Sequencing Appointments for Service Systems Using Inventory Approximations

Managing appointments for service systems with random job durations is a challenging task. We consider a class of appointment planning problems that involve two sets of decisions: job sequencing, i.e., determining the order in which a list of jobs should be performed by the server, and appointment scheduling, i.e., planning the starting times for jobs. These decisions are interconnected because their joint goal is to minimize the expected server idle time and job late-start penalty costs incurred because of randomness in job durations. In this paper, we design new heuristics for sequencing appointments. The idea behind the development of these heuristics is the structural connection between such appointment scheduling problems and stochastic inventory control in serial supply chains. In particular, the decision of determining time allowances as buffers against random job durations is analogous to that of selecting inventory levels as buffers to accommodate random demand in a supply chain; having excess buffers in appointment scheduling and supply chain settings incurs idle time and excess inventory holding costs, respectively, and having inadequate buffers leads to delays of subsequent jobs and backorders, respectively. Recognizing this connection, we propose tractable approximations for the job sequencing problem, obtain several insights, and further develop a very simple sequencing rule of ordering jobs by duration variance to late-start penalty cost ratio. Computational results show that our proposed heuristics produce close-to-optimal job sequences with significantly reduced computation times compared with those produced using an exact mixed-integer stochastic programming formulation based on the sample-average approximation approach.