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This paper considered a single-item, three-echelon (supplier, retailer, and customer) inventory problem. At random times, the supplier offers the retailer a discount. The inter-arrival times of discounts are exponentially distributed. For the retailer, whether or not to take a discount offer depends on its inventory level. If inventory is below threshold level S, the retailer will order to replenish inventory up to S+Q units. Otherwise, the retailer will pass. At the regular purchase price, the retailer uses the order-up-to reorder point inventory system. The reorder point is r, and the order-up-to quantity is R. The demand of the customer is price-elastic. Depending on its inventory level, the retailer may discounts its selling price to boost up demand. The decision variables are S, Q, R, r, and the selling prices (regular and discount selling price). The simulation experiment covered reasonable range of values for each decision variable. Each run represented one scenario, i.e., one combination of the decision variables.