Cost Efficiency in the Presence of Time Dependent Prices

In traditional cost-efficiency models, inputs and outputs, as well as input prices were known as constant values for each decision-making unit In our daily applications, however, market entry prices vary at different times. In other words, input prices for Decision-Making Units (DMUs) are time dependent. Traditional methods cannot calculate the cost efficiency of DMUs with time-dependent prices. This paper proposes a new method to calculate the cost efficiency of DMUs in the presence of time-dependent prices. The proposed model is a parametric programming problem model depending on time. In the presented model, the inputs and outputs are functions in terms of time, which is not present in the models introduced by other researchers. New definitions for time-dependent cost efficiency have also been introduced. The cost efficiency of DMUs is measured over a given time and the units are ranked according to the time obtained. Finally, a numerical example has been presented to illustrate the proposed method.