The Value of the Right Distribution for the Newsvendor Problem and a bike-sharing problem

Abstract

In this thesis, we introduce the new concept of Value of the Right Distribution, which measures the importance in Stochastic Programming of knowing the right probability distribution of the stochastic demand. We also introduce the new concepts of Recourse Penalty Bound and Maximum Recourse Penalty bound, which measure respectively the error bound and the worst-case performance bound given a certain mismatch between two probability distributions. In order to show how they apply, we study a cost-based variant of the Newsvendor problem. Moreover, we obtain closed-form and approximate expressions for the optimal quantity to order depending on the probability distribution assumed for the stochastic demand. Then, we use this new concepts to investigate bike-sharing problems. Two-stage and multi-stage stochastic optimization models are proposed. Finally, numerical results are provided.