具有不耐烦顾客的生产服务库存系统最优生产策略
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摘要
研究了基于(s,S)策略有不耐烦顾客的生产服务库存系统.建立了水平相依的拟生灭过程,通过截尾近似的方法求出系统稳态概率向量,并给出系统一些性能指标.最后,设计遗传算法并通过数值算例求解最优生产策略.
We study an(s, S) production inventory system with a positive service time and impatient customers. We formulate a level dependent Quasi-Birth-and-Death process. Using the method of truncating the tail approximately, we compute the steady-state probability vector. Furthermore, various system performance measures in the steady-state are derived.Finally, a genetic algorithm(GA) and numerical experiment are used for searching optional control strategy.
We study an(s, S) production inventory system with a positive service time and impatient customers. We formulate a level dependent Quasi-Birth-and-Death process. Using the method of truncating the tail approximately, we compute the steady-state probability vector. Furthermore, various system performance measures in the steady-state are derived.Finally, a genetic algorithm(GA) and numerical experiment are used for searching optional control strategy.
引文
[1]孔佩娟.一个基于排队/库存的生产系统的最优控制[J].宁波工程学院学报,2006, 18(2):13-16.
[2]侯玉梅.简单生产-库存系统的优化控制[J].系统工程理论与实践,2003, 23(4):1-6.
[3] Krishnamoorthy A, Viswanath N C. Stochastic decomposition in production inventory with service time[J]. European Journal of Operational Research, 2013, 228(2):358-366.
[4] Nair A N, Jacob M J. An(s, S)production inventory controlled self-service queuing system[J].Journal of Probability and Statistics, 2015, 2015(2):1-8.
[5] Jose K P, Nair S S. Analysis of two production inventory systems with buffer, retrials and different production rates[J]. Journal of Industrial Engineering International, 2017, 13(3):369-380.
[6]许茂增,王俊.基于两类需求分布的(s, S)库存系统研究[J].数学的实践与认识,2013, 43(19):55-61.
[7] Baek J W, Moon S K. The M/M/1 queue with a production-inventory system and lost sales[J].Applied Mathematics and Computation, 2014, 233(1):534-544.
[8] Baek J W, Moon S K. A production-inventory system with a Markovian service queue and lost sales[J]. Journal of the Korean Statistical Society, 2016, 45(1):14-24.
[9]张小洪,陈剑,潘德惠.有限耐期随机库存系统的最优控制[J].中国管理科学,2004, 12(2):38-43.
[10] Rajkumar M. An(s, S)retrial inventory system with impatient and negative customers[J]. International Journal of Mathematics in Operational Research, 2014, 6(1):106-122.
[11] Melikov A Z, Ponomarenko L A, Bagirova S A. Analysis of queuing-inventory systems with impatient consume customers[J]. Journal of Automation and Information Sciences, 2016, 48(1):53-68.
[12] Kwon E Y, Kang J, Ko S S. An(s, S)inventory model with level-dependent G/M/1-Type structure[J]. Journal of Industrial and Management Optimization, 2017, 12(2):609-624.
[13] Benjaafar S, Gayon J P, Tepe S. Optional control of a production-inventory system with customer impatience[J]. Operations Research Letters, 2010, 38(4):267-272.
[14] Bright L, Taylor P. Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes[J]. Communication in Statistics Stochastic Models, 1995, 11(3):497-525.
[15]丰建荣,刘志河,刘正和.混合整数规划问题遗传算法的研究及仿真实现[J].系统仿真学报,2004, 16(4):845-848.
[2]侯玉梅.简单生产-库存系统的优化控制[J].系统工程理论与实践,2003, 23(4):1-6.
[3] Krishnamoorthy A, Viswanath N C. Stochastic decomposition in production inventory with service time[J]. European Journal of Operational Research, 2013, 228(2):358-366.
[4] Nair A N, Jacob M J. An(s, S)production inventory controlled self-service queuing system[J].Journal of Probability and Statistics, 2015, 2015(2):1-8.
[5] Jose K P, Nair S S. Analysis of two production inventory systems with buffer, retrials and different production rates[J]. Journal of Industrial Engineering International, 2017, 13(3):369-380.
[6]许茂增,王俊.基于两类需求分布的(s, S)库存系统研究[J].数学的实践与认识,2013, 43(19):55-61.
[7] Baek J W, Moon S K. The M/M/1 queue with a production-inventory system and lost sales[J].Applied Mathematics and Computation, 2014, 233(1):534-544.
[8] Baek J W, Moon S K. A production-inventory system with a Markovian service queue and lost sales[J]. Journal of the Korean Statistical Society, 2016, 45(1):14-24.
[9]张小洪,陈剑,潘德惠.有限耐期随机库存系统的最优控制[J].中国管理科学,2004, 12(2):38-43.
[10] Rajkumar M. An(s, S)retrial inventory system with impatient and negative customers[J]. International Journal of Mathematics in Operational Research, 2014, 6(1):106-122.
[11] Melikov A Z, Ponomarenko L A, Bagirova S A. Analysis of queuing-inventory systems with impatient consume customers[J]. Journal of Automation and Information Sciences, 2016, 48(1):53-68.
[12] Kwon E Y, Kang J, Ko S S. An(s, S)inventory model with level-dependent G/M/1-Type structure[J]. Journal of Industrial and Management Optimization, 2017, 12(2):609-624.
[13] Benjaafar S, Gayon J P, Tepe S. Optional control of a production-inventory system with customer impatience[J]. Operations Research Letters, 2010, 38(4):267-272.
[14] Bright L, Taylor P. Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes[J]. Communication in Statistics Stochastic Models, 1995, 11(3):497-525.
[15]丰建荣,刘志河,刘正和.混合整数规划问题遗传算法的研究及仿真实现[J].系统仿真学报,2004, 16(4):845-848.