Flow shops with WIP and value added costs

A new deterministic flow shop problem is studied where the objective is to minimize the total WIP (work-in-process) cost. Based on a value added model, the unit time WIP cost increases as a job passes through various stages in the production process.The recognition version is unary NP-Complete even for two machines. Several simple and intuitive heuristics are presented. For each heuristic, we determine asymptotically attainable upper bounds on the relative error. Finally, the heuristics are empirically evaluated.

[1]  F. D. Croce,et al.  The two-machine total completion time flow shop problem , 1996 .

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

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

[4]  V. Sridharan,et al.  Scheduling with Inserted Idle Time: Problem Taxonomy and Literature Review , 2000, Oper. Res..

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

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

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

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

[9]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[10]  Hans Röck,et al.  Some new results in flow shop scheduling , 1984, Z. Oper. Research.

[11]  Stanley F. Bullington,et al.  An effective heuristic for flow shop problems with total flow time as criterion , 1993 .

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

[13]  Johnny C. Ho,et al.  Flowshop sequencing with mean flowtime objective , 1995 .

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

[15]  Gerhard J. Woeginger,et al.  Polynomial time approximation algorithms for machine scheduling: ten open problems , 1999 .

[16]  Yih-Long Chang,et al.  A new heuristic for the n-job, M-machine flow-shop problem , 1991 .

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

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

[19]  William L. Berry,et al.  Manufacturing Planning and Control Systems , 1984 .

[20]  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..

[21]  Chelliah Sriskandarajah,et al.  A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process , 1996, Oper. Res..

[22]  Han Hoogeveen,et al.  Non-approximability Results for Scheduling Problems with Minsum Criteria , 1998, IPCO.

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

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