A Mathematical Optimization Approach to Supply Chain Disruptions Management Considering Disruptions to Suppliers and Distribution Centers


Author

Syed Mithun Ali
Department of Architecture, Civil Engineering and Industrial Management Engineering, Nagoya Institute of Technology, Japan

Koichi Nakade
Department of Architecture, Civil Engineering and Industrial Management Engineering, Nagoya Institute of Technology, Japan


Content

We develop an analytical framework of a multiproduct supply chain system composed of multiple suppliers, multiple distribution centers and multiple customers considering disruptions risk. Unlike traditional single sourcing strategy which is mostly discussed in supply chain literature, we apply multi-sourcing strategy in both procurement and distribution of commodities. The model thus developed determines the location of distribution centers from a set of potential location, shipment decisions from multiple suppliers to multiple distribution centers and shipment decisions from multiple distribution centers to multiple customers. Moreover, the model evaluates potential amount of products shortages in the event of disruptions. In our work, we consider disruptions at candidate locations for distribution centers and to the suppliers. The analytical framework is formulated as a mixed integer programming (MIP) model which minimizes the sum of investment cost, the transportation cost and the expected shortage cost. We consider several numerical instances to examine the benefit and practicability of the proposed model. Finally, we compare the results of the risk concern optimization framework to the basic optimization framework. From the results, it is expected that risk concern model would outperform the basic model in the case of disruptions.

Keywords: distribution centers disruptions, multi-echelon supply chain, supply chain disruptions, supply disruptions

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In recent times, supply chain disruptions have gained increased attention from researchers and practitioners in the competitive business domains. Any events or collection of events that prevent a supply chain network from its regular operations might be defined as disruptions. Whatever might be the nature and magnitude of a disruption, it produces undesirable effects. For example, it might stop shop floors/distribution centers/warehouses from their day to day operations. In addition, it might stop flow of goods from one point to another in a network. Moreover, the on-hand raw material or finished products might be damaged due to disruptions. Therefore, disruptions hamper the entire plan of an organization thereby causing financial and reputational losses (Paul et al., 2014). Furthermore, it is advocated that designing a proper supply chain network is extremely important in order to facilitate overall business operations of an organization successfully (Chatzipanagioti at al., 2011). However, a well-designed supply chain might not perform up to its standard because of the presence of uncertainty (Wang & Abareshi, 2014) and risks in the chain. Supply chain risks appear in a diversified nature on the different parts of a chain. Of all the various types of risks discussed in supply chain literature (Chopra & Sodhi, 2004; Heckmann et al., 2015; Ma et al., 2010; Tang, 2006; Vilko & Ritala, 2014), supply chain disruption risk is one of them. The interesting concept of disruptions management is firstly articulated by Clausen et al. (2001). They successfully apply the idea to airlines industry to resolve airline flight and crew scheduling problems. Next, the concept of disruption management appears for a wider range of applications such as production planning (Yang et al., 2005), machine scheduling (Qi et al., 2006), project scheduling (Zhu et al., 2005) and supply chain management (Qi et al., 2004).

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This paper involves formulation of an optimization framework of a multi-product, multi-echelon supply chain subject to supply and storage facility disruptions. The supply chain consists of multiple suppliers, one or more distribution centers (DCs), and multiple customers as shown in Figure 1. A family of products (? ∈ ?) is outsourced from multiple suppliers ( ? ∈ ? ) and then shipped to the distribution centers ( ? ∈ ? ). Afterwards, the received products are shipped from the distribution centers to the customers (? ∈ ? ). Our problems involve selecting DCs among a set of candidate locations, the number of DCs to be selected and establishing distribution strategy while considering disruptions at the location of distribution centers (DCs) and to the suppliers. For the sake of simplicity of analysis, two assumptions are made herein. First, it is assumed that each and every distribution centers can receive products from each of the suppliers. Second, each customer receives products from each of the distribution centers. Therefore, our strategy is a multi-multi allocation (MMA) strategy in both procurement and distribution of the products. The objective of our work is to minimize the sum of investment cost, the transportation cost and the expected shortage cost in the event of disruptions. We further assume that the supplies from the suppliers and from the DCs are partially disrupted while disruptions happen. In addition, it is pointed out that while disruptions happen to the suppliers, the products received to the distribution centers in the subsequent time periods would be lower than the regular flow amount. In the time period when the system is recovered from disruptions, the suppliers start to supply regular flow amount. Further, while suppliers and DCs are disrupted, the system cannot meet all the demand of the customers. In this case, the system might incur shortage cost for unsatisfied demand. This cost might be a lost sales cost or the cost of purchasing the products from a local supplier during disruptions. It is noted here that we are not interested to explore the cases of complete failure of suppliers and/or facilities that might turn out a supply chain to be out of service partially or totally thus imposing a threat on organizational existence.

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In the 21st century, the key to business success and business continuity would rely on effective response and recovery from supply chain disruptions. Increasingly, considering and managing disruptions risk has become one of the important concerns in modern business paradigm over traditional philosophies. This paper addresses the issues of formulating an analytical framework of a multi-commodity multi-stage supply chain considering disruptions risk at the location of distribution centers (DCs) and suppliers. We formulate a mixed integer programming (MIP) model and solve by GAMS/CPLEX software. Decisions such as number and location of distribution centers, distribution strategies from suppliers to distribution centers (DCs) and from distribution centers (DCs) to customers and amount of shortages due to potential disruptions are considered. Unlike traditional supply chain literatures, we allow multiple sourcing strategy in both procurement and distribution decisions. This philosophy adds flexibility to deal with disruptions in a supply chain.

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About Author

Syed Mithun Ali is a graduate student in the Department of Architecture, Civil Engineering and Industrial Management Engineering in Nagoya Institute of Technology, Nagoya, Japan. Previously he served as an Assistant Professor in the Department of Industrial and Production Engineering (IPE) in Bangladesh University of Engineering and Technology (BUET), Bangladesh. His research appears in International Journal of Production Research, Management Science Letters, International Journal of Operations and Quantitative Management, Innovations and Supply Chain Management etc. His research interest includes supply chain disruptions management and application of artificial intelligence in manufacturing /service planning and decision making.

Koichi Nakade is from Japan. This author is a member of the Operations Research Society of Japan. The author has achieved both his Bachelor of Science and Master of Science in Engineering from Kyoto University, Kyoto, Japan in 1986 and 1988 respectively. He received a PhD from Nagoya Institute of Technology, Nagoya, Japan. His research is focused in the area of Operations Research. Currently, he is a Professor in the Department of Architecture, Civil Engineering and Industrial Management Engineering at Nagoya Institute of Technology, Japan. His research appears in European Journal of Operational Research, Computers and Industrial Engineering, International Journal of Productions Economics, etc. His research interest covers the Analysis of Stochastic Models as Queues, Markov Processes, Game Theory, and Inventory Models and their Applications to Production Systems and Supply chain.