Uniform Parallel Machine Scheduling Problem with Controllable Delivery Times

Abstract This paper considers the uniform parallel machine scheduling problem with controllable delivery times, which assumes that the delivery times of jobs are linear decreasing functions of the consumed resource. It aims to minimize the maximum completion time under the constraint that the total resource consumption does not exceed a given limit. For this NP-hard problem, we propose a resource allocation algorithm, named RAA, according to the feasible solution of the uniform parallel machine scheduling problem with fixed delivery times. It proves that RAA algorithm can obtain the optimal resource allocation scheme for any given scheduling scheme in O(n log n)time. Some algorithms based on heuristic algorithm LDT, heuristic algorithm LPDT and simulated annealing are proposed to solve the uniform parallel machine scheduling problem with controllable delivery times. The accuracy and efficiency of the proposed algorithms are tested based on those data with problem sizes varying from 40 to 200 jobs and 2 to 8 machines. The computational results indicate that the SA approach is promising and capable of solving large-scale problems in a reasonable time.

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