Lagrangian bounds for just-in-time job-shop scheduling

We study the job-shop scheduling problem with earliness and tardiness penalties. We describe two Lagrangian relaxations of the problem. The first one is based on the relaxation of precedence constraints while the second one is based on the relaxation of machine constraints. We introduce dedicated algorithms to solve the corresponding dual problems. The second one is solved by a simple dynamic programming algorithm while the first one requires the resolution of an NP-hard problem by branch and bound. In both cases, the relaxations allow us to derive lower bounds as well as heuristic solutions. We finally introduce a simple local search algorithm to improve the best solution found. Computational results are reported.

[1]  Rolf H. Möhring,et al.  Solving Project Scheduling Problems by Minimum Cut Computations , 2002, Manag. Sci..

[2]  Erik Demeulemeester,et al.  Project scheduling : a research handbook , 2002 .

[3]  Martin E. Dyer,et al.  Formulating the single machine sequencing problem with release dates as a mixed integer program , 1990, Discret. Appl. Math..

[4]  Laurent Perron,et al.  Structured vs. Unstructured Large Neighborhood Search: A Case Study on Job-Shop Scheduling Problems with Earliness and Tardiness Costs , 2003, CP.

[5]  E. Rothberg,et al.  CPAIOR ’ 03 Integrating Mixed Integer Programming and Local Search : A Case Study on Job-Shop Scheduling Problems , 2003 .

[6]  Francis Sourd,et al.  Efficient neighborhood search for the one-machine earliness-tardiness scheduling problem , 2006, Eur. J. Oper. Res..

[7]  Peter B. Luh,et al.  An alternative framework to Lagrangian relaxation approach for job shop scheduling , 2003, Eur. J. Oper. Res..

[8]  M. Caramanis,et al.  Efficient Lagrangian relaxation algorithms for industry size job-shop scheduling problems , 1998 .

[9]  Francis Sourd,et al.  PERT scheduling with convex cost functions , 2003, Theor. Comput. Sci..

[10]  Franz Kappel,et al.  An Implementation of Shor's r-Algorithm , 2000, Comput. Optim. Appl..

[11]  Safia Kedad-Sidhoum,et al.  The One-Machine Problem with Earliness and Tardiness Penalties , 2003, J. Sched..

[12]  Erik Demeulemeester,et al.  An Exact Procedure for the Resource-Constrained Weighted Earliness–Tardiness Project Scheduling Problem , 2001, Ann. Oper. Res..

[13]  Chengbin Chu,et al.  An improvement of the Lagrangean relaxation approach for job shop scheduling: a dynamic programming method , 1998, IEEE Trans. Robotics Autom..

[14]  J. Christopher Beck,et al.  A Hybrid Approach to Scheduling with Earliness and Tardiness Costs , 2003, Ann. Oper. Res..