Unrelated Parallel Machine Selection and Job Scheduling with the Objective of Minimizing Total Workload and Machine Fixed Costs

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IEEE Transactions on Automation Science and Engineering


This paper is concerned with scheduling of a set of n single-operation tasks/orders on a set of m unrelated parallel machines where subcontracting is allowed. When a machine/subcontractor is chosen to do a set of orders/tasks, it incurs a one-time fixed cost. When a job/order is performed by a machine/subcontractor, there is a cost that depends on the machine/subcontractor. The objective is to choose a subset of k machines and/or subcontractors from the set of all m available machines and/or subcontractors to perform all jobs to minimize the sum of total workload costs and total fixed costs. We discuss the complexity of the problem, and prove NP-hardness of the problem. Simplified mathematical development is provided that allows efficient implementation of two-exchange algorithms. An efficient tabu search heuristic with a diversification generation component is developed. An extensive computational experiment of the heuristic for large-scale problems with comparison to the results from CPLEX software is presented. We also solved 40 benchmark k-median problems available on the Internet that have been used by many researchers. Note to Practitioners - To be competitive in the global market, companies must be prudent in the use of their resources. This paper considers a parallel scheduling environment where choosing in-house machines and/or subcontractors as resources to perform the orders/jobs is the main objective. Processing time (or cost) of a job to be performed by different machines or subcontractors can be different. Furthermore, if a machine or a subcontractor is chosen to perform a set of orders, there is a one-time fixed cost (in the case of subcontractor it can be considered transportation cost) that depends on the machine or subcontractor. The scheduling criteria are to choose a subset of k machines and/or subcontractors to do all orders/jobs while minimizing the sum of the total workload and total fixed costs. The complexity of the problem is discussed and shown to be NP-hard. An efficient tabu search that solves large-scale problems in fraction of a second of CPU time is presented and an extensive computational experiment is provided.

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