector (NACE 10) has two companies at the Level 5 and four companies at the Level 4. Finally, manufacture of wearing apparel sector (NACE 14) has two companies at the Level 5. In terms of readiness levels, it could be observed that there is significant heterogeneity even among companies in the same industry. For example, there are 2 food production companies at level 5, none at level 3 and 18 companies at level 0.

Discussion and Conclusion

This study represents the first step in analyzing the readiness of Serbian manufacturing companies for Industry 4.0. It bases on an established methodology of the Fraunhofer ISI from Germany and uses Serbian data of the European Manufacturing Survey representing the most detailed and widest survey on industrial value-added processes and modernization strategies of companies in the manufacturing industry.

The results indicate that the majority of companies in Serbian manufacturing sector have not started the transformation based on advanced digital technologies yet. Even those companies which have started to uptake some digital technologies, are on a very low level of readiness for Industry 4.0. In our sample, we could find only few companies dealing with higher levels of readiness representing rather an exception in Serbia.

One of the reasons for this situation might be the strong market-pool-oriented strategy of the manufacturing sector in Serbia following the needs and requirements of customers instead of a self-initiative in terms of the technological catch-up imitative. In other words, instead of following a technology-based competitiveness, the majority of manufacturing companies follow solely low-price market strategies. An additional argument might be the lack of political instruments for providing technological catchup in the Serbian manufacturing sector. To identify the barriers for up-taking digital technologies, an in-depth study is to be conducted.

Looking at individual sectors within the manufacturing industry, we could identify three sectors with somewhat higher readiness levels: manufacture of rubber and plastic products, manufacture of food products and manufacture of wearing apparel. The further research should involve the deeper analysis of the underlying factors that positively influence the implementation in these sectors, with the aim to develop policy recommendation for the whole industry.

Despite the solely descriptive characteristic of methodology, the study gives a first overview of the state of the art in terms of usage of digital technologies. As such, it contributes significantly to the current research on Industry 4.0 in emerging economies. Moreover, giving a first statistical overview, it plays an crucial role for further more comprehensive as well as in-depth studies including additional nontechnological areas like human resources and competences in digital surroundings as well as the improvement of organizational and management concepts, new business models and digital innovations.

Fig. 1 .

 1 Fig.1. Levels of I4.0 Readiness[START_REF] Lerch | Wie digital ist Deutschlands Industrie wirklich?[END_REF]

Fig. 2 .

 2 Fig. 2. Distribution of firms by level of general readiness for Industry 4.0.

Table 1 .

 1 Table 1 depicts the sample distribution regarding size. EMS databasedistribution of firms by size.

	Firm size	n	%
	20 to 49 employees	110	45.8
	50 to 249 employees	103	42.9
	250 and more employees	27	11.3
		Total 240	100.0

Table 2 .

 2 General readiness assessment of Serbian manufacturing companiesdistribution of firms by level of readiness.

	Industry	Level	Level	Level	Level	Level	Level	Share on total sample
		0	1	2	3	4	5	(%)
	10	18	4	11		4	2	16.3
	11	3	2		1			2.5
	12	1						0.4
	13	2					2	1.7
	14	6	3	1	1	1	2	5.8
	15	5		2				2.9
	16	6	1	3		1		4.6
	17	3		3				2.5
	18	2	2	1	1	3		3.8
	19	1		1				0.8
	20	3	2		1			2.5
	21	1		1				0.8
	22	6	4	4	2	1	4	8.8
	23	7		2	2			4.6
	24	3		1	1			2.1
	25	14	7	9	5		1	15.0
	26	1	1	1	1	1		2.1
	27	5	1	4	2	2	1	6.3
	28	4	4	6			1	6.3
	29	3	4	2	1			4.2
	30	2						0.8
	31	3	2	1	2		1	3.8
	32	1		1	1			1.3
	33						1	0.4
	% of total	41.7	15.4	22.5	8.8	5.4	6.3	100.0

Table 3 .

 3 General readiness assessment of Industry 4.0 in Serbian manufacturing companiesdistribution of firms of top 3 industries.

	Industry Level 0	Level 1	Level 2	Level 3	Level 4	Level 5	Rank
	22	6	4	4	2	1	4	1
	10	18	4	11	-	4	2	2
	14	6	3	1	1	1	2	3


Julia Schulz

Felix Rosenberg

Valerie M Scharmer

Michael F Zaeh

Characterization of energy consumers in production systems with renewable on-site power generation

Keywords: Energy consumption, demand side management, micro-grid

The amount of renewable energy is increasing in the German energy system. As a result, grid expansion, consumer regulation (demand response), innovative storage solutions or intelligent grid operation are measures to avoid system instabilities. The development of energy prices and regulatory charges is difficult to predict against this dynamic background. The technological development of small power plants is in progress and many of the offered technologies are reaching grid parity. To increase independency from the grid and to avoid grid supply in periods of high prices, the integration of decentral, renewable power generation technologies is a reasonable solution for manufacturing companies. Therefore, a procedure for industrial companies to use their self-produced energy in a sustainable manner is introduced. This paper focuses on the characterization of industrial energy consumers, which is one of the first steps in the procedure. Different consumer criteria are descripted to define 48 consumer groups. Certain factories include consumers that can be described by a multitude of these consumer groups.

Introduction and State of the art

It has been noted recently that the energy revolution of the electricity system is proceeding ahead in all corresponding fields. Because of their volatile electricity production, the increasing share of renewable energy will challenge grid operators to establish a stable energy supply. So far, there is no economic solution to store electrical power in the utility grid. Therefore, consumption and production need to be balanced at all times. As a result, the instability of the grid could increase the number of power outages. This can lead to high breakdown costs for manufacturing companies caused by interruptions of the production line. Moreover, the volatile power supply has an impact on the electricity market. Fluctuating prices and power quality issues could lead the manufacturer to become more independent from the utility grid. In addition, the customers' demand for environmentally friendly produced products is on the rise. To increase the independency from the utility grid and to meet the costumers' demands, a reasonable solution is to integrate renewables into the industrial grid. A holistic procedure for the integration of suitable technologies within manufacturing companies was introduced recently [START_REF] Schulz | Energy self-sufficient manufacturing systemsintegration of renewable and decentralized energy generation systems[END_REF] (Fig. 1). Renewable, decentral power generation technologies include tech-nologies whose energy source is renewable and which are on the scale of the distribution network level. Starting from company-specific goals, the analysis of the consumers, installed in the regarded production systems, is an important step, since its outcome influences all the subsequent activities. The selection and dimensioning of power generation technologies, the choice of the electro-technical micro-grid structure and the development of suitable operation strategies are based on the type of consumers within the system. Against the background of Big Data, several methods from data collection to data processing have also been considered in literature in the field of energy consumption analyses. Liebl et al. [START_REF] Liebl | Approach for a Systematic Energy Data Generation and Evaluation[END_REF] provide a review of methods for energy data generation and evaluation differentiated by development depth (concept to prototype) and environmental depth (company to component level). So far, the introduced methods mainly aim at transparency enhancement to improve efficiency and do not pursue the objective of classifying and evaluating individual consumers with regard to the necessary decentral energy supply. Therefore, this paper introduces a qualitative characterization of manufacturing energy consumers considering the subsequent procedure steps.

Fig. 1. Procedure for the integration of a renewable, decentral power generation acc. to [START_REF] Schulz | Energy self-sufficient manufacturing systemsintegration of renewable and decentralized energy generation systems[END_REF].

Electrical and thermal consumers in manufacturing

A broad literature review resulted in the following summary of distinctive criteria of loads in factories divided into functional characteristics and process-related properties.

Functional characteristics

Compared to the electrical loads of households, the range of power requirements in an industrial application is much higher. Devices in industrial micro-grids considerably exceed the values of power consumption in households, where loads such as instantaneous water boilers or charging stations for electric vehicles (up to 22 kW) represent the highest power requirements. Large electrical loads can strongly influence the industrial grid which is exemplarily shown for an arc furnace by Chang et al. [START_REF] Chang | Harmonic analysis of the industrial power system with an AC electric arc furnace[END_REF]. Depending on the maximum power requirement, industrial loads may be operated either at low or medium voltage level. Furthermore, in industrial micro-grids, direct current (DC) and alternating current (AC) loads can coexist [START_REF] Alfieri | On the optimal management of the reactive power in an industrial hybrid microgrid: A case study[END_REF]. Depending on the type and level of operating voltage, industrial grids may have different requirements concerning grid configuration. In AC-grids, the power factor (ratio of effective power and apparent power) is an important functional feature. The idle power in industrial micro-grids is higher compared to conventional grids, e.g. due to a high number of electrical machines. The balance of idle and effective power in an industrial grid is of high relevance to ensure a stable grid operation [START_REF] Alramlawi | Optimal Operation of PV-Battery-Diesel MicroGrid for Industrial Loads Under Grid Blackouts[END_REF]. A large number of inductive linear (e.g. transformers, asynchronous machines) and non-linear (e.g. power converters, welding equipment, frequency converters) operating devices are used. The current of linear loads runs approximately sinusoidal. The non-sinusoidal current of non-linear loads can be divided into operation strategies for power generation, conversion, storage and consumption electro-technical micro-grid structure consumer analysis selection and dimensioning of power generation technology company-specific goal description a base current with grid frequency and several harmonics [START_REF] Kiank | Planungsleitfaden für Energieverteilungsanlagen: Konzeption, Umsetzung und Betrieb von Industrienetzen[END_REF]. These harmonics can lead to thermal overloads and disturbances in electrical systems such as control systems, measuring units, capacitors, or circuit breakers [START_REF] Chhor | Modular power conditioner concept for improving quality of supply[END_REF]. Since almost every device within a production line is integrated into the control system, a failure of this system can affect the entire electrical, thermal and mechanical energy supply [START_REF] Schael | Risk evaluation of a chemical production system regarding power quality implications[END_REF] and consequently single machines, the entire process or the product quality. Devices for compensation of the harmonics must be taken into account in the grid planning. Especially in industrial grids with large non-linear loads and low-dimensioned power supply, non-linear loads can cause voltage fluctuations and oscillations [START_REF] Chhor | Modular power conditioner concept for improving quality of supply[END_REF]. Voltage dips may lead to interruptions in process-relevant devices. A large number of single-phase loads, typically at low voltage levels, leads to voltage asymmetries. In industrial grids, rotating electrical machines in particular are influenced by these asymmetries. This leads to counter currents, high thermal losses, torque reduction and vibrations [START_REF] Chhor | Modular power conditioner concept for improving quality of supply[END_REF]. In contrast to conventional consumers, many industrial consumers are three phase loads.

Process-related properties

In micro-grids with a high share of renewable energies and a low share of synchronous generators, the rotating reserve of the grid is low. Therefore, micro-grids are more sensitive to faults than distribution grids. In addition to feed-in voltage and frequency regulation, demand side management is necessary in industrial micro-grids [START_REF] Mondal | Operation and impact of energy storage system in an industrial microgrid[END_REF]. The potential of consumer-side control in an industrial grid depends, among other things, on the controllability of the loads. Controllable loads are characterized, for example, by the adjustment of the power requirement and the starting or shut-down behavior [START_REF] Bracale | A cost minimization strategy for the control of hybrid AC-DC microgrids in industrial systems[END_REF]. Energy flexibility describes the ability of production devices to adjust their energy demand to environmental circumstances [START_REF] Graßl | Bewertung der Energieflexibilität in der Produktion[END_REF]. Energy-flexible production lines offer organizational energy-flexible measures, whereas single machines provide technical energyflexible potential for balancing the grid [START_REF] Beier | Energy flexibility of manufacturing systems for variable renewable energy supply integration: Real-time control method and simulation[END_REF]. According to Schenk et al. [START_REF] Schenk | Fabrikplanung und Fabrikbetrieb: Methoden für die wandlungsfähige, vernetzte und ressourceneffiziente Fabrik[END_REF], in a manufacturing factory the energy consumers are considered with different priorities for effective design and planning. Consumers of the first periphery are directly dependent on the production program (e.g. assembling robots, spindle drives). Consumers of the second periphery are not directly dependent on the production program, but on the equipment of the main process (e.g. hydraulic or compressed air units). Within the third periphery, consumers are independent of the production process (e.g. technical building equipment) and are known as cross-sectional technologies as well [START_REF] Moog | Energieflexibilitätspotenziale in der Produktionsinfrastruktur[END_REF]. Even if their energy demand is mostly lower than the one of the main process consumers, they are considered technologies that are very adjustable and consequently suitable for application in dynamic systems. In these systems, loads have to be specifically removed from the grid in order to avoid load peaks and balance the system [START_REF] Croce | Operation and management of the electric system for industrial plants: an expert system prototype for load-shedding operator assistance[END_REF]. Electrical loads in an industrial environment can have a uniform power demand or an intermittent demand [START_REF] Haj-Ahmed | Investigation of Protection Schemes for Flexible Distribution of Energy and Storage Resources in an Industrial Microgrid[END_REF][START_REF] Mondal | Design and operation of smart loads in an industrial microgrid[END_REF]. Intermittent loads may lead to significant fluctuations in voltage and frequency in the grid, which in turn can lead to instabilities, especially in self-sufficient operation making the integration of distributed energy resources challenging [START_REF] Mondal | Operation and impact of energy storage system in an industrial microgrid[END_REF]. Electrical loads can cause grid interferences due to functional characteristics and process-related re-quirements. In contrast, consumers may have certain requirements for supply reliability or voltage quality. Many consumers, such as motors, just tolerate limited supply quality since fluctuations of the torque can affect the manufacturing process and subsequently the product quality. In addition, low supply quality leads to increased wear or defects of the equipment and may cause decreases in productivity [START_REF]Bayerische Industrie-und Handelskammer: Energiewende im Strommarkt -Chancen für Unternehmen[END_REF].

Consumer characterization

Based on the introduced properties of consumers in industrial (micro-) grids, the characterization of the consumers and the formation of consumer groups can be described.

Overall classification

Before characterizing the consumers within production systems, the area of application of the procedure has to be defined. First, the different industry sectors are analyzed regarding important features. Gaining independency from the varying and non-transparent electricity price for industry may be one reason for on-site generation. While the electricity price for households undergoes only small price differences, these differences can be significantly higher for industrial customers. This is mainly due to the exemption from various taxes, which relieves the energy-intensive industry in particular. In addition, the absolute electricity consumption and the full-load hours influence the electricity price [START_REF] Prognose | Forschungsvorhaben: Weiterentwicklung des EEG 2014 im Hinblick auf die Kosten industrieller Verbraucher[END_REF]. The share of energy costs in the gross production value (Fig. 2b) allows more significant conclusions because others than electricity costs are considered and related to the produced outcome. The higher this share, the greater is the incentive for a company to find a more cost-effective alternative than grid procurement.

In addition to the energy costs, the share of electricity or heat in the company's energy consumption can be considered as criteria (Fig. 2a). Regarding the required heat, the temperature level is of particular importance since many decentralized and regenerative heat generation processes work at a low temperature level (Fig. 2c). Based on the described criteria, the possibilities for on-site power generation for each industry sector can be evaluated. Fig. 2d gives a qualitative evaluation of the sectors regarding the onsite generation of heat and electricity. The qualitative evaluation is based on the data given for each sector. If the electricity share is higher than 50 %, the sector is valuated with electricity +. If the temperature level is mainly < 500 °C, the sector is valuated with heat +. The share of electricity costs increases the valuation in positive direction if the share is > 2.0 %. Sustainable decisions take economic efficiency, the security of supply and the environmental impact into account. In order to assess the economic viability of a power plant, a comparison of energy production costs and the procurement costs of electricity and heat is usually carried out. In case of a grid-connected plant, a possible feed-in as well as the associated payments have to be considered in addition [START_REF] Matzen | Industrielle Energiestrategie: Praxishandbuch für Entscheider des produzierenden Gewerbes[END_REF]. The manufacturing industry in Germany is strongly characterized by medium-sized companies that represent 97.2 % of all companies [21]. Despite the dominant number, only about 40 % of the total energy consumption in the manufacturing industry is caused by them [START_REF] Bauernhansl | Energieeffizienz in Deutschland -eine Metastudie[END_REF]. Energy costs play a subordinate role for small companies due to their small share in total costs. Energy measures are usually given lower priority than investments in the core business. Therefore, small to medium-sized companies often avoid investing in their own power generation facilities due to a lack of the necessary capital [START_REF] Bauernhansl | Energieeffizienz in Deutschland -eine Metastudie[END_REF]. It can be assumed that the willingness to invest in the integration of on-site, renewable energy generation does expand with increasing company size. For high-revenue companies, there are different possibilities for the self-production. About a quarter of the companies in the German manufacturing sector work in shifts due to high fixed costs for plant and machinery or due to continuous processes [START_REF] Parent-Thirion | 6th European Working Conditions Survey: 2017 update[END_REF].

Different working hours cause high varying load profiles among companies. The range from smaller companies in one-shift operation to large companies in three-to five-shifts and weekend operation are summarized in standard load profiles divided into one-shift load profiles and multi-shift load profiles [START_REF]Verband der Elektrizitätswirtschaft: Repräsentative VDEW-Lastprofile[END_REF].

Fig. 2. Sector-wise characterization for Germany regarding a) the share of electricity of total energy consumption according to [START_REF] Energiebilanzen | Energiebilanz der Bundesrepublik Deutschland[END_REF], b) the share of energy costs of the gross production value according to [START_REF]Kostenstruktur der Unternehmen des Verarbeitenden Gewerbes sowie des Bergbaus und der Gewinnung von Steinen und Erden[END_REF], c) the distribution of heat demand by temperature level according to [START_REF] Mai | Energieeffizienz in der Wärmenutzung und -erzeugungein Langfristprogramm[END_REF] and d) evaluation of the sectors regarding the on-site generation of heat and electricity (sectors are valuated as very suitable (++), suitable (+) for on-site renewable power generation).

Renewable power generation technologies have various requirements. Depending on the industrial company, the available areas can vary. According to VDI 3644 [START_REF]VDI 3644: Analyse und Planung von Betriebsflächen -Grundlagen, Anwendung und Beispiele (2010) / Analysis and planning of factory areas -Fundamentals, application and examples[END_REF], only undeveloped green and open spaces, or reserve areas on factory sites, are relevant for the integration of renewable energies. Suitable roof structures can also be used [START_REF] Grundig | Fabrikplanung[END_REF].

Relevant distinguishing features

The manufacturing industry comprises very heterogeneous economic sectors with very different operational structures, production processes and energy intensities. Companies are to be classified with regard to possible concepts for the integration of renewable energies. Small, medium and large industrial plants can differ greatly in their consumer structure. In section 2, it was shown that loads can differ in multiple functional characteristics and process-related properties. To model individual factories, the aim of this section is to identify the characteristics of loads that are crucial for the integration of on-site, renewable power generation. The power demand of consumers is an essential parameter for the integration of power generators. A classification of the loads into two groups is sufficient to be able to estimate the voltage hierarchies (low-voltage or medium-voltage level) and grid interferences (strong or weak). Accordingly, required generators or storage units can be optimally selected, dimensioned and placed. Small consumers include all loads with a maximum power requirement of up to P = 100 kVA. These loads usually have an operating voltage at the low voltage level (400 V/230 V). The loads have a small tendency towards system interferences, which are very small. Large loads have a maximum power requirement of more than 100 kVA. The operating voltages of these loads are usually at the medium-voltage level (1 kV -50 kV) and the system interferences may have large effects on the grid. Due to their characteristics, industrial loads can cause grid interferences that consequently may have negative effects on the quality of supply. This danger exists particularly in weak grids in isolated operation. Through a suitable integration of generation technologies and storage, negative influences on the supply quality can be eliminated. Impulsive or intermittent loads, non-linear loads and inductive loads with a low power factor have a high potential for system interferences. Accordingly, loads are classified into loads with high risk of interferences and loads with a low risk of interferences. The classification of loads into the two groups is sufficient to assess the extent to which loads are compatible with sensitive loads and whether measures need to be taken to isolate sensitive loads from loads with a high potential for system interferences. The organizational classification serves the purpose of estimating the potential of loads with regard to their use for demand side management. A distinction is made between loads of the main process and peripheral loads. The first group contains loads that are directly related to the main process and that will significantly impair the process in case of supply interruptions. The suitability for load shedding and the controllability is low. Therefore, a low potential for demand side management is attributed. The group of peripheral loads is assigned with a medium and high suitability for load shedding. These loads are either always disconnected from the grid in isolated operation or continue to be operated until there is an imbalance between supply and demand. Then they can be temporarily disconnected from the grid without noticeably affecting the production process. Poor supply quality of the grid can have far-reaching consequences in production and must be taken into account accordingly when integrating power generation and storage facilities. Due to diverse requirements of the consumers for supply reliability, the selection of power generation technologies has to be adapted. Consumers can be classified into sensitive loads that allow for supply interruptions of less than one second and insensitive loads that allow for supply interruptions of more than one second. The differentiation of the required voltage quality is based on DIN EN 61000-2-4 [START_REF]2003-05 Elektromagnetische Verträglichkeit: Umgebungsbedingungen -Verträglichkeitspegel für niederfrequente leitungsgeführte Störgrößen in Industrieanlagen[END_REF]. Sensitive loads have a high demand on the voltage quality of the network, whereas insensitive loads have standard requirements for the necessary voltage quality of the network. Furthermore, the required temperature level has to be considered. Fig. 3 summarizes the defined criteria and the distinguishing features with their parametrization. Furthermore, it is described which features relate to which next steps in the procedure for integrating renewable power generation.

Conclusion and further steps

The introduced criteria allow for characterization of the divers consumers in an industrial electrical and thermal grid. Based on the given parametrization, which can be further subdivided, different consumer groups are described. Taking into account invalid combinations of characterization, industrial consumers can be divided into 48 alternative type groups (six features, two or three parametrizations). The consumers within the considered system are typically allocated to several of these groups. Depending on the distribution of consumers among the introduced groups, appropriate generation technologies can be selected and dimensioned. The application of the presented characterization will be carried out exemplarily for a machine tool. Further steps consider a quantitative analysis of the consumers, taking their specific load profile into account.

Fig. 3 .

 3 Fig. 3. Characterization of industrial energy consumers in consumer groups.

•

  on-site electricity generation • grid interferences, voltage level • supply quality of the grid • compensation by on-site electricity generation • potential for demand side management • on-site electricity generation • on-site electricity generation • structure of industrial micro-grids • on-site electricity generation • structure of industrial micro-grids • on-site heat generation relevant to:

  quarrying of stone and earth; 3 nutrition, beverage and tobacco; 4 textiles, clothing, leather, leather goods and shoes; 5 wood, wicker and cork products, furniture; 6 paper, cardboard and articles thereof; 7 printed matter, duplication of recorded audio, video and data media; 8 chemical products; 9 other chemical industry (e.g. pharmaceutical products); 10 rubber and plastic goods; 11 glass and glassware, ceramics, stone and earthwork; 12 metal production; 13 metal working and metal products; 14 data processing equipment, electronic and optical products; 15 electrical apparatuses; 16 mechanical engineering; 17 automotive engineering; 18 other sectors.

	(shaded bar describe average values)	a) share of electricity of total energy consumption in % 0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 60 40 20 0 1 2 3 4 5 6 8 9 10 11 12 13 14 15 not available not available not available 7 not available not available	b) share of energy costs of the gross production value in % 0,0 1,0 2,0 3,0 4,0 5,0 6,0 5.0 4.0 3.0 2.0 1.0 0 not available not available	c) distribution of heat demand by temperature level in % not available not available not available 0 10 20 30 40 50 60 70 80 90 100 100 < 100 C 100 C -500 C 80 60 40 20 0 not available not available > 500 C	heat d) + ++ + electricity + + ++ + + + + + + ++ ++ + + ++ + + ++
	sectors	16 17 18			+ + +	+ +
	1 mining; 2

Acknowledgment

The authors would like to thank the German Federal Ministry of Education and Research (BMBF) and the Project Management Jülich for funding the project SynErgie (03SFK3E1-2).


Masayuki Yabuuchi
email: yabuuchi@kaede.cs.kobe-u.ac.jp

Toshiya Kaihara
email: kaihara@kobe-u.ac.jp

Nobutada Fujii
email: nfujii@phoenix.kobe-u.ac.jp

Daisuke Kokuryo
email: kokuryo@port.kobe-u.ac.jp

Satoko Sakajo
email: sakajo.satoko@ds.mitsubishielectric.co.jp

Yoshito Nishita
email: nishita.yoshito@cb.mitsubishielectric.co.jp

A basic study on scheduling method for electric power saving of production machine

Keywords: flexible flow shop scheduling, power saving, optimization, production machine

At present, energy consumption all over the world is increasing, and various approaches to energy issues such as the Sustainable Development Goals (SDGs) are in progress. In Japanese manufacturing industry, the introduction of factory Energy Management System (EMS) and the improvement of production equipment are being carried out in order to reduce energy consumption. Accordingly similar considerations are also important issues for production scheduling. In this paper, based on the assumption that renewable energy and EMS will eventually be introduced in the future, we focus on factories and utility companies, and at the same time, try to realize a scheduling method that improves energy efficiency with keeping production performance, and evaluate it by computational experiments.

Introduction

As energy demand in the world increases with the development of the economy, problems such as the depletion of fossil fuels due to the increase of energy consumption and increase of CO 2 emissions causing global warming becomes more serious. Therefore, various countries around the world collaborate altogether for Sustainable Development Goals (SDGs), and work on energy issues with the aim of realizing a sustainable society [START_REF] Nilsson | Towards an integrated framework for SDGs: Ultimate and enabling goals for the case of energy[END_REF]. The industrial sector, including the manufacturing sector, accounts for more than 50% of the total energy consumption, and in today's era of rapid electrification, power saving in the industrial sector is considered an important initiative [2]. In the manufacturing industry, energy saving is promoted by introducing an Energy Management System (EMS) with energy-efficient equipment, and by scheduling in consideration of power consumption. Among them, research on scheduling aimed at improving production efficiency and energy efficiency has attracted attention because it could be realized at a lower investment cost than such as purchasing a new system or equipment [START_REF] Gahm | Energy-efficient scheduling in manufacturing companies: A review and research framework[END_REF].

In the target model (Fig. 1), electricity used in the factory is supplied by purchasing from a utility company or by generating electricity from renewable energy such as PhotoVoltaic(PV). A storage battery stores electricity from a utility company during the time when the electricity charge is low, and discharges the electricity to factory during the time when the electricity charge is high. In addition, efficient use of renewable energy is realized by positioning multiple Electric Vehicles (EVs) as moving batteries. Furthermore EMS predicts power demand and PV power generation, and determines the operation plan of each power generation facility and the EV charging and discharging schedule.

In this paper, we first focus on two models, utility company and factory, and perform scheduling for power saving and production efficiency.

Problem statement

In this paper, the problem is formulated based on the reference [START_REF] Ruiz | Modeling realistic hybrid flexible flowshop scheduling problems[END_REF]. A Flexible Flow Shop (FFS) covered in this paper (Fig. 2) is described as follows: J jobs must be processed in the I stages, and all jobs are processed in the same order. There are L machines in each stage, and each machine has difference in ability. No machine failure occurs. All jobs and machines are available from the start of production. Each job is assigned to only one machine in each stage, and each machine can process at most one job at a time. No interruption occurs during job processing. Setup occurs when processing different jobs. Each machine belongs to one of the three states of processing, idle, and setup, and the power consumption differs depending on each state.

Notation

The definition of the characters used in the formulation is as follows:

-Index • j,

Formulation

The formulation of this paper is shown below.

Min. α * T EC SOT EC + (1 -α) * C max SOC max ( 1
)
where

T EC = ∑ i∈I ∑ l∈L (pe il + se il + ie il ) (2) C max = max{c ij }, {∀i ∈ I, ∀j ∈ J} ( 3
)
pe il = pt il * P E il , {∀i ∈ I, ∀l ∈ L} ( 4
)
se il = st il * SE il , {∀i ∈ I, ∀l ∈ L} (5) ie il = it il * IE il , {∀i ∈ I, ∀l ∈ L} (6) pt il = ∑ j∈{0,J} ∑ k∈J,k̸ =j
x iljk * P ilk , {∀i ∈ I, ∀l ∈ L} (7)

st il = ∑ j∈J ∑ k∈J,k̸ =j x iljk * ST iljk , {∀i ∈ I, ∀l ∈ L} (8) it il = t2 il -t1 il -pt il -st il , {∀i ∈ I, ∀l ∈ L} (9) t1 il = 0, {∀i ∈ I, ∀l ∈ L} (10) t2 il = C max , {∀i ∈ I, ∀l ∈ L} (11) sub.to ∑ j∈{0,J},j̸ =k ∑ l∈L x iljk = 1, {∀i ∈ I, ∀k ∈ J} (12) ∑ j∈J,j̸ =k ∑ l∈L x ilkj ≤ 1, {∀i ∈ I, ∀k ∈ J} (13) ∑ h∈{0,J},h̸ =j,h̸ =k x ilhj ≥ x iljk , {∀i ∈ I, ∀l ∈ L, ∀j, k ∈ J, j ̸ = k} (14) ∑ l∈L (x iljk + x ilkj ) ≤ 1, {∀i ∈ I, ∀j ∈ J, k = j + 1, ..., Job, j ̸ = k} (15) ∑ k∈J x il0k ≤ 1, {∀i ∈ I, ∀l ∈ L} (16) c i0 = 0, {∀i ∈ I} (17) c ik + BigM (1 -x iljk ) ≥ c ij + ST iljk + P ilk , ( 18
) {∀i ∈ I, ∀l ∈ L, ∀j ∈ {0, J}, ∀k ∈ J(k ̸ = j)} c ik + BigM (1 -x iljk ) ≥ c (i-1)j + P ilk , ( 19
) {∀i ∈ I, ∀l ∈ L, ∀j ∈ {0, J}, ∀k ∈ J(k ̸ = j)} x iljk ∈ {0, 1}, {∀i ∈ I, ∀l ∈ L, ∀j ∈ {0, J}, ∀k ∈ J(k ̸ = j)} (20) c ij ≥ 0, {∀i ∈ I, ∀j ∈ J} (21)
x iljk and c ij are the decision variables. When x iljk is 1, job j precedes job k at machine l on stage i, otherwise, x iljk is 0. c ij is integer decision variable that indicates completion time of job j on stage i.

Objective function ( 1) is intended for minimizing the weighted sum of the total energy consumption of equation ( 2) and the makespan of equation ( 3). The reason for using these two as an evaluation index is that to change the degree of consideration of total energy consumption and makespan in scheduling by changing the value of a weight parameter α. SOT EC and SOC max are obtained by setting the objective function to T EC or C max for the same formulation. Equation (2) is sum of the total energy consumption in each state (processing, idle, setup). Equation ( 3) is the completion time of the last job on the last machine. Equations ( 4)-(6) calculate the power consumption in each state(processing, idle and setup) of machine l on stage i. Equations ( 7)-( 9) calculate the time in each state (processing, idle and setup) of machine l on stage i. Equations ( 10) and (11) set the work start time and work end time of machine l on stage i. Equations ( 12)-( 19) are constraint equations and have the same meanings as the constraint equations (2) to (9) in the formulation in chapter 5 in reference [START_REF] Ruiz | Modeling realistic hybrid flexible flowshop scheduling problems[END_REF]. In this paper, constraint (18) considers only setup time between different jobs. Constraint (19) considers only the completion time of the previous stage of the job.

Computational experiment

In order to evaluate the influence of the weight parameter α of the objective function, the computational experiments are performed. In the experiments, we perform the sensitivity analysis for α which is the weighting factor of the total energy consumption and makespan. CPLEX12.9 [START_REF]ILOG CPLEX-IBM[END_REF] is used to solve the scheduling problem. The evaluation criteria are as follows:

-T EC: total energy consumption -C max : makespan

Experimental condition

The initial setup conditions are hypothetically determined. In general higher speed machine with powerful actuators requires more electric energy. We consider this assumption is commonly observed in real shop floor. Therefore, this experiment assumes that each stage has two type machines: Machine 1 in each stage has a high job processing speed but high power consumption. Machine 2 in each stage has a slower job processing speed than Machine 1, but consumes less power than Machine 1. The experimental conditions are as follows. [ ] indicates a uniform random number.

-I: total number of stages = 2 -L: number of machines in each stage = 2 -J: total number of jobs = 8 -P i1j : processing time of job j at machine 1 on stage i = [10, 20] -P E i1 : power consumption per TS at machine 1 on stage i during processing = 80 -IE i1 : power consumption per TS at machine 1 on stage i during idle = 8 -P i2j : processing time of job j at machine 2 on stage i = [30, 40] -P E i2 : power consumption per TS at machine 2 on stage i during processing = 10 -IE i2 : power consumption per TS at machine 2 on stage i during idle = 1 -ST iljk : setup time from job j to job k at machine l on stage i l = 5 -SE il : power consumption per TS at machine l on stage i during setup = 5

Experimental result

In the experiment, the parameter α used for the weighted sum of the objective function is changed between 0 and 1. When α is increased, the weight for minimizing the total energy comsumption in the objective function increases. Whereas if it is decreased, the weight of the minimization of the makespan increases. Table 1 shows the results of total energy consumption and makespan when α is changed. Considering the results in Table 1, when the weight of the total energy consumption increased, total energy consumption is reduced and makespan is increased. And when we increased the weight of makespan, total energy consumption is increased and makespan is reduced. So, there is a trade-off relationship between total energy consumption and makespan under this experimental conditions, and a decision maker can decide the priority degree of total energy consumption and makespan in a scheduling by deciding α. However, when α exceeds 0.7, the values of total energy consumption and makespan change significantly, so it is difficult to finely adjust the α value close to the total energy consumption and makespan schedule assumed by decision makers.

Conclusion

In this paper, we proposed a scheduling method aiming at productivity improvement and power saving for a flexible flow shop type production line. In this method, it is assumed that more detailed and specific energy management can be provided by dividing the state of the machine into three states: processing, idle, and setup. And we solved the optimization problem related to both productivity and energy efficiency in our hypothetical target production line as basic research. In the computer experiment, scheduling that saves total energy was possible by deciding the value of α, and changing the degree of consideration of makespan and total energy consumption. However, it is not clear how to set the value of α so that the decision maker can create a schedule of total energy consumption in this experiment. Therefore, as the next step, it is necessary to clearify the relationship between the degree of consideration of makespan and the degree of consideration of total energy consumption, for each value of α, by scheduling with experimental conditions set according to a more realistic factory model.

In addition, it is also important to reduce the cost in the manufacturing industry, so we aim to reduce not only the power consumption but also the power cost in this research. Therefore, we assume that the long-term goal is to propose not only factory scheduling but also an energy allocation plan that reduces the power cost according to the power demand of the factory resulting from the scheduling. The installation of renewable energy system, batteries, or EVs, is now spreading into factory operation. Therefore, in factories including those systems, the analysis between production performance and energy saving with sophisticated scheduling methodology becomes more important issues, and it is our obvious next step.

Fig. 1 .

 1 Fig. 1. Target model

Fig. 2 .

 2 Fig. 2. An example of flexible flow shop

Table 1 .

 1 Results of experiment

	α	0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
	T EC Avg. 14790.7 14357.4 14155.5 14084.3 13974.4 13923.9 13730.2 13681.5 13126.0 11725.2 11364.6
		S.D. 337.22 482.01 550.60 552.73 531.65 505.70 552.07 556.72 473.18 398.17 182.71
	Cmax Avg. 119.9 119.9 120.2 120.5 121.1 121.5 123.8 124.9 145.7 233.6 290.0
		S.D. 4.18	4.18	4.13	3.81	4.23	4.14	4.66	4.38	25.87 41.96 18.38