Cost Malmquist Productivity Index Based on Piecewise Linear Cost Function in Data Envelopment Analysis

One of the effective factors in calculating the Malmquist productivity index (MPI) is to calculate cost efficiency changes. In some cases, especially when the issue of saving and observance of the consumption pattern is considered, prices are usually considered stepwise, so this research introduces a method for calculating cost Malmquist productivity index (CMPI) when the prices are stepwise and the cost function is a linear piece.

In this paper, due to the presence of stepwise prices and piecewise linear costs, the stepwise linear cost efficiency model, as well as the (CMPI), were used as the baseline models to develop the calculating method of cost Malmquist index as the prices are stepwise.

By applying the proposed method to calculate the index of 14 confectionaries in the city of Islam Abad Gharb during the years of 2019 and 2020, it was found that four confectionaries had an increase in productivity and ten confectionaries had a drop in productivity; and in total the average efficiency of 2020 declined compared to 2019. Also, the main factor in the loss of productivity in units was the loss of their efficiency in 2020 compared to 2019.

According to the findings of the paper, the models presented in the proposed method have increased the capability of classical models to calculate (MPI) in such a way that if the costs are piecewise linear, the more acceptable and real results can be achieved with the help of proposed models than the classical models.