Scheduling of unrelated parallel machines: an application to PWB manufacturing

In this paper, we tackle scheduling the bottleneck operation of a Printed Wiring Board (PWB) manufacturing line. The problem may be characterized as unrelated parallel machines and we are interested in several performance measures including: makespan, the average finish time, mean flow time, utilization, the number of lots and the total amount of overtime beyond the release interval. Due to setup reduction techniques employed by the company, setups are negligible, and we construct an Integer Programming (IP) model with a special structure – unimodularity. Thus, the corresponding linear programming optimal solution always satisfies the integrality constraints. In order to account for multiple objectives of the scheduling system, we introduce preference constraints and bring them into the objective function by Lagrangian Relaxation (LR). We give a heuristic procedure to select constraints to be relaxed, and formulations to determine the Lagrange multipliers. To verify the validity of the proposed method, we compare it with a network model and with a modified FIFO method. The proposed method presents very promising results in terms of our measures of interest.

[1]  Linet Özdamar,et al.  Hybrid heuristics for the capacitated lot sizing and loading problem with setup times and overtime decisions , 1998, Eur. J. Oper. Res..

[2]  Dipak Chaudhuri,et al.  Bicriteria scheduling problem for unrelated parallel machines , 1996 .

[3]  Linet Özdamar,et al.  Simultaneous lot sizing and loading of product families on parallel facilities of different classes , 1998 .

[4]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[5]  C. N. Potts,et al.  Analysis of a linear programming heuristic for scheduling unrelated parallel machines , 1985, Discret. Appl. Math..

[6]  Paolo Toth,et al.  Exact and Approximation Algorithms for Makespan Minimization on Unrelated Parallel Machines , 1997, Discret. Appl. Math..

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

[8]  David Dornfeld,et al.  Manufacturing Systems Engineering , 1981 .

[9]  John E. Beasley,et al.  Lagrangian relaxation , 1993 .

[10]  Chris N. Potts,et al.  Heuristics for scheduling unrelated parallel machines , 1991, Comput. Oper. Res..

[11]  Jan Karel Lenstra,et al.  Approximation algorithms for scheduling unrelated parallel machines , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[12]  Oscar H. Ibarra,et al.  Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors , 1977, JACM.

[13]  Ellis Horowitz,et al.  Exact and Approximate Algorithms for Scheduling Nonidentical Processors , 1976, JACM.

[14]  T.C.E. Cheng,et al.  A state-of-the-art review of parallel-machine scheduling research , 1990 .

[15]  Katta G. Murty,et al.  Network programming , 1992 .

[16]  Steef L. van de Velde.  Duality-Based Algorithms for Scheduling Unrelated Parallel Machines , 1993, INFORMS J. Comput..

[17]  Leo Kroon,et al.  On the computational complexity of (maximum) class scheduling , 1991 .

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

[19]  N. Piersma,et al.  A local search heuristic for unrelated parallel machine scheduling with efficient neighborhood search , 1996 .