Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 473172, 13 pages

http://dx.doi.org/10.1155/2015/473172

## Integrated Location-Production-Distribution Planning in a Multiproducts Supply Chain Network Design Model

^{1}Department of Industrial Management, National Taiwan University of Science and Technology, No. 43, Section 4, Keelung Road, Taipei 10607, Taiwan^{2}Industrial and Manufacturing Engineering, Asian Institute of Technology, 58 Moo 9, Paholyothin Highway Klong Luang, Pathumthani 12120, Thailand

Received 31 October 2014; Revised 7 February 2015; Accepted 23 February 2015

Academic Editor: Xuefeng Chen

Copyright © 2015 Vincent F. Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes integrated location, production, and distribution planning for the supply chain network design which focuses on selecting the appropriate locations to build a new plant and distribution center while deciding the production and distribution of the product. We examine a multiechelon supply chain that includes suppliers, plants, and distribution centers and develop a mathematical model that aims at minimizing the total cost of the supply chain. In particular, the mathematical model considers the decision of how many plants and distribution centers to open and where to open them, as well as the allocation in each echelon. The LINGO software is used to solve the model for some problem cases. The study conducts various numerical experiments to illustrate the applicability of the developed model. Results show that, in small and medium size of problem, the optimal solution can be found using this solver. Sensitivity analysis is also conducted and shows that customer demand parameter has the greatest impact on the optimal solution.

#### 1. Introduction

A supply chain is a network that consists of a set of geographical facilities (suppliers, plants, and warehouses or distribution center). Through those facilities, there is material flow from supplier, plant, warehouse, and end in the customer. It aims at bringing the right amount of the right product to the right place at the right time [1]. Moreover, a supply chain network design is a strategic decision that has high risk and long-term impact in the supply chain system. The impact of efficiency supply chain has become more important on the business competitiveness [2]. The topic has triggered both researchers and practitioners to pay more attention to the supply chain network design. Many studies have been conducted to help the practitioner in making the best decision on a supply chain network. Indeed, determining the best supply chain network is a challenge, starting with problem identification, problem formulation, and its final solution and decision.

Today’s competition among companies and market’s globalization have resulted in firms developing a supply chain that can respond quickly to customers’ need. In the current business environment, a company has to reduce costs while improving its customer service level to remain competitive [3], which also helps maintain profit margins. In order to achieve these goals, a company should appropriately select the location of the factory and the distribution center [4–6]. According to Altiparmak et al. [7], an optimal, efficient, and effective supply chain platform is provided by supply chain network (SCN) design, which also helps to improve supply chain performance. Moreover, Ballou [8] noted that the SCN design goal is to maximize the financial ratio, which is relevant to the objective of gaining the maximum return of investment at the minimum cost.

Supply chain management is divided into two levels: strategic and operational. The strategic level primarily is about the cost-effective location of facilities (plants and distribution centers), the flow of products throughout the entire supply chain system, and the assignment in each echelon [9–12]. The operational level is about the safety stock of each product in each facility, the replenishment size, frequency, transportation, and lead time, and the customer service level. According to Beamon [13], determining an effective supply chain is an important component in supply chain design. In addition, the decisions regarding in which facilities the product should be made and how to serve customers are very critical [14].

This paper provides a system optimization perspective in strategic planning for a supply chain network design that allows simultaneously determining the best location of facilities, raw material flow, and product flow on various echelons. Previous research on strategic planning for supply chain starts by considering the basic problems that have several characteristic, namely, single-period, single-product, single-echelon, and deterministic [15–25]. However, this is not sufficient to cope with the realistic problem. Therefore, many extensions to the basic problem are needed to make the problem more realistic. In this case, our paper considers multiperiod, multiproduct, and multiechelon which are still in deterministic situation to make the basic strategic planning problem more reasonable. A supply chain network design model helps managers conduct strategic planning for their company by selecting the best facility location that minimizes the total cost of the supply chain. The proposed multiproduct supply chain network design model herein helps in choosing the appropriate location of a new plant and distribution center as well as the distribution of the product and raw materials when the demand varies during the different time period. Moreover, multiechelon which represents the multitype of facility is the crucial aspect to be considered in strategic planning.

The paper is organized as follows. Section 2 presents previous research to find the gap between this study and earlier related research. Section 3 describes the problem definition and the proposed mathematical model. Section 4 contains the numerical experiments for the small and medium cases. Section 5 offers a sensitivity analysis result of the proposed model. Finally, Section 6 consists of the conclusion and suggestions for future research.

#### 2. Literature Review

Several research integrated supply chain network designs have been developed to help practitioners solve their supply chain planning. Syarif et al. [26] studied a multiechelon, single-product logistic chain network model and proposed a novel technique as the solution method, called the spanning tree-based genetic algorithm (st-GA). The model is formulated by using a mixed integer liner programming (MILP) model. Their model only considers a single-product. To demonstrate the effectiveness and efficiency of their proposed method, it is compared to the traditional matrix-based genetic algorithm (m-GA). The experiment result shows that the proposed method presents a better solution almost all time and also performs better in computational time and memory for computation.

Jakeman et al. [27] considered the strategic and operational planning level decision in their research by developing a static model for a multiechelon, multiproduct supply chain network design. They examined the single source distribution system. For their solution, they used Lagrangian relaxation and a heuristic algorithm that utilizes the Lagrangian solution. The result of their computation shows that the solution method is both efficient and effective.

Shen [20] proposed a supply chain network design model with profit maximization as the objective function, but it considers only a single-product. In addition, the company may lose the customer if the product’s price is higher than the customer reserve price. Altiparmak et al. [28] studied a single-product, multiechelon, and multiobjective SCN design. They set up a solution procedure based on the genetic algorithm (GA) to find the optimal solution to their problem. The multiobjective optimization problem consists of many optimal solutions, called Pareto-optimal solutions. The problem is formulated as a multiobjective mixed integer nonlinear programming model. The objectives are to minimize total cost, maximize customer service, and maximize utilization of the distribution centers (DCs).

Altiparmak et al. [7] presented a solution procedure for a multiproduct supply chain network (SCN) design based on the steady-state genetic algorithm (ssGA) with a new encoding structure. They considered a single source, multiproduct, and multiechelon supply chain network design in which the number of customers and their demands are assumed to be known. The problem, which is the NP-hard problem, is provided in mixed integer programming formulation. In order to investigate the effectiveness of the ssGA, three other heuristic approaches are also used: Lagrangian heuristic (LH), hybrid genetic algorithm (hGA), and simulated annealing. The experiment’s results show that ssGA has a better solution than the other heuristic approaches used. Ying-Hua [29] adopts the model developed by Altiparmak et al. [7], which considers a single source, multiproduct, and multiechelon supply chain network design, but the model only has multisources instead of a single source. Additionally, the plants and DCs that are open are known. To verify the efficiency of his proposed method, he compared it to other algorithms, such as mathematical programming, the simple genetic algorithm, the coevolutionary genetic algorithm, and the constraint-satisfaction genetic algorithm. The experimental result in Taiwan’s textile industry shows that the proposed method of Ying-Hua [29] performs better than other researchers’ methods.

Bhutta et al. [30] developed an integrated location, production, distribution, and investment mixed integer linear programming (MILP) model in a two-echelon, multiproduct, multiperiod, and flexible facility capacitated with maximum profit as the objective function. Cóccola et al. [31] set up an integrated production and distribution MILP model in a multiechelon, multiproduct, and single-period setting with minimum total cost as the objective function. They conducted an empirical numerical experiment on six European countries. Fahimnia et al. [32] presented an integrated production and distribution planning MILP model for a two-echelon SC that considers several real world variables and constraints. They used GA to optimize the model and solved the medium-size case problem in their numerical experiment. In addition, Bashiri et al. [33] and Badri et al. [34] developed a multiple-echelon, multiple-commodity mathematical model for strategic and tactical planning. The model is developed as a MILP model in four echelons, but they did not consider satisfying the demand constraint.

Many papers have developed a supply chain network design through a mixed integer programming (MIP) model [35, 36]. However, in fact, the quantity of the commodity is usually an integer. Our paper considers location, production, and distribution planning in the supply chain network design problem with multiechelon, multiproduct, and multiperiod characteristics in which the proposed model is pure integer linear programming (PILP) model, having four echelons, multiproduct, and multiperiod demand and satisfying a demand constraint. Consideration of using PILP is intended for providing quality guarantees of optimality [37]. Moreover, its application can be used for low volume discrete manufacturing company of large equipment. In terms of multiplicity, our paper considers the most complex model in the area of integrated production and distribution planning.

#### 3. Problem Definition and Model Formulation

Development of an efficient and effective supply chain is very critical to achieving good performance. Therefore, in-depth analysis is needed when opening a new plant and new distribution center in the appropriate location. Aside from that, multiple products instead of a single-product need to be considered in the problem of supply chain network design and taking into account that the integer quantity in the supply chain network design is more applicable. To deal with this problem, this paper develops a pure integer linear programming (PILP) model that focuses on determining the locations of the plants and distribution centers, as well as the number of those facilities, so that customer needs are satisfied at a minimum total cost during the planning horizon.

This research focuses on the supply chain design problem with the following characteristics.(1)The distribution network under consideration is a multiechelon and multiproduct supply chain network.(2)Demand in each time period (yearly) is deterministic and known.(3)The plant or DC does not need to be opened at the beginning of the planning horizon, and when one is opened, it will not be closed.(4)Customers can receive the product from multiple DCs.

This research develops a mathematical model that helps to determine the number and locations of plants and distribution centers in a supply network and the assignment-related demand allocation in each echelon. Figure 1 depicts the system considered in this research. According to Jayaraman and Pirkul [38], the key components of supply chain modeling that should be considered by the model builder are supply chain drivers, supply chain constraints, and supply chain decision variables of the model. Supply chain drivers represent the goal setting of the model, supply chain constraints represent the limitations on the range of decision alternatives, and supply chain decision variables are the components that set limits on the range of decision outcomes.