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2 International Journal of Applied Mathematics and Computer Science

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Exact approaches to late work scheduling on unrelated machines

Liu Xinbo, Wang Wen, Chen Xin, Sterna Malgorzata, Blazewicz Jacek

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 2

285--295

We consider the scheduling problem on unrelated parallel machines in order to minimize the total late work. Since the problem is NP-hard, we propose a mathematical model and two dedicated exact approaches for solving it, based on the branching and bounding strategy and on enumerating combined with a dynamic programming algorithm. The time efficiencies of all three approaches are evaluated through computational experiments.

Two meta-heuristic algorithms for scheduling on unrelated machines with the late work criterion

Wang Wen, Chen Xin, Musial Jędrzej, Blazewicz Jacek

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 3

573--584

A scheduling problem in considered on unrelated machines with the goal of total late work minimization, in which the late work of a job means the late units executed after its due date. Due to the NP-hardness of the problem, we propose two meta-heuristic algorithms to solve it, namely, a tabu search (TS) and a genetic algorithm (GA), both of which are equipped with the techniques of initialization, iteration, as well as termination. The performances of the designed algorithms are verified through computational experiments, where we show that the GA can produce better solutions but with a higher time consumption. Moreover, we also analyze the influence of problem parameters on the performances of these metaheuristics.