Sequencing and scheduling appointments for multi-stage service systems with stochastic service durations and no-shows
研究了多阶段服务系统中客户随机服务时长和爽约下的预约排序与调度问题，提出基于Benders分解的算法以最小化客户等待和空闲时间的加权成本，并通过数值实验验证算法效率。
In this work, we consider a joint sequencing and scheduling appointments problem with stochastic service times and no-shows in multi-stage service systems. The objective is to minimise the total expected weighted costs of customers' waiting times and service providers' idle times over multiple stages. For the problem, we first formulate it as a stochastic program and exploit the sample average approximation approach to reformulate it as a mixed-integer program in further. Then we transform the stochastic program into a two-stage optimisation problem and develop a standard Benders decomposition algorithm. To overcome the long running time of Benders decomposition, we simplify the master problem in the algorithm and propose a Benders decomposition-based algorithm to find a near-optimal solution. Finally, we conduct a series of numerical experiments to illustrate the efficiency of our proposed algorithm, examine the impact of the number of stages, stochastic service times and no-shows on the optimal job allowances and performance indicators (i.e. waiting times and idle times) and investigate two easy-to-implement sequence rules. The computational results show that both our proposed Benders decomposition-based algorithm and easy-to-implement sequence rules perform well.