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# Period Order Quantity

The EOQ attempts to minimize the total cost of ordering and carrying inventory and is based on the assumption that demand is uniform. Often demand is not uniform, particularly in MRP and using the EOQ does not produce a minimum cost. The period order quantity lot-size rule is based on the same theory as the EOQ. It uses the EOQ formula to calculate an economic time between orders. This is calculated by dividing the EOQ by the demand rate. This produce a time interval for which orders are placed. Instead of ordering the same quantity (EOQ), orders are placed to satisfy requirements for the calculated time interval. The number of orders placed in a year is the same as for an EOQ, but the amount ordered each time varies. Thus, the ordering cost is the same but , because the order quantities are determined by actual demand, the carrying cost is reduced.

Period-order quantity = EOQ / Average weekly usage

Practical considerations when using the EOQ

**Lumpy demand
**The EOQ assumes that demand is uniform and replenishment occurs all at once. When this is not true, the EOQ will not produce the best results. It is better to use the period-order quantity.

**Anticipation inventory
**Demand is not uniform and stock must be built ahead. It is better to plan a buildup of inventory based on capacity and future demand.

**Minimum order
**Some suppliers require a minimum order. This minimum may be based on the total order rather than an individual items. often these are C items where the rule is to order plenty, not an EOQ.

**Transportation inventory
**Carriers give rates based on the amount shipped. A full load costs less per ton to ship than a part load. This is similar to the price break

given by suppliers for large quantities. The same type of analysis can be used.

**Multiples**

Sometimes, order size is constrained by package size. In these case, the unit used should be the minimum package size.

__ Periodic Review System__Using the periodic review system, the quantity ordered is usually predetermined at specified, fixed-time intervals and an order is placed. Thus the review period is fixed and the order quantity is allowed to vary. The quantity on hand plus the quantity ordered must be sufficient to last until the next shipment is received.

That is, the quantity on hand plus the quantity ordered must equal the sum of the demand during the lead time plus the demand during the review period plus the safety stock.

This sum of quantities is called the target level or maximum-level inventory:

T = D(R + L) + SSWhere

T = Target (maximum) level inventory,

D = Demand per unit of time,

L = Lead-time duration,

R = Review period duration,

SS = Safety stock.

The order quantity (Q) is equal to the maximum-inventory level (T) minus the quantity on hand (I) at the review period:

Q = T – I

The periodic review system is useful for the following:

- Where there are many small issues from inventory and posting transactions to inventory records are very expensive. Supermarkets and retailers are in this category.

- Where ordering costs are small. This occurs when many different items are ordered from the one source. A regional distribution center may order most of all of its stock from a central warehouse.

- Where many items are ordered together to make up a production run or fill a truckload. A good example of this regional distribution center that orders a truckload once a week from a central warehouse.