Some results on relocation policies

Abstract

In this paper, we derive general results concerning optimal relocation policy under some assumptions. We consider a firm that is located in a specific location, producing at a certain level of efficiency. With time, the firm can decide to change its location to a new and more efficient site, paying relocation costs. Moreover, we assume that these new sites become available according to a Poisson process, and that the levels of efficiency improvement inherent to each one of these sites are random variables. With this framework, we characterise certain parameters of the optimal relocation policy. In particular, we characterise the expected relocation time and we prove that it depends on the distribution of the level of efficiency improvement only through an expected value. Therefore, the optimal policy shows a kind of robustness in terms of the stochastic assumptions of the problem, which has a major impact in the application of relocation policies. In addition, we also characterise the optimal relocation time. Impacts on the final results driven by the characteristics of the firm's original location site, the market environment and the way in which risk is modelled are studied numerically. The overall results are in line with economic intuition.

Keywords:

• finance
• relocation
• project scheduling
• real options
• optimal timing
• Erlang distribution

Acknowledgements

The research was supported in part by Programa Operacional ‘Ciência, Tecnologia, Inovação’ (POCTI) of the Fundação para a Ciência e a Tecnologia (FCT), cofinanced by the European Community fund FEDER and the projects UTAustin/MAT/0057/2008, PTDC/EIA-CCO/098910/2008 and UTA-CMU/MAT/0006/2009.

Notes

In order to derive simpler algebraically expressions, we assume these parameters, so that, in particular, the expected value is μ.