The main purpose of this paper is the allocation of orders to suppliers in an agile and flexible manner suitable to the automobile industry. In this paper, parts supplied by a single source were eliminated from the set of parts. Using mathematical modeling and through the interval-valued fuzzy-rough numbers best worst method (IVFRN-BWM), we try to achieve the results that can meet the proposed model's needs and provide the ideal results by introducing new modes. This paper addressed some new aspects of the subject and achieved robust results by considering five objective functions. These five functions are as follows: minimization of production line disruptions due to the performance of suppliers, minimization of the complaints of production line about supplied parts, minimization of defective parts received from suppliers (PPM), maximization of on-time delivery services, and minimization of overall costs of supplied parts. Reviewing the literature, the originality of this study are as follows: 1) identifying the structure of a supply chain (SC) in general and particularly in an automobile industry SC; 2) investigating the modeling techniques of the existing SC models for coordinating all the members of a product SC; 3) building a hybrid model of IVFRN-BWM and a robust goal programming agile and flexible supply chain in an uncertain situation; and 4) identifying the suitable scenarios/cases for testing the proposed models to validate the models. This paper can help decision makers and managers to opt for the best suppliers and also allocate the right numbers of parts to those supplier(s) based on a real situation of each firm. INDEX TERMS Robust optimizations, IVFRN-BWM, allocation, agile and flexible SC, automobile industry.

The development of supply chain distribution systems from single-to multi-channel networks for delivering items to end customers has effected many changes in the retail sector. Following the adoption of multi-channel distribution strategies and rapid development of relevant technologies, the Omni-channel approach can yield significant benefits and facilitate trade with customers. This paper aims to optimize a multi-product, multi-level Omni-channel distribution network and shipping flows of products within the network under uncertain conditions. A multi-objective mathematical model is developed that minimizes the costs of supply chain while maximizing customer satisfaction over different scenarios. In order to solve the proposed model, a combined algorithm is developed based on Benders Decomposition (BD) and Lagrangian Relaxation (LR). The presented model and solution approach is implemented in a case study of a distribution system, a large e-commerce startup and online store. Five different scenarios with various service levels are investigated and the numerical results are discussed compared to previous findings. The efficiency of the proposed combined BD-LR solution algorithm is also demonstrated. The results obtained from the case study show that higher service levels are correlated with higher levels of customer satisfaction and lower cost of the system.

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Norway. She has worked on risk management, operations research, green and sustainable supply chain, logistics and distribution networks. She is currently studying on stochastic optimization. She is also a reviewer of Cleaner Production Journal.

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