The optimal choice of inputs under time-of-use pricing and fixed-proportions technology

In this paper we describe the optimal choice of capital, labor and electricity during a representative day of a firm operating under time-of-use (TOU) pricing of electricity and labor. The objective of the firm is to minimize production costs over the day subject to a given output level and several scheduling constraints on the availability of capital and labor. While the underlying theoretical production process of the firm may be ‘flexible’, possibly with substantial substitution among the inputs, most firms find it difficult if not impossible to specify the production process analytically. Thus, we assume that the technology is represented by a set of fixed-proportions activities. This representation is easy to apply in actual situations since the optimal choice of inputs can be formulated as a linear programming (LP) problem. Our analysis shows that the use of a small number of fixed-proportions production activities can result in a good approximation of the optimum. The LP formulation is applied to data sets for two manufacturing firms, and the optimal quantities of output and inputs are close to those actually observed.