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Optimal Cyclic Multi-Hoist Scheduling: A Mixed Integer Programming Approach

Systems Engineering and Engineering Management Department, The Chinese University of Hong Kong, Shatin, Hong Kong
Industrial and Manufacturing Systems Engineering Department, University of Windsor, Windsor, Ontario, Canada N9B 3P4
Key Laboratory of Management, Decision, and Information Systems, Institute of Systems Science, The Chinese Academy of Sciences, Beijing, China
Planning and Engineering Department, Asia Pacific Division, FedEx Express, Hong Kong
Division of Commerce, City University of Hong Kong, Kowloon, Hong Kong
janny{at}se.cuhk.edu.hk
gzhang{at}uwindsor.ca
xgyang{at}iss.ac.cn
wmak{at}fedex.com
cmkklam{at}cityu.edu.hk

In the manufacture of circuit boards, panels are immersed sequentially in a series of tanks, with upper and lower bounds on the processing time within each tank. The panels are mounted on carriers that are lowered into and raised from the tanks, and transported from tank to tank by programmable hoists. The sequence of hoist moves does not have to follow the sequence of processing stages for the circuit boards. By optimising the sequence of hoist moves, we can maximise the production throughput.

We consider simple cyclic schedules, where the hoist move sequence repeats every cycle and one panel is completed per cycle. Phillips and Unger (1976) developed the first mixed integer programming model for finding the hoist move schedule to minimise the cycle time for lines with only one hoist. We discuss how their formulation can be tightened, and introduce new valid inequalities. We present the first mixed integer programming formulation for finding the minimum-time cycle for lines with multiple hoists and present valid inequalities for this problem. Some preliminary computational results are also presented.

Subject classifications: mixed integer programming; applications, formulation; production/scheduling; applications, cyclic scheduling; industries; chemical, electric, hoist scheduling.
History: Received February 2001; revision received September 2002; accepted August 2003.

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