A multi-retailer supply chain model with backorder and variable production cost

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The modern marketing environment involves variability and randomness within the numerous parties of any supply chain network. Thus, formation of a supply chain model including multiple buyers and variable production rate is more acceptable than assuming a single-buyer with constant production rate model. This paper considers a supply chain network, where a single-vendor manufactures products in a batch production process and supplies them to a set of buyers over multiple times. Instead of assuming a fixed production rate, as commonly used in the literature, a variable production rate is introduced by the vendor and the production cost of the vendor is treated as a function of production rate. The continuous review inventory model is applied for multiple buyers to inspect inventory levels and a crashing cost is incurred by all buyers to reduce their lead times. The lead time demand follows a normal distribution. The unsatisfied demands at the buyers end are partially backordered. A model is formulated to minimize the joint expected cost of the vendor-buyers supply chain system. A classical optimization technique is utilized to solve the model. An improved algorithm is developed to obtain the numerical solution of the model. Finally, numerical examples are given to illustrate the model.