Returns system with rebates

The demand for goods like seasonal fashion apparel is uncertain but the lead time needed for production is long, and so it is necessary to set the production quantity before the demand is fully known. Once sale begins, if demand is less than anticipated, the price will be low. In a futile attempt to avoid losses themselves, a competitive retail industry selling such merchandise will order too little, which will diminish the producer profit. A returns system is one response but it has problems also. Under a returns system in which retailers are fully reimbursed by the producer for any unsold merchandise, retailers will set their order quantities at the highest level allowed, which is also sub-optimal. So what to do? A slightly more sophisticated returns system is the answer. We show that a returns system with rebates implements the optimal production and sales strategy, attaining maximum expected profit in the channel.