We study a two-stage, finite-scenarios stochastic 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.

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View Approximation algorithm for the two-stage stochastic set multicover problem with simple resource