A PTAS for the chance-constrained knapsack problem with random item sizes

Authors:
Vineet Goyal;R. Ravi
Affiliations:
Operations Research Center, Massachusetts Institute of Technology, United States;Tepper School of Business, Carnegie Mellon University, United States
Venue:
Operations Research Letters
Year:
2010

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Abstract

We consider a stochastic knapsack problem where each item has a known profit but a random size that is normally distributed independent of other items. The goal is to select a profit maximizing set of items such that the probability of the total size exceeding the knapsack bound is at most a given threshold. We present a Polynomial Time Approximation Scheme (PTAS) for the problem via a parametric LP reformulation that efficiently computes a solution satisfying the chance constraint strictly and achieving near-optimal profit.