Addressing dynamic lot size problems with quantity discounts in information forecasting environments

Quantity discount is one of the promotion policies adopted by suppliers in practice. Therefore, upstream suppliers always provide quantity discounts to downstream buyers. This study investigates the dynamic lot size problem with a quantity discount. We consider three kinds of models and propose dynamic programming algorithms to work out the three models based on structural properties in the optimal solutions. More importantly, forecast horizons are studied for the dynamic lot size problems. We first establish the monotone property for procurement and regeneration points and then offer sufficient conditions to find forecast horizons. Useful insights on the discount breakpoints and discount rates on the forecast horizons’ length are acquired through numerical experiments.