Production inventory model of deteriorating items with holding cost, stock, and selling price with backlog

This paper deals, production-inventory model with stock-dependent and selling price dependent demand. Demand rate is linearly increasing with stock and time, decreasing with a selling price of the item. Shortages are allowed and partially back ordered at the rate of decreasing waiting time of next replenishment. This model is classified as the deterioration rate is constant, and holding cost-based as constant. The model is solved numerically and analytically by minimising the total inventory cost and maximises the total profit at the last sensitivity analysis has been performed to show the nature of model in every parameter on the optimum solution. We have presented a solution-search procedure to find the preservation technology and optimal production time.