Single-machine scheduling to minimize total convex resource consumption with a constraint on total weighted flow time

• Published in: Computers & operations research Vol. 39; no. 3; pp. 492 - 497
• Main Authors: Wang, Ji-Bo, Wang, Ming-Zheng
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2012; Elsevier; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Branch & bound algorithms; Computation; Convex resource allocation; Dominance; Exact sciences and technology; Heuristic; Heuristic methods; Job shops; Mathematical models; Operational research and scientific management; Operational research. Management science; Optimization; Optimization algorithms; Production scheduling; Resource allocation; Scheduling; Scheduling, sequencing; Single-machine; Studies; Convex resource allocation; Single-machine; Scheduling; Lower bound; Optimal algorithm; Branch and bound method; Resource allocation; Dominance; Processing time; Polynomial method; Computational complexity; Polynomial time; Production management; Optimal allocation; Resource constraint; Heuristic method; Open systems; Convex function; Resource management; Single machine; Completion time; Execution time
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2011.05.026

In this paper, we consider single-machine scheduling problem in which processing time of a job is described by a convex decreasing resource consumption function. The objective is to minimize the total amount of resource consumed subject to a constraint on total weighted flow time. The optimal resource allocation is obtained for any arbitrary job sequence. The computational complexity of the general problem remains an open question, but we present and analyze some special cases that are solvable by using polynomial time algorithms. For the general problem, several dominance properties and some lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm proposed to solve the problem. A heuristic algorithm is also proposed, which is shown by computational experiments to perform effectively and efficiently in obtaining near-optimal solutions. The results show that the average percentage error of the proposed heuristic algorithm from optimal solutions is less than 3%. ► Problem with convex resource dependent processing times is modeled and studied. ► A branch-and-bound algorithm and a heuristic algorithm were proposed. ► Experimental results show that the proposed algorithms run very efficiently.