1Assistant Professor, Dep. of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
2Assistant Professor, Dep. of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran
3M. S. Dep. of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
In some situations the producers desire to maximize total profit of Decision Making Units (DMUs) while the inputs and outputs prices of DMUs change from one time period to another. In this paper, the researchers develop productivity index when producers are going to maximize total profit when the price of inputs and outputs are known.The proposed method uses all price information about inputs and outputs for determining productivity index while previous methods use only cost of inputs to determine index of productivity .Therefore, the proposed Mulmquist productivity index in this paper is more precise than the other Mulmquist productivity index. Here, productivity change is decomposed into profit efficiency and profit technical change. Furthermore, profit efficiency change is decomposed into technical and allocative efficiency change and profit technical change into a part capturing shifts of input and output quantities and shifts of input and output prices. These decompositions provide a clearer picture of the root sources of productivity change. Finally, the proposed fractional programming problems are converted to the linear programming problems. By an illustrative example, we explain the proposed profit Malmquist productivity index.