This research deals with a distributive or tree-type three-echelon production-distribution supply chain system with allowable backorder. Allowing backorder could reduce the total of a production-distribution system by reducing holding cost due to the lower average inventory, even though backorders carry some cost and lower a company's goodwill. The main purpose of this research is to develop replenishment policies for a tree-type three-echelon supply chain system with allowable backorder. The supply chain network is composed of a producer, multiple distributors, and multiple retailers. This research attempts to improve service rate by reducing the backorder at the retailer level. The distributors are allowed to ship product to retailer quicker in order to reduce backorder. The total cost function of the proposed model is developed. Since the total cost function contains some integer variables, differentiating the function with respect to the variables could not be used as a basis to solve for the optimal solutions. A branching search process was utilized to find the integer solutions. A numerical example is used to demonstrate improvement in service rate and total cost using the model. © 2014 Operational Research Society Ltd.
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