Joint pricing and inventory problem with price dependent stochastic demand and price discounts

The market today is very dynamic and competitive. Many products, such as fashion apparel and technology and Christmas items, are short lived and become obsolete. Another example is grocery items. Some are either perishable or have expiry dates. They become less appealing to customers as they become less fresh with time. Many companies consider pricing and inventory decisions important to minimize losses and improve profitability due to either obsolescence or perishability. They also try to maximize truck capacity and reduce transport cost to reap additional savings. For this reason, suppliers often provide buyers with an all-unit quantity discounts. This study addresses these issues by examining a joint pricing and inventory decision problem with transport capacity and cost. It considers a single period model where a buyer purchases a single item from a dominant supplier offering all-unit quantity discounts. Product demand is stochastic and price-dependent. Two new mathematical models were developed. The results showed that discounts increase the pool of profits for the supplier and the buyer and provide a better utilization of truck capacity and lower transportation cost. The models also benefit the end customer by providing a product at a competitive price.