A Heuristic Algorithm for One-Machine Just-In-Time Scheduling Problem with Periodic Time Slots

概要

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Just-in-time scheduling problem is the problem of finding an optimal schedule such that each job finishes exactly at its due date. We study the problem under a realistic assumption called periodic time slots. In this paper, we prove that this problem cannot be approximated, assuming P≠NP. Next, we present a heuristic algorithm, assuming that the number of machines is one. The key idea is a reduction of the problem to a network flow problem. The heuristic algorithm is fast because its main part consists of computation of the minimum cost flow that dominates the total time. Our algorithm is O(n3) in the worst case, where n is the number of jobs. Next, we show some simulation results. Finally, we show cases in which our algorithm returns an optimal schedule and is a factor 1.5 approximation algorithm, respectively, and also give an approximation ratio depending on the upper bound of set-up times.
社団法人電子情報通信学会の論文
2005-05-01