Efficiency Evaluation in Hybrid Three-Stage network Data envelopment analysis from the Double-Frontier Standpoint

Document Type : Research Paper


1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

3 Department of Mathematics, Shahr.e Qods Branch, Islamic Azad University, Tehran, Iran


The efficiency evaluation of a network opens the “black box” and deliberates on the internal structures and innermost interactions of the system. In this paper, we have made efforts to consider a three-stage system, comprising of six sub-DMUs, in combination with additional inputs and undesirable outputs. The proposed models are simulations of a factory, with a production area and three warehouses for goods and two delivery points. Hence, an authentic example, in concern with production planning and inventory control in a factory for a year and within duration of 24 periods, was taken under consideration, as a dynamic structure. In this simulation, all costs are considered, including, production costs, setup cost, maintenance costs of the products, warehouse reservation costs, transportation costs, delay penalty costs and the profit obtained from the sale of products. We utilized the multiplicative DEA with a double-frontier approach to measure the efficiency of a general system and improve the accuracy of efficiencies. Moreover, a heuristic technique was used to convert non-linear models into linear models. The ranking results amongst the 24 time periods, which, indicate that the time periods 24 and 1, are the best and poorest periods in terms of efficiency, respectively. Finally, we suggest to use a k-means method to cluster DMUs into several groups with similar characteristics based on double-frontier Standpoint.


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