Deterministic price–inventory management for substitutable products

Revenue management involves the use of pricing and inventory control strategies to balance supply and demand in a revenue–maximising manner. Although pricing and inventory control decisions are closely related, they have historically been considered in isolation in both industry and academic work. This paper adds to the recent research stream on joint pricing and inventory control by investigating static deterministic optimisation models for firms managing multiple products sharing multiple resources. Firms must manage both sales (demand rationing) and pricing decisions in order to maximise profits. This paper shows that, under standard regularity assumptions on demand, the deterministic joint price–inventory control problem with substitutable products can be reduced to a pure pricing problem. This is not true if demand is uncertain and/or products exhibit complementary effects, in which case demand rationing can be profitable. Illustrative examples that consider linear demand with and without substitution effects are provided. In this case, the price–inventory control problem can be solved by optimising a concave quadratic objective function with linear constraints. Practical applications of the models, which have been successfully used by several industries, are presented.