STOCHASTIC KNAPSACK PROBLEM: APPLICATION TO TRANSPORTATION PROBLEMS

• Main Authors: Stefanie Kosuch, Marc Letournel, Abdel Lisser
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Pesquisa Operacional
• Series: Pesquisa Operacional
• Subjects: Stochastic knoasack problem; transportation problem; probabilistic constraint; Branch and Bound; Integration by parts
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382017000300597&lng=en&tlng=en

ABSTRACT In this paper, we study the stochastic knapsack problem with expectation constraint. We solve the relaxed version of this problem using a stochastic gradient algorithm in order to provide upper bounds for a branch-and-bound framework. Two approaches to estimate the needed gradients are studied, one based on Integration by Parts and one using Finite Differences. The Finite Differences method is a robust and simple approach with efficient results despite the fact that estimated gradients are biased, meanwhile Integration by Parts is based upon more theoretical analysis and permits to enlarge the field of applications. Numerical results on a dataset from the literature as well as a set of randomly generated instances are given.