Capacity Investment with Demand Learning

Operations Research, Forthcoming

64 Pages Posted: 16 Jun 2016 Last revised: 9 Nov 2016

See all articles by Anyan Qi

Anyan Qi

University of Texas at Dallas - Naveen Jindal School of Management

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business

Amitabh Sinha

University of Michigan, Stephen M. Ross School of Business

Date Written: August 22, 2016

Abstract

We study a firm’s optimal strategy to adjust its capacity using demand information. The capacity adjustment is costly and often subject to managerial hurdles which sometimes make it difficult to adjust capacity multiple times. In order to clearly analyze the impact of demand learning on the firm’s decision, we study two scenarios. In the first scenario, the firm’s capacity adjustment cost increases significantly with respect to the number of adjustments because of significant managerial hurdles, and resultantly the firm has a single opportunity to adjust capacity (single adjustment scenario). In the second scenario, the capacity adjustment costs do not change with respect to the number of adjustments because of little managerial hurdles, and therefore the firm has multiple opportunities to adjust capacity (multiple adjustment scenario). For both scenarios, we first formulate the problem as a stochastic dynamic program, and then characterize the firm’s optimal policy: when to adjust and by how much. We show that the optimal decision on when and by how much to change the capacity is not monotone in the likelihood of high demand in the single adjustment scenario, while the optimal decision is monotone under mild conditions and the optimal policy is a control band policy in the multiple adjustment scenario. The sharp contrast reflects the impact of demand learning on the firm’s optimal capacity decision. Since computing and implementing the optimal policy is not tractable for general problems, we develop a data-driven heuristic for each scenario. In the single adjustment scenario, we show that a two-step heuristic which explores demand for an appropriately chosen length of time and adjusts the capacity based on the observed demand is asymptotically optimal, and prove the convergence rate. In the multiple adjustment scenario, we also show that a multi-step heuristic under which the firm adjusts its capacity at a predetermined set of periods with exponentially increasing gap between two consecutive decisions is asymptotically optimal and show its convergence rate. We finally apply our heuristics to a numerical study and demonstrate the performance and robustness of the heuristics.

Keywords: capacity management; managerial hurdles; exploration-exploitation; Bayesian updating; data-driven.

Suggested Citation

Qi, Anyan and Ahn, Hyun-Soo and Sinha, Amitabh, Capacity Investment with Demand Learning (August 22, 2016). Operations Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2789834 or http://dx.doi.org/10.2139/ssrn.2789834

Anyan Qi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan St
R5456
Ann Arbor, MI 48109-1234
United States

Amitabh Sinha

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

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