A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

Abstract This research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective.

[1]  G. Moslehi,et al.  Two-machine flow shop scheduling to minimize the sum of maximum earliness and tardiness , 2009 .

[2]  Ying Zhang,et al.  Single-machine scheduling problems with machine aging effect and an optional maintenance activity , 2016 .

[3]  M.S. Kamel,et al.  Opposition-Based Q(λ) with Non-Markovian Update , 2007, 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning.

[4]  Reza Tavakkoli-Moghaddam,et al.  Minimizing the total completion time on a single machine with the learning effect and multiple availability constraints , 2013 .

[5]  Gerd Finke,et al.  Single machine scheduling with small operator-non-availability periods , 2012, J. Sched..

[6]  R Tavakoli Moghadam,et al.  A SINGLE MACHINE SEQUENCING PROBLEM WITH IDLE INSERT: SIMULATED ANNEALING AND BRANCH-AND-BOUND METHODS , 2008 .

[7]  Ghasem Moslehi,et al.  Minimizing the sum of maximum earliness and maximum tardiness in the single-machine scheduling problem with sequence-dependent setup time , 2011, J. Oper. Res. Soc..

[8]  M. Sheikhalishahi,et al.  An integrated fuzzy simulation–fuzzy data envelopment analysis approach for optimum maintenance planning , 2014, Int. J. Comput. Integr. Manuf..

[9]  Joaquín A. Pacheco,et al.  A single machine scheduling problem with availability constraints and sequence-dependent setup costs , 2011 .

[10]  Hamid R. Tizhoosh,et al.  Quasi-global oppositional fuzzy thresholding , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[11]  Xiwen Lu,et al.  Integrated scheduling of production and delivery on a single machine with availability constraint , 2015, Theor. Comput. Sci..

[12]  Zhijian Wu,et al.  Enhancing particle swarm optimization using generalized opposition-based learning , 2011, Inf. Sci..

[13]  Jing Bai,et al.  Single machine common flow allowance scheduling with deteriorating jobs and a rate-modifying activity , 2014 .

[14]  Chuanli Zhao,et al.  Deteriorating jobs scheduling on a single machine with release dates, rejection and a fixed non-availability interval , 2015 .

[15]  Marcello Braglia,et al.  Harmony search algorithm for single-machine scheduling problem with planned maintenance , 2014, Comput. Ind. Eng..

[16]  Ching-Jong Liao,et al.  A variable neighborhood search for minimizing single machine weighted earliness and tardiness with common due date , 2007, Comput. Ind. Eng..

[17]  Amir Azaron,et al.  A branch-and-bound algorithm for a single machine sequencing to minimize the sum of maximum earliness and tardiness with idle insert , 2006, Appl. Math. Comput..

[18]  Shahryar Rahnamayan,et al.  Opposition-Based Differential Evolution Algorithms , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[19]  Dan Simon,et al.  Oppositional biogeography-based optimization , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[20]  Seyyed M. T. Fatemi Ghomi,et al.  Single machine scheduling with unequal release times and idle insert for minimizing the sum of maximum earliness and tardiness , 2013, Math. Comput. Model..

[21]  Amir Azaron,et al.  Optimal scheduling for a single machine to minimize the sum of maximum earliness and tardiness considering idle insert , 2005, Appl. Math. Comput..

[22]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[23]  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 .

[24]  Lin Han,et al.  A Novel Opposition-Based Particle Swarm Optimization for Noisy Problems , 2007, Third International Conference on Natural Computation (ICNC 2007).

[25]  Rym M'Hallah,et al.  A binary multiple knapsack model for single machine scheduling with machine unavailability , 2016, Comput. Oper. Res..

[26]  T. C. Edwin Cheng,et al.  Single-machine scheduling with a variable maintenance activity , 2015, Comput. Ind. Eng..

[27]  Mario Ventresca,et al.  Numerical condition of feedforward networks with opposite transfer functions , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[28]  Muhammad Rashid,et al.  Improved Opposition-Based PSO for Feedforward Neural Network Training , 2010, 2010 International Conference on Information Science and Applications.

[29]  M.M.A. Salama,et al.  Opposition-Based Differential Evolution , 2008, IEEE Transactions on Evolutionary Computation.

[30]  C. Chu,et al.  An improved exact algorithm for single-machine scheduling to minimise the number of tardy jobs with periodic maintenance , 2016 .

[31]  Zhizhong Mao,et al.  Single-Machine Scheduling with Job Rejection, Deteriorating Effects, and Deteriorating Maintenance Activities , 2013 .

[32]  Robert G. Reynolds,et al.  A Testbed for Solving Optimization Problems Using Cultural Algorithms , 1996, Evolutionary Programming.

[33]  Cherif Sadfi,et al.  A branch-and-bound method for the single-machine scheduling problem under a non-availability constraint for maximum delivery time minimization , 2015, Appl. Math. Comput..

[34]  Mehmet Emin Aydin,et al.  Parallel variable neighbourhood search algorithms for job shop scheduling problems , 2007 .

[35]  Ghasem Moslehi,et al.  AN OPTIMUM ALGORITHM FOR SINGLE MACHINE WITH EARLY/TARDY COST , 2000 .

[36]  Abdelhakim Artiba,et al.  Minimizing the weighted sum of maximum earliness and maximum tardiness costs on a single machine with periodic preventive maintenance , 2014, Comput. Oper. Res..

[37]  Min Ji,et al.  Minimizing the makespan in a single machine scheduling problems with flexible and periodic maintenance , 2010 .

[38]  Mario Ventresca,et al.  Opposite Transfer Functions and Backpropagation Through Time , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.

[39]  Chwen-Tzeng Su,et al.  A modified particle swarm optimization algorithm for a single-machine scheduling problem with periodic maintenance , 2010, Expert Syst. Appl..

[40]  Sushil J. Louis,et al.  Learning with case-injected genetic algorithms , 2004, IEEE Transactions on Evolutionary Computation.

[41]  Fariborz Jolai,et al.  A parallel machine scheduling problem with two-agent and tool change activities: an efficient hybrid metaheuristic algorithm , 2016, Int. J. Comput. Integr. Manuf..

[42]  Hans Kellerer,et al.  Approximation algorithms for maximizing the weighted number of early jobs on a single machine with non-availability intervals , 2015, J. Comb. Optim..

[43]  Hong Zhou,et al.  Hybridization of harmony search with variable neighborhood search for restrictive single-machine earliness/tardiness problem , 2013, Inf. Sci..

[44]  Sakti Prasad Ghoshal,et al.  A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems , 2012 .

[45]  Ceyda Oguz,et al.  A variable neighborhood search for minimizing total weighted tardiness with sequence dependent setup times on a single machine , 2012, Comput. Oper. Res..

[46]  Ming Liu,et al.  A branch and bound algorithm for single-machine production scheduling integrated with preventive maintenance planning , 2013 .

[47]  Fariborz Jolai,et al.  Lion Optimization Algorithm (LOA): A nature-inspired metaheuristic algorithm , 2016, J. Comput. Des. Eng..

[48]  Ling Wang,et al.  A hybrid genetic algorithm-neural network strategy for simulation optimization , 2005, Appl. Math. Comput..

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

[50]  Vitaly A. Strusevich,et al.  Single machine scheduling with general positional deterioration and rate-modifying maintenance , 2012 .

[51]  Celso C. Ribeiro,et al.  Variable neighborhood search for the degree-constrained minimum spanning tree problem , 2002, Discret. Appl. Math..

[52]  Ghasem Moslehi,et al.  A branch-and-bound algorithm for minimizing the sum of maximum earliness and tardiness with unequal release times , 2009 .

[53]  Mario Ventresca,et al.  Simulated Annealing with Opposite Neighbors , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.

[54]  Li Zhao,et al.  A review of opposition-based learning from 2005 to 2012 , 2014, Eng. Appl. Artif. Intell..

[55]  Shahryar Rahnamayan,et al.  Opposition-Based Differential Evolution for Optimization of Noisy Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[56]  Shijin Wang.  Bi-objective optimisation for integrated scheduling of single machine with setup times and preventive maintenance planning , 2013 .

[57]  Ali Azadeh,et al.  An integrated support vector regression–imperialist competitive algorithm for reliability estimation of a shearing machine , 2016, Int. J. Comput. Integr. Manuf..

[58]  Nhu Binh Ho,et al.  An effective architecture for learning and evolving flexible job-shop schedules , 2007, Eur. J. Oper. Res..

[59]  Hamid R. Tizhoosh.  Opposite Fuzzy Sets with Applications in Image Processing , 2009, IFSA/EUSFLAT Conf..

[60]  Mario Ventresca,et al.  Improving the Convergence of Backpropagation by Opposite Transfer Functions , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[61]  Ali Azadeh,et al.  An integrated multi-criteria Taguchi computer simulation-DEA approach for optimum maintenance policy and planning by incorporating learning effects , 2013 .

[62]  Ghasem Moslehi,et al.  Minimising the total completion time in a single machine scheduling problem under bimodal flexible periodic availability constraints , 2016, Int. J. Comput. Integr. Manuf..

[63]  Xiaolei Wang,et al.  A hybrid optimization method of harmony search and opposition-based learning , 2012 .

[64]  Zhiqiang Lu,et al.  Integrated production scheduling and maintenance policy for robustness in a single machine , 2014, Comput. Oper. Res..

[65]  Amir Azaron,et al.  A branch-and-bound algorithm to minimise the sum of maximum earliness and tardiness in the single machine , 2010 .

[66]  Ryszard S. Michalski,et al.  LEARNABLE EVOLUTION MODEL: Evolutionary Processes Guided by Machine Learning , 2004, Machine Learning.

[67]  Hamid R. Tizhoosh,et al.  Applying Opposition-Based Ideas to the Ant Colony System , 2007, 2007 IEEE Swarm Intelligence Symposium.

[68]  Chwen-Tzeng Su,et al.  A single-machine scheduling problem with maintenance activities to minimize makespan , 2010, Appl. Math. Comput..

[69]  Hamid R. Tizhoosh,et al.  Opposition-Based Learning: A New Scheme for Machine Intelligence , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[70]  Alcione de Paiva Oliveira,et al.  Multi-objective Variable Neighborhood Search Algorithms for a Single Machine Scheduling Problem with Distinct due Windows , 2011, CLEI Selected Papers.

[71]  Peng Wang,et al.  A Knowledge-Based Ant Colony Optimization for Flexible Job Shop Scheduling Problems , 2010, Appl. Soft Comput..

[72]  Xianpeng Wang,et al.  A population-based variable neighborhood search for the single machine total weighted tardiness problem , 2009, Comput. Oper. Res..

[73]  Chou-Jung Hsu,et al.  Single-Machine Scheduling with Aging Effects and Optional Maintenance Activity Considerations , 2013 .

[74]  D. Yang,et al.  Single machine total completion time scheduling problem with workload-dependent maintenance duration , 2015 .

[75]  Alain Hertz,et al.  A variable neighborhood search for graph coloring , 2003, Eur. J. Oper. Res..

[76]  Yong Chen,et al.  Complexity and approximation of single machine scheduling with an operator non-availability period to minimize total completion time , 2013, Inf. Sci..

[77]  Jun Tang,et al.  An Enhanced Opposition-Based Particle Swarm Optimization , 2009, 2009 WRI Global Congress on Intelligent Systems.