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This thesis introduces a inventory-routing problem under a vendor managed inventory strategy in a two-echelon supply chain. The VMI Routing problem in this study consists of multiple suppliers, multiple retailers and a single item. The suppliers plan inventory replenishments for retailers based on deterministic demand over multiple planning period. Also they allow stock-outs at retailers, which are considered lostsales. Transshipments are allowed, neither between suppliers nor between customers. Retailers can be supplied just by one assigned supplier. Model also considers some constraints on time and capacity. A mixed integer programming formulation is presented to describe the model. We...