Scandinavian Working Papers in Economics

Discussion Papers of Business and Economics,
University of Southern Denmark, Department of Business and Economics

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

Troels Martin Range (), Richard Martin Lusby () and Jesper Larsen ()
Additional contact information
Troels Martin Range: Department of Business and Economics, Postal: COHERE, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Richard Martin Lusby: Department of Engineering Management, Postal: Technical University of Denmark, Produktionstorvet, building 426, 2800 Kgs. Lyngby, Denmark
Jesper Larsen: Department of Engineering Management, Postal: Technical University of Denmark, Produktionstorvet, building 426, 2800 Kgs. Lyngby, Denmark

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

JEL-codes: C61

26 pages, March 5, 2013

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