Proposing a Bi-level Programming Model for Multi-echelon Supply Chain with an Emphasis on Reliability in Uncertainty

Providing a bi-level programming model to solve the simultaneous problem of supplier selection and order allocation in multi-echelon supply chain is sought. The model will be proposed so that at the leader level, the supplier selection problem with the objective of increasing system reliability and at the follower level, the order allocation problem with the objective of reducing cost of system are formulated and customers’ demand at the last echelon of the supply chain is considered as an uncertain parameter.

Modeling the supplier selection and order allocation problem is based on the bi-level programming model, so the robust optimization technique was used to deal with the problem of uncertainty and a bi-level genetic algorithm was used to obtain the optimal solutions.

The results obtained from solving a real problem in the steel industry under various scenarios indicated that there is an opposing relationship between reliability and cost objectives, and increasing the number of chain members can lead to an increase in system reliability and cost. On the other hand, as increased reliability can lead to higher system costs, reliability reduction, which is mainly due to lack of quality and deficiency issues, can also lead to an increase in customers' dissatisfaction and, ultimately, an increase in aggregate system costs. Moreover, the results obtained in uncertain conditions, in comparison with definite conditions, indicated an unfavorable situation.

In order to improve the reliability of supply chain, the average reliability of the echelons in supply chain, which are at the lowest (highest) level in comparison to other echelons, should increase (decrease) in order to avoid additional costs. Besides, the interactive approach in proposed methodology provides a suitable solution for maximizing the interests of leader and follower levels.