Integrated inventory optimization in supply chain for deteriorating items with partially backorder

A single vendor single buyer integrated inventory optimization in supply chain for deteriorating items with shortage allowed is studied. The demand is supposed to be exponential time-varying and the buyer is allowed to backorder partially. The total inventory costs of vendor and buyer are explored respectively. An inventory model of the supply chain is developed accordingly to optimize the integrated total costs of vendor and buyer. An optimal algorithm is designed and numerical example is presented to illustrate the results of the proposed model.