ABSTRACT

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.

摘要

在这项工作中，我们考虑了一个随机服务时间和多阶段服务系统中不出现的联合排序和调度约会问题。目的是最大程度地减少客户在多个阶段的等待时间和服务提供商的空闲时间的预期加权总成本。对于这个问题，我们首先将其表述为随机程序，然后利用样本平均近似方法进一步将其重新表述为混合整数程序。然后，将随机程序转换为两阶段优化问题，并开发了标准的Benders分解算法。为了克服Benders分解的长时间运行，我们简化了该算法中的主要问题，并提出了一种基于Benders分解的算法来寻找接近最优的解决方案。最后，我们进行了一系列数值实验，以说明我们提出的算法的效率，研究阶段数，随机服务时间和未出现次数对最佳工作津贴和绩效指标（即等待时间和空闲时间）的影响，并进行调查两个易于实现的序列规则。计算结果表明，我们提出的基于Benders分解的算法和易于实现的序列规则都表现良好。