Joint ordering inventory policy for deteriorating substitute products with price and stock dependent demand

The paper deals with a single period joint ordering inventory policy of two deteriorating substitute products. Here customers' demands are linear functions of prices and instantaneous stocks of the products. When both products are available, the demand of a substitute product decreases against its own price and other's stock and increases with other's price and own stock. During stock-out of one product, a portion of demand of stock out product opts the available product because of urgent requirement. Different scenarios depending on the exhaustion of the products and nature of the demand are considered. As particular cases, models with substitutability with respect to prices and stocks separately are presented. The models are formulated to determine the optimal order quantities of each product to maximize the average total profit. The problems are solved by the generalized reduced gradient method using LINGO 12.0. The models are illustrated with numerical experiments and the impact of the model parameters on the objective function is demonstrated with the help of sensitivity analyses. Some interesting nature/ behaviour of average total profit is also outlined