Milovan Medojevic
email: medojevicm@uns.ac.rs

Bojan Lalic
email: blalic@uns.ac.rs

Exploring the impact of Industry 4.0 concepts on energy and environmental management systems: Evidence from Serbian manufacturing companies

Keywords: Industry 4.0, ISO 50001, ISO 14001, EMS

It became more than evident that the era of Industry 4.0 is upon us, where industrial manufacturing companies are facing strong demand to increase their productivity and profitability by realizing or upgrading to smart factories and resource-efficient manufacturing processes. Having this in mind the aim of this paper is to provide insight regarding best practices in implementing Industry 4.0 concepts and their implications on manufacturing energy and environmental management systems and overall manufacturing energy efficiency. Our analysis used the Serbian dataset from the European Manufacturing Survey conducted in 2018. Furthermore, non-parametric correlation (Spearman's) analysis of the introduction of technologies on the one hand and EN ISO 50001 and EN ISO 14001 on the other was carried out. Results indicated significant correlation among Industry 4.0 concepts and both manufacturing energy and environmental management systems.

Introduction

Energy Management Systems (EnMS) and Environmental Management Systems (EnvMS) have emerged over the last two decades as a proven best practice methodology to ensure sustainable and progressing energy and environmental efficiency performance manufacturing firms [START_REF]Global Superior Energy Performance Partnership: Models for Driving Energy Efficiency Nationally Using Energy Management[END_REF]- [START_REF] Petrovic | Importance and role of the state, ISO 50001 standards and regulations in the introduction of the energy management system[END_REF]. EnMS outlines a structured and systematic approach on how to integrate energy efficiency in an enterprise management culture [START_REF] Medojevic | ISO 50001 as a tool to establish an adequate energy management system[END_REF]. In contrast, Industry 4.0, a German strategic initiative, aims at creation of smart factories where manufacturing technologies are upgraded and transformed by Cyber-Physical Systems, the Internet of Things (IoT), and cloud computing [START_REF] Lee | A cyber-physical systems architecture for industry 4.0-based manufacturing systems[END_REF], [START_REF] Lasi | Industry 4.0[END_REF]. In the Industry 4.0 era, manufacturing systems can monitor physical processes, by generating so-called "digital twin" (or "cyber twin") of the physical system/process to make smart decisions through real-time communication and cooperation between humans, machines, and sensors [START_REF] Wang | Towards smart factory for Industry 4.0: A selforganized multi-agent system with big data based feedback and coordination[END_REF], [START_REF] Medojevic | Energy management in industry 4.0 ecosystem: A review on possibilities and concerns[END_REF]. Today, factors driving Industry 4.0 are paving the path for intelligent energy management. Nevertheless, when companies embark on efforts to introduce Industry 4.0, they mostly focus on the 'core' parameters of production efficiency, quality and cost. This is obviously what drives revenue. However, there is a strong case to also include EnMS in such projects. After all, systematically tracking energy consumption, production and costs is a major challenge nowadays in most industries -and one that has a lot in common with Industry 4.0 way of thinking. The development of technologies for instrumentation and monitoring of industrial processes enables data capture in ever-increasing resolutions, allowing increasingly powerful analyses. In the field of energy management, sophisticated physical meters (instruments) can interpret physical quantities that allow precise understanding of processes of interest, as well as monitoring variables that range from applied power, to harmonics that describe the quality of the electricity consumed. From the energy management perspective, Industry 4.0 is realized in the connectivity between measuring instruments and the entire information and automation architecture of industrial organizations. Bearing in mind a combination of environmental aspects, cost pressure, and regulation as well as the proactiveness of organizations when it comes to efficient consumption of energy, energy management becomes one of the main pillars of Industry 4.0. In energy management, the data available can give rise to prediction models for energy consumption (or generation) of operations, starting from planned production levels or other contextual variables. This study reveals how and whether integrated EnMS, EnvMS and Industry 4.0 concepts influence on manufacturing efficiency. In addition, it provides insight on correlation between integrating energy management systems and Industry 4.0 concepts into daily practices. Our study relies on a unique dataset from the European Manufacturing Survey (EMS) with a sample of 240 industrial companies from the Republic of Serbia. Serbia is developing country with great foreign investments inflow into various types of manufacturing process. For instance, cost savings vs. EU-28 average 41% in electricity [START_REF]Why Invest in Serbia[END_REF].

2

Background and related work

Implications of Industry 4.0 concepts on industrial energy strategies

For manufacturers to be competitive in the 4 th industrial revolution, reducing production costs is of crucial importance. One way to achieve this is by creating a solid strategy when it comes to EnMS in Industry 4.0 environment. Among many factors that need to be optimized in order to stay competitive, one is energy efficiency which is still easily forgotten in most companies. While improved energy efficiency, as well as effectively implemented EnMS, is always welcome, it is rarely the main driver of Industry 4.0 deployments. However, energy savings have been reported by those organizations that have attempted to make Industry 4.0 a reality. For example, Daimler in Germany has reported a 30% improvement in energy efficiency for its robot systems that use Industry 4.0 techniques. Another example is Canadian Forest Products, which reported a 15% reduction in energy consumption by using real-time alerts for energy consumption outside of anticipated norms [START_REF] Medojevic | Energy management in industry 4.0 ecosystem: A review on possibilities and concerns[END_REF].

In previous literature, the highest impact on energy strategy is brought by IoT [START_REF] Ashton | That "Internet of Things[END_REF]. As a consequence of vast IoT solutions implementation, huge amount of data is being generated, introducing the Big Data term used to describe sets of data characterized by high volume, high velocity, and high variety [START_REF] Mauro | What is big data? A consensual definition and a review of key research topics[END_REF], and for which the use of advanced analytical tools is required in order to process data into actionable information by identifying patterns, trends, and relationships [START_REF] Lycett | Datafication': making sense of (big) data in a complex world[END_REF]. However, it is estimated that less than 1% of all available data is currently analyzed [START_REF] Gantz | The Digital Universe in 2020: Big Data, Bigger Digital Shadows, and Biggest Growth in the Far East United States[END_REF]. Big data therefore creates important challenges and opportunities now and in the coming years. In addition, presence of Big Data opens the door to Blockchain technologies which represents distributed databases and ledgers made of blocks stored on a large number of machines, so that any changes made to the database are permanently recorded, while any record is made publicly available thanks to the distributed design [START_REF] Crosby | Blockchain technology: Beyond bitcoin[END_REF]. This puts the spotlight on new opportunities for reducing or eliminating the need for a trusted middleman in many operations, ensuring a supply of certified renewable electricity coming from distributed energy generation, verification of legal energy provisions, etc. From the aspect of EnMS, Blockchain technology provides companies with the potential to analyze their energy consumption with greater accuracy and efficiency, monetize the data collected and validate energy consumption and savings in real-time. Additionally, this technology provides a new solution to record and monetize carbon credits where applicable. Rising electricity costs and energy sustainability are a critical risk for factory owners and asset managers worldwide. For instance, German energy executives see a wide range of possible applications for Blockchains in the energy sector and believe the technology could have the potential to reduce costs and spur new business models in it [START_REF] Burger | Blockchain in the energy transition: A survey among decision makers in the German energy industry[END_REF]. However, the Blockchain technology faces many challenges, privacy and data security issues, but also technical issues such as the currently still rather long time needed to conduct a transaction [START_REF] Nagasawa | Accelerating clean energy through Industry 4.0: Manufacturing the next revolution[END_REF].

Rapid Prototyping technologies represent one of the major developments in the modern manufacturing [START_REF] Kruth | Progress in Additive Manufacturing and Rapid Prototyping[END_REF]. Beyond prototyping, technologies such as additive-layer manufacturing also provide benefits to serial or mass manufacturing processes. For example, General Electric's LEAP engine, with 3D-printed fuel nozzles, has enabled to go from 18 sub-parts to only 1 [START_REF] Nagasawa | Accelerating clean energy through Industry 4.0: Manufacturing the next revolution[END_REF]. This not only multiplied the durability of the component by 5% and reduced its weight by 25%, but also enabled a better optimized geometry to achieve higher combustion efficiency [START_REF] Ford | Additive manufacturing and sustainability: an exploratory study of the advantages and challenges[END_REF]. This caused to fuel savings throughout the life of the engine and reducing its CO 2 emissions. Another example is Augmented Reality (AR). Wide spread of AR use in EnMS through "Open Energy" concept is noticed [START_REF] Brackney | Augmented reality building operations tool[END_REF]. For instance, Lobby Showcase of the Fraunhofer Center for Sustainable Energy Systems use thousands of sensors inside and outside of their headquarters, ensuring 5CC building to become living laboratory gathering and sharing live data.

Research questions

Given the, the following research questions were proposed in the attempt to identify the relationship between implementation of digital technologies and implementation of energy and environmental management systems:

• RQ1: What is the relationship between implementation of Industry 4.0 concepts and energy management system in Serbian manufacturing companies? • RQ2: What is the relationship between implementation of Industry 4.0 concepts and environmental management system in Serbian manufacturing companies?

Data and methodology

For the analysis purposes Serbian dataset from the EMS conducted in 2018 was used. EMS is a survey on the manufacturing strategies and the application of innovative organizational and technological concepts in production in European manufacturing industry [START_REF] Lalić | Use of Industry 4.0 and Organisational Innovation Concepts in the Serbian Textile and Apparel Industry[END_REF]- [START_REF] Lalic | The impact of organizational innovation concepts on new products and related services[END_REF]. The survey was conducted among manufacturing companies (NACE Rev 21 codes from 10 to 33) having at least 20 employees. Each survey has been carried out based on a proportionally size-and industry-based stratified random sample. The dataset includes 240 companies of all manufacturing industries as given in Table 1. The comparison of data regarding firm size distribution shows no significant size bias. The largest industry in the sample is the manufacture of food products (NACE 10; 16.3%), followed by manufacture of fabricated metal products (NACE 25; 15.0%) and manufacture of rubber and plastic products (NACE 22; 8.8%). Tables 1 and2 depict the sample distribution of the dataset from Serbia. Lastly, to analyze the relationships between implementation of digital technologies on one side and EnMS and EnvMS on the other we employed non-parametric correlation (Spearman's) analysis.

Results and Discussion

Table 3 depicts results of the correlation analysis (i.e. Spearman correlation coefficient values) between implementation of Industry 4.0 concepts and implementation of energy (RQ1) and environmental (RQ2) management systems. Given analysis revealed that there is a significant positive relationship between implementation of each Industry 4.0 concept on one hand and implementation of EnMS and EnvMS on the other. These results provide evidence that Serbian manufacturing companies recognize the importance of e EnMS and EnvMS integration along with implementation of indicated Industry 4.0 technology concepts. However, as it could be seen from the results, although this linkage is statistically significant, it is characterized as a low strength correlation. On the other hand, this cognition can be interpreted as verification of the previously given statement that implemented EnMS and EnvMS have been deployed by those organizations that have attempted to make Industry 4.0 a reality. Nowadays, manufacturing systems worldwide implement advanced manufacturing or Lean Manufacturing principles, in which minimal resources to bring maximum value to the business are applied. These same principles can and should be used for energy utilization. From this perspective, it is all about being efficient in the way the energy within manufacturing system is being used, with aim to reduce consumption where necessary, and transfer adequate knowledge to relevant personnel across the organization in order to bring the same value with less energy and thus reduced harmful emissions [START_REF] Medojevic | Energy management in industry 4.0 ecosystem: A review on possibilities and concerns[END_REF]. However, it is strongly believed that majority of manufacturing companies, both in Serbia and throughout the world, still lacking well-tailored developing strategies to integrate environmental sustainability into manufacturing which is in any case of utmost importance to gain competitiveness. Successfully implementing energy and resource efficiency programs, pollution prevention and control programs, or sustainability initiatives is of urgent need [START_REF] May | Energy management in manufacturing: Toward eco-factories of the future -A focus group study[END_REF]- [START_REF] Vieira | Setting an Industry 4.0 Research and Development Agenda for Simulation -a Literature Review[END_REF], which with the appropriate application of Industry 4.0 concepts, can be easily integrated into processes.

Conclusion

This study provides insight regarding best practices in implementing Industry 4.0 concepts and their implications on manufacturing EnMS and EnvMS and overall manufacturing energy efficiency. Based on analysis that used the Serbian dataset from the ENMS conducted in 2018, it was revealed that there is a significant positive relationship between implementation of each Industry 4.0 concept on one hand and implementation of EnMS and EnvMS on the other. More importantly, these results provide evidence that Serbian manufacturing companies recognize the importance of EnMS and EnvMS integration along with implementation of indicated Industry 4.0 technology concepts. However, although results indicate statistical significance, this linkage is characterized as a low strength correlation. Despite the obvious similarities and the huge potential, EnMS is not (yet) fully incorporated in most factory digitization projects. There is reason for optimism, though. Awareness is growing quickly with key decision makers in industry. Having this in mind, Industry 4.0 (with special emphasis on IoT and Big Data) and EnMS and EnvMS combined suggest an exciting future with reduced costs and emission of pollutants, while simultaneously ensuring improved performance. However, you could be left with a severe wondering where all the promise and money went. Or in other words, manufacturing decision makers should be taking full advantage of these Industry 4.0 tracking tools for EnMS and EnvMS carefully. Lastly, the sample was drawn from a single developing country, probably lacking the diversity that can be expected from a comparable sample chosen

Table 1 .

 1 EMS database -distribution of companies by size

		20 to 49	Company size	250 and more
		employees	50 to 249 employees	employees
		n (%)	n (%)	n (%)
	Serbia	110 (45.8)	103 (42.9)	27 (11.3)

Table 2 .

 2 Classification on manufacturing sectors according to share on total sample

	NACE	Manufacturing industry	Share on total
	Rev. 2		sample (%)
	10	Manufacture of food products		16.3
	25	Manufacture of fabricated metal products, except machinery and	15.0
		equipment
	22	Manufacture of rubber and plastic products		8.8
	27	Manufacture of electrical equipment		6.3
	28	Manufacture of machinery and equipment n.e.c.		6.3
	14	Manufacture of wearing apparel		5.8
	16	Manufacture of wood and of products of wood and cork, except	4.6
		furniture; manufacture of articles of straw and plaiting materials
	23	Manufacture of other non-metallic mineral products		4.6
	29	Manufacture of motor vehicles, trailers and semi-trailers		4.2
		Others		28.5

Table 3 .

 3 -Results of the correlation analysis

	Technologies

NACE Rev.

stands for Statistical classification of economic activities in the European Community (more information regarding NACE Rev.2 could be found here).

from across different economies, both developed and developing. Further research should test the model and relationships in the manufacturing companies within other EMS countries (e.g. Austria, Germany, Slovenia, Lithuania).


Ken Yamashita
email: yamashita@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

Toyohiro Umeda
email: umeda.toyohiro@kobelco.com

Rihito Izutsu
email: izutsu.rihito@kobelco.com

A proposal of order planning method with consideration of multiple organizations in manufacturing system

Keywords: Manufacturing system, Order planning, Production scheduling

Manufacturing system includes multiple business organizations having different decision criteria such as factories, salespersons and customers. It is important to maximize the overall profit while considering the objectives of each organization by appropriate adjustment. In this study, we propose the order planning method using the credibility about salespersons. This proposed method adjusts the due date between the salesperson and the customer by considering the margin time, and then derives effective production schedule by solving the optimization problem that minimizes the weighted sum of the tardiness from due date and makespan. Several computational experiments are conducted so as to evaluate the effectiveness of the proposed method.

Introduction

In manufacturing industries, the production style has shifted to high-mix lowvolume manufacturing production from small-mix high-volume production in order to respond to the consumers' needs flexibly [START_REF] Zhang | Modelling and integration of customer flexibility in the order commitment process for high mix low volume production[END_REF]. As a result, the market objective has been changed into shortening due date and product life cycle [START_REF] Nishioka | Synchronization technology for planning scheduling to respond quickly to changes in demand trends[END_REF]. In response to this situation, industries have to constantly introduce new products to the market, and at the same time establish a decision making mechanism that can respond to consumers' needs quickly. The issues are to reduce product inventory, shorten lead time, estimate due date accurately, launch new products rapidly, and manage individual specifications flexibly as mass customization [START_REF] Kuroda | Delivery estimate and production scheduling -Information sharing and cooperation under the order production status[END_REF]. In order to solve these problems, it is necessary to improve the production efficiency with rational production scheduling and to properly adjust the gap between the customers' needs and due date estimation by the sales department.

In the relevant researches, there is order acceptance and scheduling problem proposed by Guerrero and Kern [4]. This is defined as the joint decision of which orders to accept for processing and how to schedule them, and various studies have been conducted on this [START_REF] Slotnick | Order acceptance and scheduling: A taxonomy and review[END_REF].

In this study, we propose an order planning method that performs determination of the due date and production scheduling in consideration of the relationship among customers, salespersons and factories. In the determination of the due date, the response adjustment method by using sales department is used which gives margin time for the due date. In scheduling, we solve the optimization problem which minimizes the objective function using multiple indicators considering salespersons and factory managers. To evaluate the effectiveness of the proposed method, several computational experiments are performed.

Target Model

In this study, we target a factory model with multiple customers, salespersons and one factory as shown in Fig. 1. One ordering period is defined as lead time from customer's inquiry to delivery. Each business organization is set as follows.

Fig. 1. Overview of relationship diagram among entities

Customer

Customers order the desired production item and the quantity of the items to the salespersons. Each customer has a degree of credibility to the salespersons which represent the previous order conditions. The order quantity is determined by the degree of credibility and the answered due date from the salesperson. The degree of credibility varies depending on the occurrence situation of the tardiness from the due date. When the credibility reaches the lower limit, the customer temporarily stops the transaction at the subsequent ordering period.

Salesperson

Salespersons make due date estimation in response to customers' order inquiries. Based on the desired due date of the customer and the information on the production schedule at the previous ordering period, the answered due date to the customer is decided in consideration with the margin time. By reducing the margin time, it is possible to bring the answered due date closer to the desired due date from the cus-tomers. On the other hand, the tardiness may increase. In contrast, by increasing it, occurrence of the tardiness can be decreased. However, the due date is far from the customers' desired due date.

Factory

The factory creates production schedule for the orders from salespersons per ordering period and manufactures products. This study targets multi-stage flow shops.

Proposed order planning method

The proposed order planning method in this study is explained. In this method, mainly due date adjustment and scheduling are performed. The algorithm of proposed method is described in Section3.2, and the formulation of factory scheduling within the algorithm is shown in Section 3.3.

Notation

The notations used in proposed order planning method are shown as follows:

𝑠 ∶ Salesperson (𝑠 = 1, … , 𝑆) 𝑐 ∶ Customer (𝑐 = 1, … , 𝐶) 𝑝 ∶ Order period (𝑝 = 1, … , 𝑃) 𝑂𝐶 ∶
The number of time slots in one ordering period 𝐶𝑅 𝑝,𝑐 ∶ Degree of credibility to salespersons by customer 𝑐 in period 𝑝 𝐵𝑄 𝑐 ∶ Standard order quantity of customer 𝑐 𝑄 𝑝,𝑐 ∶ Original order quantity of customer 𝑐 in period 𝑝 𝑄 𝑝,𝑐 ′ ∶ Final order quantity of customer 𝑐 in period 𝑝 𝐴𝑇 𝑝,𝑐 ∶ Allowable time for order of customer 𝑐 in period 𝑝 𝑃𝐷 𝑝,𝑐 ∶ Desired due date of customer 𝑐 in period 𝑝 𝐴𝐷 𝑝,𝑐 ∶ Answered due date of the order of customer 𝑐 in period 𝑝 𝐶𝑇 𝑝,𝑐 ∶ Correction time given order when the previous end time is later than the desired due date of customer 𝑐 in period 𝑝 𝑀𝑇 𝑝,𝑐,𝑠 ∶ Margin time given to order of customer 𝑐 in period 𝑝 by salesperson 𝑠 𝐷𝐷 𝑝,𝑐 ∶ Delivery date of the order of customer 𝑐 in period 𝑝 𝑟 𝑄𝐷 ∶ Rate of decrease in order quantity 𝑎 𝐶𝑅𝐼 ∶ Amount of credibility increase when the order can be delivered within the answered due date 𝑟 𝐶𝑅𝐷 ∶ Reduction rate of credibility at the time of the occurrence of the tardiness

Algorithm of proposed method

In the proposed method using due date adjustment and production scheduling, the aim is to increase order quantity by reducing the tardiness and keeping the high credibility. The algorithm the proposed method is expressed and the flowchart of the proposed method is shown in Fig. 2.

Fig. 2. Flowchart of proposed method

STEP1. Set the ordering period 𝑝 to 1. STEP2. The customer makes an inquiry about the order to the salesperson. Inquired order includes product type, desired order quantity 𝑄 𝑝,𝑐 and desired due date 𝑃𝐷 𝑝,𝑐 as information. The desired order quantity 𝑄 𝑝,𝑐 is expressed by the following equation [START_REF] Zhang | Modelling and integration of customer flexibility in the order commitment process for high mix low volume production[END_REF]. The desired due date 𝑃𝐷 𝑝,𝑐 is determined by the following equation [START_REF] Nishioka | Synchronization technology for planning scheduling to respond quickly to changes in demand trends[END_REF].

𝑄 𝑝,𝑐 = 𝐵𝑄 𝑐 × 𝐶𝑅 𝑝,𝑐 (1) 𝑃𝐷 𝑝,𝑐 = (𝑝 -1) × 𝑂𝐶 + 𝐴𝑇 𝑝,𝑐

(2) STEP3. The salesperson estimates the due date for the order. When estimating, the salesperson obtains the end time of the schedule of the previous period from the factory. The answered due date 𝐴𝐷 𝑝,𝑐 of the order of customer 𝑐 in period 𝑝 is expressed by the following equation [START_REF] Kuroda | Delivery estimate and production scheduling -Information sharing and cooperation under the order production status[END_REF].

𝐴𝐷 𝑝,𝑐 = 𝑃𝐷 𝑝,𝑐 + 𝐶𝑇 𝑝,𝑐 + 𝑀𝑇 𝑝,𝑐,𝑠

STEP4. If the answered due date is later than the desired due date, the customer decreases the order quantity according to the tardiness. When the order quantity becomes 0 after the decreasing, the order is canceled. The final order quantity 𝑄 𝑝,𝑐 ′ is expressed by the following equation ( 4).

𝑄 𝑝,𝑐 ′ = max [0, 𝑄 𝑝,𝑐 × {1 -𝑟 𝑄𝐷 × (𝐶𝑇 𝑝,𝑐 + 𝑀𝑇 𝑝,𝑐,𝑠 )}] (4) STEP5. The salesperson inserts the order to the factory. If STEP2 to STEP4 are performed by all the customers, the process proceeds to STEP6, otherwise, returns to STEP2. STEP6. The factory divides the orders input in STEP5 into multiple jobs and formulates as a multi-stages flow shop scheduling problem. It creates a production schedule by solving the problem and manufactures products. This study uses IBM ILOG CPLEX 12.6.3 [6] to solve the problem. STEP7. If the delivery date 𝐷𝐷 𝑝,𝑐 of the order is included in the ordering period 𝑝, the factory delivers to the customer. STEP8. If the order is in time for delivery, the credibility in the customer increases, and if the tardiness 𝑑 𝑝,𝑐 𝐶𝑅𝐷 according to equation ( 5) occurs, the credibility decreases. Change in credibility 𝐶𝑅 𝑝,𝑐 of customer 𝑐 in period 𝑝 is expressed by the following equation ( 6). 𝑑 𝑝,𝑐 𝐶𝑅𝐷 = max (0, 𝐷𝐷 𝑝,𝑐 -𝐴𝐷 𝑝,𝑐 ),

𝐶𝑅 𝑝,𝑐 = { 𝐶𝑅 (𝑝-1),𝑐 + 𝑎 𝐶𝑅𝐼 , (𝑑 𝑝,𝑐 𝐶𝑅𝐷 ≤ 0) max (0, 𝐶𝑅 (𝑝-1),𝑐 -𝑟 𝐶𝑅𝐷 × 𝑑 𝑝,𝑐 𝐶𝑅𝐷 ), (𝑑 𝑝,𝑐 𝐶𝑅𝐷 > 0)

STEP9. If 𝑝 period reaches the prescribed total number of times 𝑃, the process ends. Otherwise, 𝑝 ∶= 𝑝 + 1 and return to STEP2.

Formulation of K-stage flow shop scheduling

The (16) 𝑥 𝑝,𝑗,𝑗 ′ ,𝑘 is the decision variable. When this value is 1, job 𝑗 at stage 𝑘 in period 𝑝 precedes the job 𝑗'. When this value is 0, job 𝑗 ′ at stage 𝑘 in period 𝑝 precedes job 𝑗.

Objective function ( 7) is intended for minimizing the weighted sum of the total tardiness and makespan. The reason for using these two as an evaluation index is that salespersons and the factory try to respond to customers' requests and raising productivity. The parameter 𝛼 is a weight between the total tardiness and the makespan in the objective function.

Equations ( 8), ( 9) and ( 10) are the definition of tardiness, makespan, and end time. Constraint (11) guarantees that next stage is started after the completion of previous stage. Constraint (12) limits the number of jobs that can be processed at one time. Constraints ( 13) and ( 14) represent that start time is after the end time of previous period. Constraint (15) ensures that precedence relation of jobs is either one way.

Computational experiments

In order to evaluate the influence of the weight parameter  of the objective function and the margin time 𝑀𝑇 𝑝,𝑐,𝑠 which is given by the salespersons in the due date determination, the computational experiments are performed. In Experiment 1, we perform the sensitivity analysis for α which is the weighting factor of the total tardiness and makespan. Experiment 2 evaluates the influence of 𝑀𝑇 𝑝,𝑐,𝑠 . The evaluation criteria are as follows:

 𝑇𝑂 : Total order quantity  𝐷𝐿 : Average tardiness per order [TS]  𝐴𝐶 : Average final credibility  𝑆𝐶 : The number of setup

Experimental conditions

The experiments are performed with the following conditions: In these experiments, it is assumed that salespersons do not share information of orders of other customers, so the number of customers and salespersons are the same.



Experiment 1: Comparison by objective function parameter 𝛂

In Experiment 1, we simulated by varying the parameter α used for the weighted sum of the objective function in 𝑀𝑇 𝑝,𝑐,𝑠 = 0. When α is increased, the weight for minimizing the total tardiness in the objective function increases. Whereas if it is decreased, the weight of the minimization of the makespan increases. The results when α is set to 0.1, 0.5, 0.9 are shown in Table 1. Considering the results in Table 1, when the weight of the total tardiness increased, the average tardiness 𝐷𝐿 was reduced. And when we increased the weight of makespan, the number of setup 𝑆𝐶 decreased. From the result at α = 0.9, it was confirmed that increasing the weight of the tardiness raises the average final credibility 𝐴𝐶 and the total order quantity 𝑇𝑂. In Experiment 2, we compared the simulation results at 𝛼 = 0.9 with changing 𝑀𝑇 𝑝,𝑐,𝑠 given by the salespersons. Changes in 𝑇𝑂 and 𝐷𝐿 when 𝑀𝑇 𝑝,𝑐,𝑠 is 0 to 9 are shown in Fig. 3. Considering the results in Fig. 3, it was confirmed increasing margin time suppressed the tardiness. Also, 𝑇𝑂 was the maximum and increased more than when not having margin time in 𝑀𝑇 𝑝,𝑐,𝑠 = 5. So the effectiveness of the proposed method was confirmed. However, 𝑇𝑂 was decreased with increasing in margin time at 𝑀𝑇 𝑝,𝑐,𝑠 ≥ 5. Although the degree of credibility was increased by suppressing the tardiness, for order quantity, the influence of "decrease due to the difference between desired and answered due date" was larger than one of "increase due to high credibility". So the total order quantity was decreased. Therefore, in order to increase the order quantity, the appropriate adjustment of the margin time must be required.

Conclusion

In this study, we targeted the manufacturing industry where there are multiple entities such as a factory, salespersons, and customers. And, the order planning method to decide due date including margin time and perform scheduling considering total tardiness and makespan was proposed.

In the computer experiments, we increased the weight for the total tardiness of the objective function in the scheduling problem and added the margin time to the due date. From the results, the tardiness from the due date was suppressed by them. Also, the proposed method was confirmed that the total order quantity increases as the margin time increases. However, in excessive margin time, the order quantity decreases due to being far from the customer's desired due date.

We will consider the adjustment method of the margin time as the next step.

  In addition, the notations used in scheduling are shown as follows: 𝑗 ∶ Job number (𝑗 = 1, … , 𝐽) 𝑘 ∶ Stage number (𝑘 = 1, … , 𝐾) 𝑇 𝑝,𝑗 ∶ Tardiness of job 𝑗 in period 𝑝 𝑀𝑆 𝑝 ∶ Makespan in period 𝑝 𝑃𝑇 𝑝,𝑗,𝑘 ∶ Processing time of stage 𝑘 of job 𝑗 in period 𝑝 𝑆𝑇 𝑝,𝑗,𝑗 ′ ,𝑘 ∶ Setup time from job 𝑗 to job 𝑗 ′ at stage 𝑘 in period 𝑝 𝐷 𝑝,𝑗 ∶ Due date of job 𝑗 in period 𝑝 𝑠 𝑝,𝑗,𝑘 ∶ Start time of stage 𝑘 of job 𝑗 in period 𝑝 𝐸𝑇 𝑝,𝑗,𝑘 ∶ End time of stage 𝑘 of job 𝑗 in period 𝑝 α ∶ Weight factor of objective function 𝑥 𝑝,𝑗,𝑗 ′ ,𝑘 ∶ Decision variable

  The number of customers (𝐶) ∶ 10  The number of salesperson (𝑆) ∶ 10  The number of ordering period (𝑃) ∶ 10  The number of time slots in each ordering period ∶ 100[TS]  The number of job stages (𝐾) ∶ 2  The number of product types ∶ 2  Setup time due to change of product type (𝑆𝑇 𝑝,𝑗,𝑗 ′ ,𝑘 ) ∶ 2[TS]  Customer allowable time (𝐴𝑇 𝑝,𝑐 ) ∶ 20 ≤ 𝐴𝑇 𝑝,𝑐 ≤ 100[TS] (uniform random number)  Standard order quantity of customer (𝐵𝑄 𝑐 ) ∶ 10  Initial credibility of customer (𝐶𝑅 0,𝑐 ) ∶ 1.0  Range of credibility of customer (𝐶𝑅 𝑝,𝑐 ) ∶ 0.0 ≤ 𝐶𝑅 ≤ 1.0  Rate of decrease in order quantity (𝑟 𝑄𝐷 ) ∶ 0.04  Amount of credibility increase when the order can be delivered within the answered due date (𝑎 𝐶𝑅𝐼 ) ∶ 0.1  Reduction rate of credibility at the time of tardiness occurrence (𝑟 𝐶𝑅𝐷 ) ∶ 0.04  The number of trials : 20

Fig. 3 .

 3 Fig. 3. Changes to 𝑇𝑂 and 𝐷𝐿 with various 𝑀𝑇 𝑝,𝑐,𝑠 (𝛼 = 0.9). Error bar: standard deviation

  𝑠 𝑝,𝑗 ′ ,𝑘 ≥ 𝑠 𝑝,𝑗,𝑘 + 𝑃𝑇 𝑝,𝑗,𝑘 + 𝑆𝑇 𝑝,𝑗,𝑗 ′ ,𝑘 (if 𝑥 𝑝,𝑗,𝑗 ′ ,𝑘 = 1) {∀𝑗, ∀𝑗 ′ (≠ 𝑗), ∀𝑘} (12)

				follows as
	optimization problem:
	min	α ∑ 𝑇 𝑝,𝑗 + (1 -𝛼)𝑀𝑆 𝑝 ∀𝑗	(7)
	where	𝑇 𝑝,𝑗 = max(0, 𝑠 𝑝,𝑗,𝐾 + 𝑃𝑇 𝑝,𝑗,𝐾 -𝐷 𝑝,𝑗 )	(8)
		𝑀𝑆 𝑝 = 𝑚𝑎𝑥 ∀𝑗,∀𝑘	(𝑠 𝑝,𝑗,𝑘 + 𝑃𝑇 𝑝,𝑗,𝑘 -𝐸𝑇 𝑝-1,𝑘 )	(9)
		𝐸𝑇 𝑝,𝑘 = max ∀𝑗	(𝑠 𝑝,𝑗,𝑘 + 𝑃𝑇 𝑝,𝑗,𝑘 )	(10)
	s.t.	𝑠 𝑝,𝑗,𝑘+1 ≥ 𝑠 𝑝,𝑗,𝑘 + 𝑃𝑇 𝑝,𝑗,𝑘	(11)
		𝑠 𝑝,𝑗,𝑘 ≥ 𝐸𝑇 𝑝-1,𝑘 (∀𝑗, ∀𝑘)	(13)
			𝑠 𝑝,𝑗,𝑘 ≥ 0	(14)
		𝑥 𝑝,𝑗,𝑗 ′ ,𝑘 + 𝑥 𝑝,𝑗 ′ ,𝑗,𝑘 = 1 {∀𝑗, ∀𝑗 ′ (≠ 𝑗), ∀𝑘}	(15)
		𝑥 𝑝,𝑗,𝑗 ′ ,𝑘 ∈ {0,1} {∀𝑗, ∀𝑗 ′ (≠ 𝑗), ∀𝑘}

𝐾-stage flow shop scheduling problem in STEP6 is formulated as

Table 1 .

 1 Results of Experiment 1 (𝑀𝑇 𝑝,𝑐,𝑠 = 0)

				α = 0.1	α = 0.5	α = 0.9
		𝑇𝑂	Avg. S.D.	635.07 45.68	666.11 49.39	669.37 43.00
		𝐷𝐿	Avg. S.D.	2.90 0.40	2.68 0.47	2.59 0.52
		𝐴𝐶	Avg. S.D.	0.64 0.08	0.70 0.08	0.73 0.09
		𝑆𝐶	Avg. S.D.	14.48 1.68	20.65 3.59	23.08 3.51
	4.3	Experiment 2: Comparison by margin time 𝑴𝑻 𝒑,𝒄,𝒔


Nursultan Nikhanbayev

Toshiya Kaihara

Nobutada Fujii

Daisuke Kokuryo

Multiscale modeling of social systems: scale bridging via decision making

Keywords: Multiscale modeling, Simulation, Social systems, Scale bridging

In recent years technological advancement makes it possible to connect heterogeneous systems at hierarchical levels, such as macro level where strategic decisions are made, and micro level where organizations interact with the users. Modeling of these connections alongside with systems is one of the problems, which can be solved by modeling techniques that take hierarchical nature of the systems into consideration. In this paper, we propose a multiscale modeling approach for social systems. We suggest to design a model by adopting certain entities: decision makers, resources, actions and propagation variables. The proposed approach is evaluated on an example of collaboration between two systems: electricity suppliers and manufacturers. Results of the computational experiments demonstrate the effectiveness of the proposed technique.

Introduction

Recently, due to advanced development of technology connecting heterogeneous systems has started to emerge. Usually, stakeholders of heterogeneous systems are more concerned about their own objectives and goals. On top of that, in some cases those objectives are conflicting as well, which makes connection of heterogeneous systems a very complex endeavor.

Connection of multiple systems is also one of core ideas behind the concept of Super Smart Society (or Society 5.0) [1], which was proposed by Japanese government. It was highlighted that social implementation and proper risk management are the necessary points to achieve new society without loses. Making a simulation model can be an useful tool to deal with this kind of problems. However, some processes in this setup are performed on different temporal or spatial scales. Users, systems, and the government are concerned about different objectives, that differ a lot in terms of the scope. For this reason, a novel modeling technique, which can capture multiscale nature of the problem, is necessary.

There exist different modeling techniques, such as Multimethod modeling [START_REF] Borshchev | Multi-method modeling[END_REF], and Hybrid modeling [START_REF] Hooker | Hybrid Modeling[END_REF] that try to connect multiple parts of the system in one model. In authors opinion, Multiscale Modeling would be more suitable technique in this case. Mainly, because of its ability to manage submodels with different temporal and spatial scales. This paper contributes to a certain part of multiscale modeling: a scale bridging phase. Authors suggest to connect different scales of the model by using set of entities: decision makers, resources, actions and propagation variables. In the next section more comprehensive explanation of a target model and of the technique is performed.

Target model and multiscale modeling

Target model

In a target model we consider a collaboration between two systems: electricity suppliers and manufacturers. In general, stakeholders of these systems are more concerned about their own business, and do not take into consideration decision variables of other systems. For example, if we consider connection between electricity suppliers and manufacturers, formers are interested in reducing peak demand and making electricity load pattern as flat as possible (to avoid using inefficient power plants). Meanwhile, manufacturers are focused on making profit and reducing costs. In this case, one of the scenarios of collaboration might be shift of manufacturers' work time to the later hours, which would be helping in reducing peak electricity demand. However, due to late working hours, manufacturers have to spend more money on the salary to the workers. Therefore, direct collaboration is not in interest of manufacturer, and in order to achieve a connection which will benefits both sides, more comprehensive scenarios are necessary. There are three parties considered in this example: electricity supplier, manufacturer and residents.

Electricity supplier

In reality, electricity supply is a very complex system, which includes a lot of decision makers on different levels. In our example, we consider electricity supplier to be interested in one objective: reducing peak demand(or flattening electricity load pattern). This problem can be tackled by equation of Peak-to-Average Ratio (PAR). Mathematical representation of the average (L avg ) and the peak (L max ) loads of the grid looks as follows:

L avg = 1 T ∑ t∈T L t and L max = max t∈T L t . (1)
Consequently, the PAR is calculated as

P AR = L max L avg .
Electricity provider interacts with residents at one side, and with the manufacturer at another. Resources of the electricity supplier are power plants. They are utilized to generate the electricity and satisfy demand coming from manufacturers and residents. Electricity supplier makes decisions about which kind of power plants to utilize in order to satisfy demand. This decision is represented as cost minimization problem.

Manufacturer Here we consider simple supply chain which consists of the manufacturer and users(residents). The manufacturer produces one type of product and uses certain amount of electricity. Basic electricity usage of the manufacturer is performed by using electricity load pattern. Manufacturers are mainly concerned about minimizing costs and maximizing their profit. Cost and profit are captured in the model in the straightforward way: C = F C + V C and P r = pN -C, where F C is a fixed cost, V C is a variable cost, P r is a profit, p is a price, and N is a number of sold products. In this particular case, resources of the manufacturer are its products. The propagation variable is the price of the product. An action which is performed over this resource is selling it.

Residents In this model, residents are considered to use electric appliances, based on their daily activities as shown in Fig. 1, and to demand the electricity from the electricity supplier.

Fig. 1. An example of the usage of home appliances by single working person on hourly basis

Users are mainly concerned about their spendings. They possess money and electric appliances, these resources ensure connection of users to the systems of the higher level. Through money and electric appliances to the electricity supplier, and to the manufacturer through money.

Multiscale modeling

In general terms, multiscale modeling is a way of designing a system by separating it into several scales, where each scale has its own inner dynamics. Multiscale modeling is mostly used in areas, such as meteorology, mathematics, physics, material science, chemistry, and etc. [START_REF] Horstemeyer | Multiscale Modeling: A Review[END_REF] Majority of available literature are less concentrated on the theoretical part of the approach and put their main focus on the details of the specific case. There are only a few researches concentrating on theoretical or methodological aspects of multiscale modeling [START_REF] Falcone | Mml: towards a multi-scale modeling language[END_REF][6] [START_REF] Weinan | Heterogeneous multiscale methods: a review[END_REF]. Lack of standardized theory is the only tip of the iceberg: in case of multiscale modeling for social systems, to the best of our knowledge, there are a limited number of studies which address to this topic. Accordingly adaptation of the existing methods, as well as the creation of novel methods specific for social systems would be helpful to deal with multiscale cases of social systems.

Explanation of the approach will follow two steps of creation of multiscale models mentioned by Hoekstra et all. [START_REF] Falcone | Mml: towards a multi-scale modeling language[END_REF]: Scale separation and Scale bridging.

Scale separation Scale separation is the step where we identify and clarify what our scales are, and what do they do. As it was mentioned, modeling of social systems includes several heterogeneous systems, which we are trying to connect. We made an assumption here that society is located on the lowest scale and accessible to the all systems. Each heterogeneous system can be divided into several scales, and their number might be different from each other. The main idea is to connect particular scales of one system with the appropriate scales of the other. This is going to breakdown connections into sublevels, providing more insights into modeling of connections.

Scale bridging Scale bridging is a way of connecting scales. There already exist a lot of scale bridging techniques such as sampling, projection, up-scaling, homogenization and etc. [START_REF] Weinan | Heterogeneous multiscale methods: a review[END_REF][8][9] However these techniques are used in exact sciences, therefore, due to the differences of them from social systems, an adaptation of scale bridging methods or creation of new ones is necessary. In social systems decision makers and decisions play very important role. Therefore, we propose connecting scales using decision makers. Proposed connection approach is based on four entities: 1) Decision Making Entity(DME) 2) Resource 3) Action and 4) Propagation variable. Definitions are: DME -an entity which owns and has control over particular resource; Resource (R)-an asset that is possessed by a particular DME, including but not limited to information, materials and people; Action over resource (A) -is a process which affects or alters particular resource; Propagation variable -variable that propagates through scales. DME owns resource(s) and has particular set of actions which are performed on a particular resource. Each resource has properties. Propagation variable is a property of the resource which is in interest of DME of other scale.

Scale bridging is tightly related to the timescale. In general, bottom-up propagation of decision is captured as an impact of propagation variable on resource of the higher scale. Propagation variable shifts upwards based on time step of lower scale.

Application of scale separation and scale bridging

Based on the dynamics of each actor mentioned in this example, there are two scales. First scale is the residents. They have specific dynamics like using electric appliances on hourly basis, which make them different from dynamics of the next scale. On the second scale we have manufacturer, and electricity supplier. Connection among scales is performed by using the proposed approach. In total there are three DMEs in the model: manufacturers, electricity suppliers and residents.

Bottom-up connection relies on two types of resources that residents possess, which are electric appliances and money. They use electric appliances each hour, and then send their consumption, as its property, to the electricity supplier. Residents are connected to the manufacturer through their money. If a particular resident wants to buy a certain product, amount of money is sent to the manufacturer. Top-down propagation is the price of the electricity and a product respectively for each DME of the second scale. In Figure 2, we can see how bottom-up connections are performed in the target model. In this example, upper level decision makers, such as the government, is omitted, therefore only prices of both electricity and products are sent to the users as its property. In the model where the government is also considered, more different kind of properties like volume of electricity, energy fuels that have been used, amount of sales, and etc. should be taken into consideration.

Computational experiment and discussions

In this experiment we consider collaboration between two systems. The main objective of the collaboration is an identification of an optimal scenarios. We consider collaboration in terms of incentives given by electricity supplier. Manufacturer will have a cheaper electricity bill, if it shifts the working hours to the low load hours. However, shifting working hours will lead to raising of cost of the manufacturer, because it has to pay more salary. Therefore, the objective of the simulation is to find an optimal conditions for minimizing the negative impact of the trade-off.

The main experimental setups are done in the following way. Electricity supplier: types of energy fuels -6(coal, oil, gas, nuclear, hydro, renewable), basic electricity price -20 (yen/kWh). Manufacturer: electricity usage per product: 2 kWh, number of workers: 20, salary per hour -100 yen. Users: number of residents -150. Detailed setups are omitted due to space limitation.

State of the systems before collaboration Experimental results before any type of collaboration, show the existence of the peak at the side of the electricity supplier (Fig. 3). Here, PARs look as follows: PAR of the manufacturer P AR m = 1.8017, PAR of the residents P AR r = 1.5891 and in the combined case P AR c = 1.3149.

Results of the collaboration

It is assumed that manufacturer has to pay 1.5 times more salary for working at (22:00-5:00), also electricity price is 15 yen/kWh at night(day price is 20 yen/kWh).

After several simulations obtained results show that if we setup six of the workers would work at night hours (0:00-7:00) and rest of the workers work as usual, we will get a solution which affects cost of manufacturer the least. In this case demand pattern changes as can be seen in Fig. 4. P ARs of the changed patterns are P AR m = 1.384 and P AR c = 1.3122. We can notice that as expected P AR m becomes smaller, but P AR c of combined case has not changed much. The reason behind this is related to the fact, that the changes had only affected manufacturers.

Costs of the manufacturer: night shift salary-7200 yen, day shift salary -14000 yen, spendings on night-shift electricity consumption -1843.964 yen, spendings on day-shift electricity consumption -4720.7039 yen, and total-27764.6686 yen. Those values differ from original cost only by 5.6%. Additionally if we consider collaboration of residents and electricity suppliers via home batteries [START_REF] Nikhanbayev | A study on multiscale modeling and simulation approach for social systems[END_REF], we will get more promising results. In Fig. 5, we can clearly see that combined demand pattern becomes much flatter after implementing collaboration on multiple levels. Calculating peak-to-average ratio gives us: P AR r = 1.1069, P AR m = 1.1769. That is very good results. However, it should be mentioned here, that this is only simulation, and it gives us results of what might happen under certain conditions. To sum up, the proposed technique demonstrated its ability to connect several systems in one executable social simulation model. Clarifying resources and their properties that should propagate, helps to understand how connections among several systems work, which is in general not a trivial task to deal with.

Conclusions

This paper describes an implementation of multiscale modeling to design social systems. This work contributes to existing knowledge of scale bridging by extending it to the case of social systems. More specifically, authors suggest to perform scale bridging via decision makers. Multiscale model can be designed by adopting four entities: decision makers, resources, actions and propagation variables. This way of modeling helps to clarify which kind of resources ensure connection among multiple systems. Moreover, there was presented example of collaboration between an electricity supplier and a manufacturer. Computational experiments demonstrated necessity of multiscale perspective when considering cases, similar to one mentioned in this paper. In addition, it was figured out that under certain conditions, collaboration among heterogeneous is possible to achieve.

Finally, a number of limitations need to be considered. At first, the presented example does not include certain features such as higher level decision maker, like the government, or the product market. More comprehensive cases might bring some challenges, which can help to improve the proposed technique. Secondly, theoretical part of the proposed technique still lacks concretization, and more standardized approach would be helpful in dealing with complex systems. At last, simulation models have difficult point in terms of the validation of the model, and multiscale modeling is not an exception. These limitations are subject to the future work.

Fig. 2 .

 2 Fig. 2. Scale bridging of the target model: bottom-up connections

Fig. 3 .

 3 Fig. 3. Demand pattern of electricity supplier before collaboration

Fig. 4 .

 4 Fig. 4. Demand pattern of electricity supplier after collaboration

Fig. 5 .

 5 Fig. 5. Demand pattern of electricity supplier in case of collaboration with residents and manufacturers


Sabah Belil
email: sabah.belil@emines.um6p.ma

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

Kawtar Retmi
email: kawtar.retmi@emines.um6p.ma

An integrated approach for supply chain tactical planning and cash flow valuation

Keywords: Cost model, Linear programming model, Financial valuation

This paper presents a methodology combining a flow optimization and a cost models in order to, simultaneously, realize a tactical planning of a productive system, and evaluate the financial performance of the proposed plans. The system addressed is a multi-site, multi-product supply chain structure with finite capacities of production, storage and transport. In order to model physical flow, we propose an optimization model taking into consideration all the physical system's constraints. It calculates production and transport plans while maximizing demand satisfaction rate. Then, in order to financially evaluate the solution found by the optimization model, we propose a cost model using Activity Based Costing (ABC) as a valuation method using cost drivers mechanism. Finally, in order to couple both optimization and cost models in a global integrated model, we use an approach called PREVA for PRocess EVAluation, generally used to set up a supply chain's management control system using financial and physical metrics.

Introduction

The supply chain is defined as a network composed of physical entities (factories, workshops, warehouses, etc.) crossed by flows (financial, material, informational, etc.), grouped into an integrated logistic process [START_REF] Fenies | A framework for supply chain performance evaluation[END_REF]. Thus, the supply chain management consists of modelling a set of flows, to manage them in an integrated way, and to improve their coordination to create value for the final customer [START_REF] Pagh | Supply Chain Management: More Than a New Name for Logistics[END_REF]. A supply chain is crossed at least by three flows [START_REF] Lapide | What about measuring supply chain performance[END_REF]: the physical flow (purchase of the raw material, transformation into finished product, and delivery to the customer). The financial flow, its optimization aims at satisfying the actors who contributed to the functioning of the supply chain. The information flow, which allows to coordinate between the two flows. The aim of our paper is to evaluate a supply chain performance by presenting the integration of physical and financial flows across the chain. [START_REF] Guillen-Gosalbez | A holistic framework for shortterm supply chain management integrating production and corporate financial planning[END_REF] [5] propose a methodology for analyzing supply chain performance in terms of the management of assets and flow of cash along the supply chain.

The purpose is to formalize relationships between physical and financial flow by their integration in tactical planning for an internal supply chain. The proposed approach allows the use of budgeting in order to evaluate the tactical production planning by integrating financial parameters such as payments terms into valuation models Activity Based Costing (ABC), and by coupling these kind of models with the tactical model. The rest of the article is organized as follows. In section 2 a review of the literature is presented. Section 3 gives a detailed description of the modeling framework for supply chain evaluation. Finally, section 4 conclude this paper.

2

Literature review

In this literature review, we first study tactical planning in multi-site supply chain. In the second part, we address literature that present ABC valuation method as a tool for building a cost model of an industrial system. Finally, we present some literature that link physical and financial models.

Multi-level tactical planning

Tactical planning deals with decisions about materials flow, inventory and capacity utilization during with a planning horizon from one or several months to two years. The main objective at this stage is to improve the cost efficiency (inventory) and the customer's satisfaction. In the hierarchical decision-making environment described above, lot-sizing decisions fall into the categories of either tactical or operational level. Many researchers have been interested in supply chain tactical planning using the lot sizing problem. The literature proposing its modelling is diverse and varied. Most of these papers propose mathematical models in order to achieve this goal. Multi-level lot sizing models are the models used by excellence in order to grasp the problem of horizontal synchronization of the global supply chain. [START_REF] Brahimi | Etat de l'art sur les problemes de dimensionnement des lots avec contraintes de capacité[END_REF] propose a literature review of the lot sizing dedicated to supply chain. The basic multi-level model, called the Multi-Level Capacitated Lot Sizing Problem (MLCLSP), was proposed by [START_REF] Billington | Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction[END_REF]. Its purpose is to link the end-products demand with the needs for internal components using the Gozinto matrix. Starting with this basic model, researchers have developed multi-site models that solve different problems; we cite for instance [START_REF] Gnoni | Production planning of a multi-site manufacturing system by hybrid modelling: A case study from the automotive industry[END_REF], [START_REF] Thierry | Supply chain management, models and implementation for medium-term decision support[END_REF], and [START_REF] Spitter | Linear programming models with planned lead times for supply chain operations planning[END_REF]. Although, the problems solved by these models have different configurations, the considered variables and activities are similar.

A valuation method: Activity Based Costing

According to a comparison of the various methods of cost calculation [START_REF] Retmi | An approach for an economic evaluation of operational and tactical decisions: implementation on the OCP supply chain[END_REF], no method can be excluded as each one is appropriate to a specific context. As part of our research, we chose the ABC valuation method as a tool. This choice was made in order to be able to move to Business Units (BUs) oriented industrial process in the context of an industrial system. And this, to be able to be coupled to optimization models, from industrial management control systems that are associated with cost centers per functional entity.

ABC can improve organizational performance in a number of ways: helping organizations become more efficient; provide organizations with a clear picture of where funds are spent; offer organizations a better alternative to the product based on cost; identify value-added activities and eliminate or reduce non-value-added activities. ABC provides organizations with a better understanding of cost formation using a causal approach through driver mechanics and identifies action levers leading to better organizational performance. In order to build a Decision Support System (DSS) linking optimization models to management control, we should focus on approaches combining optimization models and cost models.

Coupling and review analysis

Many works have been done on the product flow in supply chain whereas there is a little research works on the financial aspect of the supply chain. Traditional approaches for supply chain management usually focus on process operations and neglect the financial side of the problem. The study of supply chain manager interest for integration of financial impact in operational and tactical planning is done by [START_REF] Vickery | The effects of an integrative supply chain strategy on customer service and financial performance: an analysis of direct versus indirect relationships[END_REF]. [START_REF] Badell | Optimal budget and cash flows during retrofitting periods in batch chemical process industries[END_REF] addresses the implementation of financial cross-functional links with the supply chain operations and retrofitting activities at plant level. In [START_REF] Hendricks | The effect of supply chain glitches on shareholder wealth[END_REF], the authors estimate the shareholder wealth effects of supply chain glitches that resulted in production or shipment delays. [START_REF] Premachandra | A diffusion approximation model for managing cash in firms: An alternative approach to the Miller-Orr model[END_REF] considers a cash management problem of firms in a two-asset setting. [START_REF] Fenies | A decisional modelling for supply chain management in franchised networks: application in franchise bakery networks[END_REF] define an approach to assess the nature of a sale point based on supply chain activity. [START_REF] Chan | An integrated multidimensional process improvement methodology for manufacturing systems[END_REF] and [START_REF] Comelli | Modélisation, optimisation et simulation pour la planification tactique des chaînes logistiques (phdthesis)[END_REF] present a methodology to solve the problems of efficiency, process control, and discrete production system cost management. [START_REF] Mahal | Activity-Based Costing (ABC) -An Effective Tool for Better Management[END_REF] present the activity based costing method in combination with a discrete event simulation as a part of a discrete supply chain. [START_REF] Vidal | A global supply chain model with transfer pricing and transportation cost allocation[END_REF] propose a model for the optimization of a global supply that maximizes the after tax profits in strategic planning. In [START_REF] Brown | Financing constraints and inventories[END_REF], authors study the impact of financing constraints on inventory and cash management. [START_REF] Wang | Liquidity management, operating performance, and corporate value: evidence from Japan and Taiwan[END_REF] examines the relationship between liquidity management, operating performance and corporate value for firms.

Table 1. Literature analysis

A synthesis of the different studied papers, carrying the integration of the physical and the financial flows, is given in a grid (Table 1); his grid indicates for each article studied, the decision-making level studied and the modeling technics.

Strategic

Tactical Operational [

3

An approach for the physical and financial flows assessment of the supply chain

In this section we will present a detailed description of the modeling framework for supply chain evaluation.

Designing a decision support system using PREVA

In order to evaluate a supply chain based on the combined use of ABC method and the optimization model, we supposed to model the supply chain as a set of activities considers as Business Units and as autonomous entities belonging either to the entity of the supply chain or to a supplier/distributor who is integrated into the latter. We therefore assume the existence of a supply chain made up of 1 to N BUs. In order to use the ABC models to evaluate processes, we propose to allocate, for each BU (a plant, a transport activity, etc.) made up of at least one elementary supply chain process, the different items that are required to translate physical flow activities into financial flow items. This phase is realized in our case using PREVA approach, it is used repeatedly to set up management control systems for the supply chain. The robustness of the approach has been shown several times [START_REF] Fenies | A decisional modelling for supply chain management in franchised networks: application in franchise bakery networks[END_REF] [18] [START_REF] Retmi | An approach for an economic evaluation of operational and tactical decisions: implementation on the OCP supply chain[END_REF]. The design and evaluation of activities by PREVA for supply chain involves three steps: (i) the first step deals with the evaluation of physical flow performance based on an optimization model. This step involves building a mathematical model of the studied system. (ii) In the second step, we have an action model for the financial flow that is done using the ABC method with a granularity at the pace of optimization. (iii) In the third step, the results are structured into prospective scorecards.

3.2

Formalization for tactical production planning in multi-site supply chain structure.

The propose Mixed Integer Linear Program (MILP) is a multi-level, multi-product multi-product supply chain structure. The problem is modeled using a small bucket multilevel lot sizing model. The productive system consists a set manufacturing and storage sites. Each site produces a set of products intended to meet both a final demand and an intermediate demand. This product structure is modeled by the Gozinto matrix, initiated by [START_REF] Billington | Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction[END_REF]. Each plant and inventory has a finite capacity. End-products can be stored in downstream or final inventories. Final products are transported by railway road to final inventories with a transport time. The train is limited by a maximum and minimum transport capacity. In order to satisfy the demand, the model calculates for each period, the production, storage and transported plans. We present below the mathematical model: S : Set of manufacturing sites; I : Set of storage sites; T : Set of periods; P : Set of products; , it d : Final demand of a product i at period t ; , ij a : The number of units of the product i necessary to produce a unit of the product j , ,, 0

i j u a  if ji  ( j predecessor of i ); i Cap
fin i i t j j Inv Inv i t j   (5) max ,, , , ,
P Cap i t s   (6) , , , . , , , i t s i s s
, , ,

i t j i j j Inv Inv i t j   (8) max , , , .
, , ,

fin i t j i j j Inv Inv i j   (9) , , max , , , i t s
R R i t s  (10) , , min , , . , , , i t s
i t s R R i t s   (11) , , , , M 0, , , i t s
i t s R i t s     (12) int , , , , , , , , , , , 0, ,
fin i t s i t s i t s i t s Inv Inv P R i t s  (13)
  ,, 0,1 , , ,

i t s i t s   (14)
The Objective function (1) maximizes demand satisfaction rate. (2) is the stock balance equation of stocks. ( 3) and ( 4) are stock balance equations of final stocks. Constraints (5), ( 6) and ( 7) ensure the respect of the maximum production and inventory capacity respectively. Constraints (8) and ( 9) and ( 10) respectively assign the products to the plant / stocks in which they are produced / stored. Constraints [START_REF] Retmi | An approach for an economic evaluation of operational and tactical decisions: implementation on the OCP supply chain[END_REF] and ( 12) ensure maximum and minimum quantity limitations for transport by train. Constraints [START_REF] Vickery | The effects of an integrative supply chain strategy on customer service and financial performance: an analysis of direct versus indirect relationships[END_REF] and bind binary variables to corresponding decision variables. Finally, constraints ( 14) and ( 15) define the domain of the decision variables.

Cost Model

Regarding the valuation model, initially, we did a distribution of charges. Since we have no operational decision related to fixed cost, as part of our modeling, we will consider direct and indirect variable costs. Relative to these costs, we have no problem in imputing the direct costs, otherwise, in order to impute the indirect costs, it is necessary to use the cost drivers. In a second step, we built our cost drivers. These drivers must reflect the consequences of the decisions made. We can have cost drivers linked to the line and others related to processors. Then, once we have cost drivers in the supply chain, we can move from existing industrial management control systems that are associated with cost centers per functional entity, to BUs process-oriented. The construction of an ABC model thus makes it possible to evaluate the value creation for each BU constituting the supply chain and making it possible to take into account all the inputs and outputs in each process entity. This model is then coupled with the optimization model.

In our case, we did a processor division to obtain the cost per quality and per hour. This file combines the direct cost and the support cost, the latter cost represents the cost of shutdowns SC and maintenance MC and the cost of running conditions RCC plus the cost of energy EC for each product. These support costs are calculated using cost inductors, running conditions inductors RCI , stop inductors SI , maintenance inductors MI and energy inductors EI .

RCI RCC RC

Where RC are the running conditions. MD is the maintenance duration. DDM is the duration of decision making. SD is the stop duration. And pr POE is the percentage of energy per processor. Finally, we calculated a margin, per hour and per quality. Once we did a cost model per line, per hour, and per processor for all outputs, we brought all the direct variable costs of all these outputs into one matrix.

Implementation of the proposed approach to a chemical process industry

In this section, we illustrate our model on real case of a chemical process industry. The program has been solved for one-month demand. It has realized the production planning of three products P1, P2 and P3 that can be produced in two plants F1 and F2 according to two scenarios. The first scenario consists of encouraging the production of the product P1 in plant F1 (product P2 can be produced simultaneously in plants F1 and F2). The second one consist of encouraging. The production of P2 in plant F2 rather than F1. Then, using the cost model, we financially evaluated the two proposed solutions in order to choose, economically, the best one.

Table 2. Coupling results (pro-format data)

Each hypothesis is simulated using the DSS proposed in the previous section. The accounting and physical data of a month were used in the real case to validate the operation of the system. The results proposed here are based on pro forma data. Table 2 presents the results. The analysis of the results shows that over the period of analysis and taking into account the data used, the production of P2 in plants F1 and F2 (Hypothesis 1) is not relevant from a financial point of view. So, our DSS can give an economic lighting.

Conclusion

In conclusion, we proposed and integrated approach combining two model: a flowplanning model and a financial valuation model. Mixing the approach aim to model and plan physical flows, on the hand, and to evaluate the financial performance of the found solution on the other. Physical flow planning model is realized by a MILP model proposed to solve a multi-level, multi-product lot-sizing problem. Financial flow is modeled using ABC valuation method using cost drivers mechanism. In order to combine the models, we propose PREVA approach, method that models supply chain subsystems by Business Units.