Stochastic programming models for a fleet sizing and appointment scheduling problem with random service and travel times - Li, Shutian; Shehadeh, Karmel S.; Tsang, Man Yiu (Transportation research. Part C, Emerging technologies, 2024)
We propose a new stochastic mixed-integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of providers and a set of geographically distributed customers within a service region, our model solves the following problems simultaneously: (i) a fleet sizing problem that determines the number of providers required to serve customers; (ii) an assignment problem that assigns customers to providers; and (iii) a sequencing and scheduling problem that decides the sequence of appointment times of customers assigned to each provider. The objective is to minimize the fixed cost of hiring providers plus the expectation of a weighted sum of customers’ waiting time and providers’ travel time, overtime, and idle time. We compare our proposed model with an extension of an existing model for a closely related problem in the literature, theoretically and empirically. Specifically, we show that our newly proposed model is more compact (i.e., has fewer variables and constraints) and provides a tighter linear programming relaxation. Furthermore, to handle large instances observed in other application domains, we propose two optimization-based heuristics that decompose the HFASP decision process into two steps. The first step involves determining fleet sizing and assignment decisions, and the second constructs a routing plan and a schedule for each provider. We present extensive computational results to show the size and characteristics of HFASP instances that can be solved with our proposed model, demonstrating its computational efficiency over the extension. Results also show that the proposed heuristics can quickly produce high-quality solutions to large instances with an optimality gap not exceeding 5% on tested instances. Finally, we use a case study based on a service region in Lehigh County to derive insights into the HFASP. •We study a fleet sizing and scheduling problem with random travel and service times.•We propose a new sequencing-based stochastic mixed-integer linear programming model.•Our model is more compact and has a tighter relaxation than the routing-based model.•Our model has superior computational efficiency compared to the routing-based model.•We propose optimization-based heuristics that produce high-quality solutions.