Dynamic Inter-day and Intra-day Scheduling

Abstract

The simultaneous consideration of appointment day (inter-day scheduling) and time of day (intra-day scheduling) in dynamic scheduling decisions is an important theoretical and practical problem that has remained open due to its stochastic nature, complex structure, and large dimensionality. This article provides the first analytical model and associated theoretical results to address this joint problem within a tractable optimization framework. We build upon two recent studies: one from dynamic inter-day scheduling (Truong 2015), and one from static intra-day scheduling (Zacharias and Yunes 2020). We build connections between these two studies by proving new theoretical results in discrete convex analysis regarding constrained multimodular function minimization. These results, in conjunction with our novel dynamic programming framework, facilitate the development of an informed and practically implementable heuristic solution with computationally tractable theoretical performance guarantees. Our numerical experiments demonstrate that the optimality gap is less than 1% for practical instances of the problem.

Keywords: stochastic dynamic programming, discrete convexity, appointment scheduling, advance scheduling