A robust possibilistic programming model for production-routing problem in a three-echelon supply chain

Purpose This paper aims to provide an integrated production-routing model in a three-echelon supply chain containing a two-layer transportation system to minimize the total costs of production, transportation, inventory holding and expired drugs treatment. In the proposed problem, some specifications such as multisite manufacturing, simultaneous pickup and delivery and uncertainty in parameters are considered. Design/methodology/approach At first, a mathematical model has been proposed for the problem. Then, one possibilistic model and one robust possibilistic model equivalent to the initial model are provided regarding the uncertain nature of the model parameters and the inaccessibility of their probability function. Finally, the performance of the proposed model is evaluated using the real data collected from a pharmaceutical production center in Iran. The results reveal the proper performance of the proposed models. Findings The results obtained from applying the proposed model to a real-life production center indicated that the number of expired drugs has decreased because of using this model, also the costs of the system were reduced owing to integrating simultaneous drug pickup and delivery operations. Moreover, regarding the results of simulations, the robust possibilistic model had the best performance among the proposed models. Originality/value This research considers a two-layer vehicle routing in a production-routing problem with inventory planning. Moreover, multisite manufacturing, simultaneous pickup of the expired drugs and delivery of the drugs to the distribution centers are considered. Providing a robust possibilistic model for tackling the uncertainty in demand, costs, production capacity and drug expiration costs is considered as another remarkable feature of the proposed model.