Integration of Time Windows and Discounts (Per Period-per Demand) in Lot Sizing Problems for Maximizing Profit

This study focuses on the lot sizing problem for a single item without capacity constraints, incorporating time windows and dynamic pricing. The primary objective is to determine optimal production quantities and specific periods for proposing price discounts to maximize profits. We explore two pricing strategies: Offering discounts in specific periods of the planning horizon and proposing discounts for specific demands. Both strategies aim to enhance delivery schedule flexibility. Typically, customers prefer to meet their demands in the first period of their time windows. However, by offering discounts customers accept to postpone the delivery of their orders to the earliest period with a discounted price. By offering discounts for specific demands, customers may accept to shift their orders to a later period in their time windows. The problem is modeled as an integer linear program. Additionally, we present the results of a computational study that assesses the benefits of price discounts in exchange for delivery flexibility across various scenarios.