Permutation flowshop scheduling problems with maximal and minimal time lags

In this paper, we study permutation flowshop problems with minimal and/or maximal time lags, where the time lags are defined between couples of successive operations of jobs. Such constraints may be used to model various industrial situations, for instance the production of perishable products. We present theoretical results concerning two-machine cases, we prove that the two-machine permutation flowshop with constant maximal time lags is strongly NP-hard. We develop an optimal branch and bound procedure to solve the m-machine permutation flowshop problem with minimal and maximal time lags. We test several lower bounds and heuristics providing upper bounds on different classes of benchmarks, and we carry out a performance analysis.

[1]  Chengbin Chu,et al.  Single Machine Scheduling with Chain Structured Precedence Constraints and Separation Time Windows , 2004 .

[2]  T. C. Edwin Cheng,et al.  Complexity Results for Flow-Shop and Open-Shop Scheduling Problems with Transportation Delays , 2004, Ann. Oper. Res..

[3]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[4]  L. G. Mitten.  Sequencing n Jobs on Two Machines with Arbitrary Time Lags , 1959 .

[5]  A. Kan.  Machine Scheduling Problems: Classification, Complexity and Computations , 1976 .

[6]  Gerd Finke,et al.  General Flowshop Models: Job Dependent Capacities, Job Overlapping and Deterioration , 2002 .

[7]  R. A. Dudek,et al.  A Heuristic Algorithm for the n Job, m Machine Sequencing Problem , 1970 .

[8]  Mauro Dell'Amico,et al.  Shop Problems With Two Machines and Time Lags , 1996, Oper. Res..

[9]  Jan Karel Lenstra,et al.  Sequencing and scheduling : an annotated bibliography , 1997 .

[10]  Freddy Deppner,et al.  Ordonnancement d'atelier avec contraintes temporelles entre opérations. (Scheduling problems with minimal and maximal time lag constraints) , 2004 .

[11]  Wenci Yu,et al.  The two-machine flow shop problem with delays and the one-machine total tardiness problem , 1996 .

[12]  R. Gomory,et al.  Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem , 1964 .

[13]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[14]  Rajasekhar Aalla,et al.  A heuristic algorithm for flow shop sequencing problems , 1992 .

[15]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[16]  D.H.R. Price,et al.  A Microcomputer Based Solution to a Practical Scheduling Problem , 1985 .

[17]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[18]  Han Hoogeveen,et al.  Minimizing Makespan in a Two-Machine Flow Shop with Delays and Unit-Time Operations is NP-Hard , 2004, J. Sched..

[19]  Eugene L. Lawler,et al.  Chapter 9 Sequencing and scheduling: Algorithms and complexity , 1993, Logistics of Production and Inventory.

[20]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[21]  D. Yang,et al.  A two-machine flowshop sequencing problem with limited waiting time constraints , 1995 .