Optimal pricing and ordering decisions for a retailer using multiple discounts

• We optimise the selling prices for a multi-discount newsboy problem. • We show the characteristics of the optimal price structure to preset. • Our method yields remarkable benefits in both static and dynamic pricing situations. • We provide a robust method for the case where partial demand information is known. Ordering and pricing are two crucial decisions for retailers and are widely studied. We focus on a situation where a retailer uses successive discounts, and we study the joint decision of the order quantity and selling prices. Earlier works often simplify this problem by assuming that demands in the discount periods are deterministic and independent, which is unrealistic. This work proves that there exists a unique optimal order quantity when the demands are stochastic and correlated. In determining the optimal order quantity and regular selling price for the multi-discount problem, earlier studies often assume special price structures, for example, equally spaced discount prices. This study optimises the selling prices and proves that the discount schemes used in earlier multi-discount works are suboptimal. In this study, both hierarchical and joint optimisation methods are derived for when the demand distribution information is known. In the static pricing situation, using small discounts in the beginning and marking down with an accelerating increase rate can benefit the retailer instead of discounting with a constantly increasing rate. Numerical examples show that the performance of the hierarchical method, often used in earlier one-discount models, depends on the profit margin and the demand correlation ratio in a multi-discount situation. Compared with the hierarchical method, the joint optimisation method yields more benefits in profit in both static and dynamic pricing situations when the profit margin is low and demand correlation is high. We also provide a robust optimisation method for the partial-demand-information case in this study. Other insights for managers are also provided.