Multi-class, multi-resource advance scheduling with no-shows, cancellations and overbooking

• Published in: Computers & operations research Vol. 67; pp. 90 - 101
• Main Authors: Salemi Parizi, Mahshid, Ghate, Archis
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.03.2016; Pergamon Press Inc
• Subjects: Approximate dynamic programming; Approximation; Cancellation; Decision making models; Delay; Dynamic programming; Exact solutions; Heuristic; Joining; Markov decision processes; Mathematical analysis; Operations research; Scheduling; Stochastic models; Studies; Markov decision processes; Approximate dynamic programming
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2015.09.004

We investigate a class of scheduling problems where dynamically and stochastically arriving appointment requests are either rejected or booked for future slots. A customer may cancel an appointment. A customer who does not cancel may fail to show up. The planner may overbook appointments to mitigate the detrimental effects of cancellations and no-shows. A customer needs multiple renewable resources. The system receives a reward for providing service; and incurs costs for rejecting requests, appointment delays, and overtime. Customers are heterogeneous in all problem parameters. We provide a Markov decision process (MDP) formulation of these problems. Exact solution of this MDP is intractable. We show that this MDP has a weakly coupled structure that enables us to apply an approximate dynamic programming method rooted in Lagrangian relaxation, affine value function approximation, and constraint generation. We compare this method with a myopic scheduling heuristic on eighteen hundred problem instances. Our experiments show that there is a statistically significant difference in the performance of the two methods in 77% of these instances. Of these statistically significant instances, the Lagrangian method outperforms the myopic method in 97% of the instances. •Proposes a large class of advance scheduling problems with no-shows, cancellations, and overbooking.•Provides a Markov decision process model for these problems and shows that it is weakly coupled.•Applies an approximate dynamic programming approach rooted in Lagrangian relaxation.