Sample average approximation under non-i.i.d. sampling for stochastic empty container repositioning problem

The stochastic empty container repositioning (ECR) problem can be solved by the sample average approximation (SAA) method, in which a sample of random scenarios are generated and then deterministic optimization techniques can be applied to solve the problem based on this sample. Considering the scale of SAA problem with multiple scenarios and the large number of random parameters in the ECR problem, we propose a design which combines Latin hypercube design and supersaturated design, which is able to get a satisfying approximation by using only a few scenarios. The impact of several non-independent and identical distribution (i.i.d). sampling methods for the stochastic ECR problem has been computationally examined. It is shown that all these non-i.i.d. sampling methods in consideration could help to enhance the performance of the SAA method for the stochastic ECR problem. Moreover, by using the proposed sampling method, it is less probable to provide bad solutions and the bias of the expected objective value of the sampled problem could also be reduced.