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A new model and algorithm for uncertain random parallel machine scheduling problem

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Abstract

The paper presents a new model for uniform parallel machine scheduling problem with uncertainty and randomness simultaneously for processing times of jobs based on chance theory. The objective of the model is to minimize expected completion time. The constraint of the model is that uncertain random completion time of scheduling is less than or equal to expected completion time. The model is transformed to a crisp non-deterministic polynomial hard mathematical programming model based on chance theory. Firstly, simulation techniques of the objective function and the left chance constraint are proposed. Then, two heuristic methods to solve the crisp model are presented. Finally, they are integrated into two hybrid intelligent algorithms for searching the quasi-optimal schedule. Besides, the effectiveness of the model and its hybrid intelligent algorithms are verified by a numerical example generated randomly.

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References

  • Alidaee B, Womer N (1999) Scheduling with time dependent processing times: review and extensions. J Oper Res Soc 50:711–720

    Article  MATH  Google Scholar 

  • Byung D, Byung S (2016) A hybrid genetic algorithm with two-stage dispatching heuristic for a machine scheduling problem with step-deteriorating jobs and rate-modifying activities. Comput Ind Eng 98:113–124

    Article  Google Scholar 

  • Chen Z (1996) Parallel machine scheduling with time dependent processing times. Discrete Appl Math 70:81–93

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Sin CCS (1990) A state-of-the-art review of parallel-machine scheduling research. Eur J Oper Res 47:271–292

    Article  MATH  Google Scholar 

  • Cheng M, Wang G, He L (2009) Parallel machines scheduling problems with proportionally deteriorating jobs. Int J Syst Sci 40:53–57

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng H, Joseph YTL, Kangbok L, Michael L (2016) Pinedo scheduling a single machine with parallel batching to minimize makespan and total rejection cost. Discrete Appl Math 204:150–163

    Article  MathSciNet  MATH  Google Scholar 

  • Chung BD, Kim BS (2016) A hybrid genetic algorithm with two-stage dispatching heuristic for a machine scheduling problem with step-deteriorating jobs and rate-modifying activities. Comput Ind Eng 98:113–124

    Article  Google Scholar 

  • Dai W, Chen X (2012) Entropy of function of uncertain variables. Math Comput Model 55:754–760

    Article  MathSciNet  MATH  Google Scholar 

  • Daniels RL, Hua SY, Webster S (1999) Heuristics for parallel-machine flexible-resource scheduling problems with unspecified job assignment. Comput Oper Res 26:143–155

    Article  MATH  Google Scholar 

  • Ding S (2014a) Uncertain minimum cost flow problem. Soft Comput 18(11):2201–2207

    Article  MATH  Google Scholar 

  • Ding S (2014b) Uncertain random newsboy problem. J Intell Fuzzy Syst 26(1):483–490

    MathSciNet  MATH  Google Scholar 

  • Gao Y (2011) Shortest path problem with uncertain arc lengths. Comput Math Appl 62:2591–2600

    Article  MathSciNet  MATH  Google Scholar 

  • Gao Y (2012) Uncertain models for single facility location problems on networks. Appl Math Model 36(6):2592–2599

    Article  MathSciNet  MATH  Google Scholar 

  • Gao Y, Qin Z (2016) On computing the edge-connectivity of an uncertain graph. IEEE Trans Fuzzy Syst 24(4):981–991

    Article  Google Scholar 

  • Gao Y, Wen ML, Ding SB (2013) Policy for uncertain single period inventory problem. Int J Uncertainty Fuzziness Knowl-Based Syst 21(6):945–953

  • Gao Y, Yang L, Li S, Kar S (2015) On distribution function of the diameter in uncertain graph. Inf Sci 296:61–74

    Article  MathSciNet  MATH  Google Scholar 

  • Gao ZK, Suganthan PN, Pan QK, Chua TJ, Cai TX (2016) An improved artificial bee colony algorithm for flexible job-shop scheduling problem with fuzzy processing time. Expert Syst Appl 65:52–67

    Article  Google Scholar 

  • Joo CM, Kim BS (2015) Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability. Comput Ind Eng 85:102–109

    Article  Google Scholar 

  • Kahneman D, Tversky A (1979) Prospect theory: an analysis of decisions under risk. Econometrica 47:263–291

    Article  MathSciNet  MATH  Google Scholar 

  • Ke H, Liu HM, Tian GD (2012) An uncertain random programming model for project scheduling problem. Int J Intell Syst 30:66–79

    Article  Google Scholar 

  • Li D, Yang J (2004) Fuzzy linear programming technique for multiattribute group decision in fuzzy environments. Inf Sci 166:49–66

    Article  MathSciNet  Google Scholar 

  • Liao TW, Chang PC, Kuo RJ, Liao CJ (2014) A comparison of five hybrid metaheuristic algorithms for unrelated parallel-machine scheduling and inbound trucks sequencing in multi-door cross docking systems. Appl Soft Comput 21:180–193

    Article  Google Scholar 

  • Lin SW, Ying KC (2014) ABC-based manufacturing scheduling for unrelated parallel machines with machine-dependent and job sequence-dependent setup times. Comput Oper Res 51:172–181

    Article  MathSciNet  MATH  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2009) Some research problems inuncertainty theory. J Uncertain Syst 3(1):33–10

    Google Scholar 

  • Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin

    Book  Google Scholar 

  • Liu YH (2013a) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 17(4):625–634

    Article  MATH  Google Scholar 

  • Liu YH (2013b) Uncertain random programming with applications. Fuzzy Optim Decis Mak 12(2):153– 169

    Article  MathSciNet  MATH  Google Scholar 

  • Liu B (2016) Uncertainty theory, 5th edn. http://orsc.edu.cn/liu

  • Mosheiov G (2001) Scheduling problems with a learning effect. Eur J Oper Res 132:687–693

    Article  MathSciNet  MATH  Google Scholar 

  • Peng J, Liu B (2004) Parallel machine scheduling models with fuzzy processing times. Inf Sci 166:49–66

    Article  MathSciNet  MATH  Google Scholar 

  • Rothblum G, Sethuraman J (2007) Stochastic scheduling in an in-forest. Discrete Optim 5:457–466

    Article  MathSciNet  MATH  Google Scholar 

  • Shahvari O, Logendran R (2016) Hybrid flow shop batching and scheduling with a bi-criteria objective. Int J Prod Econ 77:154–176

    MATH  Google Scholar 

  • Shahvari O, Logendran R (2017) An enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes. Comput Oper Res 77:154–176

    Article  MathSciNet  MATH  Google Scholar 

  • Shen J, Zhu Y (2017) Uncertain flexible flow shop scheduling problem subject to breakdowns. J Intell Fuzzy Syst 32:207–214

    Article  MATH  Google Scholar 

  • Shen L, Wang D, Wang XY (2013) Parallel-machine scheduling with non-simultaneous machine available time. App Math Model 37:5227–5232

    Article  MathSciNet  MATH  Google Scholar 

  • Wang X, Ning Y (2016) An uncertain currency model with floating interest rates. Soft Comput. https://doi.org/10.1007/s00500-016-2224-9

    MATH  Google Scholar 

  • Wang XS, Gao ZC, Guo HY (2012) Uncertain hypothesis testing for two experts’ empirical data. Math Comput Model 55:1478–1482

    Article  MathSciNet  MATH  Google Scholar 

  • Wei M, Li X, Yu L (2015) Time-dependent fuzzy random location-scheduling programming for hazardous materials transportation. Trans Res Part C Emerg Technol 57:146–165

    Article  Google Scholar 

  • Xiao J, Yang H, Zhang C, Zheng L, JatinderGupta ND (2015) A hybrid Lagrangian-simulated annealing-based heuristic for the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times. Comput Oper Res 63:72–82

    Article  MathSciNet  MATH  Google Scholar 

  • Yang XF, Gao JW (2016) Linear-quadratic uncertain differential game with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826

    Article  MathSciNet  Google Scholar 

  • Yao K, Gao JW (2015) Uncertain random alternating renewal process with application to interval availability. IEEE Trans Fuzzy Syst 23:1333–1342

    Article  Google Scholar 

  • Yao K, Li X (2012) Uncertain alternating renewal process and its application. IEEE Tran Fuzzy Syst 20(6):1154–1160

    Article  Google Scholar 

  • Yeh WC, Lai PJ, Lee WC, Chuang MC (2014) Parallel-machine scheduling to minimize makespan with fuzzy processing times and learning effects. Inf Sci 269:142–158

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang X, Chen X (2012) A new uncertain programming model for project problem. Int Interdiscip J 15(10):3901–3911

    MathSciNet  MATH  Google Scholar 

  • Zhang X, Li X (2014) A semantic study of the first-order predicate logic with uncertainty involved. Fuzzy Optim Decis Mak 13:357–367

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang X, Ning Y, Meng G (2013) Delayed renewal process with uncertain interarrival times. Fuzzy Optim Decis Mak 12:79–87

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou J, Liu B (2003) New stochastic models for capacitated location-allocation problem. Comput Ind Eng 45:111–125

    Article  Google Scholar 

  • Zhou J, Liu B (2007) Modeling capacitated location-allocation problem with fuzzy demands. Comput Ind Eng 53:454–468

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Foundation of National Natural Science Foundation of China (No. 11471152).

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Authors and Affiliations

  1. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Weimin Ma & Yang Liu

  2. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, China

    Xingfang Zhang

Authors
  1. Weimin Ma
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  2. Yang Liu
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  3. Xingfang Zhang
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Correspondence to Yang Liu.

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Communicated by V. Loia.

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Ma, W., Liu, Y. & Zhang, X. A new model and algorithm for uncertain random parallel machine scheduling problem. Soft Comput 23, 6555–6566 (2019). https://doi.org/10.1007/s00500-018-3304-9

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