Which strategy is better for managing multi-product demand uncertainty: Inventory substitution or probabilistic selling?

Firms generally sell multiple products whose demands are uncertain. In order to manage product demand uncertainty, some firms use inventory substitution, while others use probabilistic selling. Which strategy should firms adopt is an intriguing issue. Addressing this issue, we consider a retailer that sells two substitutable products whose demands are uncertain. Based on the newsboy model, we analyze the optimal pricing and inventory decisions under the two strategies in three total market size situations, namely deterministic, discrete random, and general random. We derive closed-form optimal solutions for the former two situations and numerically find the optimal solution for the latter situation. We then compare the optimal profits under the two strategies in the three situations. We show that probabilistic selling always performs better than inventory substitution and brings more benefits to the retailer. These findings can explain that more and more firms adopt probabilistic selling in reality.