Product damage and free sampling: a newsvendor model with passive and proactive self-consumption

A retailer sells a single product for a single period. During transportation and storage, some of these products are consumed by the retailer either (1) due to unavoidable damages (passive self-consumption), or (2) distributed for free to the customers (proactive self-consumption). This creates a mismatch between the amount purchased by the retailer and the amount available for sale. We study passive self-consumption with (i) fixed and (ii) proportional consumption, and proactive self-consumption with (iii) additive and (iv) multiplicative demand. Under proactive self-consumption, the retailer holds more inventory and receives a higher profit; the reverse is true under passive self-consumption. Yet, (i), (iii) and (iv) result in a higher order quantity and same fill rate compared to no self-consumption, (ii) may result in a higher or lower order quantity with a lower fill rate. When both types of self-consumption coexist, the optimal policy can be complicated. We characterize the optimal policy and show through numerical studies that the optimal policy can take at most three formats: sell to the market with positive proactive self-consumption, sell to the market with zero proactive self-consumption and do not sell to the market. Interestingly, the optimal order quantity is not smooth in the fraction of the proportional self-consumption. Further we find that when the market adoption rate is uncertain, the optimal strategy preserves a similar structure. The retailer benefits from expediting if the difference between the high and the low market adoption rates is high and the probability of a high market adoption rate is low.