Approximation algorithm for the stochastic prize-collecting set multicover problem

Abstract

We study a scenario-based stochastic and prize-collecting version of the set multicover problem, where there is uncertainty about a demand for each element to be covered and the penalty cost is imposed linearly on the shortfall in each demand. This problem is NP-hard and has an application in shift scheduling in crowdsourced delivery services. For this problem, we present an LP-based O(ln⁡n)-approximation algorithm, where n is the number of elements to be covered.