We study a location-inventory problem in a three level supply chain network under uncertainty, which leads to risk. The (r,Q) inventory control policy is applied for this problem. Besides, uncertainty exists in different parameters such as procurement, transportation costs, supply, demand and the capacity of different facilities (due to disaster, man-made events and etc). We present a robust optimization model, which concurrently specifies: locations of distribution centers to be opened, inventory control parameters (r,Q), and allocation of supply chain components. The model is formulated as a multi-objective mixed-integer nonlinear programming in order to minimize the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. Moreover, we develop an effective solution approach on the basis of multi-objective particle swarm optimization for solving the proposed model. Eventually, computational results of different examples of the problem and sensitivity analysis are exhibited to show the model and algorithm's feasibility and efficiency.
This paper presents a multi-objective location problem in a three level supply chain network under uncertain environment considering inventory decisions. The proposed model of this paper considers uncertainty for different parameters including procurement, transportation costs, supply, demand and the capacity of various facilities. The proposed model presents a robust optimization model, which specifies locations of distribution centers to be opened, inventory control parameters (r, Q), and allocation of supply chain components, concurrently. The resulted mixed-integer nonlinear programming minimizes the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. The model also minimizes the variability of the total cost of relief chain and minimizes the financial risk or the probability of not meeting a certain budget. We use the ε-constraint method, which is a multi-objective technique with implicit trade-off information given, to solve the problem and using a couple of numerical instances, we examine the performance of the proposed approach.
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