Dynamic advance scheduling of outpatient appointments in a moving booking window

Abstract

This paper addresses the dynamic advance scheduling for outpatient medical appointments in a moving booking window. To address this problem, a finite-horizon Markov decision process (MDP) model is proposed to maximize the total expected net reward comprising the reward for accepting outpatients and the capacity usage cost. Structural properties of the optimal value function and the optimal control policy are established. For the special cases in which the lengths of the booking window are equal to 1 and to 2 periods, the antimultimodularity of the optimal value function is proved while the monotonicity and bounded sensitivity of the optimal control policy are established. For the general cases, partial characterization of the optimal policy is performed. Based on insights from the theoretical results, two efficient heuristic policies are devised, including the assignment-sequence policy and multiple-threshold policy. Numerical experiments show that both policies perform consistently well and outperform the other benchmarking heuristic policies.