Robust Multi-period Network Flows Optimization

Abstract

In this paper, we extend a deterministic multi-period network flow model developed for a third party logistics (3PL) company to a robust optimization problem with uncertain market demand. We assume we are risk adverse and seek to maximize the worst case expected total margin. Since we are only exposed to partial information about the distributions of the market demand, we develop a robust multi-period network flow optimization model. Due to the complexity of the problem, we solve the linear decision rule (LDR) approximation of the problem and obtain an approximate solution. We also examine the degree of conservativeness of the LDR approximation by finding a computational tractable upper bound of the true objective. Then we compare the upper bound with the LDR objective through a numerical study and it is shown that the LDR approximation does a good job in approximating the true optimal solution.