Technical Note—Financial Market Approaches to Facility Location under Uncertainty

James Ernest Hodder

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Facility Location and Emergency Management Capital Investment and Risk Analysis Risk and Portfolio Optimization

Abstract

This paper examines financial market approaches for facility location models incorporating uncertainty and risk aversion. As an example, it compares a model based on the Capital Asset Pricing Model with one using a mean-variance objective function. There are dramatically different computational implications; the financial market approach yields simpler procedures and is able to handle more complex problems. However, as discussed in the concluding observations, there are situations where the financial market perspective is less appropriate; consequently, the mean-variance model still has a role in analyzing facility location decisions.

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1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1976The arbitrage theory of capital asset pricing 1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1959Portfolio Selection: Efficient Diversification of Investments 1966Equilibrium in a Capital Asset Market 1976Risk Aversion in the Small and in the Large 1972Essays in the Theory of Risk-Bearing.1982Modern Portfolio Theory and Investment Analysis.

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