Heuristics for Flow Shop Scheduling with Weighted WIP Costs

This paper considers a flow shop scheduling problem where a different WIP (work-in-process) state has different weight on the duration time. The objective is to minimize the sum of the weighted WIP. For the two machine flow shop case, the recognition version is unary NP-Complete. The three simple and intuitive heuristics H0, H1, and H2 are presented for the problem. For each heuristic, we find an upper bound on relative error which is tight in limit. For heuristic H2, we show that H2 dominates the other two heuristics.

[1]  Han Hoogeveen,et al.  Minimizing Total Completion Time in a Two-Machine Flowshop: Analysis of Special Cases , 1999, Math. Oper. Res..

[2]  Neta Amit,et al.  Openshop and flowshop scheduling to minimize sum of completion times , 1984, Comput. Oper. Res..

[3]  Chelliah Sriskandarajah,et al.  The complexity of scheduling jobs in repetitive manufacturing systems , 1993 .

[4]  S. L. Velde.  Minimizing the sum of the job completion times in the two-machine flow shop by Lagrangian relaxation , 1991 .

[5]  Wen-Chiung Lee,et al.  Minimizing the total flow time and the tardiness in a two-machine flow shop , 2001, Int. J. Syst. Sci..

[6]  Han Hoogeveen,et al.  Minimizing Total Completion Time in a Two-Machine Flowshop: Analysis of Special Cases , 1996, Math. Oper. Res..

[7]  Chengen Wang,et al.  Efficient heuristic and optimal approaches for n/2/F/[sigma]Ci scheduling problems , 1996 .

[8]  Roberto Tadei,et al.  An improved branch-and-bound algorithm for the two machine total completion time flow shop problem , 2002, Eur. J. Oper. Res..

[9]  Hirofumi Matsuo.  Cyclic sequencing problems in the two‐machine permutation flow shop: Complexity, worst‐case, and average‐case analysis , 1990 .

[10]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[11]  Daniel Sipper,et al.  JIT vs. WIP— a trade-off analysis , 1989 .

[12]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[13]  William L. Maxwell,et al.  The Role of Work-in-Process Inventory in Serial Production Lines , 1988, Oper. Res..

[14]  Teofilo F. Gonzalez,et al.  Flowshop and Jobshop Schedules: Complexity and Approximation , 1978, Oper. Res..