An Efficient Approach for Solving Integrated Production and Distribution Planning Problems: Cost vs. Energy

Introduction

Presently, in the economic context, the relationship between the customer and the supplier has strongly progressed, establishing the need of products and services customization, minimizing the delivery delays, delivery channels multiplication, and satisfaction rates. This led industrial companies to search new methods to improve their performances and answer to the greater degree for customers’ expectations. Facing these goals, those companies need to set a new planning all along the supply chain network to optimize their processes.

Supply chain management is a huge field that aims to better organize the companies’ operations throughout the chain (from the initial suppliers until the distribution of the final product to the final customers) where there are so many issues to deal with. More recently, the focus on the integrated supply chain has become bigger. In fact, its benefits have been proven through the literature, optimizing many activities in a single problem, where its results are better than those of the optimization of each activity independently. For that reason, the operational research community pays more attention and gives more importance to this kind of integrated problems.

The Production Routing Problem (PRP), addressed in this paper, makes part of the above mentioned integration problems. The aim, in such a problem, is to simultaneously optimize the production decision, the inventory, and the distribution. The PRP is a NP-hard problem that combines two famous classic problems: the Lot-Sizing Problem (LSP) and the Vehicle Routing Problem (VRP), which was presented by Adulyasak et al. (2015), and both of them have been widely studied. The LSP is the problem of determining the optimal production schedule with the optimal decisions of the amounts to produce and to store according to the demands of customers, while the VRP is the problem of determining the vehicle optimal routes either in a term of cost or of distance.

The PRP may arise within a supply chain that is composed of a manufacturing factory that has the role of producing goods and delivering them to a set of customers or warehouses. According to literature, the PRP has the target of finding the optimal production and distribution schedule in a multi-period planning horizon in a way that minimizes the whole system costs.

Most of the papers dealing with the PRP consider only the total costs minimization (setup, production, inventory and transportation costs) while energy, which is a very important aspect, has not yet been considered. To this fact, and through this work, we propose to include the concept of energy into the PRP definition, and we make call, in our study, to a multi-objective method. To deal with such a problem, we provide a MILP approach that considers both classical and energy-minimizing PRP versions.

Nowadays, energy consumption has a strong relationship with the worldwide economic development, and because of the limited natural resources, energy has become a critical factor that affects the sustainable development of the industrial and transportation sector. We analyze, in this paper, the relationship between the cost and the power in the integrated Production-Routing Problem that may be important for production and distribution companies in order to optimally manage their organizations. This paper contributes to a better understanding of the conflict between the cost and the power consumption, as well as the impact of the power notion on the whole system decisions.

In the rest of this paper, a review of some relevant works from the literature is firstly presented in section 2 with an emphasis on the proposed resolution approaches for the PRP. In section 3, several tabs will be opened. We begin with a description of our problem and strengthen this description by an illustrative example of the classical PRP. Subsequently, we describe the solution procedure followed by a mathematical formulation of the PRP. The mathematical formulation takes into account, respectively, the cost minimization, the energy consumption minimization, and finally the multi-objective version using a LP-metric method. Section 4 addresses the efficiency of our approach by presenting some experimental instances. Computational results are presented in section 5 then discussed in section 6. Finally, section 7 outlines our approach limitations and opens the door to the perspectives of our study.