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

• Published in: Journal of optimization theory and applications Vol. 174; no. 3; pp. 927 - 944
• Main Authors: Sterna, Malgorzata, Czerniachowska, Kateryna
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2017; Springer Nature B.V
• Subjects: Applications of Mathematics; Approximation; Calculus of Variations and Optimal Control; Optimization; Computation; Criteria; Dynamic programming; Engineering; Functions (mathematics); Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Polynomials; Production scheduling; Scheduling; Theory of Computation; 68Q25; Late work; 90B35; Parallel machines; Polynomial time approximation scheme; Scheduling; Early work
• ISSN: 0022-3239; 1573-2878; 1573-2878
• DOI: 10.1007/s10957-017-1147-7

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.