Dynamic Inter-day and Intra-day Scheduling

39 Pages Posted: 3 Dec 2020 Last revised: 2 Mar 2022

See all articles by Christos Zacharias

Christos Zacharias

Miami Herbert Business School, University of Miami

Nan Liu

Boston College - Carroll School of Management

Mehmet A. Begen

Ivey Business School, University of Western Ontario

Date Written: November 10, 2020

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

Suggested Citation

Zacharias, Christos and Liu, Nan and Begen, Mehmet A., Dynamic Inter-day and Intra-day Scheduling (November 10, 2020). Available at SSRN: https://ssrn.com/abstract=3728077 or http://dx.doi.org/10.2139/ssrn.3728077

Christos Zacharias (Contact Author)

Miami Herbert Business School, University of Miami ( email )

United States

HOME PAGE: http://moya.bus.miami.edu/~czacharias/

Nan Liu

Boston College - Carroll School of Management ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

HOME PAGE: http://sites.google.com/site/nanliuacademic/

Mehmet A. Begen

Ivey Business School, University of Western Ontario ( email )

1255 Western Road
London, Ontario N6G 0N1
Canada

HOME PAGE: http://www.ivey.uwo.ca/faculty/MBegen

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