Robust optimization model for stochastic logistic problems

The main difficulty of a logistic management problem is in the face of uncertainty about the future. Since many logistic models encounter uncertainty and noisy data in which variables or parameters have the probability of occurrence, a highly promising technique of solving stochastic optimization problems is the robust programming proposed by Mulvey et al. and Mulvey and Ruszczynski. However, heavy computational burden has prevented wider applications in practice. In this study, we reformulate a stochastic management problem as a highly efficient robust optimization model capable of generating solutions that are progressively less sensitive to the data in the scenario set. The method proposed herein to transform a robust model into a linear program only requires adding n+m variables (where n and m are the number of scenarios and total control constraints, respectively). Whereas, the current robust programming methods proposed by Mulvey et al., Mulvey and Ruszczynski and Bai et al. require adding 2n+2m. Two logistic examples, logistic management problems involving a wine company and an airline company, demonstrate the computational efficiency of the proposed model.