SOLUTION APPROACHES FOR SIMULTANEOUS SCHEDULING OF JOBS AND OPERATORS ON PARALLEL MACHINES

In literature, most of the studies related to parallel machine scheduling problems assume that jobs require only machines as the processing resources and accordingly deal with simply job-machine scheduling problem. However, in real-life manufacturing environments, jobs may also require additional resources. A common example of additional resources is cross-training workers that perform tasks related with different machines. This study handles a real-life problem that requires simultaneous scheduling of jobs and operators over the parallel machines. Operators are responsible for monitoring the machines, unloading the parts and trimming extra material. These tasks may not require an operator’s full attention during the processing of a job at one machine. In this context, a significant distinguishing feature of the investigated problem is that an operator can be assigned to more than one machine through the specified time periods. While determining the machines that an operator has to deal with during the same scheduling periods, the physical closeness of the machines should also be taken into account. For the problem on hand, with the aim of minimizing the completion time of the last job, integer and constraint programming models have been developed. The models have been evaluated through the test problems with different parameters, and their performances have been discussed. Finally, the applicability of the proposed constraint programming model on the real-life problem has been shown.

[1]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[2]  Joseph B. Mazzola,et al.  Scheduling Parallel Manufacturing Cells with Resource Flexibility , 1996 .

[3]  Emrah Bünyamin Edis,et al.  Resource constrained parallel machine scheduling problems with machine eligibility restrictions: Mathematical and constraint programming based approaches , 2009 .

[4]  Alexander Grigoriev,et al.  Unrelated Parallel Machine Scheduling with Resource Dependent Processing Times , 2005, IPCO.

[5]  Karla E. Bourland,et al.  PARALLEL-MACHINE SCHEDULING WITH FRACTIONAL OPERATOR REQUIREMENTS , 1994 .

[7]  Jose A. Ventura,et al.  Parallel machine scheduling with earliness-tardiness penalties and additional resource constraints , 2003, Comput. Oper. Res..

[8]  Po-Chieng Hu,et al.  Minimising total tardiness for the worker assignment scheduling problem in identical parallel-machine models , 2004 .

[9]  Richard L. Daniels,et al.  Heuristics for parallel-machine flexible-resource scheduling problems with unspecified job assignment , 1999, Comput. Oper. Res..

[10]  Alexander Grigoriev,et al.  LP Rounding and an Almost Harmonic Algorithm for Scheduling with Resource Dependent Processing Times , 2006, APPROX-RANDOM.

[11]  Sally C. Brailsford,et al.  The Progressive Party Problem: Integer Linear Programming and Constraint Programming Compared , 1995, CP.

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

[13]  Irem Ozkarahan,et al.  Solution approaches for a real-life resource-constrained parallel machine scheduling problem , 2012 .

[14]  Imran Ali Chaudhry,et al.  Minimizing flow time for the worker assignment problem in identical parallel machine models using GA , 2010 .

[15]  Irem Ozkarahan,et al.  A combined integer/constraint programming approach to a resource-constrained parallel machine scheduling problem with machine eligibility restrictions , 2011 .

[16]  Jean-François Puget,et al.  Program Does Not Equal Program: Constraint Programming and Its Relationship to Mathematical Programming , 2001, Interfaces.

[17]  Gautam Mitra,et al.  Constraint Logic Programming and Integer Programming approaches and their collaboration in solving an assignment scheduling problem , 1997, Constraints.

[18]  Zhi-Long Chen,et al.  Simultaneous Job Scheduling and Resource Allocation on Parallel Machines , 2004, Ann. Oper. Res..

[19]  Po-Chieng Hu,et al.  Minimizing total flow time for the worker assignment scheduling problem in the identical parallel-machine models , 2005 .

[20]  P. Baptiste,et al.  Scheduling identical parallel machines and operators within a period based changing mode , 2009, Comput. Oper. Res..

[21]  Irem Ozkarahan,et al.  Lagrangian-Based Solution Approaches for a Resource-Constrained Parallel Machine Scheduling Problem with Machine Eligibility Restrictions , 2008, IEA/AIE.

[22]  Robert McNaughton,et al.  Scheduling with Deadlines and Loss Functions , 1959 .

[23]  Paul R. Drake,et al.  Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machines using genetic algorithms , 2009 .

[24]  Ken Darby-Dowman,et al.  Properties of Some Combinatorial Optimization Problems and Their Effect on the Performance of Integer Programming and Constraint Logic Programming , 1998, INFORMS J. Comput..

[25]  Alexander Grigoriev,et al.  Machine scheduling with resource dependent processing times , 2007, Math. Program..