Appointment scheduling for multi-stage sequential service systems with stochastic service durations

Abstract

We consider an appointment scheduling problem in multi-stage sequential service systems, in which the decision maker has to determine an appointment time for each customer in the first stage to minimize the total expected weighted costs of customers’ waiting times and service providers’ idle times over multiple stages. For the multi-stage sequential appointment scheduling problem, we first formulate it as a stochastic program. Then, we establish linear relationships among waiting times and idle times in different stages, and transform the stochastic program into a two-stage program. Moreover, we analyze properties of the second stage program, and develop an efficient L-shaped algorithm based on the properties. And finally, we conduct numerical experiments to evaluate the efficiency of our proposed algorithm, and investigate structural properties of the optimal schedule and characteristics of waiting times and idle times in each stage. The experimental results show that the optimal schedule exhibits a “dome” shape when service times of all customers are independent and identically distributed in each stage, and the “dome” shape varies with different parameters.