Approximation Algorithms for Scheduling with a Variable Machine Maintenance

In this paper, we investigate the problem of scheduling weighted jobs on a single machine with a maintenance whose starting time is prior to a given deadline and whose duration is a nondecreasing function of the starting time. We are asked not only to schedule the jobs but also the maintenance such that the total weighted job completion time is minimum. The problem is shown to be weakly NP-hard. In the case that the duration of the maintenance is a concave (and nondecreasing) function of its starting time, we provide two approximation algorithms with approximation ratio of 2 and at most 1 + √2/2 + e, respectively.

[1]  Bin Fu,et al.  Exponential inapproximability and FPTAS for scheduling with availability constraints , 2009, Theor. Comput. Sci..

[2]  Gur Mosheiov,et al.  Scheduling a maintenance activity to minimize total weighted completion-time , 2009, Comput. Math. Appl..

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

[4]  Hans Kellerer,et al.  Fully Polynomial Approximation Schemes for a Symmetric Quadratic Knapsack Problem and its Scheduling Applications , 2010, Algorithmica.

[5]  Nicole Megow,et al.  Short Note on Scheduling on a Single Machine with one Non-availability Period , 2009 .

[6]  Eugene Levner,et al.  Fast approximation algorithm for job sequencing with deadlines , 1981, Discret. Appl. Math..

[7]  Gur Mosheiov,et al.  Scheduling a deteriorating maintenance activity on a single machine , 2010, J. Oper. Res. Soc..

[8]  Zhi-Long Chen,et al.  Scheduling jobs and maintenance activities on parallel machines , 2000 .

[9]  Guoqing Wang,et al.  Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times , 2005, Ann. Oper. Res..

[10]  Imed Kacem.  Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval , 2008, Comput. Ind. Eng..

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

[12]  Hans Kellerer,et al.  Two simple constant ratio approximation algorithms for minimizing the total weighted completion time on a single machine with a fixed non-availability interval , 2009, Eur. J. Oper. Res..

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

[14]  Vitaly A. Strusevich,et al.  Planning Machine Maintenance in Two-Machine Shop Scheduling , 2006, Oper. Res..

[15]  Alessandro Agnetis,et al.  Scheduling Problems with Two Competing Agents , 2004, Oper. Res..