Two-stage flowshop earliness and tardiness machine scheduling involving a common due window |
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Authors: | W K Yeung Ceyda O
uz T C Edwin Cheng |
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Institution: | Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR |
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Abstract: | This paper studies a non-preemptive two-stage flowshop scheduling problem to minimize the earliness and tardiness under the environment of a common due window. The window size and the window location are considered to be given parameters. The just-in-time problem exists naturally and has many practical applications. The problem is shown to be NP-complete in the strong sense. We develop a branch and bound algorithm and a heuristic to solve the problem. We conduct the computational experiments to test the performances of the algorithms. A strong lower bound is derived for the branch and bound algorithm that can efficiently solve 15 jobs problem for about 5 minutes. The heuristic is shown to be efficient and effective, which can solve the problem of 150 jobs for about 20 seconds and provide near-optimal solution. We justify that the heuristic is an excellent solution approach for large problem instances. We also show that four special cases are either polynomial solvable or NP-complete in the ordinary sense. |
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Keywords: | Flowshop scheduling Earliness– tardiness Due window Dynamic programming Branch and bound Heuristic |
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