Discussion Papers on Economics,
University of Southern Denmark, Department of Economics

Abstract: We consider the assignment of jobs to agents in a stochastic and dynamic setting. Focus is on a dynamic scenario with due dates and service levels reflecting the completion of jobs within certain deadlines. Due dates and other relevant characteristics for currently uncompleted jobs generated in the past are known, but the consumption of resources needed for their completion is stochastic. Distributions for the generation of future jobs as well as their characteristics are known. Capacity is limited, and an arriving job that cannot be assigned to an agent within its due date must be outsourced. Outsourcing is accompanied by a cost. We develop an optimization model based on column generation for the assignment of known and future jobs to agents such that the expected cost of outsourcing is minimum. The model is an extension of a generalized assignment problem and provides an allocation of known as well as tentative future jobs to agents. The model is embedded in a rolling horizon framework and subjected to a series of computational tests. The results indicate that taking stochastic information about future job arrivals into account in the assignment of jobs to agents implies an improved performance. The model is highly relevant in the context of patient scheduling in an operating theater. For this reason patient scheduling constitutes the storyline in the development of the model.

Keywords: Surgery allocation; generalized assignment problem; stochastic knapsack problem; column generation; simulation

JEL-codes: C61

27 pages, June 21, 2016

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