Supply Chain Management (SCM) Optimization and Meta- heuristic

by

thesis

FULFILLEMENT OF THE REQUIREMENTS FORTHE DEGREE OF MASTER’s WITH THESIS: M. A. Sc.

Montreal,

© Copyright 2018 reserved by author’s

46

i

46

BOARD OF EXAMINERS (thesis M. A. sc.)

THIS THESIS HAS BEEN EVALUATED

BY THE FOLLOWING BOARD OF EXAMINERS

<Mr. XXX >, Thesis Supervisor

< Department > at

< Mr. XXX >, Thesis Co-supervisor

< Department > at

< Mr. XXX >, President of the Board of Examiners

< Department> at

< Mr. or Mrs. YYY>, Member of the jury

<Company’s name >

< Mr. or Mrs. ZZZ>, External Evaluator

< Company’s name >

THIS THESIS WAS PRENSENTED AND DEFENDED

IN THE PRESENCE OF A BOARD OF EXAMINERS AND PUBLIC

<defence date of the thesis>

ACKNOWLEDGMENT

I would like to thank my supervisors, Dr….and Dr……., for their valuable recommendations and efforts during the research study. I also like to thank …. and…. for awarding me with a…… I promise that I will best represent my country and serve my nation by proficiently assisting the next generation.

I would like to acknowledge my parents who devoted their life to encourage and support me, as well as, my wife who is always besides me during my happy and sad moments.

Finally, this acknowledgment will be incomplete if I did not thank all other people who helped in making this work a success that I am proud of; including fellow research students at…., authors who were a great inspiration to me, and researchers who made their work accessible to motivate others.

Thank you all!

VIII

SUPPLY CHAIN MANAGEMENT (SCM) OPTIMIZATION AND META- HEURISTIC

ABSTRACT

This Thesis presents Supply Chain Management (SCM) Optimization and Meta-heuristic approaches, specifically on issues regarding the configuration of a generic multi stage distribution network, determination of a milk-run delivery issue in lean supply chain (LSC) management. Indeed, this issue can be represented as the routing of the supply or delivery vehicle to construct multiple pick-ups or drop-offs on a regularly scheduled basis and at different locations. The optimal model for milk-run delivery issue must aim to improve vehicle load and minimize transportation distance (optimal delivery route) between facilities with optimizing the entire delivery of goods among the supply chain facilities. The set of Meta-heuristic approaches and Hybrid Meta-heuristic approaches introduced in the present research aim to became a modeling system to find an optimal solution for the transportation distance as well as for managing the transportation of goods in highly complex logistic networks. In fact, the optimal transportation distance ensures that the total cost of the entire supply chain is minimized. In particular this modeling system groups concepts about integrated supply chain management proposed by operations research practitioners, logistics experts, and strategists. Indeed, it refers to functional coordination within the firm, between the firm and its suppliers, and between the firm and its customers. It also refers to inter-temporal coordination of supply chain decisions as they relate to the firm’s operational, tactical and strategic plans. The milk-run delivery issue is studied with the genetic algorithm (GA) approach as well as the hybrid of genetic algorithm with ant colony optimization approach (HGACO). Various frameworks, models, heuristics approaches, Hybrid Meta-heuristic approaches and software tools are introduced and discussed in the following chapters. Significant case study is given to demonstrate the effectiveness of the proposed approaches. Finally, the goal of this thesis is to present a set of genetic algorithm (GA) approach as well as the hybrid of genetic algorithm with ant colony optimization approach (HGACO) to minimize total cost of supply chain. This set of proposed HGACO approach can efficiently and effectively find optimal solutions.

X

TABLE OF CONTENTS

Page

Introduction………….……………………………………………………1

1.1 Background 1

1.2 Research objectives 4

1.3 Thesis organization 5

2.1 Introduction 7

2.2 What is Supply Chain Management? 8

2.3 Objective of SCM 9

2.4 Challenges of SCM 11

2.5 Previous Methodologies that have been done in SCM 14

2.6 Scope of SCM 14

2.7 Limitation of the Previous Studies Related to SCM 15

3.1 Introduction 17

Optimization by Meta-heurtic Approaches and the Traveling Salesman Problem 19

3.2 Meta-heuristic approaches 21

3.2.1 Introduction 21

3.2.2 Genetic algorithm (GA) 22

3.2.3 Proposed of implementation of genetic algorithm (GA) 26

3.2.4 Ant Colony Optimization (ACO) 27

3.2.5 Tabu Search (HAT) 30

3.2.6 Mixed Integer Programming (MIP) 35

3.2.7 Hybridization of Meta-Heuristic Approaches 35

3.2.8 Hybridization of Genetic Algorithm GA with Ant Colony Optimization ACO 35

3.2.9 Hybridization Ant Colony Optimization ACO with Tabu Search (AT) 36

4.1 Optimization of an Automobile Industry case study with Meta-heurstic Approaches 37

4.1.1 Specific data and description of automobile industry case study (AICS) 37

4.2 Definition of the optimization problem 39

4.2.1 Optimization objective 40

4.2.2 Constraints 41

4.3 Application of meta-heuristic approaches to AICS 42

4.3.1 Application of the Genetic algorithm 42

4.3.2 Application of the hybrid genetic algorithm and ant colony optimization 45

5.1.1 Result of 47

5.2 Discussion 49

5

LIST OF TABLES

Page

Table 3 1 Geographical location of AICS facilities 38

Table 3 2 Data of manufacturing plant and supplier facilities for AICS 38

Table 3 3 Date of customer facilities for AICS 38

Table 3 4 Transportation distance matrix d among facilities of AICS 43

Table 4 1 Optimal dr from GA,HGACO and ACO 48

Table 4 2 Optimal dr with two sub-routes found from GA, HGACO and ACO 49

LIST OF FIGURES

Page

Figure ‎ 1 1 Stages of a supply chain 8

Figure ‎ 4 1 Flow chart of proposed GA for optimizing route distance (dr) 43

Figure ‎ 5 1 Optimal dr (383.30 km) with GA and HGACO 47

Figure ‎ 5 2 Optimal dr (286.22 km) with ACO 48

LIST OF ABREVIATIONS

LIST OF SYMBOLS

INTRODUCTION

0. Background

Supply chain is defined as, the network of entities through which material flows. Those entities may include suppliers, carriers, manufacturing sites, distribution centers, retailers, and customers (Lummus and Alber, 1997).” Quinn (1997) defines the supply chain as “all of those activities associated with moving goods from the raw-materials stage through to the end user. This includes sourcing and procurement, production scheduling, order processing, inventory management, transportation, warehousing, and customer service. A lot of definitions have been proposed regarding the concepts of supply chain management.

Supply Chain Management coordinates activities within organization to create value for the customers. It integrates and manages the sourcing and flow of materials via a total systems approach that accounts for several organizational functions and the several types of partners [36]. However, there is no generally accepted definition for the term “supply chain management”. While some authors use operational definitions focusing on the flow of materials, others view it as a management philosophy. On the other hand, several others interpret it as a management process or an integrated system. Christopher (1994) defined the supply chain as a network of organizations involved in different processes that create value to the customer through upstream and downstream linkages. It includes manufactures, suppliers, vendors, wholesalers, retailers and the customer.

The evolution of the concept of SCM can be dated back to 1950s, a period commonly referred to as the logistics era where the SCM concept was not valued as a strategic function [25]. However, in the early 1960s, the importance of logistics was established due to the recognition of physical distribution management as separate function of management [30]. The period was named as the first transformational era. Most importantly, the aspect of supply chain management was first introduced by logistics consultants in the 1980s [37]. This meant that the supply chain could be viewed as a single entity that the top-level management was entitled to make decisions in their original formulation. The concept was universally accepted by logistics experts and the marketing theorists who focused on management of channels to expand the understanding of logistics (Gripsrud, 2006). Today, SCM has evolved to become an important management function that affects the ability of organizations to run profitable enterprises.

Both the cooperation and the competition between companies in the international business arena create a variety of logistical challenges that emanate from the planning and control of the supply chains. Ideally, companies should minimize the production costs and optimize the location of various business points such as; the sources of raw material, manufacturing points, distribution centers, and retail/wholesale branches [26]. They should also manage the product flows between manufacturing plants and warehousing facilities in addition to the allocation of customer demand to production activities.

Solving the facility location problem is essential in optimizing SCM [26]. FL is defined by the taking of simultaneous decisions regarding design, management, and control of a generic production and distribution network. In this case it is essential that the demand points influence the location of the facility. In addition, the transportation network should be configured in a manner that enhances planning, designing, and execution of supply chain activities.

In order to survive and develop in the fierce pressures of globalization, enterprises relentlessly seek measures to enhance the performance of their supply chain (SC). Among several SC models have been studied and applied, Lean Supply Chain (LSC) is evaluated as an “ideal SC” (Srinivasan, 2012) owing to ability of supplying final products/ services to consumers promptly, economically in a seamless manner. Paschal et al. (2012) state that when Lean Manufacturing (LM) concepts are implemented across entire SC, the SC is considered as LSC. Anand and Kodali (2008) summarize 59 LM tools/ techniques used to transform fat SC into LSC, in which milk-run delivery is prevalent technique.

In SC management, Milk-run is one of the most efficient and regular transportation model (Kitamura & Okamoto, 2012). It is defined as “A route on which a truck either delivers product from a single supplier to multiple retailers or goes from multiple suppliers to a single buyer location” (Sunil & Peter, 2013). This network maximizes the capacity of vehicle by conveying item in small quantity with high frequency among all members instead of large stuffs from individual company. To balance with milk-run pace, companies keep production at the level that their output at a time window fits with the amount of products received/ picked up by each milk-run.

As a result, waste relating to inventory in LSC is eliminated and total cost (TC) is saved up. Meanwhile, it speeds up the circulation of materials through facilities which improves responsiveness of whole chain (Du et al., 2007). Other advantages of milk-run are analyzed in detail by exhausted review of Sadjadi (2009). With such striking advantages, milk-run is widely applied in both inbound and outbound logistics (Kilic & Durmusoglu, 2013) or even in plants among assembly lines or workstations (Pesce et al., 2000).

In reality, Toyota and Seven-Eleven are the worldwide successful cases of the milk-run application. Moreover, milk-run logistics refers to a strategy of goods collection where the manufacturer releases one vehicle at a time to collects input goods from a number of suppliers using a predefined route and to deliver them back to the production plant [34]. The concept originates from the daily industry where one truck covers the input and output requirements of several stations using a predefined schedule. It is also inherent in the American culture where the milkman distributes bottles on a daily basis [34]. In this case, he follows a daily routine where full bottles are distributed and the empty ones collected along the daily route. In the end, the milkman returns with the empty bottles to his milk facility location. This implies that families that do not deliver empty bottles would not receive milk.

The milk-run logistics target the reduction of transportation costs resulting from the effectiveness of travelling paths and the reduced consumption of fuel [43]. It also focuses on promoting efficiency and effectiveness in the procurement of materials. At first, managers calculate the volume of supplies that should meet production plans of subsequent periods. During this stage, potential suppliers are identified in addition to the breaking down of the volume into smaller quantifiable parts. Secondly, the management creates a master milk-run pickup route which accounts for different supplier locations. Incremental changes in previous route plans are idealized. Thirdly, suppliers are informed about the master route plan to open a platform for negotiations [34].

This approach is economical when several supplier stations deliver smaller volumes than the truckload. In most cases, it is used internally to deliver raw materials, finished goods or wastes to manufacturing plants and warehouses of an enterprise. Xu and Han (2010) proposed that milk run logistics could be used by manufacturers during the financial crisis in china to overcome the resultant difficulties. The proposed plan was supported by reductions in inventory costs and transportation costs. The scholars noted that the milk run logistics translated to a 67.5% reduction in transportation costs.

The benefits of milk run logistics include the consolidated approach to transportation which reduces the resultant costs. Additionally, the efficiency of this system enhances Just in time delivery and continuity in production by simplifying both distribution and collection. It also counts on maximum demand and minimum transportation distance to meet the requirements simultaneously at the lowest costs. Small volumes delivered at higher frequencies with the aim of meeting the customer’s demand [(Zhang, Zou & Hu, 2016) By improving loading rates and reducing the number of vehicles and travel distances, milk rum logistics minimize the amount of exhaust gases to concur with the environmental policy [34]. For example, Carbon dioxide is a greenhouse gas which is addressed by state and federal laws. In this context, Milk run logistics help firms in environmental compliance. Lastly, the use of information technology in milk run logistics implies that high accuracy is observed in path planning and pickup management [43].

To identify solution for milk-run logistics, numerous approaches are used from a specific software (Thanatorn, 2013) to Heuristic (Kilic & Durmusoglu). Nowadays, general Meta- Heuristics have been employed in order to define the best milk-run path. Some effective ones are ACO (Zhou & Kelin, 2011; Yang et al., 2013), Tabu Search (Jiang, 2010) or Genetic Algorithm (Sadjadi; Wang, 2013). After reviewing the application of Meta-heuristics in SC and logistics, Stanley et al. (2012) conclude that although the results found from Meta- Heuristics are acceptable, hardly do they obtain optimal values.

Research objectives

The following thesis establishes the initiatives that organizations should take to utilize the competencies of SCM. It explores the various approaches that organizations can use to optimize SCM. The hypothesis of the research is based on the assumption that the hybrid of genetic algorithm and ant colony optimization approach (HGACO) for the best approach in obtaining an optimal solution for the milk-run delivery and minimize total cost of supply chain management. The thesis compares various mathematical models to identify the best meta-heretic approach.

Thesis organization

The thesis starts with an introductory part which explores the background of supply chain management. It also dwells on the definitions of a milk run system and its implementation in the context of SCM. Chapter 2 explains essential definitions required for the reader to understand the studied topic and reviews literature concerning Supply Chain Management while presenting various studies in this area. In addition, we introduce elements that are closely related to system’s supply chain along with the area of attention in previous works concerning lean supply chain. Chapter 3 presents an overview on optimization and meta-heuristic approaches. Chapter 4 analyzes the problematic of milk-run delivery in LSC then re-addresses its modeling proposed by Zhou and Kelin. The following part particularly details the proposed approaches of MIP and HAT before presenting the results of testing stage from case study in chapter 5 which is the main targets to be addressed in this research. We demonstrate the applicability of our work and its efficiency in modeling small-scale networks with higher certainty by testing the proposed approaches on a few certified networks with different properties. Finally, the three last parts discuss obtained solutions as well as express the conclusions and propose future work

Chapter 1 CHAPTER 1

SUPPLY CHAIN MANAGEMENT

Introduction

There is a great deal of confusion regarding exactly what supply chain management involves. In fact, many people using the term supply chain management treat it as a synonym for logistics or as logistics that includes customers and suppliers [16]. Others view supply chain management as the new name for purchasing or operations [20]. or the combination of purchasing, operations and logistics [19]. However, increasingly supply chain management (SCM) is being recognized as the management of relationships across the supply chain. Strictly speaking, the supply chain is not a chain of businesses, but a network of businesses and relationships. SCM offers the opportunity to capture the full potential of intra- and inter-company integration and management. In that sense, SCM deals with business process excellence and represents a new way of managing the business and relationships with other members of the supply chain.

The Global Supply Chain Forum, a group of non-competing firms and a team of academic researchers, has been meeting regularly since 1992 with the objective to improve the theory and practice of SCM. The definition of SCM developed and used by the members of The Global Supply Chain Forum is:

Supply chain management is the integration of key business processes from end-user through original suppliers that provides products, services,
and information that add value for customers and other stakeholders [21].

A supply chain consists of all stages involved, directly or indirectly, in fulfilling a customer request. The supply chain not only includes the manufacturer and suppliers, but also transporters warehouses, retailers, and customers themselves.

A supply chain is dynamic and involves the constant flow of information, production and funds between different stages. Each stage of the supply chain performs different processes and interacts with other stages of the supply chain. A typical supply chain may involve a variety of stages such as:

Component/raw material suppliers

Manufacturers

Wholesalers/distributors

Retailers

Customers

Furthermore, some supply chain involves all stages of supply chains but some has less supply chain relying on the business’ environment. Fig. 1 shows the different stages of the supply chain.

Figure ‎11 Stages of a supply chain

What is Supply Chain Management?

As stated earlier, there is not a single definition in the context of SCM. However, it can be argued that Supply chain management entails the integration of manufacturing, transportation, purchasing, operations and the physical distribution of products into one universal function. This process is characterized by close and beneficial links between various partners who play fundamental roles in the supply chain. These include organizational departments, vendors, third party service providers, carriers and IT service providers. In a general overview, supply chain management encompasses certain core activities such as transportation, procurement, warehouse management, sourcing and inventory control. Additionally, production planning, scheduling, the processing of orders, forecasting and customer service all point to supply chain management [27].

According to La londe (2010) supply chain management refers to the delivery of value to customers through a well-planned flow of products and related information starting from sourcing to the consumption stage. This definition highlights the importance of external partners in an efficient SCM. Organizations which create the greatest value for customers gain a considerable market share. As a result, the resultant competitive advantage guarantees cheaper warehousing, little wastage and reduced inventory levels

According to the Supply Chain Council, SCM refers to the management of supply and demand parameters, sourcing of raw materials, assembly and manufacture, control of inventory, order tracking, warehousing, management of channels of distribution and the delivery of finished products to the customer. On the other hand, the institute of supply management defines SCM as the processes involved in designing flawless value-added elements in conjunction with various partners to reach the aspirations of the customer. Pyke, Robb and Farley (2000) summarize these definitions by articulating that SCM entails the initiatives taken by firms to take advantage of suppliers’ competencies, technological advancements, competitive advantage capabilities and the close monitoring of manufacturing operations, logistics and the management of material with the ultimate aim of increasing customer value.

Objective of SCM

SCM enables managers to survive the competitive global environment by getting goods to customers at a faster rate [27]. In this case, Sales increase when firms supply their markets with timely products. In addition, profit advantage is realized when the competitor is out of the market. SCM also ensures that firms deliver goods in the right quality, quantity, price, place and at the right time of delivery. This aids in reducing inventories along the supply chain pipeline. Similarly, it enables firms to respond to the changing expectations of customers. In this case, cost consciousness represents a new direction in the buying behavior of customers. The contemporary customer only buys products that he feels satisfy the concept of ‘value for money’. In addition, the market offers unlimited choices which give the customer an upper hand. With this in mind, SCM provides a tool through which firms can minimize overhead costs. Consequently, the finished products can be priced in a customer sensitive approach. Similarly, the modern customer tends to be choosy and buys goods which have significant value addition. In this context, SCM enables firms to partner with various players along the supply chain with the intention to add more value to the final products [27].

On the other hand, SCM enhances the timely delivery of information regarding goods to customers. This implies that customers are updated on delivery changes, ordering mistakes or possible delays in delivery using a well-structured communication network. In addition, the modern technologies used in contemporary SCM take into consideration the sensitivity of information and enhance a well-structured communication. This has the potential to yield customer satisfaction, customer loyalty and the subsequent increase in sales

Thirdly, SCM recognizes the customers need for reliability [38]. The firms strive to enhance a constant supply of goods or services to the target customers. In this case, the managers ensure that there are minimal interruptions and that the customers do not experience shortages. This is enhanced by the maintenance of effective communication networks and the improved warehousing and inventory control. As a result, more sales are realized through improved customer loyalty

From a different perspective, SCM helps firms to address the threat of increased competition by reducing lead times. This means that the period between acquisition of raw materials and the re-introduction of the finished products to the market is significantly reduced. In this context, competitors who use outdated system to monitor supply chains lag behind in the competitive business environment. On the other hand, firms with integrated systems of SCM have the upper hand by the virtue of reducing lead times. Similarly, SCM improves a firm’s competitive position by reducing the cost of doing business. In this case, optimized supply management systems save on transport and inventory costs. They also address the problems of vehicle routing and optimize the loading rate. This minimizes fuels costs and prevents the misuse of vehicles. As a result, the firms minimize the expenses that characterize the supply chains.

It also recognizes the need for integration and partnerships to increase the value delivered to customers [38]. In this case, SCM starts when firms identify suppliers, distributors and retailers and enter into an agreement with them. Most successful organizations such as Apple have a suppliers’ code of conduct which ensures that high standards are met in line with the expectations of customers. These agreements are fundamental in controlling the supply chains and dictating the standards that partners must observe. Lastly, SCM compels managers to engage their firms in continuous improvement of processes that seek to maintain the respective competitive positions. In this case, managers influence the various [partners along the supply chains to continually innovate their products in the attempt to meet changing customer demands. They also change the information systems to adapt to the changing technological trends. This has the aim to improve the processes of manufacturing, distribution, inventory control and customer service

The objective of every supply chain is to maximize the overall value created. So, effective supply chain management is the management of flows among supply chain stages to maximize total supply chain surplus.

The value a supply chain generates is the difference between what the final product is worth to the customer and the effort the supply chain expends in filling the customer’s request. Moreover, the success in supply chain should be measured by the total supply chain profitability, not by profits at an individual stage.

Lean supply chain (LSC) is a network of integrated organisations in which the capabilities of all entities are aligned with customer demand [1]. The supply chain (SC) is referred as a LSC when lean is implemented across the entire Supply Chains (SC) [2].

Challenges of SCM

First, the varying needs of customers complicate decisions related to SCM. In this case, it is the customer who determines the firm’s initiatives as it operates its supply chains. For example, customers may dictate certain shipment methods or carriers that the firm cannot afford. This causes hitches in the SCM processes.

Secondly, globalization creates a new challenge in the context of SCM. In this case, the geographical distances between various global locations increases the transportation costs undertaken in the delivery of goods or supply of raw materials. In addition, globalization complicates inventory management due to higher lead times witnessed in global supply chains.

Thirdly, Chopra and Meindl (2004) articulate a supply chain design problem which results from an array of decisions regarding the facility location and the number of production facilities. In addition, managers face a challenge determining the capacities of each production facility. They also face difficulties in allocating market segments and suppliers for each of the selected locations.

On the other hand, SCM is confronted with an organizational flexibility challenge. This entails the adaptability of the firm’s mission to maintain the focus on SCM. This means that since SCM is a new concept, firms should rethink their mission statement to include the objective of supply chain management and how those objectives may be met. The organizational flexibility determines the success in this ordeal. The performance metrics and decision-making parameter should reflect the goals of SCM. From a different perspective, SCM should enhance the collaboration within the organization and with key supply chain partners to eliminate wastes along the supply chains

Conflicts that arise among partners in the supply chain present a new challenge for SCM. The management of conflicts through mediation is time consuming and sometimes it does not arrive at a mutual solution. This paves way for lawsuits which are usually expensive when they occur. Additionally, the conflicts disorient the supply chains and this affects the continuity of production. Consequently, the firm’s reliability decrease in the eyes of the customer

Firms also encounter difficulties in instilling values, skill and training to partners along the supply chain. This means that the supply chains may not be effective in meeting the needs of the customers. Alternatively, the firms have to invest huge sums in training to align with the modern concepts of SCM.

Firms also encounter a lot of Uncertainties in SCM. For instance, a supplier may be incapacitated within a planning period causing deficiencies in production and distribution systems. Similarly, the production plant might breakdown due to no fault of the company. Political changes may also render the activities of a supplier unlawful to end und influencing the firm’s activities. Similarly, weather changes may affect the transport network which in turn affects the collection and delivery cycles. Such uncertainties make SCM a complex concept that should be approached with considerable professionalism.

From a different perspective, firms encounter challenges as the attempt to match supply and Demand. Sometimes, the market might become volatile in a manner that disables predictions of demand. Additionally, the initiatives taken by competitors may affect the demand of the firm’s products. Alternatively, the seasonality of demand means that it is difficult to match it to supply.

On the other hand, service firms have a problem in striking a balance between cost and service level. This is because services are intangible and cannot be quantified in the same way that goods are measured. This implies that the costs involved cannot be effectively used to determine the levels of corresponding services. In this light, SCM managers can only use the levels of customer satisfaction as a basis for measuring how the firm meets customer demands

The product cycles of High Technology products are shorter implying that SCM is more complicated. In this case, SCM has to make sure that all the supply chain factors are closely monitored to ensure that customers do not experience shortages. For example, minor delays in the supply of parts results to serious deficiencies in the market that have the potential to deprive firms of customer loyalty

Lastly, SCM strategies tend to vary over time because of seasonality trends and unforeseen competitor strategies. The dynamic business environment of the 21st century implies that firms have to keep adapting their SCM methods. However, abrupt changes disorient the supply chain timelines and schedules. This phenomenon results to inconveniencies within the entire supply chain management

Previous Methodologies that have been done in SCM

La Londe (2010) argues that SCM has been implemented in three phases since its initiation. The first was the Physical Distribution Management phase which took manufacturing as a sole function. Additionally, finished goods were taken to an output warehouse awaiting sale

Secondly, the Integrated Logistics Management phase recognized sales, warehousing, procurement, transportation and manufacturing and integrated them into one system that enhanced a better distribution network

Thirdly, the change of logistics management to SCM was realized in phase 3. This provided links where external partners such as suppliers and customers would enhance the creation of value to the final customer. In this new approach, SCM enhance the flow of information and cash between the partners in a synchronized system of management.

Scope of SCM

Supply Chain management entails several functions that can be classified in a single department. These include; Inventory management, Transportation, procurement, Materials management and Warehousing management.

Strive to oversee order fulfillment through’ Customer service performance monitoring, Order processing and the forecasting of SCM budgets.

It also shares some functions with other departments such as Third-party invoice audit for members of the supply chain. In addition, sales forecasting is shared with the sales department.

Other functions of SCM include; (Pyke, Robb & Farley, 2000)

Master production planning

Operational and materials management

Distribution management

Computer Systems management and simulation

Warehouse related Project Management

Operational Commissioning

Computer Simulation

Organizing training and technical seminars

Limitation of the Previous Studies Related to SCM

Early scholars ignored the flow of information along the supply chain. For instance, Jones and Riley, Houlihan, and Novack and Simco agree that SCM occurs as a single function where all its elements are managed as a whole. They also recognize the flow of materials in a single system starting from raw materials where manufacturers interact with suppliers to the finished products where distributors work with customers. Similarly, Scott and Westbrook emphasized on the importance of reducing inventory levels to enhance SCM efficiency by managing fluctuations along the supply chains. They neglected the importance of enhancing better communication networks

One of the most significant paradigm shifts of modern business management is that individual businesses no longer compete as solely autonomous entities, but rather within supply chains. In this emerging competitive environment, the ultimate success of the business will depend on management’s ability to integrate the company’s intricate network of business relationships [17]. The members of The Global Supply Chain Forum refer to the management of this network of relationships as supply chain management. Successful supply chain management requires cross-functional integration within the firm and across the network of firms that comprise the supply chain. It is focused on relationship management and the improvements in performance that result from better management of key relationships. However, in many companie’s executives struggle to achieve the necessary integration. By understanding the supply chain management processes and how they should be implemented, executives will be able to create more integrated supply chains which will lead to higher revenues and increased profitability for all member firms [16].

Supply Chain Management is the integration of key business processes from end user through original suppliers that provides products, services, and information that add value for customers and other stakeholders.

Logistics is that part of the supply chain process that plans, implements, and controls the efficient, effective flow and storage of goods, services, and related information from the point-of-origin to the point-of-consumption 3 in order to meet customers’ requirements [18].

31

Chapter 2 CHAPTER 2 OPTIMIZATION AND META-HEURISTIC APPROACHES

Introduction

According to Michael and Claudia (2009) the milk run system can be used to optimize the transport of materials to and from production plants. In this research, the scholars designed routes for the supply of parts to a number of manufacturing stations while using one transport. In the end, the use of clustered routes translated to more frequent trips between the production lines. As a result, the inventory volume in the production plants reduced to an optimum level. Essentially, the number of transports is reduced and this optimizes the use of transport related equipment. Consequently, inventory and transport costs fall to within desired levels.

On the other hand, Lin and Cha (2010) optimized the assimilation of both inventory and transportation aspects to the distribution network. They also presented Genetic Algorithm of natural number coding with the aim of solving the vehicle scheduling model of milk-run. In addition, they put in place a stepwise iterated algorithm that balanced inventory and transportation costs with the goal of reducing to total costs of the milk run logistics system.

In the same way that Ricoh Express implemented the milk run logistics, production plants should develop a system that optimizes vehicle routing by confirming shipment volumes with suppliers before collection using telephone communication or a well-developed network. This increases efficiency by shortening transportation distances and increasing the loading rate. Alternatively, the optimization model suggested by Chen and Shuaiying (2009) can be adopted

On the other hand, Yun, Xian-Long and Chao-Chun (2010) present an optimization model that addresses the vehicle scheduling problem (VSP) and the vehicle routing problem (VRP). They visualize the effective utilization of a vehicle’s space by delivering fully loaded trucks to specified points. This improves vehicle load factors and avoids the misuse of vehicles. Similarly, effective path planning shortens the distribution distance and prevents the waste of time during delivery or collection. To minimize the total cost of freight, the picking time and the routes to be used by vehicles should be planned. The vehicles leave demand points after considerations of the optimal loading rate have been met. Yun, Xian-Long and Chao-Chun (2010) stipulate a mathematical modeling that is effective in setting the milk run route taking into consideration the loading rate. The use of a modern heuristic algorithm such as the Tabu Search can be used in optimizing milk-run routes.

Gaonkar and Viswanadham (2001) suggest that a linear programming model for integrated supply chain planning would aid the sharing of information by partners via web based platforms. It simplifies the selection of partners and minimizes the cost of procurement. Most importantly, the linear programming model satisfies demand for various materials in light of flow balancing constraints. Later in their research, Viswanadham and Gaonkar (2003) developed an optimization technique which took more insight into capacities and costs. In this context, managers should allocate sub-optimal order quantities to all suppliers. The optimization technique adopted a multi integer programming for the manufacturing network.

On the other hand, Talluri and Baker (2002) suggest that a three-phase mathematical programming approach should be used in an attempt to address the complexities of a supply chain design. This approach encompasses both multi-criteria efficiency models and linear and integer programming methods. The first two phases cover the network design for the supply chain while the third focuses on operational issues such as routing. Jang et al. (2002) propose a different approach consisting of three modules to solve the complexities of decision making. These include an optimization module, production and distribution planning module, model management and data management modules. While the first module strives to minimize transport costs, the second module stipulates the production and distribution plans within a specific period of time. For the first module Lagrangian heuristics are applicable while the second module is solved by a a genetic algorithm. The last two modules save managers from the hustle of interpreting data and mathematical models

One of the earliest problems for which an Meta-heurstic approaches was implemented was the traveling salesman problem (TSP): the “Ant System” (AS) Colorni et al., (1992). The graduation of the metaphor to the algorithm is relatively easily understood and the traveling salesman problem is well known and extensively studied.

The traveling salesman problem consists in finding the shortest path connecting n cities specified, each city has to be visited only once. The problem is more generally defined like a totally connected graph (N, A), where the cities are the nodes N and the paths between these cities are the edges A.

The domain of meta-heuristic optimization comprises methods such as Evolutionary Algorithms (EAs) [44], Simulated Annealing (SA) [45], Particle Swarm Optimization (PSO) [46], and Differential Evolution (DE) [47]. These methods are successfully applied to complex real-world problems from different domains where exact optimization techniques like Linear Programming (LP), Quadratic

Programming (QP), or Geometric Programming (GP) are not applicable due to their restrictive expressiveness. The targeted problems of meta-heuristic optimization might comprise multiple non- linear objectives or constraints. In contrast to common optimization benchmarks, the complexity of realistic problems might be also characterized by the problem structure where multiple heterogeneous sub tasks have to be optimized concurrently. For instance, such a complex optimization task might be the optimization of automotive networks that requires the concurrent determination of the allocation of hardware resources, the binding of software tasks, the routing of messages, and the scheduling.

During optimization procedure, usually there will be more than one acceptable design that satisfies the functional and other requirements of the problem, and the purpose of optimization is to choose the best one of the many acceptable designs available. Thus a criterion for selecting the best one by comparing the different alternative acceptable designs has to be defined. When this criterion expressed as a function of the design variables, is known as the objective function [11]. The choice of objective function is governed by the nature of problem. In structural optimization, the objective is usually taken as minimization of weight, displacement in a given direction, effective stress or total cost. In some situations, there may be more than one criterion to be satisfied simultaneously. An optimization problem involving multiple objective functions is known as a multi-objective optimization.

Meta-heuristic approaches

Introduction

Meta-heuristics approaches provide a reliable approach for obtaining optimal solutions to complex and multi-objective problems (Jones, Mirrazavi & Tamiz, 2002). They refer to well-known approaches such as the tabu search, simulated annealing, genetic algorithm, evolutionary algorithm and Ant Colony Optimization (Shanmugam, 2011). Rather than combining a multi-objectives problem into a single objective using the weighted sum approach that sums individual weights to obtain the optimal value, Meta- heuristic approaches accept several criteria to determine the non-dominated set by utilizing several alternatives that serve as potential solutions for the multiple objectives (Shanmugam, 2011). In this case, through solution trade-offs, the user can choose the best alternatives for desired outcomes. This approach is idealized for multi objective optimization (Corner & Buchanan, 1995). There are 5 main heuristic algorithms developed in recent years, namely Genetic Algorithms, Simulated Annealing, Particle Swarm Optimization, Ant Colony Optimization and Neural-network-based Methods (Kaveh, et al., 2008, Li and Au, 2010, Madeira, et al., 2009, Martí and González-Vidosa, 2010, Perea, et al., 2008). The genetic algorithms are based on the principles of natural genetics and natural selection. Simulated annealing is based on the simulation of thermal annealing of critically heated solids. The particle swarm optimization is based on the behavior of a colony of living things, such as a swarm of insects, a flock of birds, or a school of fish. Ant colony optimization is based on the cooperative behavior of real ant colonies, which are able to find the shortest path from their nest to a food source. In neural-network-based methods, the problem is modeled as a network consisting of several neurons, and the network is trained suitably to solve the optimization problem efficiently [11].

According to Silva et al. (2005), the supply chain consists of a number of logistical steps such as order arrival, the request for parts, the arrival of the parts, assignment and subsequent delivery. He proposed that the resultant scheduling problem should be handled using genetic algorithms (GA) and ACO. On the other hand, Altiparmak et al. (2006) presented a GA oriented procedure for optimizing a supply chain that was made up of suppliers, plants, warehouses and customers. His approach accounts for fixed costs involved in opening and running plants together with the expenses related to the acquisition of raw materials and distribution of products. Secondly, it focuses on the customer demand that the firm can deliver before the due date stipulated ion orders. Thirdly the approach has the objective of determining the capacity utilization ratio with regard to the plant and the warehouses.

Silva et al. (2005) proposed a mix approach that combined ACO and Multi-agent system. He recognized the presence of three sub-systems in a supply chain. First, the Logistic sub-system receives customers’ orders, acquires several pats from well known suppliers and initiates the process of scheduling. Secondly, the supplying sub-system operates as a network of suppliers that produces several components and enhances cooperation. It also encompasses the Distribution sub-system which has an aim of alleviating the Vehicle Routing Problem for timely delivery of orders. The significance of ACO is exhibited by each subsystem because individual tasks are separately accomplished. It is considered a multi-agent system because it covers a number of independent agents solving their own problems and communicating among each in order to solve discrepancies

Genetic algorithm (GA)

The Genetic Algorithm model provides solutions for complicated non-linear and programming problems (Glover, 1986). It is a new approach which relies on the evolutionary paths similar to the ones followed in biological evolution. It generates a number of solution sets (similar to generations in biological evolution) and tries to advance towards the optimal solution. Genetic algorithm method is a kind of optimization algorithms that finds the optimal solution(s) to a given computational problem that maximizes or minimizes a function. The genetic algorithm method represents one branch of the area of study that is called evolutionary computation. In that, it is based on the principles of natural genetic and natural selection to solve for the ‘fittest’ solutions. Like in evolution, many of genetic algorithm’s processes are random; however, this optimization technique allows one to set the level of randomization and the level of control.

In executing the genetic algorithm, the user starts with the selection of the current population to generate an intermediate population. Afterwards, the next population is created through the application of mutation and recombination to the intermediate population (Glover, 1986). The completion of this cycle constitutes a single generation in the execution process. This approach has an evaluation function which measures performance. On the other hand, the fitness function translates the measured component into an allotment of reproductive opportunities.

It works with a number of individuals which represent feasible solutions to the problems being investigated. The individuals are given a fitness score base on the suitability of the solutions. Most importantly, the algorithm only allows the highly fit individuals the chance of reproduction via the cross- breeding process (Holland, 1975). New off-springs have desirable characteristics from both parents. This implies that a new population of feasible solutions is created every time those individuals are selected from the current population and mated. In a matter of generations, good characteristics are attained. With a well designed GA approach, an optimal solution can be found (Holland, 1975)

The steps of a genetic algorithm (AG) are:

1- Choose initial population.

2- Evaluate fitness function.

3- Create a new population through:

· Selection

· Crossover

· Mutation

4- Replace random /worst ranked part of population with offspring.

5- Evaluate the individual fitness of the offspring.

The primary advantage of genetic algorithm comes from the crossover operation.

1- Initial population:

It begins with randomly initial generated states. which are satisfactory to the problem.

Example of states:

· N- queens

· Each state must have n queens.

· One queen in each column.

· Usually represented by a bit-string or chromosome.

Example: [1 2 3 4 5 6 7 8 9]

2- Fitness function:

The fitness function produces the next generation of states by choosing a good fitness to each state. Thus, the probability of being chosen for reproduction is based on your fitness.

3- Create a new population through:

3.1 Selection:

Selected two parents’ chromosomes to reproduce new parents. They are selected based on their fitness function. The better fitness has the biggest chance to be selected. However, one may be selected more than once where as one may not be selected at all.

Note:

There are different techniques, which can be used to choose the best fitness such as Roulette Wheel, Binary tournament and elitist… etc.

3.2 Crossover:

For each chromosome to be mated a crossover point is chosen at random from within the bit-string to create offspring by exchange between parents at crossover point.

Note:

Normal crossover operators will often lead to inadmissible solutions:

· Two chromosomes produce chromosomes offspring.

· There is a chance that the chromosomes of the two chromosomes s are copied unmodified as offspring.

· There is a chance that the chromosomes of the two chromosomes are randomly recombined to form offspring.

Example:

There are many specialized operators have been devised to focus on combining order or adjacency information of the two parents.

· Order one crossover: the idea is to preserve the relative order in which elements occur.

Informal procedure:

1- Choose an arbitrary port from the first parent.

2- Transfer this part to the child.

3- Copy the numbers that are not in the child, from the second parent to the child.

Note:

· Staring right from the cut point of the part, using the order of the second parent, and wrapping around at the end.

4- Analogous for the second child with parent roles reversed.

Copy rest from second parent in order 1,9, 3,8, 2

3.3 Mutation:

Mutation changes some of the bits in the new offspring, which can help to converge faster by getting different solutions.  After the change, calculating the fitness must be done again and check. If the fitness better than before, that means good mutation, else, the mutation should be canceled.

Example:

4- Replace:

Replace the current population with the new population.

5- Evaluate the individual fitness of the offspring:

Test new population whether the end condition is satisfied. If yes, it will stop. If not, it will return the best solution in current population and go back to step 2.

Proposed of implementation of genetic algorithm (GA)

GA approach is a type of optimization algorithms which is used to find the ideal solution(s) for a given computational problem that maximizes or minimizes a function [5]. The GA approach represents one branch of the area of study that is called evolutionary computation. This is based on the principles of natural genetic and natural selection to find the fittest solutions. Like in evolution, many of the genetic algorithms processes are random and feature factors such as selection, crossover, and mutation. After encoding the solution in an appropriate way, GA works iteratively, evolving to obtain the global optimum. In addition, the individuals in a population are manipulated by the genetic operators to improve their fitness values while searching for global optimum solutions. This optimization technique allows one to set the level of randomization. The following section lists the seven steps of GA [9]:

1) Initiate: Randomly create the initial population of the chromosome.

2) Evaluate the fitness function: Evaluate the fitness of each chromosome in the population.

3) Create a new population of chromosomes: Repeat the process of reproduction with the following sub-steps (a, b, c) until an optimal solution that satisfies the optimization criteria is obtained:

a. Selection: select chromosomes depending on each chromosome’s fitness function score. The better a chromosome’s fitness, the more likely it is to be chosen. Various techniques can also be used to pick the best chromosomes’ fitness, such as a roulette wheel selection.

b. Crossover: Perform the crossover to produce new chromosomes, which are off-springs by exchange between two chromosomes at the crossover point. There are many types of crossovers. In this study, an order one crossover has been used to produce off-springs.

c. Mutation: After off-springs are produced, perform the mutation, which is the modification of a few randomly chosen genes in off-springs to produce a new off-spring. However, the primary advantage of genetic algorithm comes from the crossover operation.

4) Re-evaluate the fitness function: Evaluate the fitness of each off-spring that has been produced to find out the best fitness.

5) Replace: Replace the worst random fitness chromosomes of population with off-springs.

6) Return processes: Repeat processes 2 to 5 until the conditions are satisfied.

7) Stop: Terminate the process.

Ant Colony Optimization (ACO)

Ant colony optimization (ACO) uses meta-heuristic, colonies of artificial ants which work together to find optimal solutions for complicated problems (Dorigo & Blum, 2005). In the real situation, ants can smell and deposit a chemical known as pheromones which allow them to communicate as they move around a specific location. Upon leaving the nest, ants take a random route but change this approach when they encounter a pheromone trail along the way. In this case, the ants make a decision on whether to follow the trails or not. They deposit their own pheromones adjacent to the previous trails if they decide to use a particular route. Notably, a statistician can calculate the probability of selection of a route relative to the others paths. The probability is based on the amount of chemical deposited on the paths.

As time elapses, the pheromones evaporate leaving little room for use of probabilities. Consequently, the colony has to use all possible routes in equal number in order to determine the shortest route between the nest and the food source (Dorigo & Blum, 2005). They also deposit the pheromones as the maneuver in search for food but the ant that uses a shorter route returns to the nest first. In this case, the shorter route will be marked by more pheromones because the chemical is fresh and not subject to evaporation. Such a path would be more attractive to other ants that may return to the food source.

For the optimization model, the artificial ants travel through a network where they deposit ‘pheromones’ over either the vertices or edges. The initial condition is interpreted as the nest in real ants while the food source is represented by the terminal condition (Dorigo & Blum, 2005). The selection of node or vertex for stepping forward is based on a probabilistic model which depends on the quantity of ‘pheromone’ deposited on either the edge or vertex. Additionally, the artificial ants deposit and smell the chemical based on a pheromone matrix (PM). On the other hand, the set of constraints that call for the evaluation of each and every selection represents the problem.

From a different perspective, Pareto optimization (PO) aims to achieve a comprehensive Pareto Optimal Set of solutions (POS) for problems that have a number of objectives. The solutions obtained using the approach are referred to as non-dominated solutions. P-ACO uses ant colonies that have a characteristic number of ants to compute the set of non-dominated solutions. In this case, every ant generates a solution. However, after comparison, deposition of ‘the chemical’ over the PM is only allowed for the non-dominated solutions (Dorigo & Blum, 2005).

The research is concerned with the supply chain design problem where the total cost and order lead time should be minimized. Pitakaso et al. (2007) found that the MAX−MIN Ant System (MMAS) provided the best model (ACO algorithm) for solving the supply chain design problem. In this approach, the ant that provides a desirable solution is permitted to deposit pheromones implying that other ants use the best design in all iterations. The problem with this method is that it could result to stagnation or the attainment of sub-optimal solutions. However, Dorigo and Blum (2005) argue that the use of heuristic information rather that the information provided by the ants avoids the effect. In addition, the ACO algorithm embraces an evaporation factor to account for the evaporation of pheromones in generating solutions

Bell and McMullen (2004) argue that ant colony optimization may be used in the combinatorial optimization. According to Baker and Ayechew (2003), when a 2-opt heuristic was used in vehicle routing optimization, desirable results were obtained since they were only slightly inferior to those of Tabu search. Lastly, Doerner et al (2007) argue that Pareto Ant Colony Optimization (PACO) can be used to solve the location-routing problem using a number of objective functions. They classify it as a multi objective meta-heuristic approach

Tabu Search (HAT)

The tabu search uses a basic and direct searching algorithm to optimize complicated problems. It working principle is similar to the human memory which creates a list of the most recent points of investigation (Glover & Laguna, 1997). In this context, the creation of this list prevents the possibility of transformation to the points that were investigated on a previous date. The tabu search is based on the premise that intelligent problem-solving requires one to incorporate the adaptive memory. In this light , it is important to note that the tabu list comprises of certain forbidden moves (Glover & Laguna, 1997)..

For a problem whose current solution is x, the tabu search is interested with its neighborhood N(x) which it identifies as x’ to meet the condition of a best neighbor (not in the tabu list). There exists subset of neighborhood points known as candidate points which simplify the search. The addition of the new solutions to the tabu list results to the subsequent removal of the oldest member on the list. In this way, it disallows the repetition of moves to prevent the possible entrapment in local minima (Glover & Laguna, 1997).. In addition, the aspiration criterion allows the algorithm to accept some solutions even if they are in the tabu list. In addition diversification and intensification allow users to jump to different parts of the search space and to search for solutions with desirable characteristics respectively (Glover & Laguna, 1997).. The user can also dictate the search process by discouraging solutions that are likely to be duplicates of other solutions attained at a previous date. This can be applied by the imputing certain restrictions on defined attributes that are related to the search history. In this case, recency and frequency memories aid the exploration of the tabu search history to impose the said restrictions. The difference between recency and frequency memories can be attributed to the fact that recency memory is short term and is managed through tabu lists while the frequency memory is long term.

In its standard form, the recency memory disallows moves that end up delivering solutions similar to the ones recently visited. On the other hand, the standard form of frequency memory accounts for moves that are disallowed based on the possibility of yielding solutions with attributes that occasionally been shared by solutions obtained in previous searches (Glover & Laguna, 1997). It also encourages solutions with characteristics that seldom occur in previous searches.

According to Golden, Laporte and Taillard (1997), the Tabu search uses an adaptive memory procedure to solve the vehicle routing problem with a min-max objective.

Mixed Integer Programming (MIP)

Evolutionary Algorithms

This is classified into the category of Soft Computing. It may be made up of Genetic Algorithms, Evolutionary Programming, Evolutionary Strategies and Genetic Programming (Coello Coello, 2014). In most cases, It adopts a structure where;

· The Search space allows users to get possible solutions

· The Population represents candidates for a solution.

· The String space denotes individuals in the population.

· There are Functions for coding and decoding

· genetic operators generate new strings and new individuals

· The Fitness function determines the fitness of each individual

· There is Stochastic control of genetic operators.

To use this type of algorithm, the following basics are followed;

· Initialization to get a population

· Evaluation for fitness of individual members

· Selection

· Recombination

· Repeating previous steps until the finish criteria is attained

The pareto concept is applicable in this context (Zitzler, Deb & Thiele, 2000)

Simulated Annealing

In statistical mechanics, the annealing process of solids forms the basis for simulated annealing [20]. The concept revolves around the heating of solids to high temperatures before cooling them gradually for crystallization to take place. While the heating process excites atoms to move randomly, the cooling procedure allows the atoms to drop to minimum energy of equilibrium after aligning themselves. Tavakkoli-Moghaddam et al (2006) articulates that this approach can be used in combinatorial optimizations where the possible solution is represented by the sated of solid and the energy realized at each state relates to improvements in the objective function. On the other hand, the optimal solution in simulated annealing is denoted by the minimum energy.

Hybridization of Meta-Heuristic Approaches

The hybrid algorithm uses the meta-heuristics approaches (one or more) together with an optimization/ heuristic method that guarantees fast, easier and accurate solutions. For vehicle routing problems, Potvin, Dub and Robillard (1996) suggest that a two-stage hybrid algorithm may be used. He uses the simulated annealing algorithm in the first stage to decrease the number of routes before adopting the neighborhood search in the second step to decrease the costs of travel. Other options include using the genetic algorithm in the first stage together with neural networks in the second and the use of neighborhood search and the genetic algorithm [9].

Bres et al. (1980) suggest that using the hybrid approach for meta-heuristics such as tabu search and promises the best results since the method combines the most important features of both.

Hybridization of Genetic Algorithm GA with Ant Colony Optimization ACO

GA and ACO algorithms are population-based search algorithms capable of wide applications for solving hard and complex problems across various branches of sciences and engineering. These algorithms can be hybridized with other algorithms [15]. The first ACO was used through focussing on the conduct of real ants [3]. In the ACO algorithm, artificial ants search a graph probabilistically and with the guidance of the pheromone, in order to create candidate solutions. These solutions are then evaluated and used for pheromone updates. Various versions of the ACO have been developed, but they all follow the same idea of solution construction guided by pheromone levels [10]. Many attempts have been made to hybridize these algorithms in order to improve the quality of the solutions. Based on previous studies, hybrid of genetic algorithm and ant colony optimization (HGACO) provides acceptable solutions in a reasonable time [6]. This is because several meta-heuristic approaches work together in order to benefit from the best characteristics of each. In view of the foregoing, we propose a hybrid of genetic algorithm and ant colony optimization to solve the milk-run delivery issue in LSC management for AICS.

Hybridization Ant Colony Optimization ACO with Tabu Search (AT)

Chapter 3 CHAPTER 3 CASE STUDY

Optimization of an Automobile Industry case study with Meta-heurstic Approaches

The automobile industry case study (AICS) was studied by Zhou and Kelin (2011). They built up a theoretical total cost (TC) model for the milk-run delivery issue in LSC by considering the three factors that most influence the total cost of supply chain: production, delivery and inventory costs. Hence, they developed an equation to minimize TC (Equation (1)) and then solved it by applying the improved ant colony optimization (ACO). Later, Nguyen and Dao (2015) worked on the same case study but with different approaches: mixed integer programming (MIP), along with a hybrid of ant colony optimization (ACO) and tabu search (HAT). They compared their results with those of the original ACO, finding that the MIP results outperformed the previously obtained ACO results as well as the HAT results. Thus, MIP can minimize the total cost of an entire supply chain. The AICS involves only a few facilities (less than 10) making it a small-scale LSC. So, the previous results indicated that the use of MIP is pertinent in a small-scale LSC. However, MIP, HAT and ACO were also tested with random data in large-size LSC [8]. The results showed that MIP encounters significant difficulties in such cases. When the number of facilities is greater than 15, the time spent in finding the optimal dr makes MIP all but useless as an industrial application [8]. In fact, compared with ACO and HAT, MIP requires a very long processing time when handling a large-scale LSC. When random data were tested with 100 iterations, optimal dr from the HAT was superior to ACO in most cases [8].

Specific data and description of automobile industry case study (AICS)

The supply chain in an AICS has just one manufacturing plant facility. This is identified as facility number 1, because the route will always start and end here. Facilities 2, 3, and 4 are considered as suppliers, while facilities 5, 6, 7, 8 and 9 play the role of customers. The geographical location of each AICS facility is listed in Table 1.

Table 31 Geographical location of AICS facilities

To integrate the supply chain, we need to consider the transportation distance delivery model to minimize the transportation cost between the manufacturing plant, the suppliers and the customers by going to each AICS facilities only once. The goal is to minimize the total cost of the supply chain by applying the following strategy: the shortest delivery route (dr) and the optimal delivery frequency (n). This strategy will have a significant impact on the level of stock and the quantity of goods with regard to the manufacturing plant, suppliers and customers. The supply chain values of the AICS are given in Tables 2 and 3 and will be utilized as input data for Equation (1).

Table 32 Data of manufacturing plant and supplier facilities for AICS

Table 33 Date of customer facilities for AICS

Definition of the optimization problem

The optimization problem is defined by the parameters to be adjusted and the objective to be optimized. We will apply both the genetic algorithm (GA) approach as well as the hybrid of the genetic algorithm and ant colony optimization (HGACO) approach to study their advantages and disadvantages compared to each other and to the ACO approach, using the same data from AICS and applying the same TC function (Equation 1) developed by Zhou and Kelin (2011).

(1)A list of the parameters is given below:

Dc: productivity/demand rate from customers;

dij: transportation distance from facility i to facility j;

dr: total transportation distance for one route;

F: number of facilities;

FDC: delivery start-up cost (1000);

FOC: order fixed cost of parts;

FOC’: order fixed cost of finished products;

i: a manufacturing plant /customer/ supplier facility;

j: a manufacturing plant /customer/ supplier facility;

K: number of customers;

N: number of suppliers;

n: delivery frequency;

Pm: productivity/demand rate from a manufacturing plant;

Ps: productivity/demand rate from suppliers;

SIm: part safety stock quantity of a manufacturing plant;

SIs: part safety stock quantity of suppliers;

SI’c: finished safety stock quantity of customers;

SI’m: finished safety stock quantity of a manufacturing plant;

T: manufacture’s production cycle (30 days);

TC: minimum total cost of supply chain;

UDC: unit delivery cost (5 per km);

UICd: parts unit inventory cost of in-transit;

UICm: parts unit inventory cost of a manufacturing plant;

UICs: parts unit inventory cost of suppliers;

UIC’c : finished product unit inventory cost of customers;

UIC’d: finished product unit inventory cost of in-transit;

UIC’m: finished product unit inventory cost of a manufacturing plant;

UPCm: unit production cost of manufacturing plant;

UPCs: unit production cost of suppliers;

USCm: production start-up cost/batch of a manufacturing plant;

USCs: production start-up cost/batch of suppliers;

V: average speed of delivery vehicle (50 km/h);

W: delivery vehicle capacity (20 tons);

w: weight (mass) of part (kg);

w’: weight (mass) of finished product (kg).

Optimization objective

The main objective here is to minimize the transport distance between the facilities, which can be modelled as the sum of the distances to all the facility locations in just one route.

 (2)

Constraints

1- Ensure that each customer/supplier is serviced/supplied only once and included in one route:

2- Ensure that a route is fully connected and that there is no sub-route:

K is the set of all transportation distances in one route.

3- Ensure that the vehicle starts and ends at the same facility. As shown below, [1] means facility number 1, which is both the start and the end of the same route:

Route = [1]: [F+1]

However, the path from the second facility [2] to the last facility [F] is random:

Random route= [2]: [F]

Mathematically, we can obtain the minimum n and the minimum TC by the following equations:

· delivery frequency [8]:

 (3)

· total cost [8]:

Min TC= A*dr + B*n + C*n*dr + D/n + E (4)

where:

C = UDC

Application of meta-heuristic approaches to AICS

Application of the Genetic algorithm

GA is proposed to find the best solution for the shortest route in a complicated logistics network. In this study, the steps defined by Potvin et al. (1996) and presented at section 3.1 have been used as illustrated in Figure 1. GA is first applied on data from the transportation distance matrix d of AICS, as shown in Table 4. Each facility is given a unique integer value index from 1 to F, and every chromosome is designed to represent a solution for the problem, keeping in mind that the route must not repeat facilities. The length of the chromosome, which is one delivery route (dr), is selected to be equal to the number of facilities of AICS.

Figure ‎41 Flow chart of proposed GA for optimizing route distance (dr)

Encoding:

Permutation encoding can be used in ordering problems and it can also be used in this problem. In permutation encoding, every chromosome is a string of numbers that randomly represents the number of facilities. The number of facilities in each chromosome is fixed. From AICS data, as mentioned previously, there are nine facilities: a single manufacturing plant, three suppliers and five customers. The optimal dr is calculated from (1, 2, 3, …, F, 1). Different routes are based on the same geographical location of facilities (Table 1) with different transportation distances defined by Equation (5) and presented in Table 4:

(5)Table 34 Transportation distance matrix d among facilities of AICS

	0.00	34.66	24.19	55.04	14.14	62.39	12.65	45.00	31.38
	34.66	0.00	58.41	84.12	20.52	95.38	31.38	60.03	13.93
	24.19	58.41	0.00	35.44	38.01	38.60	29.41	53.67	52.63
	55.04	84.12	35.44	0.00	66.10	21.21	52.89	88.77	73.82
=	14.14	20.52	38.01	66.10	0.00	75.58	14.14	49.04	19.10
	62.39	95.38	38.60	21.21	75.58	0.00	64.35	85.99	87.20
	12.65	31.38	29.41	52.89	14.14	64.35	0.00	57.14	23.35
	45.00	60.03	53.67	88.77	49.04	85.99	57.14	0.00	66.71
	31.38	13.93	52.63	73.82	19.10	87.20	23.35	66.71	0.00

Identification of the optimal dr:

The optimal dr is obtained by the following steps, which have been adapted for this study. They are illustrated in Figure 1:

1) Find all possible solutions (F-1)! where F=9 is the number of facilities.

2) Set random permutation for (9-1)! that contains the number of all different facilities.

3) Choose 9 random chromosomes (routes) as the initial population from the data of transportation distance matrix d of AICS.

4) Check the validity of the routes (all facilities ≠ 0, no sub-route).

5) Compute fitness function (optimal route dr) for each route with Equation (2).

6) Select the best 4 chromosomes (routes) by roulette wheel selection. The selection is based on current population fitness (dr value) by probability of selection [11].

7) Randomly create 2 off-spring populations from 4 existing chromosomes (routes) by applying an order one crossover operator. In this case, each group of 2 chromosomes (routes) produces one off-spring. Two crossover points will be chosen randomly from the third gene (facilities) and seventh gene (facilities) for the first chromosome. This part is then transferred to the off-spring (new route). After that, the genes (facilities) which are not in the off-spring are copied from the second chromosome (route) to the off-spring (new route). This last step is done by starting from the right of the cut point of the part of the first chromosome (route) and by using the order of the second chromosome (route), which is wrapped around at the end.

8) Mutate randomly by choosing 2 genes (facilities) in the off-spring and by switching them. However, if the new off-spring (new route) value is bigger than the old off-spring (old route), the mutation is canceled.

9) Compare the 2 off-springs (new route value dr) with the old chromosome (old route dr).

10) Continue to check other possible values of the route until all successive GA iterations no longer produce better results.

11) Stop when the optimal dr is found.

In summary, GA checks all possible dr to identify the optimal dr. Afterwards, the delivery frequency (n) is computed as well as the total cost of the supply chain (TC) (Figure 1).

Application of the hybrid genetic algorithm and ant colony optimization

Hybrids of genetic algorithm and ant colony optimization are used to obtain the best result in terms of the optimal route (dr) by using transportation distance matrix d of AICS as shown in Table 4. In the ACO approach, artificial ants probabilistically search a graph, with the guidance of pheromone, in order to create candidate solutions. Candidate solutions are then evaluated (dr) and pheromone updates repeated until the stop condition is met (9 iterations). This can be achieved by following a temporary memory or tabu list before being selected as the initial population for GA approach. The alternative is selecting random initial population and then following the stages as in the previous GA approach, including identifying optimal n and TC. The framework is used as guide to find the optimal route (dr) for hybrid genetic algorithm and ant colony optimization. All the codes were written and implemented in MATLAB 2015.

1) Set the parameters and assign the initial pheromone value on each path to the same constant value.

β=1: Heuristic Exponential Weight M=9: Number of Ants (Population Size)

α=1: Pheromone Exponential Weight E=0.05: Evaporation Rate

Q=1: constant value

2) Solution Construction. Each ant begins at a start facility and constructively builds a solution based on the pheromone values. Ants choose to move from the facility (i) to facility (j) based on a probabilistic decision , and then onto a facility that has not yet been visited, as shown in Equation (6) [3]:

 (6)

where:

mi is the feasible neighborhood of facility (i). The neighborhood of facility (i) is the set of all facilities that an ant can move to when at facility (i).

Tij is the pheromone value between facility i and j.

is a heuristic value, =1/dij.

3) Update Pheromone. Once all ants have finished constructing their routes, the pheromone trails are updated. This is done first by lowering the pheromone trails by a constant factor (evaporation) and then by allowing the ants to deposit pheromone on the transportation distance they have visited.

4) The solution construction and pheromone update are repeated until the stop condition is met by the selected first 9 iterations.

5) The best four chromosomes (routes) are then selected by roulette wheel the from first 9 iterations of ACO, becoming the initial population for GA and then following the same stages as the previous GA approach, including identifying optimal n and TC.

45

Chapter 4 CHAPTER 4 EXPERIMENTAL RESULTS

Experimental results

Result of the genetic algorithm

Result of the hybrid genetic algorithm and ant colony optimization

The main results obtained from this study is the optimal delivery route which is illustrated in Figures 2 and 3 and Table 5. As can be seen from the results, the proposed genetic algorithm starts from facility 1 and then does a full array equation cross of other facilities to find the optimal value. As can be seen in figure 2, the optimal value is 283.30 km after 18 – 36 iterations. This optimal solution is the optimal delivery route which is 1-5-2-9-7-4-6-3-8-1 presented in Table 5. However, HGACO shows superior performance when compared to other existing meta-heuristic by getting the best optimal route (dr) with slightly fewer iterations than GA. A comparison between the three approaches (GA, HGACO and ACO) is presented in Figures 2 and 3. As shown, HGACO and GA have obtained the same optimal dr (283.30 km) which is slightly better than ACO (286.22 km) as presented in Table 5.

Figure ‎51 Optimal dr (383.30 km) with GA and HGACO

Figure ‎52 Optimal dr (286.22 km) with ACO

Table 41 Optimal dr from GA,HGACO and ACO

Approach	dr (km)	Best sub-Route
GA	283.30	1 – 5 – 2 – 9 – 7 – 4 – 6 – 3 – 8 – 1
HGACO	283.30	1 – 5 – 2 – 9 – 7 – 4 – 6 – 3 – 8 – 1
ACO	286.22	1 – 5 – 9 – 2 – 8 – 3 – 6 – 4 – 7 – 1

However, because this optimal route does not meet the vehicle capacity by delivering to all the facilities in one delivery route distance, it needs to be divided into two sub-route distances, as follows: (dr1) is 1-8-3-6-4-7-1 and (dr2) is 1-9-2-5-1. With these sub-routes, the dr becomes 295.94 km. Once again, the two sub-routes obtained from GA are the same as those obtained from HGACO (Table 6). Equations (3) and (4) were then used to calculate the delivery frequency (n): for dr1 and dr2, the delivery frequency is equal to 30 (Table 6). The total cost of the supply chain (TC), as calculated with Equations (3) and (4) is found to be 14,265,635.58 $ (Table 6). With the same sub-routes, GA also has the same TC as HGACO.

Table 42 Optimal dr with two sub-routes found from GA, HGACO and ACO

Approach	dr (km)	Best sub-Route	n	TC ($)	Note
GA	295.94	dr1 = 1 – 8 – 3 – 6 – 4 – 7 – 1 dr2 = 1 – 9 – 2 – 5 – 1	30 30	14,265,636.58	Optimal TC
HGACO	295.94	dr1 = 1 – 8 – 3 – 6 – 4 – 7 – 1 dr2 = 1 – 9 – 2 – 5 – 1	30 30	14,265,636.58	Optimal TC
ACO	301.75	dr1= 1 – 5 – 9 – 2 – 8 – 1 dr2= 1 – 7 – 4 – 6 – 3 – 1	19 19	14, 766,546.0

Discussion

The final TC offered by MIP achieves optimal value. Comparing with original, the LSC can save TC up to $1,500,909.42 and shorten the delivery path by 5.81 km/ milk run. The optimal dr and greater n obtained from MIP, contribute to the reduction of TC globally (9.52%) thanks to the decrease of inventory holding cost of all members in chain. The result matches with the conclusion of Gurinder and Gagan which emphasizes the importance of cost improvement though high delivery frequency in short distances of milk-run. However, MIP confronts monumental trouble with large m since there are total (m-1)! feasible values of dr need to be checked for optimal dr. When m reaches to 15, the processing time of CPU (with processor can solve 2 million procedures per second) exceeds a week. When m larger than 15, the vast time spending in finding optimal dr makes MIP’s meaningless in industrial application.

Regarding factor “short distance” dr, results from HAT with different LSC sizes in Table 7, and Figure 6 indicate that HAT provides smaller average value optimal dr than ACO. In the test, with 100 iterations, optimal dr from the hybrid approach is superior to ACO in most of cases. Yet, while m increases, the linear regression model of ACO-HAT variation appears a gradual downward trend (Table 8 and Figure 7) or with very large size LSC, the difference between two methods becomes small. However, in practical size of milk-run as shown, HAT proves worthy applying. By providing shorter dr, HAT can offer better solution for milk-run issue than ACO at each certain m. What is more, other advantage of HAT is emphasized regarding processing time. When m reaches 100, find optimal dr from HAT costs only 163.65s while it is completely impractical for MIP.

CONCLUSION

In this thesis, the integrated optimization of the supply chain management — lean supply chain management —is used in order to improve the relationships between the various facilities. In addition to being more effective, responsive and flexible, the approach seeks to gain a sustainable competitive advantage through high quality and cost minimization. This study confirms that the genetic algorithm approach (GA) along with the hybrid of genetic algorithm and ant colony optimization approach (HGACO) for the design of a logistic distribution network is effective in achieving an optimal solution. HGACO gives encouraging results that can be obtained by using fewer iterations than the GA approach. In addition, since GA and HGACO have superior performance compared to ACO, these approaches seem quite promising for industrial applications. However, they would first have to be applied in larger-scale.

21

RECOMMENDATIONS

Firms have a role in is synchronizing customers’ needs with the inflow of goods from suppliers in order to establish a balance between the apparently divergent goals of outstanding customer service, minimal unit cost and low inventory (Stevens 1989]. This means that a cost benefit analysis with reference to the customers should influence the decisions regarding cost analysis of suppliers and the optimal distance between stores. In the end, the firms should address the response capacity of their respective supply chains

The decision making process in SCM , should prescribe solutions for a number of problems. Kumar et al. (2004] argues that the problems arise from internal needs and external factors such as traffic. In this context, firms should embrace the stochastic search techniques that have been discussed in the thesis to ease the decision making constraints. This avoids the problem of undesired locally optimal solutions with inferior functional values which characterizes the traditional methods of optimization (Deb and Kalyanmoy 2001; Davies 1991). Moreover Ko et al (2010] argue that the Genetic algorithm addresses constraints that the traditional methods could not find solutions for.

The problems of order delivery, demand management, supplier relations and routing should be addressed effectively using the GA (Shen 2007]. The Genetic algorithm should also be used in reducing the total cost of the distribution network (Lawrynowicz 2011) Additionally, the problems of batching orders, logistics scheduling and routing inventory should be solved by designing an integer encoded GA that represents the cargo item sequence (Hsu et al. 2005)

Since GA and HGACO have superior performance compared to ACO, these approaches seem quite promising for industrial applications. However, they would first have to be applied in larger-scale. The problematic issue with meta-heuristic approaches is that they require expertise tailoring, customization and the fine tuning of the algorithm (Jones, Mirrazavi, & Tamiz, 2002). This means that metaheuristic techniques must be adapted to the problems where solutions are being sought for them to be efficient. To alleviate this problem, the meta-heuristic approaches (GA and HGACO) should be designed within appropriate standards.

27

<TITLE>

<

11

<TITLE>

<

12

APPENDIX <If necessary>

<

59

LIST OF BIBLIOGRAPHICAL REFERENCES

[1] Bowersox, D. J., Closs, D. J. & Copper, M. B. (2002). Supply chain logistics management. New York, N.Y: McGraw-Hill/Irwin.

[2] Chopra, S. & Meindl, P. (2013). Supply chain management: Strategy, Planning and Operation (5th edition). New Jersey: Pearson.

[3] Dorigo, M., Birattari, M. & Stutzle, T. (2006). Ant colony optimization. IEEE Computational Intelligence Magazine, 1(4), 28-39.

[4] Eroğlu, D. Y., Rafele, C., Cagliano, A.C., Murat, S. S. & Ippolito, M. (2014). Simultaneous routing and loading method for milk-run using hybrid genetic search algorithm. XII International Logistics and Supply Chain Congress, 48-57.

[5] Gonen, B. (2011). Genetic algorithm finding the shortest path in networks. International Congress in Computer Science, Computer Engineering and Applied Computing.

[6] Lee, Z. (2004). A Hybrid algorithm applied to travelling salesman problem. IEEE International Conference in Networking, Sensing and Control, 1, 237-242. doi: 10.1109/ICNSC.2004.1297441

[7] Manrodt, B., Abbott, J. & Vitasek, K. (2005). What makes a lean supply chain? Supply Chain Management Review, 9(7), 39-45.

[8] Nguyen, D. H. T. & Dao, M. T. (2015). New approaches for optimization of milk-run delivery issue in lean supply chain management. The Journal of Management and Engineering Integration, 8 (1).

[9] Potvin, J., Duhamel, C. & Guertin, F. (1996). A genetic algorithm for vehicle routing with backhauling. Applied Intelligence, 6 (4), 345-355.

[10] Qiu, Q. & Xie, X. (2012) Theoretical Analysis on Initial Pheromone Values for ACO. In B. Cao & X. Xie. (eds), Fuzzy Engineering and Operations Research (pp. 339-349). doi: 10.1007/978-3-642-28592-9_35

[11] Rao, S. S. (2009). Engineering Optimization: Theory And Practice (4th edition). Hoboken, N. J: John Wiley and Sons.

[12] Rivera, L., Wan, H., Chen, F. F. & Lee, W. M. (2007) Beyond Partnerships: The Power of Lean Supply Chains. In H. Jung, B. Jeong & F.F Chen. (eds), Trends in Supply Chain Design and Management (pp. 241-268). https://doi.org/10.1007/978-1-84628-607-0_10

[13] Ugochukwu, P., Engström, J. & Langstrand, J. (2012). Lean in the supply chain: a literature review. Management and Production Engineering Review, 3(4), 87-96. doi:10.2478/v10270-012-0037-6

[14] Zhou, M. & Kelin, X. (2011). Modeling and simulation of lean SC with the consideration of delivery consolidation. Key Engineering Materials, 467-469, 853-858.

[15] Zukhri, Z. & Paputungan, I. V. (2013). A hybrid optimization algorithm based on genetic algorithm and ant colony optimization. International Journal of Artificial Intelligence and Applications, 4(5), 63.

[16] ‘’D.Lambert_Executive Summary_SCM-book’’

[17]

[18] Presented at the annual business meeting, Council of Logistics Management (CLM), in Anaheim, California, in October 1998. The definition is posted at the CLM’s homepage at http://www.CLM1.org.

[19]

[20] Tavakkoli-Moghaddam, R., Safaei, N., & Gholipour, Y. (2006). A hybrid simulated annealing for capacitated vehicle routing problems with the independent route length. Applied Mathematics and Computation, 176(2), 445-454.

[21]

[22]

[23]

[24]

[25] Ballou, R. (1978). Basic Business Logistics, Prentice-Hall, Englewood Cliffs, NJ

[26] Chen , J., & , and Shuaiying. (2009). A Cost Optimization Model Based on the Milk Run System for the Three-Level Supply Chain. Journal of WUT (Information and Management Engineering), 31, 831-842.

[27] Chopra, S., & Meindl, P. (2004). Supply Chain Management. Strategy, Planning & Operation. Das Summa Summarum des Management, 265-275.

[28] Christopher, M.(1994). Logistics and Supply Chain Management, Pitman Publishing, New York.

[29] Gaonkar, R., & Viswanadham, N. (2001). Collaboration and information sharing in global contract manufacturing networks. IEEE/ASME Transactions on Mechatronics, 6(4), 366-376.

[30] Heskett, J., Ivie, R. & Glaskowsky, N. (1964). Business Logistics, Management of Physical Supply and Distribution, the Ronald Press Company, New York

[31] Jang, Y. J., Jeng, S. Y., Chang, B. M. & Park, J. (2002). A combinated model of network design and production/distribution planning for a supply network. Computers & Industrial Engineering. 43, 263-281.

[32] La londe . (2010). Evolution of Supply Chain Management (SCM). Adaptive Supply Chain Management, 1-17.

[33] La Londe, Bernard J. (1997). “Supply Chain Management: Myth or Reality?” Supply Chain Management Review. 1, 6-7

[34] Ma, H. J., & Wei, J. (2012). Milk-Run Vehicle Routing Optimization Model and Algorithm of Automobile Parts. Applied Mechanics and Materials, 253-255, 1463-1467.

[35] Michael M., & Claudia, N. (2009). A Report on the Current Event on the WMS Market. WMS Market Overview.

[36] Monczka, Trent R., & Handfield R. (1994). Purchasing and Supply ChainManagement, Cincinnati, OH: South-Western College Publishing

[37] Oliver, R.K. & Webber, M.D. (1992).“Supply-chain management: logistics catches up withstrategy”, in Christopher, M. (Ed.), Logistics: The Strategic Issues, Chapman & Hall, London

[38] Pyke, D., Robb, D., & Farley, J. (2000). Manufacturing and supply chain management in China:. European Management Journal, 18(6), 577-589.

[39] Sadjadi, S. J., Jafari, M., & Amini, T. (2008). A new mathematical modeling and a genetic algorithm search for milk run problem (an auto industry supply chain case study). The International Journal of Advanced Manufacturing Technology, 44(1-2), 194-200.

[40] Talluri, S., & Baker, R. (2002). A multi-phase mathematical programming approach for effective supply chain design. European Journal of Operational Research, 141(3), 544-558.

[41] Viswanadham, N., & Gaonkar, R. (2003). Partner selection and synchronized planning in dynamic manufacturing networks. IEEE Transactions on Robotics and Automation, 19(1), 117-130.

[42] Xu, J., & Han, X. (2010). Analysis on Linkage Mechanism between Manufacturing and Logistics Industry. 2010 International Conference on E-Business and E-Government.

[43] You, Z., & Jiao, Y. (2014). Development and Application of Milk-Run Distribution Systems in the Express Industry Based on Saving Algorithm. Mathematical Problems in Engineering, 2014, 1-6.

[44] T. Bäck. Evolutionary Algorithms in Theory and Practice: Evolution Strategies,Evolutionary Programming, Genetic Algorithms. Oxford University Press,USA, 1996

[45] V.Cˇerny`.ThermodynamicalApproachtotheTravelingSalesmanProblem:An Efficient Simulation Algorithm. Journal of Optimization Theory and Applications, 45(1):41–51, 1985.

[46] J. Kennedy and R. C. Eberhart. Particle Swarm Optimization. In Proceedings of the IEEE International Conference on Neural Networks (ICNN 1995), pages 1942–1948, 1995.

[47]

INDEX (If necessary)

28

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

{

}

(

)

{

}

(

)

(

)

(

)

(

)

11

1

1

1

‘

””

‘

1

22

NK

ij

ss

i

ii

dc

jj

mmcccm

jjj

ij

sm

i

mm

mi

sm

i

s

i

N

dm

i

mmms

i

i

i

K

j

i

UICPdr

UICSIUICSIPUPC

VT

UICDdr

UICSIUICSIDUPC

VT

USCFOCUSCFOCFDCUDCdrn

UICP

P

UICP

P

MinTC

==

=

=

=

+++

´+++

+++´

-+

=

++

ìü

íý

îþ

ìü

íý

îþ

+

ìæöü

+

íý

ç÷

îèøþ

+

åå

å

å

(

)

(

)

(

)

(

)

(

)

2

1

‘

‘

22

ccc

jjj

mc

j

m

NK

j

DUICD

UICDn

P

=

-+

æö

ìæöü

ïï

ç÷

+

ç÷

íý

ç÷

ç÷

ïï

îèøþ

èø

åå

11

FF

ijij

ij

Minimizedr

dx

==

=

åå

1 if vehicle travels from i to j

0 otherwise

x

=

ì

í

î

,

xK1 Ki,2KF2

ij

ijF

Î

=-Ì££-

å

(

)

()

nBDdrC

=+´

A = UICd ⎛

⎝ ⎜⎜

⎞

⎠ ⎟⎟iPm

VT

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟

+ i=1

N ∑

UIC’d ⎛

⎝ ⎜⎜

⎞

⎠ ⎟⎟ j Dc

⎛

⎝ ⎜⎜

⎞

⎠ ⎟⎟ j

VT

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟

j=1

K ∑

A=

UIC

d

æ

è

ç

ç

ö

ø

÷

÷

i

P

m

VT

æ

è

ç

ç

ç

ç

ç

ö

ø

÷

÷

÷

÷

÷

+

i=1

N

å

UIC’

d

æ

è

ç

ç

ö

ø

÷

÷

j

D

c

æ

è

ç

ç

ö

ø

÷

÷

j

VT

æ

è

ç

ç

ç

ç

ç

ç

ö

ø

÷

÷

÷

÷

÷

÷

j=1

K

å

B = USCs( )i + FOC( )i{ }i=1 N

∑ + USCm + FOC ‘( ) j{ }+ FDCj=1 K

∑

B=USC

s

()

i

+FOC

()

i

{ }

i=1

N

å

+USC

m

+FOC’

()

j

{ }

+FDC

j=1

K

å

D = UICs⎛⎝⎜ ⎞⎠⎟i Pm 1 – Pm 2Ps⎛⎝⎜

⎞ ⎠ ⎟i

⎛

⎝

⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟

+ UICm⎛⎝⎜

⎞

⎠ ⎟iPm 2

⎧

⎨

⎪ ⎪

⎩

⎪ ⎪

⎫

⎬

⎪ ⎪

⎭

⎪ ⎪

+ UIC ‘m Dc( ) j – Dc( )i

⎛

⎝ ⎜

⎞

⎠ ⎟ 2

2Pm

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟

+ UIC ‘c( ) j Dc( ) j

2

⎧

⎨

⎪ ⎪⎪

⎩

⎪ ⎪ ⎪

⎫

⎬

⎪ ⎪⎪

⎭

⎪ ⎪ ⎪

j=1

K ∑i=1

N ∑

D=UIC

s

æ

è

ç

ö

ø

÷

i

P

m

1 –

P

m

2P

s

æ

è

ç

ö

ø

÷

i

æ

è

ç

ç

ç

ç

ö

ø

÷

÷

÷

÷

+

UIC

m

æ

è

ç

ö

ø

÷

i

P

m

2

ì

í

ï

ï

î

ï

ï

ü

ý

ï

ï

þ

ï

ï

+UIC’

m

D

c

()

j

–

D

c

()

i

æ

è

ç

ö

ø

÷

2

2P

m

æ

è

ç

ç

ç

ç

ç

ç

ö

ø

÷

÷

÷

÷

÷

÷

+

UIC’

c

()

j

D

c

()

j

2

ì

í

ï

ï

ï

î

ï

ï

ï

ü

ý

ï

ï

ï

þ

ï

ï

ï

j=1

K

å

i=1

N

å

E = UICs⎛⎝⎜⎜ ⎞

⎠

⎟ ⎟i SIs ⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟i+UICm

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟i SIm ⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟i+PmUPCs

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟i

⎧ ⎨ ⎪

⎩⎪

⎫ ⎬ ⎪

⎭⎪i=1

N ∑ + UIC’m⎛⎝⎜⎜ ⎞⎠⎟⎟SI’m+UIC’C⎛⎝⎜⎜ ⎞⎠⎟⎟ j SI’c

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ j+Dc

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ j UPCm

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟{ }j=1

K ∑

E=UIC

s

æ

è

ç

ç

ö

ø

÷

÷

i

SI

s

æ

è

ç

ç

ö

ø

÷

÷

i

+UIC

m

æ

è

ç

ç

ö

ø

÷

÷

i

SI

m

æ

è

ç

ç

ö

ø

÷

÷

i

+P

m

UPC

s

æ

è

ç

ç

ö

ø

÷

÷

i

ì

í

ï

î

ï

ü

ý

ï

þ

ï

i=1

N

å

+UIC’

m

æ

è

ç

ç

ö

ø

÷

÷

SI’

m

+UIC’

C

æ

è

ç

ç

ö

ø

÷

÷

j

SI’

c

æ

è

ç

ç

ö

ø

÷

÷

j

+D

c

æ

è

ç

ç

ö

ø

÷

÷

j

UPC

m

æ

è

ç

ç

ö

ø

÷

÷

{ }

j=1

K

å

dij = xix j -1( ) 2 + yiy j -1( )

2

i

F ∑

d

ij

=x

i

x

j

-1

()

2

+ y

i

y

j

-1

()

2

i

F

å

dij

d

ij

(

)

t

p

k

ij

(

)

[

]

[

]

[

]

[

]

ï

ï

î

ï

ï

í

ì

Î

×

×

=

å

Î

otherwise

allowed

m

i

t

T

t

T

t

p

m

allowed

m

ij

ij

ij

ij

m

ij

m

0

f

)

(

)

(

b

a

b

a

h

h

ij

h

You Need a Professional Writer To Work On Your Paper?