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.