Evaluating the efficiency of two-stage systems under Stackelberg game and imprecise data conditions

Document Type : Original Paper


Department of Mathematics, Tafresh University, Tafresh 39518 79611, Iran


Many production processes have a two-stage structure in which production takes place through two stages with separate inputs and outputs for each stage. In these production systems, some outputs of the first stage form inputs for the second stage. These factors are called intermediate data. Since in many practical situations, data is not deterministic and is given in interval form, the efficiency evaluation under interval data is very important. In this paper, some data envelopment analysis models are proposed to evaluate the performance of two-stage systems with interval data and Stackelberg game tradeoff between the stages. By exploiting the mathematical properties of the models, some simplifications are provided to determine the interval efficiency of each stage. For optimistic and pessimistic scenarios, it is shown that the upper and lower bounds of efficiency scores are obtain at the upper/lower bounds of all data except the intermediate data. Using a numerical example, the application of the model and analysis of the results are described.


Main Subjects

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