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Cyclic hoist scheduling in large real-life electroplating lines

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Abstract

This paper addresses cyclic scheduling of a single hoist in large real-life electroplating lines, where a part visits some processing tanks more than once and multiple duplicate tanks are used at some production stages having long processing times. We present a formal analysis of the problem and propose an efficient branch-and-bound algorithm. The developed analytical properties allow us to considerably eliminate dominated or infeasible solutions in the branch-and-bound procedure. Computational results on benchmark and real-life instances show that the algorithm is very efficient in scheduling large electroplating lines.

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Acknowledgements

This work was in part supported by the Scientific and Technological Innovation Foundation from the Northwestern Polytechnical University and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China.

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Authors and Affiliations

  1. School of Management, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Ada Che

  2. ISTIT, Université de Technologie de Troyes, 12 Rue Marie Curie, BP 2060, 10010, Troyes, Cedex, France

    Chengbin Chu

  3. Hefei University of Technology, Tunxi Road 193, Hefei, 230009, Anhui, People’s Republic of China

    Chengbin Chu

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  1. Ada Che
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Correspondence to Ada Che.

An example in which flexible move times lead to a shorter cycle time

An example in which flexible move times lead to a shorter cycle time

We use the following example, which is similar to the one in Ng 1996, to illustrate the fact that flexible move times longer than constant ones can lead to a shorter cycle time. There are four tanks in the line. The loading station and the unloading station are the same one (tank 0). The travel time for an empty hoist from tank i to tank j is 5|i−j|  s, 0≤i, j≤3. The constant times required for the hoist to transport a part from tank i to tank i+1 (including unloading a part from tank i, traveling from tank i to tank i+1, and loading the part onto tank i+1) for i=0, 1, 2, 3, are 10, 10, 10, and 20 s, respectively. The minimum processing times for tanks 0, 1, 2, and 3 are 40, 30, 30, and 20 s, respectively. The corresponding maximum processing times are 100, 60, 35, and 60 s.

With flexible move times, the optimal cycle time for this example is 105 s. The corresponding optimal hoist schedule is shown in Fig. 6. In this solution, the hoist pauses 5 s (from time instant 75 to 85) during its loaded travel from tank 1 to tank 2. As a result, the transportation of a part from tank 1 to tank 2 takes 15 s instead of 10 s. For this example, if no pause was allowed during the hoist’s loaded travel from tank 1 to tank 2, then the processing of the part in tank 2 will begin at time instant 80 instead of 85. Note that the part will be unloaded from tank 2 and complete the processing at time instant 120 in the next cycle. Therefore, the processing time for any part in tank 2 will be (120−80)=40. Thus, the processing time window in tank 2 will be violated. As a consequence, the corresponding schedule is infeasible. Thus, a feasible solution with flexible move times may be identified as an infeasible one with the constant travel time assumption. In fact, with the constant hoist move times, the optimal cycle time for this example is 110 s. Thus, flexible move times longer than constant ones lead to a shorter cycle time.

Fig. 6
figure 6

The optimal cyclic hoist schedule with flexible loaded move times

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Che, A., Chu, C. Cyclic hoist scheduling in large real-life electroplating lines. OR Spectrum 29, 445–470 (2007). https://doi.org/10.1007/s00291-006-0040-9

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