Incorporating location, routing, and inventory decisions in a bi-objective supply chain design problem with risk-pooling

Reza Tavakkoli-Moghaddam,Fateme Forouzanfar,Sadoullah Ebrahimnejad

doi:10.1186/2251-712x-9-19

Reza Tavakkoli-Moghaddam, Fateme Forouzanfar + Show 1 more

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This paper considers a single-sourcing network design problem for a three-level supply chain. For the first time, a novel mathematical model is presented considering risk-pooling, the inventory existence at distribution centers (DCs) under demand uncertainty, the existence of several alternatives to transport the product between facilities, and routing of vehicles from distribution centers to customer in a stochastic supply chain system, simultaneously. This problem is formulated as a bi-objective stochastic mixed-integer nonlinear programming model. The aim of this model is to determine the number of located distribution centers, their locations, and capacity levels, and allocating customers to distribution centers and distribution centers to suppliers. It also determines the inventory control decisions on the amount of ordered products and the amount of safety stocks at each opened DC, selecting a type of vehicle for transportation. Moreover, it determines routing decisions, such as determination of vehicles' routes starting from an opened distribution center to serve its allocated customers and returning to that distribution center. All are done in a way that the total system cost and the total transportation time are minimized. The Lingo software is used to solve the presented model. The computational results are illustrated in this paper.

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Nowadays, rapid economic changes and competitive pressure in the global market make companies pay more attention on supply chain topics
Indices (a) I, set of plants indexed by i (b) J, set of candidate distribution centers (DCs) locations indexed by j (c) K, set of customer demand zones indexed by k (d) Nj, set of capacity levels available to DCj (j ∈ J) (e) Ωjl2, set of all feasible routes using a vehicle of type l2 from DCj (j ∈ J) (f ) LPij, set of vehicles l1 between nodes i and j (g) LWjk, set of vehicles l2 between nodes j and k
Decision variables (a) Unj, 1 if distribution center j is opened with capacity level n, and 0 otherwise (b) Aijl1, binary variable equal to 1 if vehicle l1 connecting plant i and DCj is used, and equal to 0 otherwise (c) Bjk l2, binary variable equal to 1 if vehicle l2 connecting DCj and customer k is used, and equal to 0 otherwise (d) Xr, 1 if and only if route r is selected, and 0 otherwise (e) Xijl1, quantity transported from plant i to DCj using vehicle l1

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Introduction

Rapid economic changes and competitive pressure in the global market make companies pay more attention on supply chain topics. In this paper, we present a multi-objective model to concurrently optimize location, allocation, capacity, inventory, selection of vehicles, and routing decisions with risk-pooling in a stochastic supply chain system for the first time.

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