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The paper presents a two-echelon inventory-transportation problem in Vendor Managed Inventory (VMI) system. We consider a distribution system composed with single supplier, single distribution center and multiple retailers. Single kind of products are required to deliver from the manufacturer through distribution center to the retailers within soft time window. The objective of the problem is to minimize total logistics cost in the distribution network, including inventory cost, distribution cost, and time penalty cost. The upper echelon model focuses on minimizing inventory cost while the lower echelon model on vehicle routing problem. A mixed algorithm is designed to solve the problem with simulated annealing and ant colony with local search. The solution of upper and lower echelon model are substituted into each other based on the mixed algorithm step by step to get the optimization solutions. Computational experiments are executed to compare the performance of independent and integrated inventory-transportation optimization from the dimension of to verify the effectiveness of the model and the algorithms.
Teng et al. (Tue,) studied this question.