Price discounts in exchange for reduced customer demand variability and applications to advance demand information acquisition

We consider a supplier and a customer operating under a service agreement that requires the supplier to cover the random customer demand with high probability. To fulfill the service agreement, the supplier carries a certain amount of safety stock. The customer has some bearing on its demand variability, possibly through activities such as acquiring advance demand information, employing more sophisticated forecasting techniques or smoothing its product consumption, but these activities bring an extra cost to the customer. Since a reduction in the customer demand variability helps the supplier reduce its safety stock, the supplier is willing to offer a price discount in exchange for reduced demand variability.