Decision rules for allocating a limiting factor across products in a stochastic production environment: a real options approach

This paper develops a real option framework to extend the current class of managerial decision rules appropriate for selecting a multi-product firm's optimal product mix in the presence of a limiting factor of production. The rules are relevant for both tactical and strategic decision making when managers are operating in an environment of earnings uncertainty. The analysis makes several contributions. The central result derives a decision rule for allocating a limiting factor across products based upon the ranking of the different products' real option values per unit of the limiting factor. This rule is shown to give a more efficient allocation of the limiting factor than other potential methods for dealing with uncertainty, for example, an allocation rule based upon a product's expected profit contribution per unit of limiting factor. Furthermore, the paper extends the results to an environment of generalised production uncertainty, clarifying the relevance of two important, but often neglected sources of production flexibility, namely intra-product and inter-product flexibility. Intra-product flexibility denotes the ability of the firm to vary the time at which a given amount of the limiting factor is dedicated to the production of a specific product, depending upon the resolution of uncertainty over the deferral period. Inter-product flexibility enables the firm to re-allocate productive capacity across products, hence alter the composition of the final product mix, for similar reasons. The analysis reveals that the value to the firm of such production flexibility depends critically upon both the revealed value of the option to defer, and the nature and extent of any correlation of price and cost changes across products.