Price-dependent inventory models with discount offers at random times

We consider an inventory model with a supplier offering discounts to a reseller at random epochs. The offer is accepted when the inventory position is lower than a threshold level. We compare three different pricing policies in which demand is induced by the reseller's price variation. Policy 1 is the EOQ policy without discount offers. Policy 2 is a uniform price, stock-independent policy. Policy 3 is a stock level-dependent, discriminated price policy. Assuming constant demand rates, expressions are obtained for the optimal order quantities, prices, and profits. The numerical experiments show that if it is better to accept a supplier's discount, then it benefits the reseller to transfer the discount to downstream customers.