Preemptive multiprocessor order scheduling to minimize total weighted flowtime

• Published in: European journal of operational research Vol. 190; no. 1; pp. 40 - 51
• Main Authors: Leung, Joseph Y.-T., Lee, C.Y., Ng, C.W., Young, G.H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2008; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Complexity theory; Exact sciences and technology; Flexible machines; Heuristic; Heuristics; Inventory control, production control. Distribution; NP-hard; Operational research and scientific management; Operational research. Management science; Order scheduling; Production scheduling; Studies; Total weighted completion time; Total weighted completion time; NP-hard; Order scheduling; Flexible machines; Heuristics; Preemption; Lower bound; Multiple machine; Worst case method; Priority; Empirical method; Parallel machines; Finished product; Processing time; Scheduling; Order picking; Computational complexity; Multiprocessor; Production management; Minimum time; Heuristic method; NP hard problem; Completion time; Execution time
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2007.05.052

Consider m identical machines in parallel, each of which can produce k different product types. There is no setup cost when the machines switch from producing one product type to another. There are n orders each of which requests various quantities of the different product types. All orders are available for processing at time t = 0, and preemption is allowed. Order i has a weight w i and its completion time is the time when its last requested product type finishes. Our goal is to find a preemptive schedule such that the total weighted completion time ∑ w i C i is minimized. We show that this problem is NP-hard even when all jobs have identical weights and there are only two machines. Motivated by the computational complexity of the problem, we propose a simple heuristic and show that it obeys a worst-case bound of 2 − 1/ m. Finally, empirical studies show that our heuristic performs very well when compared with a lower bound of the optimal cost.