Hierarchical P-hub center problem for perishable goods

In supply chains of perishable goods, paying attention to product freshness during delivery to customers is very important because perishable goods deteriorate during the transportation process and their quality decreases. Therefore, how to design the distribution system of perishable goods to transfer products from origins to destinations impacts the responsiveness of the transportation system. This paper presents a bi-objective model for designing a capacitated hierarchical hub network with multiple allocation for perishable goods. In the proposed model, transportation costs and maximum travel time (as a measure of network responsiveness) are optimized simultaneously. To get Pareto-optimal solutions, three exact methods, namely the augmented epsilon constraint method, Torabi-Hassini method, and augmented weighted Tchebycheff procedure, are applied. Validation of the proposed model is performed using some test problems on the Turkish network dataset. Also, sensitivity analyses are performed on the critical parameters of the model. The results show that multiple allocation can be effective in the variety of Pareto solutions. Also, designing the network with economic and responsiveness considerations costs more than designing the network with only economic considerations.