Supply chain optimization : location, production, inventory and distribution

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Supply chain optimization:

location, production, inventory and distribution

Thèse

Maryam Darvish

Doctorat en Sciences de l’administration – opérations et systèmes de décision

Philosophiæ doctor (Ph.D.)

Québec, Canada

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Supply chain optimization:

location, production, inventory and distribution

Thèse

Maryam Darvish

Sous la direction de:

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Résumé

L’environnement concurrentiel des affaires et la mondialisation oblige actuellement les entreprises à accorder une importance particulière à la performance de leur chaîne d’approvisionnement. Afin de se démarquer, les entreprises sont contraintes de prévoir et de gérer des paramètres de performance souvent contradictoires à savoir réduire le coût de leur chaîne d’approvisionnement et augmenter la qualité du service offert à leur clientèle. À cet égard, la planification intégrée de la chaîne logistique c’est-à-dire que les décisions relatives à la l’emplacement des usines, l’approvisionnement, la production, le stockage et la distribu-tion s’avèrent majeures dans le gain d’efficience des entreprises et la réactivité d’une chaîne d’approvisionnement.

La production et la planification de la distribution constituent deux opérations fondamentales dans la gestion de la chaîne logistique. Couramment, elles sont traitées de manière distincte du fait de leur complexité. Les coûts d’inventaire sont élevés dans cette approche dite aussi linéaire ou hiérarchique, eu égard à la nécessité de respecter les délais de traitement des commandes et d’assurer la satisfaction des clients. Cependant, il devient impératif de ne plus négliger les liens existants entre les décisions prises pour gérer la production et la distribution, afin de réaliser des économies de coûts dans la chaîne d’approvisionnement. Bien que l’intérêt pour la planification intégrée de chaîne d’approvisionnement soit grandissant, les modèles d’optimisation actuels laissent encore place à l’amélioration afin d’être plus réalistes.

Dans cette recherche, nous étudions des problèmes logistiques riches et intégrés. La perti-nence de notre apport réside dans l’ajout de variables opérationnelles telles que les fenêtres de temps de service ou la configuration de réseaux flexibles ainsi que de certaines caractéristiques environnementales, dans des modèles logistiques. Notre objectif est de mettre en évidence les valeurs d’intégration, en termes d’économies de coûts et de réduction de gaz à effet de serre. Premièrement, nous décrivons, modélisons et résolvons le problème qui se présent chez un partenaire industriel qui fabrique un seul produit. Dans ce système, la capacité de production et le niveau d’inventaire sont limités, les transferts inter-usines sont permis et les fenêtres de

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délais de livraison sont flexibles. En nous appuyant sur un vaste ensemble de données réelles collectées chez notre partenaire, nous comparons l’approche intégrée avec plusieurs scénarios de pratique courante. Nous utilisons une méthode exacte qui permet de résoudre chacun des scénarios et étudions les compromis entre les coûts et les niveaux de service dans une analyse de sensibilité détaillée. Les résultats obtenus démontrent ainsi comment l’application d’une approche synchronisée et holistique dans la prise de décision apporte de nombreuses opportunités bénéfiques pour les systèmes logistiques en général.

Nous étendons par la suite notre étude aux systèmes de production produits et multi-échelons. Cette nouvelle configuration du problème implique que les produits sont expédiés aux clients par l’intermédiaire d’un ensemble de centres de distribution dont le producteur peut contrôler l’emplacement. Dans cette analyse, la conception de notre réseau de transport est flexible puisqu’il peut varier au cours du temps. Plus le problème est riche et s’approche de la réalité, plus le problème devient difficile et compliqué à résoudre. Les meilleures solu-tions issues de l’approche intégrée sont obtenues au détriment d’une plus grande complexité d’implémentation et de l’allongement du temps d’exécution. Nous décrivons, modélisons et résolvons le problème en utilisant d’abord des approches de prise de décision intégrées puis des approches séquentielles afin de déterminer à quel le moment l’usage d’une approche plus complexe est avantageuse pour résoudre le problème. Les résultats confirment la pertinence de l’approche intégrée comparativement à l’approche séquentielle.

Pour illustrer l’importance des économies réalisées grâce au caractère flexible de la conception de réseaux et des fenêtres de temps de livraison, nous décrivons, modélisons et résolvons un problème de localisation-tournées de vehicules intégré et flexible à deux échelons. Dans ce pro-blème, le fournisseur livre la marchandise à ses clients grâce à un réseau d’approvisionnement à deux échelons, avec une pénalité pour chaque demande non réalisée dans la fenêtre de li-vraison prédéterminée. La problématique est ici traitée dans une configuration plus riche; la livraison est planifiée en tournées de véhicules.

Le quatrième volet de cette thèse s’intéresse aux impacts environnementaux des décisions lo-gistiques. En effet, le plus souvent, les recherches scientifiques sur l’optimisation des chaînes d’approvisionnement se concentrent uniquement sur les aspects économiques du développe-ment durable et tendent à ignorer les deux autres dimensions. Nous abordons donc des pro-blématiques d’optimisation connues sous de nouveaux angles. Nous étudions deux systèmes intégrés de production, d’inventaire, de localisation et de distribution dans lesquels une mar-chandise produite à une usine est livrée aux détaillants dans un horizon de temps fini. Une analyse de sensibilité élaborée nous permet d’améliorer nos connaissances sur les coûts et les émissions dans les chaînes d’approvisionnement intégrées, en plus d’améliorer notre

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compré-hension des coûts associés à l’implantation de solutions respectueuses de l’environnement. Dans cette thèse, nous visons non seulement une meilleure compréhension de l’approche en-globante de logistique intégrée mais nous développons également des outils opérationnels pour son application dans des cas complexes concrets. Nous proposons ainsi de nouveaux mo-dèles d’affaires capables d’améliorer la performance de la chaine d’approvisionnement tout en développant des techniques d’implémentation mathématiques efficaces et efficientes.

Mots Clés: Optimisation intégrée, Problème de dimensionnement dynamique de lots, Fe-nêtres de temps de livraison, Problèmes de localisation, Distribution.

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Abstract

Today’s challenging and competitive global business environment forces companies to place a premium upon the performance of their supply chains. The key to success lies in understanding and managing several contradicting performance metrics. Companies are compelled to keep their supply chain costs low and to maintain the service level high. In this regard, integrated planning of important supply chain decisions such as location, procurement, production, in-ventory, and distribution has proved to be valuable in gaining efficiency and responsiveness. Two fundamental operations in supply chain management are production and distribution planning. Traditionally, mainly due to the high complexity and difficulty of these operations, they have been treated separately. This hierarchical or sequential decision making approach imposes high inventory holding cost, as in the traditional approach inventory plays an impor-tant role in timely satisfying the demand. However, in the era of supply chain cost reduction, it is becoming increasingly apparent that the interrelations between different decisions, and especially production and distribution decisions, can no longer be neglected. Although the research interest in the integrated supply chain planning has been recently growing, there is still much room to further improve and make the existing models more realistic.

Throughout this research, we investigate different rich integrated problems. The richness of the models stems from real-world features such as delivery time windows, flexible network designs, and incorporation of environmental concerns. Our purpose is to highlight the values of integration, in terms of cost savings and greenhouse gas emission reduction.

First, we describe, model, and solve a plant-customer, single product setting in which pro-duction and inventory are capacitated and inter-plant transshipment is allowed. The problem is flexible in terms of delivery due dates to customers, as we define a delivery time window. Using a large real dataset inspired from an industrial partner, we compare the integrated ap-proach with several current practice scenarios. We use an exact method to find the solution of each scenario and study the trade-offs between cost and service level in a detailed sensitivity analysis. Our results indicate how the use of a synchronized and holistic approach to decision

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making provides abundant opportunities for logistics systems in general.

We further extend our study by considering a multi-product and multi-echelon setting. In this problem, products are shipped to customers through a set of distribution centers, and the producer has control over their locations. In this study our network design is flexible since it may change over time. As the problem gets richer and more realistic, it also becomes more complex and difficult to solve. Better solutions from the integrated approach are obtained at the expense of higher implementation complexity and execution time. We describe and model the problem, and solve it with both integrated and sequential decision making approaches to indicate when the use of a more complex approach is beneficial. Our work provides insights on the value of the integrated approach compared to the sequential one.

To highlight how the two types of flexibility, from the network design and from the delivery time windows, lead to economic savings, we describe, model, and solve an integrated flexible two-echelon location routing problem. In this problem a supplier delivers a commodity to the customers through a two-echelon supply network. Here, we also consider a penalty for each demand that is not satisfied within the pre-specified time window. The problem is studied in a richer setting, as the distribution is conducted via vehicle routing.

The fourth part of this thesis addresses the environmental impacts of logistic decisions. Tradi-tionally, supply chain optimization has merely concentrated on costs or the economic aspects of sustainability, neglecting its environmental and social aspects. Aiming to compare the effect of operational decisions not only on costs but also on greenhouse gas emissions, we reassess some well-known logistic optimization problems under new objectives. We study two integrated systems dealing with production, inventory, and routing decisions, in which a com-modity produced at the plant is shipped to the retailers over a finite time horizon. We provide elaborated sensitivity analyses allowing us to gain useful managerial implications on the costs and emissions in integrated supply chains, besides important insights on the cost of being environmentally friendly.

In this thesis, we aim not only to better understand the integrated logistics as a whole but also to provide useful operational tools for its exploitation. We propose new business models capa-ble of enhancing supply chain performance while at the same time developing mathematical and technical implementation for its effective and efficient use.

Keywords: Integrated optimization; Dynamic lot-sizing; Delivery time window; Location analysis; Distribution

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List of Tables

1.1 Supply chain integrated planning . . . 6

1.2 Single product production-distribution problems . . . 15

1.3 Multi-product production-distribution problems . . . 19

1.4 Numerical experiments and case studies on integrated production-distribution problems . . . 22

2.1 Notations of the model . . . 29

2.2 Total costs for different production scenarios . . . 32

2.3 Percentage of contribution to the total cost per component . . . 33

2.4 Percentage of cost changes with respect to the optimized solutions . . . 35

2.5 Combined effects for the transportation and setup costs . . . 36

3.1 Integrated production-distribution problems . . . 41

3.2 Notation used in the model . . . 45

3.3 Input parameter values. . . 54

3.4 Results from the branch-and-bound algorithm . . . 55

3.5 Heuristics results for r = 0. . . 56

3.9 Average time for the proposed method to obtain its best solution . . . 58

4.1 Input parameter values. . . 70

4.2 DC availability in the fixed network design with r = 0 . . . 72

4.3 Fixed vs. flexible network designs with r = 0 . . . 73

4.4 Value of flexibility from due dates for 3 DCs and fixed network design . . . 74

4.5 Value of flexibility from due dates for 3 DCs and flexible network design . . . . 75

4.6 Cost of fixed and flexible designs for 3 DCs with different due dates. . . 76

4.7 Comparison between the most inflexible and the most flexible scenarios . . . . 77

4.8 Computation time of fixed and flexible network designs . . . 78

5.1 Performance summary for IRP . . . 88

5.2 Comparison of solutions with different objective functions for the IRP . . . 89

5.3 Performance summary for PRP . . . 90

5.4 Comparison of solutions with different objective functions for PRP-Class I . . . 90

5.5 Comparison of solutions with different objective functions for PRP-Class II . . 91

5.6 Comparison of solutions with different objective functions for PRP-Class III . . 92

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5.8 Average inventory KPIs for IRP. . . 93

5.9 Average delivery KPIs for IRP . . . 94

5.10 Average load KPIs for IRP . . . 95

5.11 Average inventory KPIs for PRP . . . 95

5.12 Average delivery KPIs for PRP . . . 96

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List of Figures

2.1 An instance of the dynamic multi-plant lot-sizing and distribution problem with

two plants and three customers . . . 28

2.2 Feasibility of a delivery plan with respect to the maximum lateness allowed . . 31

2.3 An example of production and inventory capacities in high (a) versus low (b)

demand periods . . . 34

3.1 Comparison between time (s) and gap (%) of CPLEX and the proposed

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Acknowledgments

First and foremost, I wish to thank my advisor, Professor Leandro C. Coelho. This work would have not been possible without his support, guidance, and continuous encouragement. The way he cared about my research and his prompt replies to my questions and emails have been just exceptionally awesome. His passion and enthusiasm for applied research had and will always inspire me. Thank you for showing me the light.

I will forever be thankful to my former supervisor and mentor Professor Remy Glardon. I have been extremely lucky to have had his enormous support. In 2011 he welcomed me to his team at École polytechnique fédérale de Lausanne, and he never stopped caring since then and finally, he helped me to start my studies at Laval University. Thanks Remy for caring like family.

I wish to thank my committee members: Jacques Renaud, Yan Cimon, Claudia Archetti, and Raf Jans for their time and support.

I would like to thank administrative and technical staff members at the Faculty of Business Administration, the Ph.D. program committee, and the CIRRELT for their support. I would also thank the professors, my friends, and colleagues from the CIRRELT and the faculty of business administration.

Last but not least, I would like to offer my heartfelt thanks to my friends and family who have been with me throughout this journey. I want to express sincere gratitude to my family for all their love, never-ending patience, and encouragement. I would like to thank my parents who supported me in all my pursuits. Thanks for being the ultimate role models in my life.

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Preface

This thesis presents my work as a Ph.D. student completed during the program of study at the Centre Interuniversitaire de recherche sur les Réseaux d’Entreprise, la Logistique et le Transport (CIRRELT) at the Faculty of Business Administration of Laval University. The thesis consists of four papers; each of which is written in collaboration with other researchers, mainly my director Leandro Callegari Coelho. One of these papers is already published and the other three are currently under revision. In all four papers, I remain the first author and have played the major role of setting up and conducting the research, modeling and implementation of the the problem, analyzing the results, preparing and writing the papers.

The first paper entitled A dynamic multi-plant lot-sizing and distribution problem is written in collaboration with Homero Larrain and Leandro C. Coelho. The paper is accepted by the International Journal of Production Research (IJPR) on February 8, 2016 and published online on March 2, 2016.

The second paper entitled Sequential versus integrated optimization: production, location, inventory control and distribution is written under supervision of my director Leandro C. Coelho.

The third paper entitled Flexible two-echelon location routing is written in collaboration with Claudia Archetti, Leandro C. Coelho, and Maria Grazia Speranza.

The fourth paper entitled Minimizing emissions in integrated distribution problems is written in collaboration with Claudia Archetti and Leandro C. Coelho.

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Introduction

Supply chain is an integrated network of facilities performing several logistics functions of procurement, production, storage, and distribution of products to the market. The goal of a supply chain is to offer the final customer, the right product, at the right time, price, quantity, quality, and location [Christopher and Towill, 2001, Katz et al., 2003]. To attain this goal, a set of decisions and actions are to be made and taken. Thus, a supply chain could be considered as a network of interrelated decisions. Among all supply chain decisions, procurement, location, production, inventory and distribution constitute the essential and fundamental components of planning processes. Traditionally, these decisions were treated independent from one another, mainly by considering a hierarchical approach toward decision making. Therefore, in this approach, all the interactions among different interrelated supply chain functions are overlooked [Cohen and Lee, 1988]. Ignoring the dependencies between supply chain decisions results in higher costs, as any attempt in minimizing cost in one area, mostly results in cost increase in other areas [Adulyasak et al.,2012].

With the competition among companies becoming more intense, the keys to the success of the supply chains are known to be their efficiency and responsiveness level [Manatkar et al.,

2016]. These two have become the new strategies for supply chains; efficiency aims at deliv-ering products at reduced costs, but competitive advantage is gained not only by reducing supply chain costs but also by providing a faster and more flexible service to customers. As companies have realized that dramatic improvements are to occur by exploiting integrated production systems, the linchpin of success in today’s medium and large companies is known to be the supply chain integration [Archetti et al.,2011]. It is not long since it was realized how integration and coordination of supply chain decisions yield competitive and economic advantage [Hein and Almeder, 2016]. The modern world both facilitates and necessitates a more comprehensive and holistic view of supply chains. Coordinating and integrating decisions of the supply chain is a complex task and mainly due to its complexity, they were investi-gated separately [Ekşioğlu et al., 2006]. However, with the improvement of computational ability of modern computers, we are now able to solve problems far larger and more complex

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than previously thought in much less time. From the academic point of view, in the past few decades, the idea of simultaneously considering different functions of the supply chain has attracted growing attention. The new models integrate several functions of supply chains into single models and optimize them. In most industries, transportation and distribution costs are the main contributors to the total cost [Boudia et al., 2007]. Therefore, several supply chain decisions are mainly integrated with distribution planning.

Building upon the insightful literature, this research contributes to the integrated optimization literature by adding distinctive features to the problems and making them more real-world relevant. This thesis first shows the advantages of taking an integrated approach to decision making in complex decision settings, then it explores the idea of flexibility, in terms of delivery to customers and the supply chain network design, and finally it investigates the trade-offs between emission reduction and economic performance objectives in an integrated optimization context.

A number of success stories dealing with the integration of different supply chain planning problems are reported in the literature, e.g.,Pyke and Cohen[1994],Pooley[1994],Erlebacher

and Meller [2000], Brown et al. [2001], Çetinkaya et al.[2009], Baboli et al.[2011], Degbotse

et al. [2013] and Meisel et al. [2013]. This research also supports the positive effect of the

integrated optimization on the supply chain performance [Chandra and Fisher,1994,Coelho

et al.,2014,Acar and Atadeniz,2015,Adulyasak et al.,2015]. Although integrating different

functions into a single model makes it more complex and difficult to solve, it mostly achieves better results in terms of cost saving and improving the service level. Aiming to highlight the values of the integrated approach, in this research, we compare the results obtained from this approach with the ones from the traditional hierarchical decision making approach. We also explore different types of flexibility: obtained from time windows and from the network design.

The classical dynamic lot sizing problem (LSP) mainly considers a finite time horizon, a set of customers, and deals with satisfying the demand of a particular period by delivering the requested products to customers in the same period [Brahimi et al., 2006a, Hwang, 2010]. However, in practice, this assumption mostly does not hold true, as a delivery time window is considered for fulfilling the demand. Lee et al.[2001] introduce the LSP with delivery time windows and today it is recognized as one of the topics with a significant research opportunity

[Claassen et al., 2016]. In this research, we describe, model, and solve the rich integrated

problem, also considering a delivery time window.

In a typical supply chain, a number of plants produce one/several product(s); these are either stored at the plant or shipped to one/several distribution center(s) (DCs) of the next echelon.

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In order to fulfill the demands of customers, these products are then transported to the last echelon (retailers, or final customers). The solution mainly needs to determine 1) where to locate the plants and DCs, 2) the production quantities at plants and inventory allocation at both plants and DCs, 3) assignment of DCs to plants as well as customers to DCs, and 4) the shipment quantities from plants to DCs and from DCs to the final customers. This problem simultaneously addresses several supply chain decisions such as lot sizing, facility location, and distribution. Despite numerous studies on jointly optimization of production and distribution problems, their integration with facility location decisions is not extensively studied. The facility location problem (FLP) has long been considered as a strategic decision [Klose and

Drexl, 2005] and therefore, its integration with other tactical or operational level decisions

has received less attention [Nagy and Salhi, 2007]. However, in the era of shareconomy, renting or leasing facilities has become a current practice. As the location of facilities can periodically change, the FLP could be easily integrated with other operational level decisions. A contribution of this research is to simultaneously optimize facility location, production and/or inventory, and distribution decisions.

Integrated supply chain problems are reducible to problems such as the LSP, FLP, or vehicle routing problem (VRP). Each of these problems are known to be very hard to solve. Most variants of the LSP are proved to be complex and difficult to solve [Jans and Degraeve,2007].

Florian et al. [1980] prove that the single-product capacitated problem is NP-hard, and Maes

et al. [1991] show how finding a feasible production plan for a capacitated production system

with no setup cost is an NP-complete problem. Mostly, small size instances of integrated supply chain optimization problems could be easily solved to optimality using exact methods, but finding a good solution in a reasonable time for large complex real-world integrated prob-lems has been a challenge [Fahimnia et al.,2013]. Throughout this thesis, we first solve each problem with exact methods, and if necessary, we propose approximate methods to accelerate the solution procedure.

The remainder of this thesis is organized as follows. Chapter 1 provides an overview on single stage integrated production and distribution optimization problems. Integration of production and distribution decisions is an important and widely studied area in the integrated supply chain literature. Independently, both production and transportation problems have several well-studied variants, and so does their integration. In that chapter, the existing research is grouped into two broad categories: single versus multi-product models and then their characteristics and applications are elaborated.

In Chapter 2, we investigate a single-product, multi-plant production planning and distri-bution problem for the simultaneous optimization of production, inventory control, demand

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allocation, and distribution decisions. The objective of this rich problem is to satisfy the dynamic demand of customers while minimizing the total cost of production, inventory and distribution. By solving the problem we determine when the production needs to occur, how much has to be produced in each of the plants, how much has to be stored in each of the warehouses, and how much needs to be delivered to each customer in each period. On a large real dataset inspired by a case obtained from an industrial partner we show that the proposed integration is highly effective. Moreover, we study several trade-offs in a detailed sensitivity analysis.

Chapter 3 extends the problem by considering multiple products and a leasing period for DCs. This chapter contributes to the integrated optimization literature by simultaneously addressing location, production, inventory, and distribution problems, and to the production economics literature by comparing and assessing the performance of sequential and integrated solution techniques. We develop an exact method and several heuristics, based on separately solving each part of the problem. In this study, we show the limitations of the exact methods in handling large size integrated optimization problems and the poor performance of sequential approaches. Then, we introduce a hybrid adaptive large neighborhood search (ALNS) heuristic to overcome these limitations. Our results and analysis not only compare solution costs but also highlight the value of an integrated approach.

By a flexible two-echelon location routing problem presented in Chapter 4, we aim to assess the value of flexibility. The chapter deals with an integrated location routing problem in which a supplier delivers a commodity to its customers through a two-echelon supply network. The objective is to minimize the total shipping costs from the central depot/plant to the DCs, the traveling costs from DCs to customers, the locations costs and the penalty costs for the unfulfilled demands. We present a mathematical formulation of the problem together with different classes of valid inequalities. Computational results and business insights are discussed. The results show that the combined effect of the network design and delivery flexibility lead to considerable savings for supply chains.

Research and practice show that taking an integrative approach to supply chain planning en-hance the business performance. Despite the ever increasing attention towards environmental impacts of operational decisions, the research is still limited. Chapter 5 aims to identify the trade-offs between cost and emission reduction potential within an integrated supply chain planning system. To this end, the two well-known problems of inventory routing and produc-tion routing are investigated. By means of several key performance indicators, we shed light on the values of integration when it comes to emission reduction.

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Chapter 1

Literature review

Supply chain is viewed as a network of facilities engaged in procurement of raw material, production and storage of finished products, and their distribution to reach the final customers

[Hugos,2011]. Supply chain planning processes mainly include facility location, procurement,

production, inventory, and distribution decisions [Stadtler, 2005, Christopher, 2016]. The goal of any supply chain is to ensure that customers are provided with the right products or services at minimum cost and time. To date, several definitions for the term supply chain management exist but despite all their differences, generally what they have in common is that supply chains coordinate and integrate interdependent activities and processes within and between companies [Ellram, 1991, Cooper et al., 1997, Carter and Rogers, 2008]. Due to the vital role supply chain planning integration plays in today’s business, it is believed to be the new source of achieving and retaining competitive advantage [Lei et al., 2006, Hein

and Almeder, 2016]. However, despite the abundance of conceptual and empirical studies on

supply chain integration and coordination, e.g.,Stevens [1989],Power [2005],Mustafa Kamal

and Irani [2014], until recently integrated models of the supply chains have been very sparse

on the operations research literature.

Simultaneous optimization of all supply chain planning decisions by integrating them into a single model has been such a complex and difficult task that traditionally each decision was treated separately from the others, or the problem was decomposed to smaller and easier to solve problems. For example, location, lot sizing, and distribution have traditionally been solved independently from one another, e.g., Erlenkotter [1978], ReVelle and Laporte [1996],

Florian et al.[1980],Barany et al.[1984],Maes et al.[1991],Desrochers et al.[1992],Gendreau

et al. [1994] and Taillard et al.[1997]. A sequential hierarchical approach was often taken in

which the solution obtained from one decision level is passed and imposed to the next. In a hierarchical approach, the decisions at each level are taken in isolation and once decisions are

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made in a level, they are considered to be fixed and all other decisions follow on. Since every function tries to optimize its own decisions, this approach often leads to sub-optimal solutions

[Vogel et al., 2017]. Whereas, in integrated paradigm, various functions of the supply chain

are simultaneously taken into consideration and jointly optimized.

In this chapter we aim to provide a comprehensive summary of the well-studied integrated production and distribution problems. The remainder of this chapter is organized as follows. Section 1.1 provides a brief overview on the well-known integrated problems of the supply chain. The integrated production-distribution problem is presented in Section1.2. Section1.3

presents directions for further research and our conclusions are given in Section1.4.

1.1 Well-known integrated problems

Generally, integrated models combine decisions of at most two functions from the supply chains and due to their nature, operational level decisions have been the main targets for integration. To date, a number of review papers have attempted to provide a comprehensive overview of each integrated problem. In what follows, we present the integrated problems and the existing reviews on them. In Table 1.1 we present the well-studied integrated supply chain planning models, adopting from the work of Adulyasak et al. [2012].

Table 1.1: Supply chain integrated planning

Problem Location Production Inventory Routing

Location-Routing Problem (LRP) X X

Location-Inventory Problem (LIP) X X

Lot Sizing Problem (LSP) X X

Inventory-Routing Problem (IRP) X X

Production-Routing Problem (PRP) X X X

Location-routing problem (LRP): includes both facility location planning (FLP) and vehicle routing problem (VRP). Being closely related to the supply chain network design, has long been regarded as a critical strategic issue in the literature [Aikens,1985] dealing with decisions such as establishing a new facility, relocating the existing ones, or any capacity expansion plans

[Melo et al.,2006]. In FLPs, a set of alternative locations are available to serve geographically

dispersed customers and the goal is to select locations such that the cost and/or time of reach-ing the customer is minimized [Melo et al., 2009]. Literature reviews published on the FLP classify the models and algorithms and provide a comprehensive picture for a large variety of studies on FLP (e.g.,Francis et al.[1983],Brandeau and Chiu[1989],Owen and Daskin[1998],

Klose and Drexl[2005],Snyder[2006],Şahin and Süral[2007],Melo et al.[2009],Farahani et al.

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been associated to location decisions; therefore, integrating this problem with other tactical or operational decisions was less prevalent in the integrated optimization literature [Nagy and

Salhi,2007]. However, joint efforts, such as the one between Proctor & Gamble and Walmart,

to manage the distribution flows efficiently and collaboratively have recently become more common [Amiri, 2006], to the extent that the dynamic selection of partners in supply chains is identified as one of the new trends and research opportunities in the supply chain man-agement [Speranza,2018]. Adapting to the reality of the new business environment, location decisions could now enjoy more flexibility and should be revised periodically, and hence, they could easily be combined with other tactical/operational level decisions. Even if considered as a long term decision, the facility location is interrelated with other decisions, in particular with transportation decisions [Drexl and Schneider,2015]. Boventer [1961] recognizes the re-lationship between transportation costs and location rent and introduces the location-routing problems (LRPs) as the combination of facility location and routing decisions. A few papers such as Nagy and Salhi [2007], Prodhon and Prins [2014], and Drexl and Schneider [2015] discuss different variants and extensions of the LRP. In LRP the questions of which facilities should be selected, which customers should be served, and in which order are to be answered

[Drexl and Schneider,2015]. The objective is to minimize the total costs of locating facilities

and distributing the products.

Location inventory problem (LIP): the LIP combines the strategic location decisions with the operational inventory management. The literature deals with the inventory and location problems separately. First the location and number of DCs or warehouses are decided solving facility location problems and then assuming these decisions to be fixed, the optimal inventory replenishment policies are determined [Daskin et al.,2002]. By decomposing the LIP into two separate problems, all the interrelated costs are ignored; this approach becomes questionable specially in dealing with uncertain demands [Shen et al.,2003]. Farahani et al.[2015] provide a review on the models that jointly consider facility location decisions and inventory management problems. In the LIP, the questions of which facilities to be selected and how much inventory to be kept at each facility are to be answered. The objective is to minimize the total costs including locating facilities and inventory holding.

Lot sizing problem (LSP): as an important and challenging problem in production planning, the LSP integrates the production and inventory decisions and deals with the trade-off between production and storage costs [Karimi et al.,2003]. The objective is to minimize the total costs of production, setup, and inventory [Jans and Degraeve, 2007]. Since the seminal paper of

Wagner and Whitin [1958], several studies have investigated the LSP. Florian et al. [1980]

prove that the single-product capacitated problem is NP-hard, and Maes et al. [1991] show that finding a feasible production plan for a capacitated production system with no setup

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cost is an complete problem; even multi-plant, uncapacitated lot sizing problem is NP-complete [Sambasivan and Schmidt, 2002]. Numerous reviews of the literature (e.g., Karimi

et al. [2003], Brahimi et al. [2006b], Jans and Degraeve [2007, 2008], Robinson et al. [2009],

Buschkühl et al. [2010],Glock et al. [2014],Axsäter [2015]) have provided an overview of the

variants, models and formulations, and algorithms of LSPs.

Inventory-routing problem (IRP): as the name indicates, the IRP is the integration of inven-tory management and routing decisions. An indispensable part of many integrated supply chain models entails the delivery/transportation decisions. On one hand, in most industries, transportation cost is the major component of the total logistics cost [Boudia et al., 2007], and on the other hand, the ever-rising transportation costs, and increasing customer sensitiv-ity to lead time have become the salient reasons behind the supply chain literature emphasis on transportation cost reduction and performance increase. The road-based transportation methods mentioned in different existing integrated optimization problems could be classified into two broad categories of direct shipment and routing decisions. A very well-known and well-researched area in distribution and transportation planning is the VRP [Toth and Vigo,

2014]. A number of papers review the variants, models and algorithms of this problem (e.g.,

Laporte[1992],Eksioglu et al.[2009],Laporte[2009],Pillac et al.[2013],Lahyani et al.[2015c],

Koç et al.[2016a],Psaraftis et al.[2016], Ritzinger2016). The problem concerns the design of

vehicle routes to make deliveries to customers in each period. The IRP first appeared on the literature as a variant of the VRP [Coelho et al.,2014]. The reviews on the IRP ofCampbell

et al.[1998],Moin and Salhi[2007],Andersson et al.[2010], andCoelho et al.[2014] provide an

exhaustive overview on its variants, applications, models and formulation, and solution meth-ods. In the IRP, the questions of how much of the inventory needs to be kept at each center, which customers should be served and in which order are to be answered. The objective is to minimize the total of the inventory and transportation costs.

Production-routing problem (PRP): the PRP is an integration of the IRP with production decisions [Coelho et al.,2014] or equivalently, the LSP with the VRP [Adulyasak et al.,2015]. The most recent reviews on the PRP [Adulyasak et al., 2015, Díaz-Madroñero et al., 2015] thoroughly investigate the various solution techniques, formulations, applications and classi-fications of the problem. The PRP answers the questions of how much to be produced in each period, how much of the inventory needs to be kept at each facility, and which customers should be served and in which order. The PRP jointly minimizes the production (setup and variable), inventory, and transportation costs. It belongs to the vast class of integrated production-distribution problems.

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area of supply chain literature, as according to Chen[2004], production and distribution are the most important operational decisions of supply chains. In order to better understand, classify the broad integrated production-distribution literature, and provide directions for future research, in what follows we review several existing research on the topic and discuss the assumptions, main problems, methods, and results. In this work, we also review studies in which the strategic decisions, such as facility location, are simultaneously optimized with short-term and operational level decisions, such as transportation and distribution are addressed.

1.2 Integrated production-distribution problems

Independently, both production and transportation problems have several well-studied vari-ants, and so does their integration. Here, we focus only on integrated approaches. Depending on the variant of the integrated problem, it is known by different names in the literature. In some cases, despite the difference in what they are called, they tackle the same problem.

Chan-dra and Fisher [1994] deal with production scheduling and distribution problem (PSD). The

integration of production and routing is called the production-inventory-distribution-routing problem (PIDRP) in Bard and Nananukul[2009b],Lei et al.[2006] and Bard and Nananukul

[2010], it is also considered as integration of an inventory-routing problem with a produc-tion planning problem and is called integrated producproduc-tion-distribuproduc-tion problem (IPDP) by

Armentano et al. [2011] andBoudia and Prins[2009] or PRP by Absi et al.[2014],Adulyasak

et al. [2012], and Adulyasak et al. [2015]. Karaoğlan and Kesen [2017] study the integrated

production and transportation scheduling problem (PTSP). The lot-sizing problem with pro-duction and transportation (LSPT) is studied in Hwang and Kang [2016], the same problem is called operational integrated production and distribution problem (OIPDP) in Belo-Filho

et al. [2015]. Finally, when location decisions are incorporated into the

production-distribu-tion model, the problem becomes a producproduction-distribu-tion-distribuproduction-distribu-tion system design problem (PDSDP)

[Elhedhli and Goffin,2005].

As of now, a number of reviews on the coordination and integration of production and trans-portation decisions exist. Cohen and Lee [1988] and Sarmiento and Nagi [1999] survey inte-grated production and distribution systems, Mula et al.[2010] review mathematical program-ming models for supply chain production and transport planning, Chen[2010] and Meinecke

and Scholz-Reiter [2014] review integrated production and outbound distribution scheduling

(IPODS), integrated production-distribution planning is reviewed inFahimnia et al. [2013]. In the what follows, we review the literature that present mathematical models to solve single stage integrated optimization problems. Therefore, integrated production-distribution models that schedule the production are out of the scope of this research. With regards to the

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integra-tion of producintegra-tion and distribuintegra-tion, it is present in two distinct streams of research. One deals with integrated facility location and production planning decisions and the other integrates production with distribution decisions. Looking at the cost structure of the integrated facility location and LSP in single echelon, single product/period models, the distinction between these two streams of literature becomes less evident. By putting the common elements of both objective functions aside, i.e., production variable, transportation, and inventory han-dling costs, in both streams a binary decision is present to decide whether or not a product is produced in a plant. This decision is called facility location allocation in FLP, and setup decision in LSP. Therefore, we consider facility location as a characteristic of the model only if a distinct binary decision is defined to indicate whether a facility is operational in a period or to select a/several facility(ies) among a set of available ones. Our criteria for selection of the paper is that both production (either variable or fixed setup) and transportation costs must be present in the objective function. Generally, the common assumptions of most papers deal-ing with integration of production and distribution are that the plants are multi-functional, therefore, all products can be produced in any of the plants; when routing is the delivery method, each customer can be visited at most once per day; a fleet of homogeneous vehicles with limited capacity are considered; the demand cannot be split; no shortage, stockouts or backlogging is allowed; and finally, transfer between sites is not allowed. The cost functions are often linear, however fixed-charge and general concave cost structures are also considered in some studies. In what follows, when economies of scale are present, we call the cost function concave. Unless otherwise specified, these are the assumptions of the problems studied here. We organize our revision around two broad categories of single versus multi-product models, and then categorize them based on the following characteristics:

• the number of echelons (single or multiple); • the number of plants (single or multiple); • the number of periods (single or multiple); • whether production/inventory capacities exist; • whether the demand is deterministic or stochastic;

• whether the production setup cost is considered in the objective function; • whether location decision is addressed in the model.

Variants of production-distribution models with single product are presented in Section 1.2.1

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1.2.1 Single-product production-distribution models

In this section we review integrated production-transportation models for single product prob-lems. To better analyze the variants and characteristics of each problem, we divide them into two categories of models with direct shipment and those with routing. We notice that in production integrated with direct shipment more variants of the production problem are con-sidered, but the joint production and routing literature has been mainly focused on finding faster and more efficient solution algorithms. Therefore, majority of the PRP studies compare their results and performance of the algorithms with the existing methods on the literature.

van Hoesel et al.[2005] present a model to integrate production, inventory and transportation

decisions in a serial multi-echelon supply chain. All cost functions are concave and a produc-tion capacity is present. They model the problem as a capacitated minimum-cost network flow problem and study different transportation and inventory holding cost structures in the integrated problem. In general, their dynamic programming algorithms runs in polynomial time in the number of periods and echelons. Ekşioğlu et al.[2006] also formulate the produc-tion and transportaproduc-tion planning problem as a network flow and propose a primal-dual based heuristic to solve it. In their model, the plants are multi-functional, the production and setup cost vary from one plant to another as well as from one period to the next, and transportation costs are concave. They claim that their problem is a special case of the facility location problem and an extension of the classical lot sizing problem as the facility selection decision is also present in the model. Ahuja et al.[2007] study a multi-period single-sourcing problem in a dynamic environment in which they consider production, inventory and throughput, as well as the perishable products constraints. The single-sourcing suggests that the customer de-mand during the whole planning horizon is fulfilled from the same facility and cannot be split among different facilities. They formulate the problem as a nonlinear assignment problem to link retailers to facilities, taking timing, location and production quantities into consideration. They first propose a greedy heuristic and then a very-large-scale-neighborhood (VLSN) search method to improve the greedy solutions. Hwang[2010] investigates integrated economic LSP with production and transportation. Using stepwise cost for transportation, the model con-siders economies of scale in shipment and consequently production. The number of vehicles is assumed to be unlimited and the production cost is concave. While backlogging is allowed, the results are provided for both cases of with and without backlogging assumptions. Romeijn

et al. [2010] study the integration of facility location and production planning decisions. They

introduce the idea of generalizing LSP by integrating it with facility location decision [Liang

et al., 2015]. The objective function is to minimize the location, production, inventory, and

transportation costs. They study a new approximation method for cases with special produc-tion and inventory cost structures and seasonal demand patterns. Akbalik and Penz [2011]

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combine distribution decisions and LSP with delivery time windows. They aim to compare the just-in-time and time window policies. Under the just-in-time policy, the customer re-ceives a fixed quantity on the due date of the demand but with the time window policy the deliveries are constrained by the time windows and advanced shipment is possible. In their model, costs change over time and they assume a fixed transportation cost per vehicle. A dynamic programming (DP) algorithm is used to solve the problem. They show that the time window policy has a lower cost than the just-in-time one and they also compare the Mixed Integer Linear Programming (MILP) and DP methods, and conclude that even for their large size instances, the DP outperforms the MILP. Sharkey et al. [2011] apply a branch-and-price algorithm for an integration of the location and production planning problem similar to the one studied inRomeijn et al. [2010]. In their model, single sourcing is considered. Their find-ings show the potential benefits of integrating facility location decisions with the production planning. The proposed branch-and-price algorithm works better when the ratio of the num-ber of customers to the numnum-ber of plants is low. Hwang et al. [2016] reduce the complexity of the algorithm proposed in van Hoesel et al. [2005] by utilizing only the information on the aggregated production quantities and considering only those periods in which transportation occurs. A concave transportation cost consisting of a fixed and variable cost of shipment, and a linear holding cost function is assumed. Later Hwang and Kang [2016] propose a stepwise transportation function and consider a production-distribution problem in which backlogging is allowed. They further improve the O(T3_{) algorithm of} _{Hwang et al.} _[₂₀₁₆_{] and reduce its} complexity to O(T2 _{log T) where T is the number of periods.}

Lei et al. [2006] consider integration of production, inventory, and distribution routing

prob-lems and associate a heterogeneous vehicle to each plant. They propose a two-phase heuristic approach to solve the PRP. In the first phase, the routing decisions are relaxed and the prob-lem is solved considering direct shipments, in the second phase, they propose a heuristic for the routing part of the problem. Single product PRP with capacity constraints is studied in

Boudia et al. [2007, 2008] and Boudia and Prins [2009]. In their application, the customers

are served at most once a day based on a first-in-first-out (FIFO) policy by a limited fleet of capacitated vehicles. The customers cannot receive a late service, however, if the capacity permits, their demand can be fulfilled in advance. Although the inventory held at the plant and customer levels is capacitated, the holding cost at the customer is negligible compared to the one at plant. Boudia et al. [2007] suggest a greedy randomized adaptive search procedure (GRASP) to solve the PRP but in order to change production and delivery days for some of the demands the local search is used and to reinforce the combination either a reactive mechanism or a path relinking is added. Boudia et al. [2008] propose two greedy heuristics followed by two local search procedures to solve the problem. The same problem is solved using

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a memetic algorithm with population management (MA|PM) and with dynamic population management in Boudia and Prins [2009]. Their memetic algorithm yields better results than the GRASP, and shows 23% saving in cost compared to the classical hierarchical approach

[Boudia and Prins,2009]. The same problem is addressed in Bard and Nananukul[2009a,b,

2010], in which a single plant serves a set of customers over a multi-period time horizon. The demand is satisfied either from the inventory held at the customer or daily distribution of the product. Two cases are considered for the distribution: to fulfill the demand of the day by vehicle routing or routing is replaced by allocation and aggregated vehicle capacity con-straints replace the routing concon-straints [Bard and Nananukul,2010]. InBard and Nananukul

[2009a], they solve the problem with a reactive tabu search which is followed by a path

re-linking procedure to improve the solution. Compared toBoudia et al.[2007], the results from

Bard and Nananukul [2009a] are slightly better. Bard and Nananukul [2009b] use

branch-and-price algorithm and compare several heuristics for the IRP in the context of PIDRP. To take advantage of the efficiency of a heuristic and accuracy of the branch-and-price, in Bard

and Nananukul [2010], they improve their former method by proposing a hybrid algorithm

combining exact and heuristic methods within the branch-and-price framework. Within 30 minutes of run time, the algorithm is able to find optimal solutions only for instances with up to 10 customers, two periods, and five vehicles. Moreover, the lower bounds they obtain are not strong [Adulyasak et al., 2014]. The problem discussed in Ruokokoski et al. [2010] con-siders a single uncapacitated vehicle. As in Bard and Nananukul [2010], the maximum level (ML) inventory policy is used for the quantities delivered to each retailer [Absi et al., 2014]. They introduce several strong reformulations for the problem, inequalities to strengthen them and a branch-and-cut algorithm to solve them. Their results support the cost saving benefits of the coordinated approach compared to the uncoordinated one. The proposed algorithm can solve instances with up to 80 customers and eight periods, but finds larger instances still challenging. Archetti et al. [2011] compare the ML and order-up to level (OU) inventory policies in the PRP context. The demand is delivered to the customers using an unlimited fleet of capacitated vehicles. Using a branch-and-cut algorithm, they conclude that the ML policy outperforms OU in short time horizons, but with increase in the number of periods, the difference between the costs obtained from these two policies also reduces. However, within two hours of execution, the proposed branch-and-cut approach does not provide optimal solu-tion for all instances. Adulyasak et al. [2012] compare the performance of the adaptive large neighborhood search (ALNS) heuristic against GRASP [Boudia et al.,2007], MA|PM [Boudia

and Prins,2009], reactive tabu search [Bard and Nananukul,2009a], tabu search with path

re-linking [Armentano et al.,2011], and the branch-and-cut approach proposed inArchetti et al.

[2011]. Their proposed heuristic outperforms the former heuristics. Absi et al. [2014] propose a two-phase iterative heuristic approach for PRP with a limited fleet of capacitated vehicles

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and an ML inventory policy. Their decomposition method addresses the lot sizing decisions in the first phase and determines the routing in the second one. The comparisons of this method against the ALNS proposed byAdulyasak et al.[2012], and the other five heuristics compared

inAdulyasak et al.[2012] reveal that while the second phase outperforms all existing methods

using less running time, developing fast heuristics that can yield good results for the lot sizing phase still remains a challenge. Adulyasak et al. [2014] consider both PRP with ML or OU policies. A main difference between their model and that ofArchetti et al.[2011] is that prod-ucts could be delivered to the customers on the same period as the demand happens, and there is no need to wait until the products are replenished in the facility. Using a single core and within two hours of execution, instances with up to three periods and three vehicles, and up to 25 customers are solved to optimality. The PRP with demand uncertainty is addressed for the first time inAdulyasak et al.[2015]. They propose and compare branch-and-cut algorithm with Benders decomposition method to solve the two-stage and multi-stage stochastic PRP.

Solyalı and Süral [2017] use a multi-phase heuristic to solve a single echelon PRP with

pro-duction and inventory capacities. They evaluate the performance of their proposed heuristics on the benchmark instances of Boudia et al. [2007] and Archetti et al.[2011]. Although the multi-phase heuristic finds new best solutions for 65% of instances, for larger instances, the better solution is found at the cost of higher computation time.

Table 1.2 presents the papers that consider only one product in their models. As indicated in Table 1.2, only Adulyasak et al. [2015] consider the demand to be stochastic. Except for

van Hoesel et al. [2005], models address a single plant-retailer echelon. In a few number of

papers, the model does not consider the fixed or setup cost of production but they assume the production cost to be a function of the quantities produced. Exact methods (mostly DP) and metaheuristics are exploited when the direct shipment is the delivery method. Prior to 2010, the common solution approach to tackle the PRP was metaheuristics, however, matheuristics are more common since they proved to be better in terms of efficiency and performance.

1.2.2 Multi-product production-distribution models

In this section we present the integrated production-distribution models with multiple prod-ucts. The number of publications in this category is less than the ones with single product models. Obviously adding multiple products to the model makes it more difficult to solve, therefore, in this section fewer papers consider routing as the shipment method. Here, we first present those studies that consider only one echelon in the model, mostly considering a set of plants and customers. Then, multi-echelon problems are surveyed.

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T able 1.2: Single pro duct production-distribution problems Reference Num b er of Capacit y In v en tory Demand Setup Lo cation Shipmen t Solution meth o d Ec helons Pe rio ds Plan ts Pro du ction In ven tory van Ho esel et al. [ 2005 ] M M S X P,DC,C D DS D ynamic programmin g Ekşioğlu et al. [ 2006 ] S M M P D X DS Primal-dual based heurist ic Ah uja et al. [ 2007 ] S M M X X P S DS Greedy adap tiv e searc h pro cedure/v ery-large-scale-neigh borho od-searc h metho d Hw ang [ 2010 ] S M S P D DS Dynamic programming Romeijn et al. [ 2010 ] S M M P S X DS Greedy algorithm and cost-scaling Akbalik and Penz [ 2011 ] S M M X P,C D X DS Dynamic programming Shark ey et al. [ 2011 ] S M M P D X DS Branc h-and-price Hw ang et al. [ 2016 ] S M S X P, C D DS Dynamic programming Hw ang and Kang [ 2016 ] S M M P D DS Geometric te chnique with re sidual zoning Lei et al. [ 2006 ] S M M X X P,DC D R Decomp osition metho d Boudia et al. [ 2007 ] S M S X X P,C D X R Greedy adaptiv e searc h pro cedure Boudia et al. [ 2008 ] S M S X X P,C D X R Gree dy heuristics and lo cal sea rc h Boudia and Prins [ 2009 ] S M S X X P,C D X R MA|PM Bard and Nanan ukul [ 200 9a ] S M S X X P,C D X R Reactiv e tabu searc h Bard and Nanan ukul [ 200 9b ] S M S X X P,C D X R Branc h and pr ice Ruok ok oski et al. [ 2010 ] S M S P,C D X R Branc h and cut Bard and Nanan ukul [ 201 0 ] S M S X X P, C D X R Branc h and pr ice Arc hetti et al. [ 201 1 ] S M S X P,C D X R Branc h and cut A duly asak et al. [ 2012 ] S M S X X P,C D X R ALNS and MCNF Absi et al. [ 2014 ] S M S X X P,C D X R Tw o-phase iterativ e metho d A duly asak et al. [ 2014 ] S M S X X P,C D X R ALNS and branc h-and-cut A duly asak et al. [ 2015 ] S M S X X P,C S X R Branc h-and-cut and Benders decomp osition Soly alı and Süral [ 2017 ] S M S X X P,C D X R A m ulti-phase heuristic Num b er of ec helons, p erio ds and plan ts: S: Single -M: Multiple Demand: D: Deterministic ; S: Sto chastic In v en tory at: P: Plan t -DC: Dis tr ibution cen ter -C: Customer Shipmen t: DS: Direct shipmen t -R: R outing

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Chandra and Fisher [1994] are among the firsts to compare the hierarchical decision making approach with the integrated one. Their PRP model considers an unlimited number of vehicles split deliveries to the customers, a storage capacity but no inventory holding cost at the plant [Boudia and Prins,2009]. The integrated problem is solved using a local improvement heuristic. They investigate the value of integrating production and routing decisions and show that compared to the sequential approach, PRP yields to 3–20% cost savings. The model presented in Fumero and Vercellis[1999] differs from other PRP studies as partial delivery to customers is allowed, the transportation cost is obtained considering both distances and loads, and a fixed cost per each identical capacitated vehicle and finally, the demand of the customer may be fulfilled in advance. They propose a Lagrangian relaxation approach to solve the problem. Comparing results from the synchronized and the decoupled approach, they show the value of the integrated approach. Armentano et al. [2011] consider a multi-product PRP with a fleet of identical vehicles, and evaluate the performance of the proposed tabu search with path relinking approach exploiting their own generated instances for the multi-product case and the single-product instances generated by Boudia et al. [2007]. On single product instances, their approach outperforms the MA|PM [Boudia and Prins,2009] and reactive tabu search [Bard and Nananukul, 2009a]. They also show that for multiple product instances, tabu search with path relinking always yields better solutions than the tabu search, but on large instances it requires a very high running time. Brahimi and Aouam[2016] are the firsts to consider backordering in the context of PRP. They combine a decomposition relax-and-fix method with the local search heuristic. They compare their approach with the performance of a commercial solver, concluding that for most cases, the hybrid relax-and-fix heuristic outperforms the commercial solver.

The fact that the capacity is extendable, distinguishes the model presented in Jolayemi and

Olorunniwo [2004] from others. In their profit maximization model, any shortfall in demand

can be overcome by extension in the capacity or subcontracting. If the resources are not suf-ficient to satisfy the demand, the model identifies where and how much extension in capacity is required. They introduce a procedure to reduce the size of the zero-one MILP, and using a numerical example, they show that the reduced and full-size models generate exactly the same results. Another paper with a profit maximization objective function is that of Park

[2005]. Plants and retailers are controlled by an OU inventory policy and the model allows stockouts; identical capacitated vehicles are used for direct shipments. A two-phase heuristic is developed: in the first phase the production and distribution plans are identified and in the second phase, the plans are improved by trying to consolidate the deliveries into the full truckloads. This heuristic generates good results only for the small instances. The paper inves-tigates the benefits of the integrated approach compared to the decoupled planning procedure

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concluding that with the integrated approach the profit increases on average by 4.1% and the demand fill rate by 2.1%. The sensitivity analysis reveals that the integrated approach is more advantageous when production capacity, fixed cost per vehicle, and unit stockout costs are high and the vehicle capacity is small. Ekşioğlu et al. [2007] extend the problem studied in Ekşioğlu et al.[2006] by considering multiple rather than single-product integrated production-transportation problem. They apply the Lagrangean decomposition heuristic to solve the problem. The problem investigated by Melo and Wolsey [2012] is similar to that of

Park [2005]. Melo and Wolsey [2012] develop formulations and heuristics that yield solutions

with 10% gap for instances with limited transportation capacity but up to 40% for instances with joint production/storage capacity restrictions. Nezhad et al.[2013] tackle an integration of location, production with setup costs, and distribution decisions. This is one of the few papers in which only one period is considered. In their problem all plants are uncapacitated and single-source. The only fixed cost incurred in the model is the setup cost of producing a certain product in a plant.

The integrated production-distribution problem addressed in De Matta et al. [2015] assumes that each plant uses either direct shipment or a consolidated delivery mode using a third party logistics firm. They use Benders decomposition to solve integrating consolidated deliveries in the production and distribution problem. Liang et al. [2015] extend the model presented in

Romeijn et al. [2010] by allowing backlogging and propose a hybrid column generation and

relax-and-fix method. Th exact approach provides the lower bounds and the decomposition yields the upper bounds of the problem. Comparing their results to the ones from CPLEX, it is superior in obtaining lower and upper bounds and it is not as sensitive as CPLEX to the number of facilities in the problem size. Over a long planning horizon,Pirkul and Jayaraman

[1996] present a Lagrangean relaxation based heuristic to tackle a production-distribution, and facility location-allocation problem. They present a single source model, therefore each customer is served from a single warehouse selected among a limited number of available ones. The number of open plants is also limited. They test the performance of a Lagrangean relaxation based heuristic over randomly generated set of instances. The solution time is between 46 and 76 seconds and the gap ranges between 0.8% to 2.7%. A similar approach is also applied in Barbarosoğlu and Özgür [1999]. They present an integrated model for production and distribution decisions, but propose a decomposition technique to divide the problem into two subproblems. The focus is to find good solutions for each of the decomposed sub problems. As an extension ofPirkul and Jayaraman [1996],Jayaraman and Pirkul [2001] incorporate procurement of the raw material and supply side of the problem into the model. Generating several instances, first they compare the bounds from the Lagrangean approach with the optimal solution obtained from a commercial solver. Then, they apply the method

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to the data obtained from a real case. The gap between the proposed method and the feasible solution ranges between 1.36% and 2.65% and is obtained between 45 and 88 seconds. A production-distribution system design is addressed in Elhedhli and Goffin [2005]. The stable demand of customers is fulfilled from a single DC (single-sourcing), but the system design is reconfigured by opening and closing the DCs. The problem is considered over a very large planning horizon. They integrate Lagrangean relaxation, interior-point methods, and branch-and-bound to solve the complex problem. They obtain better results compared to the classical Lagrangean approach. Also, in the context of supply chain network design, Correia

et al. [2013] consider integration of production/storage facility costs, fixed maintenance cost,

unit operation costs per product family, and unit shipment costs. They use a branch-and-cut algorithm to solve their randomly generated instances.

Hein and Almeder [2016] highlight the benefits of the integrated approach toward decision

making using numerical experiments, but their study differs from the former papers in which they also include the supply side routing to their model, and therefore, combine lot sizing and supply scheduling. They minimize the setup, inventory holding, and transportation costs while ignoring the variable cost of production. The transportation costs are load and distance-based. They consider both just-in-time and keeping inventories at the plants scenarios. Their results show that the potential savings are higher when inventories are not involved.

A summary of the integrated production-distribution models with multiple products is pre-sented in Table1.3.

1.3 Discussions and analysis

Findings from several studies confirm the many benefits of the integrated approach in sup-ply chain decision making and we have also identified a rapidly growing interest in these approaches. A substantial number of papers, especially on PRP, are published recently. How-ever, the literature still poses several challenges need to be further investigated. We summarize them as follows.

Demand uncertainty: only very few studies have considered the stochasticity of the dynamic environments. The majority of studies assume the demand to be known in advance, and plan the production and distributions based on this assumption. A future research opportunity would be to investigate stochastic production-distribution integra-tion.

Effective exact algorithms: integrated lot sizing with distribution problems are mostly solved exploiting decomposition or relaxation techniques. The set of binary

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T able 1.3: Multi-pro duct production-distribution p roble ms Reference Num b er of Capacit y In v e n tory Demand Setup Lo cation Shipmen t Solution metho d Ec helons Perio ds Plan ts Pro duc tion In ven tory Chandra and Fisher [ 1994 ] S M S P,C D X R Lo cal impro vemen t heuristic Fumero and V ercellis [ 1999 ] S M S X P,C D X R Lagrangean relaxation Armen tano et al. [ 201 1 ] S M S X X P,C D X R Tabu searc h wit h path relinking Brahimi and A ouam [ 2016 ] S M S X X P,C D X R Relax-and-fix heuristic Jola yemi and Olor unniw o [ 2004 ] S M M X X C D X DS MILP Park [ 2005 ] S M M X X P,C D X DS Lo cal impro vemen t heuristic Ekşioğlu et al. [ 2007 ] S M M X P D X DS Lagrangean decomp ositi on heuristic Melo and W olsey [ 2012 ] S M S X X C D X DS Hybrid heu ristic Nezhad et al. [ 2013 ] S S M – D X DS Lagrangian relaxation De Matt a et al. [ 2015 ] S/M M M DC D X DS Benders decomp osition and DP Liang et al. [ 2015 ] S M M X C D X X DS Column generati on Pirkul and Ja yaram an [ 1996 ] M S M X X P, DC D X DS Lagrangian relaxation Barbarosoğlu and Özgür [ 1999 ] M M S X P D X DS Lagrangian relaxation Elhedhli and Goffin [ 2005 ] M M M X – D X DS La grangian relaxat ion and branc h-a nd-price Ja yaraman and Pirku l [ 2001 ] M S M X – D X X DS Lagrangian relaxation Correia et al. [ 2013 ] M M M X X P, DC D X X DS Branc h-and-cut Hein and Almeder [ 2016 ] M M S X P D X R Branc h-and-b ound Num b er of ec helons, p erio ds, and plan ts: S: Single -M: Multiple Demand: D: Deterministic -S: Sto chastic In v en tory at: P: Plan t -DC: Dis tr ibution cen ter -C: Customer Shipmen t: DS: Direct shipmen t -R: R outing

Supply chain optimization : location, production, inventory and distribution

Supply chain optimization:

location, production, inventory and distribution

Supply chain optimization:

location, production, inventory and distribution

Résumé

Abstract

Contents

List of Tables

List of Figures

Acknowledgments

Preface

Introduction

Chapter 1

Literature review

1.1

Well-known integrated problems

1.2

Integrated production-distribution problems

1.3

Discussions and analysis