AIS-SFHM APPROACH FOR OPTIMIZATION OF MULTI OBJECTIVE JOB SHOP PROBLEMS

The n-job, m-machine Job shop scheduling (JSP) problem is one of the general production scheduling problems. The JSP problem is a scheduling problem, where a set of ‘n’ jobs must be processed or assembled on a set of ‘m’ dedicated machines. Each job consists of a specific set of operations, which have to be processed according to a given technical precedence order. Job shop scheduling problem is a NP-hard combinatorial optimization problem.  In this paper, optimization of three practical performance measures mean job flow time, mean job tardiness and makespan are considered. The hybrid approach of Sheep Flocks Heredity Model Algorithm (SFHM) is used for finding optimal makespan, mean flow time, mean tardiness. The hybrid SFHM approach is tested with multi objective job shop scheduling problems. Initial sequences are generated with Artificial Immune System (AIS) algorithm and results are refined using SFHM algorithm. The results show that the hybrid SFHM algorithm is an efficient and effective algorithm that gives better results than SFHM Algorithm, Genetic Algorithm (GA). The proposed hybrid SFHM algorithm is a good problem-solving technique for job shop scheduling problem with multi criteria

Selected heuristic algorithms for solving job shop and flow shop scheduling problems

Importance of job shop and flow shop scheduling has increased to a high extent. Nowadays, each and every industry focuses largely on how to schedule their machine working, since it is an important factor which decides the net productivity. All manufacturing systems including flexible manufacturing system follow a planned schedule of machine operation depending on the demand criterion. With the increase in number of machines and jobs to be scheduled, complexity of the problem increases which demands the need of a proper scheduling technique. Here this thesis shows some of the essential methods of solving a job shop and flow shop scheduling problems. This thesis focuses on finding the most efficient way of scheduling in a flow shop environment with the help of heuristics algorithms that include Palmer’s algorithm, CDS algorithm and NEH algorithm. Comparison was also done between the various heuristics algorithms. For getting the optimum make span for job shop scheduling we have used branch and bound algorithm and shifting bottleneck algorithm. Basis input parameters are given in the problem which are then used for computing the make span. A C programming code was generated to find the optimum results of the scheduling problem

An Enhanced Estimation of Distribution Algorithm for Energy-Efficient Job-Shop Scheduling Problems with Transportation Constraints

[EN] Nowadays, the manufacturing industry faces the challenge of reducing energy consumption and the associated environmental impacts. Production scheduling is an effective approach for energy-savings management. During the entire workshop production process, both the processing and transportation operations consume large amounts of energy. To reduce energy consumption, an energy-efficient job-shop scheduling problem (EJSP) with transportation constraints was proposed in this paper. First, a mixed-integer programming model was established to minimize both the comprehensive energy consumption and makespan in the EJSP. Then, an enhanced estimation of distribution algorithm (EEDA) was developed to solve the problem. In the proposed algorithm, an estimation of distribution algorithm was employed to perform the global search and an improved simulated annealing algorithm was designed to perform the local search. Finally, numerical experiments were implemented to analyze the performance of the EEDA. The results showed that the EEDA is a promising approach and that it can solve EJSP effectively and efficiently.This work was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 17KJB460018), the Innovation Foundation for Science and Technology of Yangzhou University (No. 2016CXJ020 and No. 2017CXJ018), Science and Technology Project of Yangzhou under (No. YZ2017278), Research Topics of Teaching Reform of Yangzhou University under (No. YZUJX2018-28B), and the Spanish Government (No. TIN2016-80856-R and No. TIN2015-65515-C4-1-R).Dai, M.; Zhang, Z.; Giret Boggino, AS.; Salido, MA. (2019). An Enhanced Estimation of Distribution Algorithm for Energy-Efficient Job-Shop Scheduling Problems with Transportation Constraints. Sustainability. 11(11):1-23. https://doi.org/10.3390/su11113085S1231111Wu, X., & Sun, Y. (2018). A green scheduling algorithm for flexible job shop with energy-saving measures. Journal of Cleaner Production, 172, 3249-3264. doi:10.1016/j.jclepro.2017.10.342Wang, Q., Tang, D., Li, S., Yang, J., Salido, M., Giret, A., & Zhu, H. (2019). An Optimization Approach for the Coordinated Low-Carbon Design of Product Family and Remanufactured Products. Sustainability, 11(2), 460. doi:10.3390/su11020460Meng, Y., Yang, Y., Chung, H., Lee, P.-H., & Shao, C. (2018). Enhancing Sustainability and Energy Efficiency in Smart Factories: A Review. Sustainability, 10(12), 4779. doi:10.3390/su10124779Gahm, C., Denz, F., Dirr, M., & Tuma, A. (2016). Energy-efficient scheduling in manufacturing companies: A review and research framework. European Journal of Operational Research, 248(3), 744-757. doi:10.1016/j.ejor.2015.07.017Giret, A., Trentesaux, D., & Prabhu, V. (2015). Sustainability in manufacturing operations scheduling: A state of the art review. Journal of Manufacturing Systems, 37, 126-140. doi:10.1016/j.jmsy.2015.08.002Akbar, M., & Irohara, T. (2018). Scheduling for sustainable manufacturing: A review. Journal of Cleaner Production, 205, 866-883. doi:10.1016/j.jclepro.2018.09.100Che, A., Wu, X., Peng, J., & Yan, P. (2017). Energy-efficient bi-objective single-machine scheduling with power-down mechanism. Computers & Operations Research, 85, 172-183. doi:10.1016/j.cor.2017.04.004Lee, S., Do Chung, B., Jeon, H. W., & Chang, J. (2017). A dynamic control approach for energy-efficient production scheduling on a single machine under time-varying electricity pricing. Journal of Cleaner Production, 165, 552-563. doi:10.1016/j.jclepro.2017.07.102Rubaiee, S., & Yildirim, M. B. (2019). An energy-aware multiobjective ant colony algorithm to minimize total completion time and energy cost on a single-machine preemptive scheduling. Computers & Industrial Engineering, 127, 240-252. doi:10.1016/j.cie.2018.12.020Zhang, M., Yan, J., Zhang, Y., & Yan, S. (2019). Optimization for energy-efficient flexible flow shop scheduling under time of use electricity tariffs. Procedia CIRP, 80, 251-256. doi:10.1016/j.procir.2019.01.062Li, J., Sang, H., Han, Y., Wang, C., & Gao, K. (2018). Efficient multi-objective optimization algorithm for hybrid flow shop scheduling problems with setup energy consumptions. Journal of Cleaner Production, 181, 584-598. doi:10.1016/j.jclepro.2018.02.004Lu, C., Gao, L., Li, X., Pan, Q., & Wang, Q. (2017). Energy-efficient permutation flow shop scheduling problem using a hybrid multi-objective backtracking search algorithm. Journal of Cleaner Production, 144, 228-238. doi:10.1016/j.jclepro.2017.01.011Fu, Y., Tian, G., Fathollahi-Fard, A. M., Ahmadi, A., & Zhang, C. (2019). Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraint. Journal of Cleaner Production, 226, 515-525. doi:10.1016/j.jclepro.2019.04.046Schulz, S., Neufeld, J. S., & Buscher, U. (2019). A multi-objective iterated local search algorithm for comprehensive energy-aware hybrid flow shop scheduling. Journal of Cleaner Production, 224, 421-434. doi:10.1016/j.jclepro.2019.03.155Liu, Y., Dong, H., Lohse, N., Petrovic, S., & Gindy, N. (2014). An investigation into minimising total energy consumption and total weighted tardiness in job shops. Journal of Cleaner Production, 65, 87-96. doi:10.1016/j.jclepro.2013.07.060Liu, Y., Dong, H., Lohse, N., & Petrovic, S. (2016). A multi-objective genetic algorithm for optimisation of energy consumption and shop floor production performance. International Journal of Production Economics, 179, 259-272. doi:10.1016/j.ijpe.2016.06.019May, G., Stahl, B., Taisch, M., & Prabhu, V. (2015). Multi-objective genetic algorithm for energy-efficient job shop scheduling. International Journal of Production Research, 53(23), 7071-7089. doi:10.1080/00207543.2015.1005248Zhang, R., & Chiong, R. (2016). Solving the energy-efficient job shop scheduling problem: a multi-objective genetic algorithm with enhanced local search for minimizing the total weighted tardiness and total energy consumption. Journal of Cleaner Production, 112, 3361-3375. doi:10.1016/j.jclepro.2015.09.097Salido, M. A., Escamilla, J., Giret, A., & Barber, F. (2015). A genetic algorithm for energy-efficiency in job-shop scheduling. The International Journal of Advanced Manufacturing Technology, 85(5-8), 1303-1314. doi:10.1007/s00170-015-7987-0Masmoudi, O., Delorme, X., & Gianessi, P. (2019). Job-shop scheduling problem with energy consideration. International Journal of Production Economics, 216, 12-22. doi:10.1016/j.ijpe.2019.03.021Mokhtari, H., & Hasani, A. (2017). An energy-efficient multi-objective optimization for flexible job-shop scheduling problem. Computers & Chemical Engineering, 104, 339-352. doi:10.1016/j.compchemeng.2017.05.004Meng, L., Zhang, C., Shao, X., & Ren, Y. (2019). MILP models for energy-aware flexible job shop scheduling problem. Journal of Cleaner Production, 210, 710-723. doi:10.1016/j.jclepro.2018.11.021Dai, M., Tang, D., Giret, A., & Salido, M. A. (2019). Multi-objective optimization for energy-efficient flexible job shop scheduling problem with transportation constraints. Robotics and Computer-Integrated Manufacturing, 59, 143-157. doi:10.1016/j.rcim.2019.04.006Lacomme, P., Larabi, M., & Tchernev, N. (2013). Job-shop based framework for simultaneous scheduling of machines and automated guided vehicles. International Journal of Production Economics, 143(1), 24-34. doi:10.1016/j.ijpe.2010.07.012Nageswararao, M., Narayanarao, K., & Ranagajanardhana, G. (2014). Simultaneous Scheduling of Machines and AGVs in Flexible Manufacturing System with Minimization of Tardiness Criterion. Procedia Materials Science, 5, 1492-1501. doi:10.1016/j.mspro.2014.07.336Saidi-Mehrabad, M., Dehnavi-Arani, S., Evazabadian, F., & Mahmoodian, V. (2015). An Ant Colony Algorithm (ACA) for solving the new integrated model of job shop scheduling and conflict-free routing of AGVs. Computers & Industrial Engineering, 86, 2-13. doi:10.1016/j.cie.2015.01.003Guo, Z., Zhang, D., Leung, S. Y. S., & Shi, L. (2016). A bi-level evolutionary optimization approach for integrated production and transportation scheduling. Applied Soft Computing, 42, 215-228. doi:10.1016/j.asoc.2016.01.052Karimi, S., Ardalan, Z., Naderi, B., & Mohammadi, M. (2017). Scheduling flexible job-shops with transportation times: Mathematical models and a hybrid imperialist competitive algorithm. Applied Mathematical Modelling, 41, 667-682. doi:10.1016/j.apm.2016.09.022Liu, Z., Guo, S., & Wang, L. (2019). Integrated green scheduling optimization of flexible job shop and crane transportation considering comprehensive energy consumption. Journal of Cleaner Production, 211, 765-786. doi:10.1016/j.jclepro.2018.11.231Tang, D., & Dai, M. (2015). Energy-efficient approach to minimizing the energy consumption in an extended job-shop scheduling problem. Chinese Journal of Mechanical Engineering, 28(5), 1048-1055. doi:10.3901/cjme.2015.0617.082Hao, X., Lin, L., Gen, M., & Ohno, K. (2013). Effective Estimation of Distribution Algorithm for Stochastic Job Shop Scheduling Problem. Procedia Computer Science, 20, 102-107. doi:10.1016/j.procs.2013.09.246Wang, L., Wang, S., Xu, Y., Zhou, G., & Liu, M. (2012). A bi-population based estimation of distribution algorithm for the flexible job-shop scheduling problem. Computers & Industrial Engineering, 62(4), 917-926. doi:10.1016/j.cie.2011.12.014Jarboui, B., Eddaly, M., & Siarry, P. (2009). An estimation of distribution algorithm for minimizing the total flowtime in permutation flowshop scheduling problems. Computers & Operations Research, 36(9), 2638-2646. doi:10.1016/j.cor.2008.11.004Hauschild, M., & Pelikan, M. (2011). An introduction and survey of estimation of distribution algorithms. Swarm and Evolutionary Computation, 1(3), 111-128. doi:10.1016/j.swevo.2011.08.003Liu, F., Xie, J., & Liu, S. (2015). A method for predicting the energy consumption of the main driving system of a machine tool in a machining process. Journal of Cleaner Production, 105, 171-177. doi:10.1016/j.jclepro.2014.09.058Dai, M., Tang, D., Giret, A., Salido, M. A., & Li, W. D. (2013). Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm. Robotics and Computer-Integrated Manufacturing, 29(5), 418-429. doi:10.1016/j.rcim.2013.04.001Beasley, J. E. (1990). OR-Library: Distributing Test Problems by Electronic Mail. Journal of the Operational Research Society, 41(11), 1069-1072. doi:10.1057/jors.1990.166Zhao, F., Shao, Z., Wang, J., & Zhang, C. (2015). A hybrid differential evolution and estimation of distribution algorithm based on neighbourhood search for job shop scheduling problems. International Journal of Production Research, 54(4), 1039-1060. doi:10.1080/00207543.2015.1041575Van Laarhoven, P. J. M., Aarts, E. H. L., & Lenstra, J. K. (1992). Job Shop Scheduling by Simulated Annealing. Operations Research, 40(1), 113-125. doi:10.1287/opre.40.1.113Wang, L., & Zheng, D.-Z. (2001). An effective hybrid optimization strategy for job-shop scheduling problems. Computers & Operations Research, 28(6), 585-596. doi:10.1016/s0305-0548(99)00137-9Dorndorf, U., & Pesch, E. (1995). Evolution based learning in a job shop scheduling environment. Computers & Operations Research, 22(1), 25-40. doi:10.1016/0305-0548(93)e0016-mPark, B. J., Choi, H. R., & Kim, H. S. (2003). A hybrid genetic algorithm for the job shop scheduling problems. Computers & Industrial Engineering, 45(4), 597-613. doi:10.1016/s0360-8352(03)00077-

A tabu search algorithm for scheduling a single robot in a job-shop environment

We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the travelling-salesman problem with time windows, where additionally generalized precedence constraints have to be respected. The objective is to determine a sequence of all nodes and corresponding starting times in the given time windows in such a way that all generalized precedence relations are respected and the sum of all travelling and waiting times is minimized. We present a local search algorithm for this problem where an appropriate neighborhood structure is defined using problem-specific properties. In order to make the search process more efficient, we apply some techniques which accelerate the evaluation of the solutions in the proposed neighbourhood considerably. Computational results are presented for test data arising from job-shop instances with a single transport robot

An Efficient Solution to the Mixed Shop Scheduling Problem Using a Modified Genetic Algorithm

The mixed job shop scheduling problem is one in which some jobs have fixed machine orders and other jobs may be processed in arbitrary orders. In past literature, optimal solutions have been proposed based on adaptations of classical solutions such as by Johnson, Thompson and Giffler among many others, by pseudopolynomial algorithms, by simulation, and by Genetic Algorithms (GA). GA based solutions have been proposed for flexible Job shops. This paper proposes a GA algorithm for the mixed job shop scheduling problem. The paper starts with an analysis of the characteristics of the so-called mixed shop problem. Based on those properties, a modified GA is proposed to minimize the makespan of the mixed shop schedule. In this approach, sample instances used as test data are generated under the constraints of shop scheduling problems. A comparison of our results based on benchmark data indicate that our modified GA provides an efficient solution for the mixed shop scheduling problem

Optimal job insertion in the no-wait job shop

The no-wait job shop (NWJS) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is given. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The NWJS problem consists in finding a schedule that minimizes the makespan. We address here the so-called optimal job insertion problem (OJI) in the NWJS. While the OJI is NP-hard in the classical job shop, it was shown by Gröflin & Klinkert to be solvable in polynomial time in the NWJS. We present a highly efficient algorithm with running time $\mathcal {O}(n^{2}\cdot\max\{n,m\})$ for this problem. The algorithm is based on a compact formulation of the NWJS problem and a characterization of all feasible insertions as the stable sets (of prescribed cardinality) in a derived comparability graph. As an application of our algorithm, we propose a heuristic for the NWJS problem based on optimal job insertion and present numerical results that compare favorably with current benchmark

A hybrid algorithm for flexible job-shop scheduling problem with setup times

[EN] Job-shop scheduling problem is one of the most important fields in manufacturing optimization where a set of n jobs must be processed on a set of m specified machines. Each job consists of a specific set of operations, which have to be processed according to a given order. The Flexible Job Shop problem (FJSP) is a generalization of the above-mentioned problem, where each operation can be processed by a set of resources and has a processing time depending on the resource used. The FJSP problems cover two difficulties, namely, machine assignment problem and operation sequencing problem. This paper addresses the flexible job-shop scheduling problem with sequence-dependent setup times to minimize two kinds of objectives function: makespan and bi-criteria objective function. For that, we propose a hybrid algorithm based on genetic algorithm (GA) and variable neighbourhood search (VNS) to solve this problem. To evaluate the performance of our algorithm, we compare our results with other methods existing in literature. All the results show the superiority of our algorithm against the available ones in terms of solution quality.Azzouz, A.; Ennigrou, M.; Ben Said, L. (2017). A hybrid algorithm for flexible job-shop scheduling problem with setup times. International Journal of Production Management and Engineering. 5(1):23-30. doi:10.4995/ijpme.2017.6618SWORD233051Allahverdi, A. (2015). The third comprehensive survey on scheduling problems with setup times/costs. European Journal of Operational Research, 246(2), 345-378. doi:10.1016/j.ejor.2015.04.004Azzouz, A., Ennigrou, M., & Jlifi, B. (2015). Diversifying TS using GA in Multi-agent System for Solving Flexible Job Shop Problem. Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics. doi:10.5220/0005511000940101Azzouz, A., Ennigrou, M., Jlifi, B., & Ghedira, K. (2012). Combining Tabu Search and Genetic Algorithm in a Multi-agent System for Solving Flexible Job Shop Problem. 2012 11th Mexican International Conference on Artificial Intelligence. doi:10.1109/micai.2012.12Bagheri, A., & Zandieh, M. (2011). Bi-criteria flexible job-shop scheduling with sequence-dependent setup times—Variable neighborhood search approach. Journal of Manufacturing Systems, 30(1), 8-15. doi:10.1016/j.jmsy.2011.02.004Brandimarte, P. (1993). Routing and scheduling in a flexible job shop by tabu search. Annals of Operations Research, 41(3), 157-183. doi:10.1007/bf02023073Cheung, W., & Zhou, H. (2001). Annals of Operations Research, 107(1/4), 65-81. doi:10.1023/a:1014990729837Fattahi, P., Saidi Mehrabad, M., & Jolai, F. (2007). Mathematical modeling and heuristic approaches to flexible job shop scheduling problems. Journal of Intelligent Manufacturing, 18(3), 331-342. doi:10.1007/s10845-007-0026-8González, M. A., Rodriguez Vela, C., Varela, R. (2013). An efficient memetic algorithm for the flexible job shop with setup times. In Twenty-Third International Conference on Automated, pp. 91-99.Hurink, J., Jurisch, B., & Thole, M. (1994). Tabu search for the job-shop scheduling problem with multi-purpose machines. OR Spektrum, 15(4), 205-215. doi:10.1007/bf01719451Imanipour, N. (2006). Modeling&Solving Flexible Job Shop Problem With Sequence Dependent Setup Times. 2006 International Conference on Service Systems and Service Management. doi:10.1109/icsssm.2006.320680KIM, S. C., & BOBROWSKI, P. M. (1994). Impact of sequence-dependent setup time on job shop scheduling performance. International Journal of Production Research, 32(7), 1503-1520. doi:10.1080/00207549408957019Moghaddas, R., Houshmand, M. (2008). Job-shop scheduling problem with sequence dependent setup times. Proceedings of the International MultiConference of Engineers and Computer Scientists,2, 978-988.Mousakhani, M. (2013). Sequence-dependent setup time flexible job shop scheduling problem to minimise total tardiness. International Journal of Production Research, 51(12), 3476-3487. doi:10.1080/00207543.2012.746480Naderi, B., Zandieh, M., & Fatemi Ghomi, S. M. T. (2008). Scheduling sequence-dependent setup time job shops with preventive maintenance. The International Journal of Advanced Manufacturing Technology, 43(1-2), 170-181. doi:10.1007/s00170-008-1693-0Najid, N. M., Dauzere-Peres, S., & Zaidat, A. (s. f.). A modified simulated annealing method for flexible job shop scheduling problem. IEEE International Conference on Systems, Man and Cybernetics. doi:10.1109/icsmc.2002.1176334Nouiri, M., Bekrar, A., Jemai, A., Niar, S., & Ammari, A. C. (2015). An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem. Journal of Intelligent Manufacturing, 29(3), 603-615. doi:10.1007/s10845-015-1039-3Oddi, A., Rasconi, R., Cesta, A., & Smith, S. (2011). Applying iterative flattening search to the job shop scheduling problem with alternative resources and sequence dependent setup times. In COPLAS 2011 Proceedings of the Workshopon Constraint Satisfaction Techniques for Planning and Scheduling Problems, pp. 15-22.Pezzella, F., Morganti, G., & Ciaschetti, G. (2008). A genetic algorithm for the Flexible Job-shop Scheduling Problem. Computers & Operations Research, 35(10), 3202-3212. doi:10.1016/j.cor.2007.02.014Sadrzadeh, A. (2013). Development of Both the AIS and PSO for Solving the Flexible Job Shop Scheduling Problem. Arabian Journal for Science and Engineering, 38(12), 3593-3604. doi:10.1007/s13369-013-0625-ySaidi-Mehrabad, M., & Fattahi, P. (2006). Flexible job shop scheduling with tabu search algorithms. The International Journal of Advanced Manufacturing Technology, 32(5-6), 563-570. doi:10.1007/s00170-005-0375-4Vilcot, G., & Billaut, J.-C. (2011). A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem. International Journal of Production Research, 49(23), 6963-6980. doi:10.1080/00207543.2010.526016Shi-Jin, W., Bing-Hai, Z., & Li-Feng, X. (2008). A filtered-beam-search-based heuristic algorithm for flexible job-shop scheduling problem. International Journal of Production Research, 46(11), 3027-3058. doi:10.1080/00207540600988105Wang, S., & Yu, J. (2010). An effective heuristic for flexible job-shop scheduling problem with maintenance activities. Computers & Industrial Engineering, 59(3), 436-447. doi:10.1016/j.cie.2010.05.016Zandieh, M., Yazdani, M., Gholami, M., & Mousakhani, M. (2009). A Simulated Annealing Algorithm for Flexible Job-Shop Scheduling Problem. Journal of Applied Sciences, 9(4), 662-670. doi:10.3923/jas.2009.662.670Zambrano Rey, G., Bekrar, A., Prabhu, V., & Trentesaux, D. (2014). Coupling a genetic algorithm with the distributed arrival-time control for the JIT dynamic scheduling of flexible job-shops. International Journal of Production Research, 52(12), 3688-3709. doi:10.1080/00207543.2014.881575Zhang, G., Gao, L., & Shi, Y. (2011). An effective genetic algorithm for the flexible job-shop scheduling problem. Expert Systems with Applications, 38(4), 3563-3573. doi:10.1016/j.eswa.2010.08.145Zhang, G., Shao, X., Li, P., & Gao, L. (2009). An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem. Computers & Industrial Engineering, 56(4), 1309-1318. doi:10.1016/j.cie.2008.07.021Zhou, Y., Li, B., & Yang, J. (2005). Study on job shop scheduling with sequence-dependent setup times using biological immune algorithm. The International Journal of Advanced Manufacturing Technology, 30(1-2), 105-111. doi:10.1007/s00170-005-0022-0Ziaee, M. (2013). A heuristic algorithm for solving flexible job shop scheduling problem. The International Journal of Advanced Manufacturing Technology, 71(1-4), 519-528. doi:10.1007/s00170-013-5510-zZribi, N., Kacem, I., Kamel, A. E., & Borne, P. (2007). Assignment and Scheduling in Flexible Job-Shops by Hierarchical Optimization. IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), 37(4), 652-661. doi:10.1109/tsmcc.2007.89749

Flow shop scheduling with two machines

A flow shop problem has n jobs (i = 1.. , n) on m machines (j = 1, . . . , m) and a job consists two operations and the jth operation of each job must be processed on machine j. Any job can start only on machine j if it is completed on machine j-1 and if machine j is free. Each operation has a known processing time pij. The work here focuses on the case m = 2 where the objective is to minimize (1) the makespan (Cmax) and (2) the average completion time (sumCi); We first review an efficient greedy algorithm by Johnson for Cmax and give detailed proofs; The we note that in the case of sumCi the problem is harder, in fact it is NP-hard. To tackle this problem we have implemented a branch and bound algorithm to find the optimal schedules in some cases. We also constructed a genetic algorithm under MIT\u27s GALib C++ package. Solutions from the branch and bound algorithm are used as benchmarks for the solutions found by the genetic algorithm