A Permutation-Based Approach for Solving the Job-Shop Problem

In this paper, we deal with the famous job-shop scheduling problem, which has been being a constant subject of study for many years due to its high computational complexity (NP-hard in the strong sense). We present a permutation-based scheme for solving the problem, which in the abstraction level differs from the classical one of Jacques Carlier and Eric Pinson. In particular, we specify the differences both in the fashion of stating the constraints (the use of the generalized sorting constraint) and in the search strategy (splitting intervals of task orders). We will first give a constraint program for solving the problem, which involves only primitive constraints and which is clean and simple to understand. We then study some special techniques based on testing variable bounds that allow us to solve two hard instances la21 and la38. These two instances have been open problems recommended in a paper of David Applegate and William Cook in 1991.

[1]  Alain Colmerauer,et al.  An introduction to Prolog III , 1989, CACM.

[2]  P. Hall.  On Representatives of Subsets , 1935 .

[3]  Eugene C. Freuder,et al.  Constraint satisfaction using constraint logic programming , 1994 .

[4]  J. Carlier,et al.  An algorithm for solving the job-shop problem , 1989 .

[5]  Philippe Baptiste,et al.  Constraint-Based Optimization and Approximation for Job-Shop Scheduling , 1995 .

[6]  Pascal Van Hentenryck.  Constraint satisfaction in logic programming , 1989, Logic programming.

[7]  David B. Shmoys,et al.  A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem , 1996, IPCO.

[8]  Pascal Van Hentenryck.  Improved CLP Scheduling with Task Intervals , 1994 .

[9]  Jianyang Zhou,et al.  A Constraint Program for Solving the Job-Shop Problem , 1996, CP.

[10]  J. Carlier,et al.  Adjustment of heads and tails for the job-shop problem , 1994 .

[11]  Frédéric Benhamou,et al.  Applying Interval Arithmetic to Real, Integer, and Boolean Constraints , 1997, J. Log. Program..

[12]  J. K. Lenstra,et al.  Computational complexity of discrete optimization problems , 1977 .

[13]  Yves Colombani.  Constraint Programming: an Efficient and Practical Approach to Solving the Job-Shop Problem , 1996, CP.

[14]  Nicolas Beldiceanu,et al.  Extending CHIP in order to solve complex scheduling and placement problems , 1993, JFPL.

[15]  William J. Cook,et al.  A Computational Study of the Job-Shop Scheduling Problem , 1991, INFORMS Journal on Computing.

[16]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[17]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[18]  William Older.  Constraint Arithmetic on Real Intervals William Older Andr e Vellino , 1993 .

[19]  M. H. van Emden,et al.  Adapting CLP to Floating-Point Arithmetic , 1992, FGCS.