A heuristic for scheduling jobs on two identical parallel machines with a machine availability constraint

We study a two identical parallel-machine scheduling problem in which one machine is available to process jobs in a limited time interval while the other machine is always available over the scheduling horizon. The objective is to maximize the number of on-time jobs. As the problem is NP-hard, we develop a heuristic to tackle it by incorporating the backward adjusting and two-step look-ahead strategies into some existing heuristics for similar problems without the machine availability constraint. We show that our heuristic has a worst-case ratio bound of 4/3 and the bound is tight.

[1]  Susan A. Slotnick,et al.  Order acceptance and scheduling: A taxonomy and review , 2011, Eur. J. Oper. Res..

[2]  Chung-Yee Lee,et al.  Capacitated Two-Parallel Machines Scheduling to Minimize Sum of Job Completion Times , 1993, Discret. Appl. Math..

[3]  Min Ji,et al.  Parallel-machine scheduling with an availability constraint , 2011, Comput. Ind. Eng..

[4]  Eric Sanlaville,et al.  Machine scheduling with availability constraints , 1998, Acta Informatica.

[5]  Christos Koulamas,et al.  A heuristic for maximizing the number of on-time jobs on two uniform parallel machines , 2006 .

[6]  H.-C. Hwang,et al.  Parallel Machines Scheduling with Machine Shutdowns , 1998 .

[7]  Chengbin Chu,et al.  A survey of scheduling with deterministic machine availability constraints , 2010, Comput. Ind. Eng..

[8]  Kangbok Lee,et al.  The effect of machine availability on the worst-case performance of LPT , 2005, Discret. Appl. Math..

[9]  Johnny C. Ho,et al.  Minimizing the number of tardy jobs for m parallel machines , 1995 .

[10]  Joseph Y.-T. Leung,et al.  Heuristic for Minimizing the Number of Late Jobs on Two Processors , 1994, Int. J. Found. Comput. Sci..

[11]  Chung-Yee Lee,et al.  Machine scheduling with an availability constraint , 1996, J. Glob. Optim..

[12]  Joseph Y.-T. Leung.  Improved Competitive Algorithms For Two-Processor Real-Time Systems , 2004, Int. J. Found. Comput. Sci..

[13]  F. Sibel Salman,et al.  Order acceptance and scheduling decisions in make-to-order systems , 2010 .

[14]  Günter Schmidt,et al.  Scheduling with limited machine availability , 2000, Eur. J. Oper. Res..

[15]  R. L. Bulfin,et al.  Minimizing the weighted number of tardy jobs on parallel processors , 2005, Eur. J. Oper. Res..

[16]  Sudipto Guha,et al.  Approximating the Throughput of Multiple Machines in Real-Time Scheduling , 2002, SIAM J. Comput..

[17]  Chien-Hung Lin,et al.  Minimizing the sum of job completion times on capacitated two-parallel machines , 2009, Eur. J. Oper. Res..

[18]  T.C.E. Cheng,et al.  A modified artificial bee colony algorithm for order acceptance in two-machine flow shops , 2013 .

[19]  T.C.E. Cheng,et al.  Order acceptance and scheduling in a two-machine flowshop , 2013 .

[20]  Yong Chen,et al.  Parallel machines scheduling with machine maintenance for minsum criteria , 2011, Eur. J. Oper. Res..