Uncle Nappy’s Mattress Mart stocks a private-label mattress pad for queen-sized beds in all of its stores. The pads are ordered from a contract manufacturer which produces the same basic item for several different mattress stores. The manufacturer stocks the basic mattress pads in its warehouse and then packages them with the specific customer’s branding once an order is received. The average lead time to fulfill orders is 1.5 weeks with a standard deviation of 0.6 weeks.
Uncle Nappy’s sells approximately 120 mattress pads each week, and the demand is assumed to follow a normal distribution with a standard deviation of 24 pads. The store pays the manufacturer $43 for each pad and pays $90 in delivery charges for each replenishment shipment it receives. The manager estimates that each replenishment order costs an additional $5 in administrative costs. Uncle Nappy’s uses a holding cost rate of 26% to make its inventory decisions, and the manager has established a minimum-allowable safety factor of 1.25 for the mattress pads.
Any time the mattress pads are out-of-stock, the manager contacts the manufacturer to place a rush order. The additional cost of each rush order is $300, regardless of the number of units ordered. Assuming that the store uses the EOQ to establish the order quantity for the mattress pads, determine the store’s order quantity and reorder point for this item.