Single Machine Scheduling with Chain Structured Precedence Constraints and Separation Time Windows

We consider a single machine scheduling problem which we studied to improve the efficiency of an automated medical laboratory. In this problem, there are not only chain structured precedence constraints, but also minimal and maximal times separating successive jobs in the same chain (separation time windows). The criterion to be minimized is the makespan. Potential applications are not restricted to medical analysis. This problem often arises in systems where chemical processes are involved. Therefore the problem studied in this paper is important in practice. We prove that the problem is nonpolynomial (NP)-complete. As a consequence, we propose three heuristics for large size problems and a branch and bound based algorithm for small size problems. Computational results are reported.

[1]  M. I. Dessouky,et al.  The One-Machine Sequencing Problem with Early Starts and Due Dates , 1972 .

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

[3]  Donald Goldfarb,et al.  Efficient Shortest Path Simplex Algorithms , 1990, Oper. Res..

[4]  E. Nowicki,et al.  A note on minimizing maximum lateness in a one-machine sequencing problem with release dates , 1986 .

[5]  Henry L. W. Nuttle,et al.  Hoist Scheduling For A PCB Electroplating Facility , 1988 .

[6]  B. J. Lageweg,et al.  Minimizing maximum lateness on one machine : Computational experience and some applications , 1976 .

[7]  Lei Lei,et al.  The minimum common-cycle algorithm for cyclic scheduling of two material handling hoists with time window constraints , 1991 .

[8]  Nicholas G. Hall,et al.  Average and worst-case analysis of heuristics for the maximum tardiness problem , 1986 .

[9]  Stéphane Dauzère-Pérès.  The one-machine sequencing problem with dependent jobs , 1993 .

[10]  Chengbin Chu,et al.  Cyclic scheduling of a hoist with time window constraints , 1998, IEEE Trans. Robotics Autom..

[11]  Graham McMahon,et al.  On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness , 1975, Oper. Res..

[12]  M. Florian,et al.  On sequencing with earliest starts and due dates with application to computing bounds for the (n/m/G/Fmax) problem , 1973 .

[13]  Peter B. Luh,et al.  Improving the time resolution of schedules generated via Lagrangian relaxation algorithms , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[14]  Michel Minoux,et al.  Graphes et algorithmes , 1995 .

[15]  Kenneth R. Baker,et al.  Sequencing with due-dates and early start times to minimize maximum tardiness , 1974 .

[16]  L. W. Phillips,et al.  Mathematical Programming Solution of a Hoist Scheduling Program , 1976 .

[17]  Jerzy Kyparisis,et al.  Single machine scheduling research , 1987 .

[18]  E. Nowicki,et al.  A block approach for single-machine scheduling with release dates and due dates , 1986 .

[19]  R. E. Larson,et al.  A Forward-Backward Procedure for the Single Machine Problem to Minimize Maximum Lateness , 1980 .