Estimation of cost efficiency with piecewise linear cost function in integer-valued data envelopment analysis

The cost efficiency is one of the types of the used efficiency concepts in the data envelopment analysis (DEA). In the literature of the cost efficiency, the prices are often applied to the units in a fixed and linear form, while in some cases, as the subjects of the savings and observance of the consumption patterns, the prices are usually considered in terms of stepwise (piecewise linear) and not fixed (linear). This paper proposes the new models to evaluate of the cost efficiency in the fully competitive setting by using the costs in a piecewise linear form. The models are developed for the non-fully competitive and integer-valued inputs cases. Finally, the proposed models are used to determine the cost efficiency of the confectioneries in Islam Abad Gharb city from Iran country in the case study.