Approximate Dynamic Programming for Capacity Allocation in the Service Industry

European Journal of Operational Research, Vol. 218 (1), 239-250.

27 Pages Posted: 6 Jun 2010 Last revised: 15 Aug 2012

See all articles by Hans-Jörg Schütz

Hans-Jörg Schütz

Technische Universität München - TUM School of Management

Rainer Kolisch

Technische Universität München (TUM) - TUM School of Management

Date Written: June 1, 2010

Abstract

We consider a problem where different classes of customers can book different types of service in advance and the service company has to respond immediately to the booking request confirming or rejecting it. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as cost of overtime. For the calculation of the latter, information on the underlying appointment schedule is required. In contrast to most models in the literature we assume that the service time of clients is stochastic and that clients might be unpunctual. Throughout the paper we will relate the problem to capacity allocation in radiology services. The problem is modeled as a continuous-time Markov decision process and solved using simulation-based approximate dynamic programming (ADP). We employ an adapted heuristic ADP algorithm from the literature and investigate on the benefits of applying ADP to this type of problem. First, we study a simplified problem with deterministic service times and punctual arrival of clients and compare the solution from the ADP algorithm to the optimal solution. We find that the heuristic ADP algorithm performs very well in terms of objective function value, solution time, and memory requirements. Second, we study the problem with stochastic service times and unpunctuality. It is then shown that the resulting policy constitutes a large improvement over an “optimal” policy that is deduced using restrictive, simplifying assumptions.

Keywords: Capacity Allocation, Services, Health Care Operations, Approximate Dynamic Programming, Reinforcement Learning, Semi-Markov Decision Process

JEL Classification: C61, I10, L80

Suggested Citation

Schütz, Hans-Jörg and Kolisch, Rainer, Approximate Dynamic Programming for Capacity Allocation in the Service Industry (June 1, 2010). European Journal of Operational Research, Vol. 218 (1), 239-250., Available at SSRN: https://ssrn.com/abstract=1618315 or http://dx.doi.org/10.2139/ssrn.1618315

Hans-Jörg Schütz (Contact Author)

Technische Universität München - TUM School of Management ( email )

Arcisstr. 21
D-80333 Munich
Germany

Rainer Kolisch

Technische Universität München (TUM) - TUM School of Management ( email )

Arcisstr. 21
München, 80333
Germany

HOME PAGE: http://www.som.wi.tum.de/index.php?id=16

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