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

The efficiency evaluation of a network opens the “black box” and focuses 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 of 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 were 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 of the 24 time periods indicate that the time periods 24 and 1 respectively are the best and poorest periods in terms of efficiency. Finally, we suggest using a k-means method to cluster DMUs into several groups with similar characteristics based on double-frontier Standpoint.