379 International Journal of Supply and Operations Management IJSOM November 2018, Volume 5, Issue 4, pp. 379-395 ISSN-Print: 2383-1359 ISSN-Online: 2383-2525 www.ijsom.com Performance Measurement and Productivity Management in Production Units with Network Structure by Identification of the Most Productive Scale Size Pattern Fereshteh Koushki* , a a Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran Abstract Managers tend to improve resource (input) utilization in organizations to obtain the highest level of productivity. Additionally, many industrial units have multi-stage structure in which the output of one stage is the input of the next one. This paper, for the first time, presents data envelopment analysis (DEA) approaches to achieve the most productivity in two-stage decision making units (DMUs). By considering internal activities in system, radial and non-radial models are proposed to evaluate network DMUs and radial model is developed to identify the most productive scale size (MPSS) pattern. Proposed models are applied to optimize the performance of bank branches as units with two-stage structure. Results show that efficiency scores and improvements needed in costs and paid interests (inputs) to get more incomes and facilities (outputs). This study provides managers with information to propose better strategies to improve not only the overall performance but also the efficiency of each stage. Keywords: Data envelopment analysis (DEA); Network DEA; Most productive scale size (MPSS); Scale efficient target. 1. Introduction Identification of the most productive scale size (MPSS) patterns, which are called scale efficient targets, shows the needed improvements of resources (as inputs of organization) to obtain the highest possible level of productivity. Besides, in multi-stage production systems, the performance of each stage and overall performance must be improved. In production and industrial units with network structure, the outputs of one stage are the inputs of the next. For example, in Banks, as two-stage systems, labor, physical capital, and financial equity capital are the inputs of the first stage to produce deposits as the output of this stage. In the second stage, the inputs are the deposits raised from the first stage and the outputs are loans and security investments. Assessing multi-stage systems needs special considerations including how each stage performs, what the efficiency score of each score is, how the stages are related to one another, etc. Investigations to achieve the answers, especially in managerial decisions, identify inefficiencies which may exist in internal activities and provide managers with useful insights to optimize overall performance of system. As a nonparametric technique, data envelopment analysis (DEA) is mathematical programming to evaluate the performance of homogenous decision-making units (DMUs). Traditional DEA models evaluate two-stage DMU as a black box and neglect the connectivity which may exist among the stages. We look inside the system and introduce models to optimize two-stage DMU by considering the intermediate activities between the stages. Furthermore, in network DEA models which will be mentioned in next section, constraints related to intermediate activities are considered as inequalities which, as will be shown in this paper, result in contradictions in optimality. In this paper, this point is taken into consideration. Additionally, each stage of network structure production systems may consist of parallel parts in which the inputs and the outputs of the entire stage are separated for each part. This paper addresses units with such a two-stage structure and presents radial and non-radial models to measure efficiency scores. Corresponding author email address: fkoushki@gmail.com