The Sample Average Approximation Method Appliedto Transportation Procurement Auction Problemunder Uncertainty

Abstract

This thesis proposes to apply the sample average approximation method to solve the lanebundling problem under demand uncertainty.In the previous work, we investigated thepossibility of forming packages within a company™s own distribution network and proposed astochastic model which was computationally intractable. The SAA method is an approach tosolve stochastic optimization problems by using Monte Carlo simulation and approximatingthe expected objective function by a sample average estimate from a random sample. Em-pirical results from the application of the SAA method are presented and analyzed, allowingus to discover the signiï¬cance of the stochastic model as well as the efficiency of this solutionmethodology.We have shown that although the candidate solutions from the SAA method are superior tothe traditional mean-value problem solution in an expectation sense, the mean-value problemsolution is sufficiently good if the compliance requirement needs to be absolutely satisï¬ed.However, given a slight relaxation to the compliance requirement, the estimated objectivevalue of the relaxed problem is found to be signiï¬cantly higher and the SAA method alsoprovides much better candidate solutions than the mean-value problem solution.