Incorporation of Costs of Adjustment in DEA Models: Selection of Optimal Paths

Abstract

This study focuses on the optimisation of the economic objective of firms and on the determination of the optimal paths of adjustments of their inputs. The path of adjustment is the period-to-period sequence of adjustments that change the quantities of the inputs from the initial to the optimal target values. The target quantities of the inputs are optimal in the sense that they optimise the economic objective of the firm. The adjustment of inputs is feasible only if the present value of the costs of adjustments of inputs is no less than the present value of the reduction of the costs of the inputs. Data Envelopment Analysis (DEA) is used to define the boundary of the technology or the transformation function for the productive process. The period-to-period sequence of adjustments suggests a dynamic form of DEA. This dynamic form is derived from allowing DEA for a period-to-period change of peers and of their respective weights. The change of peers may be the deletion of a peer, the incorporation of a new peer or both changes simultaneously. A peer may increase, retain or decrease its weight. The final dynamic DEA model considers time-varying outputs and time-varying technology. The final dynamic model reduces to the standard DEA model when time is not included in implicit or explicit form. A limitation of the model is that the expected or forecasted data are used as observed data. The model is used in an empirical application to 35 stores of Dijon, a Chilean retailing firm.