基于运作成本模型的不耐烦顾客预约时间安排（英文）
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摘要
研究了预约中考虑不耐烦行为的顾客到达时间安排问题.假设顾客不耐烦时长及服务时长服从指数分布,以最小化联合成本为目标,研究了固定数量顾客的最优预约到达时间安排.联合成本函数由顾客期望延迟时间和服务时间构成.根据顾客的预约到达时间间隔,推导出了每个顾客期望延迟时间的递推表达式.进一步研究了不耐烦行为对于最优预约到达时间安排及总成本函数的影响.结果表明,随着不耐烦率的增加,最优预约到达时间间隔越来越小,并且最后几名顾客的预约时间间隔逐渐接近中间的顾客,且不耐烦行为会造成联合成本的显著增加.
An appointment scheduling problem is studied with the consideration of customer impatience. On the assumption that both the time of leaving queue and the time of service are exponentially distributed, in order to minimize the joint cost, the optimal appointment schedule of the fixed number of customers is studied. The joint cost function is composed of customers' expected delay time and service availability time. The expected delay time of each customer in the queue is recursively computed in terms of customer interarrival time. Furthermore, the effect of impatience on the optimal schedule as well as the total operating cost is studied. The results show that as the impatience rate increases, the optimal interarrival time becomes shorter and the interarrival time of the last few customers gradually approaches that of the customers in the middle. In addition, impatient behaviors can increase the joint cost.
An appointment scheduling problem is studied with the consideration of customer impatience. On the assumption that both the time of leaving queue and the time of service are exponentially distributed, in order to minimize the joint cost, the optimal appointment schedule of the fixed number of customers is studied. The joint cost function is composed of customers' expected delay time and service availability time. The expected delay time of each customer in the queue is recursively computed in terms of customer interarrival time. Furthermore, the effect of impatience on the optimal schedule as well as the total operating cost is studied. The results show that as the impatience rate increases, the optimal interarrival time becomes shorter and the interarrival time of the last few customers gradually approaches that of the customers in the middle. In addition, impatient behaviors can increase the joint cost.
引文
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[3] Kuiper A,Kemper B,Mandjes M.A computational approach to optimized appointment scheduling[J].Queueing Systems,2015,79(1):5-36.DOI:10.1007/s11134-014-9398-6.
[4] Zhang Y L,Shen S Q,Erdogan S A.Distributionally robust appointment scheduling with moment-based ambiguity set[J].Operations Research Letters,2017,45(2):139-144.DOI:10.1016/j.orl.2017.01.010.
[5] Liu N.Optimal choice for appointment scheduling window under patient no-show behavior[J].Production and Operations Management,2016,25(1):128-142.DOI:10.1111/poms.12401.
[6] Jiang B W,Tang J F,Yan C J.A stochastic programming model for outpatient appointment scheduling considering unpunctuality[J].Omega,2019,82:70-82.DOI:10.1016/j.omega.2017.12.004.
[7] Movaghar A.On queueing with customer impatience until the beginning of service[J].Queueing Systems,1998,29(2/3/4):337-350.
[8] Choi B D,Kim B,Chung J.M/M/1 queue with impatient customers of higher priority[J].Queueing Systems,Theory and Applications,2001,38(1):49-66.DOI:DOI:10.1023/A:1010820112080.
[9] Daley D J.General customer impatience in the queue GI/G/1[J].Journal of Applied Probability,1965,2(1):186-205.DOI:10.2307/3211884.
[10] Choi B D,Kim B,Zhu D B.MAP/M/c queue with constant impatient time[J].Mathematics of Operations Research,2004,29(2):309-325.DOI:10.1287/moor.1030.0081.
[11] Sakuma Y,Takine T.Multi-class M/PH/1 queues with deterministic impatience times[J].Stochastic Models,2017,33(1):1-29.DOI:10.1080/15326349.2016.1197778.
[12] Wang F,Wu X Y.On the waiting time for a M/M/1 queue with impatience [EB/OL].(2017-04-06)[2019-05-23].https://arxiv.org/abs/1704.01709.
[13] Neuts M F.Matrix-geometric solutions in stochastic models:An algorithmic approach[M].Courier Corporation,1994:1-36.
[2] Wang P P.Static and dynamic scheduling of customer arrivals to a single-server system[J].Naval Research Logistics,1993,40(3):345-360.DOI:10.1002/1520-6750(199304)40:3345::aid-nav3220400305>3.0.co;2-n.
[3] Kuiper A,Kemper B,Mandjes M.A computational approach to optimized appointment scheduling[J].Queueing Systems,2015,79(1):5-36.DOI:10.1007/s11134-014-9398-6.
[4] Zhang Y L,Shen S Q,Erdogan S A.Distributionally robust appointment scheduling with moment-based ambiguity set[J].Operations Research Letters,2017,45(2):139-144.DOI:10.1016/j.orl.2017.01.010.
[5] Liu N.Optimal choice for appointment scheduling window under patient no-show behavior[J].Production and Operations Management,2016,25(1):128-142.DOI:10.1111/poms.12401.
[6] Jiang B W,Tang J F,Yan C J.A stochastic programming model for outpatient appointment scheduling considering unpunctuality[J].Omega,2019,82:70-82.DOI:10.1016/j.omega.2017.12.004.
[7] Movaghar A.On queueing with customer impatience until the beginning of service[J].Queueing Systems,1998,29(2/3/4):337-350.
[8] Choi B D,Kim B,Chung J.M/M/1 queue with impatient customers of higher priority[J].Queueing Systems,Theory and Applications,2001,38(1):49-66.DOI:DOI:10.1023/A:1010820112080.
[9] Daley D J.General customer impatience in the queue GI/G/1[J].Journal of Applied Probability,1965,2(1):186-205.DOI:10.2307/3211884.
[10] Choi B D,Kim B,Zhu D B.MAP/M/c queue with constant impatient time[J].Mathematics of Operations Research,2004,29(2):309-325.DOI:10.1287/moor.1030.0081.
[11] Sakuma Y,Takine T.Multi-class M/PH/1 queues with deterministic impatience times[J].Stochastic Models,2017,33(1):1-29.DOI:10.1080/15326349.2016.1197778.
[12] Wang F,Wu X Y.On the waiting time for a M/M/1 queue with impatience [EB/OL].(2017-04-06)[2019-05-23].https://arxiv.org/abs/1704.01709.
[13] Neuts M F.Matrix-geometric solutions in stochastic models:An algorithmic approach[M].Courier Corporation,1994:1-36.