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amount of safety analytical model backorder cost per expedited cost per unit cost substantially cycle length demand distribution demand standard deviation demand variability deterministic and stochastic dited shipment Equation 14 Equation 9 expe expedited shipment Figure fixed cost following order freight charge G increases hold some safety holding inadequate safety inadequate safety stock insure that expediting inventory carrying charge just-in-time production keeping small levels likelihood of stocking-out minimum total cost model parameters Motors Research Laboratories normal distribution number of items optimal inventory level optimal order-up-to level optimal trade-off order is placed order is received PRL/G probability density function production schedules Q(L+T reduce expediting cost reduced with various regular shipments represents safety stock inventory safety stock level Schonberger SHIPMENT ARRIVALS shipment is ordered shipment size shipping freight shows the sensitivity stochastic component STOCHASTIC COST STOCK INVENTORY COSTS Substituting Equation suppliers to meet total inventory transportation and inventory transportation cost weeks