A supply chain network design model for deteriorating items

We consider a supply chain network design problem for deteriorating items, involving a single supplier, some potential distribution centers and multiple retailers. This problem is to determine how many distribution centers to set up, where to locate them, how to serve the retailers using these distribution centers, and to determine the optimal inventory policies for the whole supply chain network. The goal is to minimize the total deterioration, inventory, transportation and facilities location cost. We formulate this problem as a nonlinear mix-integer programming model. This model is a NP-Hard problem, so we present a Lagrangian relaxation solution algorithm and a Genetic algorithm to solve our model respectively. Finally numerical examples are given to illustrate the application of these two algorithms, and our computational results show that Lagrangian relaxation algorithm is more efficient for our problem.