Exploring congestion in intermediate products by DEA: an application on Iranian cement supply chain

Evaluating the performance of a supply chain as a decision-making unit (DMU) is a significant topic for many researchers and learners. Presence congestion is one of the key events that results in lower efficiency and performance in a DMU. One of the most suitable methods to explore congestion is data envelopment analysis (DEA). A supply chain may encounter congestion in its inputs or intermediate products or both. Some studies have been conducted to explore the intermediate product congestion through solving network DEA (NDEA) models regardless of the role of intermediate products. In this study, a two-stage series supply chain with separate inputs and outputs for each stage as a DMU is considered. Then, a new linear programming problem is presented to determine extreme efficient supply chain. Since extreme efficient DMUs play an essential role in production technology, we proposed a novel linear programming problem to detect congested extreme efficient supply chain according to their intermediate products' role for the first time. To reach this end, various scenarios that congestion may arise in intermediate products have been identified. And so, for each scenario, a novel linear model was offered to determine congested extreme efficient DMU. According to this method, an extreme efficient DMU under evaluation was removed from the production technology and by comparing it with other units belonging to this technology, the presence of congestion and the status of congestion (strong congestion and weak congestion) in intermediate products were determined. Finally, 15 Iranian supply chains of cement factories have been employed to establish applicability of the suggested models.