Technology Systems Department, East Carolina University, Greenville, NC 27858-4353, USA
Department of Industrial Engineering, University of Windsor, Windsor, ON N9B 3P4 Canada
We propose a mixed integer program (MIP) based product distribution planning model for optimizing the transportation and distribution cost of a supply chain. The model takes into account production/procurement centers (PCs) and plans product delivery to customers either directly from the PCs, or through distribution centers (DCs) considering the available distribution modes. To cover the customer requirements at diverse geographic regions, the model selects optimum regions for DCs, and determines the capacities and the number of DCs to be used in each region to achieve optimum cost. Within the possible distribution modes, the model explores options of using distribution contractors (e.g., the U.S. post office; FedEx, UPS, etc.). A numerical example illustrates the applicability of the model.
Keywords: distribution planning, production/procurement centers, MIP modeling, distribution modes, regional distribution centers, supply chains.
Given the current internet-based business operations, ensuring timely receipt of the products ordered by a customer is an essential requirement for a SC to be competitive in the market. This timely receipt may be considered by the businesses as a performance metric for making service differentiation. This is because there is little difference in terms of the availability of product variety, quality, price, and product presentation among the e-market based businesses. E-market based supply chains (SCs) are similar to two phase retail network SCs as described in Jayaraman and Ross (2003) where the cost of product delivery may be considered to be a differentiating factor in the overall cost structure of the SC, and where the customer satisfaction parameters are highly dependent on the coordination of the customer demand and effective distribution planning. With the help of modern SC management software, scheduling the delivery of customer orders and planning for product realization/procurement may be performed very efficiently. However, the choice of the regions where the distribution centers (DCs) are to be located and the possible distribution modes to deliver the products according to the orders is still crucial (Lasserre, 2004). Considering that customer satisfaction is the main determinant for the overall business performance, a SC decides whether a product should be: a) sent directly to the customer by courier services; b) accumulated for a number of orders and then transported to regional DCs from where it will be sent to the customer, or to suitable customer pickup centers (markets); c) sent to the customer following both a) and b) based on the customer preferences. Each option is to be considered based on the number of regions, the number of DCs in a region, the size of DCs, the location of customer pick up points (or markets); transportation costs; distances from PCs to DCs and from DCs to customer regions; market demand; and the comparison of costs for courier and other distribution modes. All these factors should be taken into account to ensure the overall SC performance improvement and the desired customer satisfaction. Based on the above discussion, we propose an approach to the problem which incorporates the desired business performance objectives and the various operational factors in a mathematical model. The paper proposes a mixed integer programming (MIP) model that includes all the factors discussed above in order to decide on the number of regions, the number and capacity of the DCs, the choice of the suitable distribution options (SC’s own distributions and courier services), to achieve the business objectives at the optimum cost.
The remainder of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3 includes the problem statement, notations, and the formulation of the mathematical model. Section 4 illustrates a numerical example to show the applicability of the model, and discusses the results. Some concluding remarks are presented in Section 5.
Figure 1 displays the schematic diagram of the supply chain under consideration. We assume that a set of products i (iϵI) is realized by a supply chain (SC) at a set of production or procurement centers PCj (jϵJ). There is a random demand Dim for product i in a set of markets m (mϵM) in diverse geographical regions. To ensure product supply to market, the SC plans a set of distribution centers DCk (kϵK) in a set of possible marketing regions l (lϵL). The SC has contractual arrangement with several transportation and distribution contractors who deliver the products from PCs to DCs and from DCs to customers (markets). This contractual arrangement includes per-unit rates for transportation and distribution of products based on the timely delivery of a load by the contractor, as well as the distances travelled. To deliver the products directly to market places from the PCs, the SC has the option of utilizing courier services (e.g., US postal service, UPS, FedEx, etc.) by paying the per-unit delivery charges based on the same conditions of timely delivery and distances. The demand for product i in market m, Dim, is assumed to be normally distributed. The objective of the SC is to decide optimum capacity, region, number of DCs, and allocation of DCs to markets at an optimum cost. The objective of SC also includes selection of optimum distribution mode for distributing product to market.
We assume a SC that has 3 PCs where it receives orders for its 15 products from customers in 25 markets (or customer centers) located in five 5 regions. The SC has the option of opening as many as 8 DCs in the 5 regions with the required capacities to cover all the markets. The model requires a great deal of input data, and in turn generates a great deal of information. However, in this section, the data are only partially presented; we concentrate mainly on the model outcomes that are interesting and related to the objectives of the study. Also, we only present the input information that is needed to analyze the model outputs. The input data are randomly generated based on practical data range values. The model was solved using the commercial solver LINGO 14 on a standard PC. It involved a total of 23,142 variables, 1,238 integer variables, 4,108 constraints, and needed from one hour to 1.5 hours to reach the global optimum solution depending on the specific situation under consideration.
The present research proposes an efficient business planning approach for two-echelon SCs to address changes in product demand, market size, and transportation and distribution requirements. The model includes flexibility consideration in terms of deciding the regions where the DCs will be located, the number and sizes of DCs to address customer density, and their requirements effectively. The research provides managerial insights to utilize procurement centers, selection of distribution modes, and the regions where the DCs are allocation based on specific business characteristics.
Dr. Kanchan Das is an Associate Professor in the Technology Systems Department of East Carolina University, North Carolina, USA. He received his PhD in Industrial Engineering from the University of Windsor, Ontario, Canada. His research interests include mathematical modeling of cellular and flexible manufacturing systems, reliability consideration in the design of cellular manufacturing systems, design and planning of supply chain management. He also conducts research on humanitarian logistics planning. His current research foci include sustainability considerations, risk management, and resiliency planning in supply chain design and management. He is a member of INFORMS and Institute of Industrial Engineers.
Dr. Reza Lashkari is Professor (Emeritus) of Industrial Engineering at the University of Windsor, Ontario, Canada. He received his MSc and PhD in Industrial Engineering from Kansas State University, USA, and B.Sc. in Electrical Engineering from the University of Tehran, Iran. His research interests include modelling and analysis of supply chain networks, modelling of cellular manufacturing systems, and reliability engineering, and more recently, modelling the logistics systems for humanitarian disaster relief. Dr. Lashkari is on the editorial board of Production and Inventory Management Journal and Operations and Supply Chain Management: An International Journal, and is a registered Professional Engineer in Ontario.