Lagrangian-Based Solution Approaches for a Resource-Constrained Parallel Machine Scheduling Problem with Machine Eligibility Restrictions

Authors:
Emrah B. Edis;Ceyhun Araz;Irem Ozkarahan
Affiliations:
Department of Industrial Engineering, Dokuz Eylul University, Izmir, Turkey 35100;Department of Industrial Engineering, Dokuz Eylul University, Izmir, Turkey 35100;Computer Science Department, Troy University, Montgomery, USA AL 36103-4419
Venue:
IEA/AIE '08 Proceedings of the 21st international conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems: New Frontiers in Applied Artificial Intelligence
Year:
2008

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Abstract

This study is motivated by a real world scheduling problem in an injection molding department of an electrical appliance company. In this paper, a resource-constrained parallel machine scheduling problem with machine eligibility restrictions is investigated. For the problem, an integer linear program is developed with the objective of minimizing total flow time. Based on this model, a Lagrangian-based solution approach with a subgradient optimization procedure has been proposed. Additionally, a problem-specific heuristic algorithm is developed to obtain near-optimal solutions. Through randomly generated instances of the problem, it is demonstrated that the proposed algorithms generate not only very tight lower bounds but also efficient results with a small optimality gap.