Lot splitting to minimize average flow-time in a two-machine flow-shop

Lot splitting is a technique for accelerating the flow of work by splitting job lots into sublots, In this paper we investigate the lot splitting scheduling problem in a two-machine flow-shop environment with detached setups and with batch availability. The performance measure considered is the average flow-time which is indicative of the increasingly important manufacturing lead-time. Our contribution is both theoretic and practical for the case of general (not necessarily equal) sublots. We identify properties of the optimal solution and develop a solution procedure to solve the problem. We then present a computational study which indicates that our solution technique is very efficient.

[1]  Alper Sen,et al.  Optimal streaming of a single job in a two-stage flow shop , 1998, Eur. J. Oper. Res..

[2]  Dean H. Kropp,et al.  Optimal and Heuristic Models for Lot Splitting in a Flow Shop , 1990 .

[3]  Chris N. Potts,et al.  Scheduling with batching: A review , 2000, Eur. J. Oper. Res..

[4]  T.C.E. Cheng,et al.  Parallel-machine batching and scheduling to minimize total completion time , 1996 .

[5]  A. J. Clewett,et al.  Introduction to sequencing and scheduling , 1974 .

[6]  Kenneth R. Baker,et al.  Basic Techniques for Lot Streaming , 1993, Oper. Res..

[7]  David Shallcross,et al.  A polynomial algorithm for a one machine batching problem , 1992, Oper. Res. Lett..

[8]  Michael J. Magazine,et al.  Batching in single operation manufacturing systems , 1985 .

[9]  Jiang Chen,et al.  Lot streaming with attached setups in three-machine flow shops , 1997 .

[10]  Subhash C. Sarin,et al.  Optimal Solutions for the Single Batch, Flow Shop, Lot-streaming Problem with Equal Sublots , 2001, Decis. Sci..

[11]  William G. Truscott,et al.  Scheduling production activities in multi-stage batch manufacturing systems , 1985 .

[12]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[13]  Jiang Chen,et al.  Lot streaming with attached setups in three-machine flow shops , 1998 .

[14]  Chung Yee Lee.  Scheduling: Theory, Algorithms, and Systems , 1996 .

[15]  Uday S. Karmarkar,et al.  Batching to minimize flow times on parallel heterogeneous machines , 1989 .

[16]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

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

[18]  William G. Truscott.  Production scheduling with capacity-constrained transportation activities , 1986 .

[19]  Bertrand M. T. Lin,et al.  Makespan minimization in the two‐machine flowshop batch scheduling problem , 2000 .

[20]  Kenneth R. Baker,et al.  A comparative study of lot streaming procedures , 1993 .

[21]  Denis Naddef,et al.  One-pass batching algorithms for the one-machine problem , 1988, Discret. Appl. Math..

[22]  Uday S. Karmarkar,et al.  Batching to minimize flow times on one machine , 1987 .