Decision support for unrelated parallel machine scheduling with discrete controllable processing times

A scheduling problem involving discrete controllable processing times is considered.The objectives are to minimize some scheduling criteria.We develop polynomial time algorithms for the considered problems.We further consider the NP-hard problem of the makespan case.An integer programming and a heuristic are presented to solve the NP-hard problem. In a manufacturing or service system, the actual processing time of a job can be controlled by the amount of an indivisible resource allocated, such as workers or auxiliary facilities. In this paper, we consider unrelated parallel-machine scheduling problems with discrete controllable processing times. The processing time of a job is discretely controllable by the allocation of indivisible resources. The planner must make decisions on whether or how to allocate resources to jobs during the scheduling horizon to optimize the performance measures. The objective is to minimize the total cost including the cost measured by a standard criterion and the total processing cost. We first consider three scheduling criterions: the total completion time, the total machine load, and the total earliness and tardiness penalties. If the number of machines and the number of possible processing times are fixed, we develop polynomial time algorithms for the considered problems. We then consider the minimization problem of the makespan cost plus the total processing cost and present an integer programming method and a heuristic method to solve the studied problem.

[1]  Radoslaw Rudek,et al.  The single processor total weighted completion time scheduling problem with the sum-of-processing-time based learning model , 2012, Inf. Sci..

[2]  R. G. Vickson,et al.  Choosing the Job Sequence and Processing Times to Minimize Total Processing Plus Flow Cost on a Single Machine , 1980, Oper. Res..

[3]  S. S. Panwalkar,et al.  Single-machine sequencing with controllable processing times , 1992 .

[4]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[5]  T. C. Edwin Cheng,et al.  Single-machine due window assignment and scheduling with a common flow allowance and controllable job processing time , 2014, J. Oper. Res. Soc..

[6]  Wen-Chiung Lee,et al.  Scheduling with general position-based learning curves , 2011, Inf. Sci..

[7]  MengChu Zhou,et al.  Single-Machine Scheduling With Job-Position-Dependent Learning and Time-Dependent Deterioration , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[8]  Yunqiang Yin,et al.  The single-machine total weighted tardiness scheduling problem with position-based learning effects , 2012, Comput. Oper. Res..

[9]  Suh-Jenq Yang,et al.  Unrelated parallel-machine scheduling simultaneously with rate-modifying activities and earliness and tardiness penalties , 2012 .

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

[11]  Stanisław Zdrzałka,et al.  A two-machine flow shop scheduling problem with controllable job processing times , 1988 .

[12]  Dirk Biskup,et al.  A state-of-the-art review on scheduling with learning effects , 2008, Eur. J. Oper. Res..

[13]  Eugeniusz Nowicki,et al.  A survey of results for sequencing problems with controllable processing times , 1990, Discret. Appl. Math..

[14]  Shanlin Yang,et al.  Author's Personal Copy Applied Soft Computing Parallel Machine Scheduling Problem to Minimize the Makespan with Resource Dependent Processing Times , 2022 .

[15]  Raymond G. Vickson,et al.  Two Single Machine Sequencing Problems Involving Controllable Job Processing Times , 1980 .

[16]  Suh-Jenq Yang,et al.  Multi-machine scheduling with deterioration effects and maintenance activities for minimizing the total earliness and tardiness costs , 2013 .

[17]  Daniel Oron,et al.  Minimizing the number of tardy jobs on a proportionate flowshop with general position-dependent processing times , 2012, Comput. Oper. Res..

[18]  Radoslaw Rudek,et al.  A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models , 2011, Comput. Math. Appl..

[19]  Joseph B. Mazzola,et al.  Flow Shop Scheduling with Resource Flexibility , 1994, Oper. Res..

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

[21]  Alexander Grigoriev,et al.  Scheduling jobs with time-resource tradeoff via nonlinear programming , 2009, Discret. Optim..

[22]  Stanislaw Gawiejnowicz,et al.  Time-Dependent Scheduling , 2008, Monographs in Theoretical Computer Science. An EATCS Series.

[23]  Bahram Alidaee,et al.  Two parallel machine sequencing problems involving controllable job processing times , 1993 .

[24]  K. R. Baker,et al.  A bicriterion approach to time/cost trade-offs in sequencing , 1982 .

[25]  Chung-Lun Li,et al.  Parallel-machine scheduling with controllable processing times , 1996 .

[26]  Radosław Rudek,et al.  On flowshop scheduling problems with the aging effect and resource allocation , 2012 .

[27]  Peter Brucker,et al.  Scheduling Algorithms , 1995 .

[28]  Dvir Shabtay,et al.  A survey of scheduling with controllable processing times , 2007, Discret. Appl. Math..

[29]  Daniel Oron,et al.  Scheduling controllable processing time jobs in a deteriorating environment , 2014, J. Oper. Res. Soc..

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

[31]  T.C.E. Cheng,et al.  Single-machine common due-date scheduling with batch delivery costs and resource-dependent processing times , 2013 .

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

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

[34]  Joseph B. Mazzola,et al.  An analysis of heuristics for the parallel-machine flexible-resource scheduling problem , 1997, Ann. Oper. Res..

[35]  Chin-Chia Wu,et al.  Scheduling problems with two agents and a linear non-increasing deterioration to minimize earliness penalties , 2012, Inf. Sci..

[36]  Gur Mosheiov,et al.  A note: Multi-machine scheduling with general position-based deterioration to minimize total load , 2012 .

[37]  T.C.E. Cheng,et al.  Parallel-machine scheduling with controllable processing times and rate-modifying activities to minimise total cost involving total completion time and job compressions , 2014 .

[38]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[39]  Adam Janiak,et al.  Experience-Based Approach to Scheduling Problems With the Learning Effect , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[40]  Zhi-Long Chen,et al.  Single machine scheduling with discretely controllable processing times , 1997, Oper. Res. Lett..