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How to Deal with Numbers of Decision-Making Units and Number of Variables in Multiple Input-Output Production Functions

Estimating the production function is one of the most interest topics in economics, managements, and operations research. Often the number of decision-making units (DMUs) is not sufficiently large in comparison with the numbers of inputs and outputs. In this case, the available methodologies suffer to distinguish between DMUs and to provide a fair estimation of the production function. In the literature, studies usually suggest that researchers should either decrease the number of input-output variables or increase the number of DMUs. We demonstrate the reasons for such suggestions and provide a geometric visualization to address this issue. A simple but powerful model is introduced which is able to estimate a production function when the number of DMUs are small. A real-life numerical example of 32 DMUs with 45 variables is also used to demonstrate the advantages of the introduced model. From such an approach, researchers can benchmark organizations even if the number of DMUs is less than the number of input-output variables.