Short- and long-run plant capacity notions: Definitions and comparison

Abstract

Starting from the existing input-and output-oriented plant capacity measures, this contribution proposes new long-run input-and output-oriented plant capacity measures. While the former leave fixed inputs unchanged, the latter allow for changes in all input dimensions to gauge either a maximal plant capacity output or a minimal input combination at which non-zero production starts. We also establish a formal relation between the existing short-run and the new long-run plant capacity measures. Furthermore, for a standard nonparametric frontier technology, all linear programs as well as their variations are specified to compute all efficiency measures defining these short-and long-run plant capacity concepts. Furthermore, it is shown how the new long run plant capacity measures are identical to existing models of a variable returns to scale technology without inputs or without outputs (see Lovell and Pastor (1999)): thus, we offer an interesting production economic justification for these models. Finally, we numerically illustrate this basic relationship between these short-run and long-run technical concepts of capacity utilisation.

Using COVID-19 mortality to select among hospital plant capacity models: An exploratory empirical application to Hubei province

“…Finally, L (0) = { x : ( x ,0) ∈ T } is the input set compatible with a zero output level. Cesaroni et al. (2019) provide more details on these special technology definitions, and their Figs.…”

“…According to the approach and terminology introduced by Färe et al. (1989a) , we can obtain an SR output-oriented decomposition: where we decompose into a biased plant capacity measure and an unbiased measure , depending on whether we ignore inefficiency or adjust for it (see also Cesaroni et al. (2019) ).…”

“…(2017) , we also define SR input-oriented plant capacity utilization by a ratio of input efficiency measures, evaluated relative to a production technology targeting only at reducing variable inputs and an identical technology with a level of null outputs : where and are input efficiency measures aimed at reducing variable inputs for a given level of outputs or null outputs, respectively. 4 Following Cesaroni et al. (2019) , we also propose an SR input-oriented decomposition, as follows: where is a biased measure, and is an unbiased measure of input-oriented plant capacity utilization.…”

“…Thus, fixed and variable inputs no longer need to be treated differently. Cesaroni et al. (2019) introduce a measure of LR output-oriented plant capacity utilization, given as: where and are output efficiency measures relative to a standard production technology and a technology without any constraints on availability of inputs.…”

Estimating Capacity Utilization of Chinese State Farms

“…Kalai [18] developed a DEA-based framework for identifying the minima of the short-and long-run average cost curves which determined the corresponding capacities. Cesaroni et al [19] considered the short-and long-run capacity measures by imposing different assumptions on the disposability of inputs.…”