Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work

Malgorzata Sterna () and Kateryna Czerniachowska ()
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Malgorzata Sterna: Poznan University of Technology
Kateryna Czerniachowska: Poznan University of Technology

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 17, 927-944

Abstract: Abstract We study the scheduling problem with a common due date on two parallel identical machines and the total early work criterion. The problem is known to be NP-hard. We prove a few dominance properties of optimal solutions of this problem. Their proposal was inspired by the results of some auxiliary computational experiments. Test were performed with the dynamic programming algorithm and list algorithms. Then, we propose the polynomial time approximation scheme, based on structuring problem input. Moreover, we discuss the relationship between the early work criterion and the related late work criterion. We compare the computational complexity and approximability of scheduling problems with both mentioned objective functions.

Keywords: Scheduling; Parallel machines; Early work; Late work; Polynomial time approximation scheme; 90B35; 68Q25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s10957-017-1147-7

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