A New MIP Model for Parallel-Batch Scheduling with Non-identical Job Sizes

Parallel-batch machine problems arise in numerous manufacturing settings from semiconductor manufacturing to printing. They have recently been addressed in constraint programming (CP) via the combination of the novel sequenceEDD global constraint with the existing pack constraint to form the current state-of-the-art approach. In this paper, we present a detailed analysis of the problem and derivation of a number of properties that are exploited in a novel mixed integer programming (MIP) model for the problem. Our empirical results demonstrate that the new model is able to outperform the CP model across a range of standard benchmark problems. Further investigation shows that the new MIP formulation improves on the existing formulation primarily by producing a much smaller model and enabling high quality primal solutions to be found very quickly.

[1]  Mark Wallace,et al.  Principles and Practice of Constraint Programming – CP 2004 , 2004, Lecture Notes in Computer Science.

[2]  J. Christopher Beck,et al.  Recent Improvements Using Constraint Integer Programming for Resource Allocation and Scheduling , 2013, CPAIOR.

[3]  Makespan minimisation on parallel batch processing machines with non-identical job sizes and release dates , 2012 .

[4]  F. Jolai,et al.  Optimal methods for batch processing problem with makespan and maximum lateness objectives , 2010 .

[5]  J. Christopher Beck,et al.  Logic-based Benders Decomposition for Alternative Resource Scheduling with Sequence Dependent Setups , 2012, ECAI.

[6]  Meral Azizoglu,et al.  Scheduling a batch processing machine with non-identical job sizes , 2000 .

[7]  J. Christopher Beck,et al.  Combining Constraint Programming and Local Search for Job-Shop Scheduling , 2011, INFORMS J. Comput..

[8]  Petr Vilím,et al.  Edge Finding Filtering Algorithm for Discrete Cumulative Resources in O(kn log n){\mathcal O}(kn {\rm log} n) , 2009, CP.

[9]  Edward P. K. Tsang,et al.  Constraint Based Scheduling: Applying Constraint Programming to Scheduling Problems , 2003, J. Sched..

[10]  Principles and Practice of Constraint Programming — CP98 , 1999, Lecture Notes in Computer Science.

[11]  Ali Husseinzadeh Kashan,et al.  A note on minimizing makespan on a single batch processing machine with nonidentical job sizes , 2009, Theor. Comput. Sci..

[12]  Peter J. Stuckey,et al.  Solving RCPSP/max by lazy clause generation , 2012, Journal of Scheduling.

[13]  Reha Uzsoy,et al.  Efficient Algorithms for Scheduling Semiconductor Burn-In Operations , 1992, Oper. Res..

[14]  Philippe Baptiste,et al.  Constraint Propagation and Decomposition Techniques for Highly Disjunctive and Highly Cumulative Project Scheduling Problems , 1997, CP.

[15]  Laurence A. Wolsey,et al.  Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings , 2007, CPAIOR.

[16]  Xavier Lorca,et al.  Choco: an Open Source Java Constraint Programming Library , 2008 .

[17]  Clarisse Dhaenens,et al.  Minimizing the makespan on a batch machine with non-identical job sizes: an exact procedure , 2002, Comput. Oper. Res..

[18]  Paul Shaw,et al.  Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems , 1998, CP.

[19]  Philippe Baptiste,et al.  Constraint-based scheduling , 2001 .

[20]  J. A. Hoogeveen,et al.  Scheduling a batching machine , 1998 .

[21]  Eugene C. Freuder.  In Pursuit of the Holy Grail , 1996, CSUR.

[22]  Paul Shaw,et al.  A Constraint for Bin Packing , 2004, CP.

[23]  Christelle Guéret,et al.  A Branch-and-Price algorithm to minimize the maximum lateness on a batch processing machine , 2008 .

[24]  Louis-Martin Rousseau,et al.  A constraint programming approach for a batch processing problem with non-identical job sizes , 2012, Eur. J. Oper. Res..

[25]  John N. Hooker,et al.  A Hybrid Method for the Planning and Scheduling , 2005, Constraints.

[26]  Ignacio E. Grossmann,et al.  Mixed-Integer Optimization Techniques for the Design and Scheduling of Batch Processes , 1996 .

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