Lagrangian-Based Solution Approaches for a Resource-Constrained Parallel Machine Scheduling Problem with Machine Eligibility Restrictions
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.
KeywordsParallel machine scheduling Resource constraints Machine eligibility Lagrangian relaxation Subgradient optimization
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