An integrated game theoretic model and network data envelopment analysis to determine optimal export allocation to industrial units (A case study of the stone industry)

Abstract

Despite the fact that Iran is one of the main world's stone producers with more than 6000 stone-cutting centers, its share barely holds one percent of the world market. The industry, hence, awaits effective measures to increase its exports of building stone products. It is assumed in the present study that public-private partnership based on a win-win approach might not only facilitate foreign trades by different industries but also enhance export opportunities and improve production efficiency. Accordingly, efforts are made in the present study to investigate both production and supply networks in conjunction with the hitherto less heeded demand allocation. It is the objective to exploit functional criteria in each of these networks that will guarantee efficiency and functional values based on domestic and international demands. The way each player participates in its respective network and handles feedback from other players depends on the his/her conditions and the performance of the various players/components of the network they are part of. To determine these parameters, use is made in this study of the network data envelopment analysis (NDEA) with the efficiency of each industrial unit in the network considered as the weight of that unit within a game theoretic framework. More specifically, given the importance of exports and trade commodities as well as the great impacts such industrial units as R&D and sales departments have on international markets and marketing, the weights associated with each industrial unit is calculated via the network data envelopment analysis that takes into account not only the effects of all the network components but also those of the parameters affecting their efficiency. Thus, all the factors involved in the evaluation of the supply chain are initially identified based on the SCOR model and the balanced scorecard that additionally includes sustainability criteria. The model is implemented on the data extracted from a survey of 10 stone-cutting plants, the supply chain network of which is determined based on a study of their structures and the criteria considered in the relevant sub-networks. In a subsequent stage, after implementing PCA, the NDEA model is solved for each of the subnetworks in GAMS software and the efficiency of each plant is obtained using the weights obtained from the demand allocation model within a game theoretic framework. The output from the model solved in GAMS indicates that, compared to the current situation, application of the integrated model proposed in this study leads to a significant increase in the profits gained from each customer demand; the profits earned is expressed as the number of orders placed with each plant.