A Lot Sizing Model for a Deteriorating Product with Shifting Production Rates, Freshness, Price, and Stock-Dependent Demand with Price Discounting

Many production systems need to be able to change the rate at which they manufacture products for various reasons, hence, the need to find the optimal lot size under these multiple levels of production. This research addresses the need for optimizing inventory in a system with a shifting production rate and other challenging product characteristics such as product deterioration with limited life span, and product demand that is dependent on the stock level, the state of freshness of the product, and the selling price. The product also needs to be discounted as it gets close to the expiry date in order to boost demand and prevent wastage beyond its life span. Our objective is to maximize profit by determining the optimal selling price and inventory cycle time by deriving the relevant equations for these decision variables. The Newton-Raphson method was used to numerically solve for the optimal values of these variables. Sensitivity analyses were performed to derive useful insights for managerial decision-making.