Cost optimization for series–parallel execution of a collection of intersecting operation sets. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Dolgui, Alexandre; Levin, Genrikh; Rozin, Boris; Kasabutski, Igor
• Is Part Of: Engineering optimization. Volume 48:Issue 5(2016)
• Page Start: 756
• Page End: 771
• Publication Date: 2016-05-03
• Subjects: sets of operations -- series–parallel execution -- operation costs and times -- line balancing -- process planning -- batch scheduling -- optimization -- Lagrangian relaxation -- dynamic programming; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2015.1056790
• Languages: English
• ISSNs: 0305-215X

Abstract

Abstract : A collection of intersecting sets of operations is considered. These sets of operations are performed successively. The operations of each set are activated simultaneously. Operation durations can be modified. The cost of each operation decreases with the increase in operation duration. In contrast, the additional expenses for each set of operations are proportional to its time. The problem of selecting the durations of all operations that minimize the total cost under constraint on completion time for the whole collection of operation sets is studied. The mathematical model and method to solve this problem are presented. The proposed method is based on a combination of Lagrangian relaxation and dynamic programming. The results of numerical experiments that illustrate the performance of the proposed method are presented. This approach was used for optimization multi-spindle machines and machining lines, but the problem is common in engineering optimization and thus the techniques developed could be useful for other applications.