Decomposition algorithms for optimizing multi-server appointment scheduling with chance constraints

• Published in: Mathematical programming Vol. 157; no. 1; pp. 245 - 276
• Main Authors: Deng, Yan, Shen, Siqian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2016; Springer Nature B.V
• Subjects: Algorithms; Approximation; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Decomposition; Full Length Paper; Integer programming; Linear programming; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical models; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Operations research; Optimization; Packing problem; Risk; Scheduling; Servers; Studies; Surgery; Theoretical; Chance-constrained programming; 90C15 Stochastic programming; 90C10 Integer programming; Decomposition; Service scheduling; Branch-and-cut; Mixed-integer linear programming
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-016-0990-x

This paper investigates a problem of scheduling appointments with random service durations on multiple servers with operating time limits. We minimize the cost of operating servers and serving appointments, subject to a joint chance constraint limiting the risk of server running overtime. With finite samples of random service time, we consider a mixed-integer linear programming extended formulation and propose a two-stage decomposition framework with cutting planes. The first stage considers a relaxed master problem as a variant of the chance-constrained binary packing problem discussed in Song et al. (INFORMS J Comput 26(4):735–747, 2014 ), which packs appointments into servers under chance-constrained server overtime. Given appointment-to-server assignments, the second stage seeks feasible schedules on individual servers. We propose strengthening, bounding, and branch-and-cut methods for computing problems in both stages. Via testing instances with diverse sizes, we compare different decomposition schemes. In particular, we demonstrate the efficacy of our branch-and-cut algorithm that incorporates server-based decomposition for optimizing the problem.