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【正文】 efits that accrue from that control. ? In multiproduct inventory systems not all products are equally profitable. ? A large portion of the total dollar volume of sales is often accounted for by a small number of inventory items. Multiproduct Systems ABC analysis: 100 195 %80 %20 % 50 %P roduc ti on of inventor y it e msCumulative fraction of value of inventoryA B CMultiproduct Systems ABC analysis: Since A items account for the lion39。s share of the yearly revenue, these items should be watched most closely. Inventory levels for A items should be monitored continuously. More sophisticated forecasting procedures might be used and more care would be taken in the estimation of the various cost parameters required in calculating operating policies. Multiproduct Systems ABC analysis: For B items inventories could be reviewed periodically, items could be ordered in groups rather than individually, and somewhat less sophisticated forecasting methods could be used. Multiproduct Systems ABC analysis: ? The minimum degree of control would be applied to C items. For very inexpensive C items with moderate levels of demand, large lot sizes are remended to minimize the frequency that these items are ordered. ? For expensive C items with very low demand, the best policy is generally not to hold any inventory. One would simply order these items as they are demanded. Lot SizeReorder Point Systems ? In what follows, we assume that the operating policy is of the form. However, when generalizing the EOQ analysis to allow for random demand, we treat and as independent decision variables. ? ?RQ,QRLot SizeReorder Point Systems Assumptions ? The system is continuousreview ? Demand is random and stationary ? There is a fixed positive lead time for placing an order ? The following costs are assumed – Setup cost at $ per order. – Holding cost at $ per unit held per year. – Proportional order cost of $ per item. – Stockout cost of $ per unit of unsatisfied demand ?KhcpLot SizeReorder Point Systems Describing demand: The demand during the lead time is a continuous random variable with probability density function (or pdf) , and accumulative distribution function (or cdf) . Let and be the mean and standard deviation of demand during lead time. D? ?xf? ?xF ? ?DE?? ? ?Dv a r??Lot SizeReorder Point Systems Decision variables: There are two decision variables for this problem, and , where = the lot size or order quantity and = the reorder level in units of inventory. QRQRLot SizeReorder Point Systems Decision variables: Or de r a rr ivesQOr de r pla c e dTim eR?InventoryAdditional Discussion of PeriodicReview Systems Define two numbers, and , to be used as follows: When the level of on hand inventory is less than or equal to , an order for the difference between the inventory and is placed. If is the starting inventory in any period, then the policy is: ? If , order . ? If , don39。t order. s SsSu? ?Ss,su ? uS?su?Additional Discussion of PeriodicReview Systems Determining optimal values of ? ?Ss,Rs ?QRS ?
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