Scandinavian Working Papers in Economics
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Department of Business and Economics, University of Southern Denmark Discussion Papers of Business and Economics
Department of Business and Economics, University of Southern Denmark

No 5/2013:
Solving the selective multi-category parallel-servicing problem

Troels Martin Range (), Richard Martin Lusby () and Jesper Larsen ()

Abstract: In this paper we present a new scheduling problem and describe a shortest path based heuristic as well as a dynamic programming based exact optimization algorithm to solve it. The Selective Multi-Category Parallel-Servicing Problem (SMCPSP) arises when a set of jobs has to be scheduled on a server (machine) with limited capacity. Each job requests service in a prespecified time window and belongs to a certain category. Jobs may be serviced partially, incurring a penalty; however, only jobs of the same category can be processed simultaneously. One must identify the best subset of jobs to process in each time interval of a given planning horizon while respecting the server capacity and scheduling requirements. We compare the proposed solution methods with a MILP formulation and show that the dynamic programming approach is faster when the number of categories is large, whereas the MILP can be solved faster when the number of categories is small.

Keywords: Machine scheduling; dynamic programming; node-disjoint shortest-path problem; preprocessing; (follow links to similar papers)

JEL-Codes: C61; (follow links to similar papers)

26 pages, March 5, 2013

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