Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date

Abstract We study the scheduling problem on parallel identical machines in order to maximize the total early work, i.e. the parts of non-preemptive jobs executed before a common due date, and investigate mainly the model with a fixed number of machines, for which a dynamic programming approach and a fully polynomial time approximation scheme (FPTAS) are proposed. The proposal of these methods allowed us to establish the complexity and approximability status of this problem more exactly. Moreover, since our FPTAS can be also applied for the two-machine case, we improve considerably the result known in the literature for this model, in which a polynomial time approximation scheme (PTAS) was given. The new FPTAS has not only the best computational complexity, but also the much better approximation ratio than the PTAS. Finally, the theoretical studies are completed with computational experiments, performed for dynamic programming, PTAS and FPTAS, showing the high efficiencies of FPTAS both in terms of time consumption and solution quality.

[1]  Malgorzata Sterna,et al.  Metaheuristics for Late Work Minimization in Two-Machine Flow Shop with Common Due Date , 2005, KI.

[2]  N. Alon,et al.  Approximation schemes for scheduling on parallel machines , 1998 .

[3]  Malgorzata Sterna,et al.  Flow Shop Scheduling with Late Work Criterion - Choosing the Best Solution Strategy , 2004, AACC.

[4]  Kuan Yew Wong,et al.  Job shop scheduling problem with late work criterion , 2015 .

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

[6]  Chris N. Potts,et al.  A Fully Polynomial Approximation Scheme for Scheduling a Single Machine to Minimize Total Weighted Late Work , 1994, Math. Oper. Res..

[7]  Malgorzata Sterna,et al.  Complexity of late work minimization in flow shop systems and a particle swarm optimization algorithm for learning effect , 2017, Comput. Ind. Eng..

[8]  Mohammad Ranjbar,et al.  Minimizing the total weighted late work in scheduling of identical parallel processors with communication delays , 2014 .

[9]  Malgorzata Sterna,et al.  Late work minimization in flow shops by a genetic algorithm , 2009, Comput. Ind. Eng..

[10]  Kuan Yew Wong,et al.  Minimizing total carbon footprint and total late work criterion in flexible job shop scheduling by using an improved multi-objective genetic algorithm , 2018 .

[11]  Chin-Chia Wu,et al.  A Branch-and-Bound Algorithm for Two-Agent Scheduling with Learning Effect and Late Work Criterion , 2018, Asia Pac. J. Oper. Res..

[12]  Xin Chen,et al.  Scheduling on parallel identical machines with late work criterion: Offline and online cases , 2016, J. Sched..

[13]  Chris N. Potts,et al.  Single Machine Scheduling to Minimize Total Late Work , 1992, Oper. Res..

[14]  Malgorzata Sterna,et al.  Dominance relations for two-machine flow shop problem with late work criterion , 2007 .

[15]  Yuan Zhang,et al.  A note on a two-agent scheduling problem related to the total weighted late work , 2018, J. Comb. Optim..

[16]  Wang Yong,et al.  Two-agent scheduling problems on a single-machine to minimize the total weighted late work , 2017, J. Comb. Optim..

[17]  Yunqiang Yin,et al.  Using a branch-and-bound and a genetic algorithm for a single-machine total late work scheduling problem , 2015, Soft Computing.

[18]  Gur Mosheiov,et al.  Scheduling on a proportionate flowshop to minimise total late work , 2019, Int. J. Prod. Res..

[19]  Malgorzata Sterna,et al.  Metaheuristic approaches for the two-machine flow-shop problem with weighted late work criterion and common due date , 2008, Comput. Oper. Res..

[20]  Malgorzata Sterna,et al.  Open shop scheduling problems with late work criteria , 2004, Discret. Appl. Math..

[21]  T.C.E. Cheng,et al.  Approximation schemes for single-machine scheduling with a fixed maintenance activity to minimize the total amount of late work , 2016 .

[22]  Bahram Alidaee,et al.  Single machine scheduling to minimize total weighted late work: a comparison of scheduling rules and search algorithms , 2002 .

[23]  Javad Rezaeian,et al.  Design of high-performing hybrid meta-heuristics for unrelated parallel machine scheduling with machine eligibility and precedence constraints , 2016 .

[24]  B. M. T. Lin,et al.  Two-machine flow-shop scheduling to minimize total late work , 2006 .

[25]  Yuzhong Zhang,et al.  The NP-Hardness of Minimizing the Total Late Work on an Unbounded Batch Machine , 2009, Asia Pac. J. Oper. Res..

[26]  Malgorzata Sterna,et al.  A comparison of solution procedures for two-machine flow shop scheduling with late work criterion , 2005, Comput. Ind. Eng..

[27]  Dujuan Wang,et al.  A two-agent single-machine scheduling problem with late work criteria , 2017, Soft Comput..

[28]  Malgorzata Sterna,et al.  A survey of scheduling problems with late work criteria , 2011 .

[29]  Chris N. Potts,et al.  Approximation algorithms for scheduling a single machine to minimize total late work , 1992, Oper. Res. Lett..

[30]  Malgorzata Sterna,et al.  The two-machine flow-shop problem with weighted late work criterion and common due date , 2005, Eur. J. Oper. Res..

[31]  Vitaly A. Strusevich,et al.  Preemptive models of scheduling with controllable processing times and of scheduling with imprecise computation: A review of solution approaches , 2018, Eur. J. Oper. Res..

[32]  Saeed Hosseinabadi,et al.  Minimizing total weighted late work in the resource-constrained project scheduling problem , 2013 .

[33]  Jacek Blazewicz,et al.  A note on the two machine job shop with the weighted late work criterion , 2007, J. Sched..

[34]  Dachuan Xu,et al.  The complexity of two supply chain scheduling problems , 2013, Inf. Process. Lett..

[35]  Gur Mosheiov,et al.  A single machine scheduling problem to minimize total early work , 2016, Comput. Oper. Res..

[36]  Jacek Blazewicz,et al.  Scheduling preemptible tasks on parallel processors with information loss , 1984 .

[37]  Malgorzata Sterna,et al.  Total Late Work Criteria for Shop Scheduling Problems , 2000 .

[38]  Xiangjie Kong,et al.  Meta-heuristic algorithms for parallel identical machines scheduling problem with weighted late work criterion and common due date , 2015, SpringerPlus.

[39]  Gerd Finke,et al.  Minimizing Mean Weighted Execution Time Loss on Identical and Uniform Processors , 1987, Inf. Process. Lett..

[40]  Malgorzata Sterna,et al.  Late work minimization in a small flexible manufacturing system , 2007, Comput. Ind. Eng..

[41]  Malgorzata Sterna,et al.  Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work , 2017, Journal of Optimization Theory and Applications.