Optimal Portfolio of Reconfigurable and Dedicated Capacity under Uncertainty

Abstract

We address how a firm should optimally allocate its capacity investments between dedicated systems (DMS) and reconfigurable systems (RMS). Motivated by our work with machine tool makers, and auto companies who buy their tools, our model addresses the case of a firm making a single product for which demand is random. Furthermore, in stochastic time intervals, the firm introduces a new generation of products. Dedicated capacity is generally cheaper but only functional for one product generation while reconfigurable capacity can be reconfigured for future generations as well albeit at the expense of potentially higher initial investments per unit capacity, maintenance and unit production costs. Given the stochastic nature of demand, and new product introduction intervals, the firm has to decide every period how many reconfigurable and dedicated modules to buy or salvage. We first characterize the structure of the optimal investment policy when DMS and RMS module sizes are identical. In this case, we are able to use multimodularity properties of value functions (Hajek (1985)), to show that the optimal policy structure of our model is of ISD (Invest/Stay Put/Disinvest) type (Eberly and Van Mieghen (1997)). We are also able to provide comparative statics results on how the thresholds defining the ISD structure are affected by changes in problem parameters. Interestingly, the amount of reconfigurable capacity is not necessarily monotonic in the probability of new product introductions or relative cost of dedicated capacity. The ISD policy is unfortunately sub-optimal when DMS and RMS capacity have different module sizes. We provide numerical examples that display characteristics of the optimal policy with different module sizes. We are able to fully characterize the structure of the optimal investment policy under the irreversible investment assumption. For the general case, we provide structural results that significantly decrease the computational load for computing the optimal investment policy. We also show that the optimal policy has an ISD-like structure with perturbations caused by the fact that capacity is lumpy and not continuous as assumed in previous work. Our results indicate that in most situations, firms should keep a portfolio of dedicated and reconfigurable machine tools and the mix should be driven by the relative costs of each as well as the forecasts on how often new products will be introduced and the expected level of demand. In many firms we ∗Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109 †Business School, University of Michigan, Ann Arbor, MI 48109 ‡McCormick School of Engineering & Applied Science, Northwestern University, Evanston, IL 60208

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