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# Order Quantity & EOQ

In general, when products are demanded on a regular basis (i.e. daily), the logistical problems of getting goods from source of supply to inventory requires that enough goods be ordered in each order cycle to last for some reasonable period of time. The more quantity of goods that are ordered each time, the longer they will last. This is true whether the goods are purchased for resale or manufactured to supply a finished goods warehouse or distribution center.

Graphs shown above contrast two extreme policies to illustrate the range of choices available. The top inventory graph depicts the acquisition of whole year’s supply at one time. The lower graph shows the re-supply policy of one order per week, with 52 orders

placed per year.

In most cases one would conclude that only one order per year is not reasonable because of the space required for the inventory and the cost of buying so much at once. On the other hand 52 orders seems too many with constant authorization and paperwork and excessive receiving and ordering costs. A compromise is called for. But what should it be? Every order quantity decision when done intuitively is based on the comparison of two different costs - the cost to carry the inventory versus the cost to place order.

__ Economic Order Quantity__All order quantity, or lot-size, choices are based on the principle of economy of scale. It is usually less expensive to purchase (and transport) or produce a bunch of material at once than to order it in small quantities. On other hand, larger lot sizes result in more

inventories and inventory is expensive to hold.

**Assumptions**

The assumptions on which the EOQ is based are as follows:

- Demand is relatively constant and is known,

- Order preparation costs and inventory-carrying costs are constant and known,

- The items is produced or purchased in lots and not continuously,

- Replacement occurs all at once.

The assumptions are usually valid for finished goods whose demand is independent and fairly uniform. However, there are many situations where the assumptions are not valid (e.g. made-to-order items, shelf life of the product is short,…). In MRP, the lot-for-lot decision rule is often used, but there are also several rules that are variations of the EOQ.

**Development of the EOQ formula
**Under the assumptions given, the quantity of an item in inventory decreases at a uniform rate. The vertical lines represent stock arriving all at once as the stock on hand reaches zero. The quantity of units in inventory then increases instantaneously by Q, the quantity ordered.

Average lot size inventory = (Order quantity)/ 2

Number of order per year = Annual demand / Order quantity

the number of order per year is rounded neither up nor down.

Relevant costs

The relevant cost are as follows:

- Annual cost of placing orders,

- Annual cost of carrying inventory.

As the order quantities increases, the average inventory and the annual cost of carrying inventory increase, but the number of orders per year and the ordering cost decrease. The trick is to find the particular order quantity in which the total cost of carrying inventory and the cost of ordering will be a minimum.

A = annual usage in units

S = ordering cost in dollar per order

i = annual carrying cost rate as a decimal of a percentage

c = unit cost in dollars

Q = order quantity in units

Ideally, the total cost will be a minimum. For any situation in which the annual demand (A), the cost of ordering (S) and the cost of carrying inventory (i) are given, the total cost will depend upon the order quantity (Q).

**Economic-order quantity formula**

The EOQ occurred at an order quantity in which the ordering costs equal the carrying costs.

Carrying costs = ordering costs

__ How to reduce lot size__Looking at the EOQ formula, there are 4 variables. The EOQ will increase as the annual demand (A) and the cost of ordering (S) increase and it will decrease as the cost of carrying inventory (i) ant the unit cost (c) increase. The annual demand is a condition of the marketplace and is beyond the control of manufacturing. The cost of carrying inventory (i) is determined by the product itself and the cost of money to the company. As such, it is beyond the control of manufacturing.

The unit cost (c) is either the purchase cost of the SKU or the cost of manufacturing the item. Ideally both costs should be as low as possible. In any event, as the unit cost decreases, the EOQ increases.

The cost of ordering (S) is either the cost of placing a purchase order or the cost of placing a manufacturer order. The cost of placing a manufacturing order is made up from production control costs and setup costs. Anything that can be done to reduce these costs reduce the EOQ.

Just-in-time manufacturing emphasizes reduction of setup time. There are several reasons why this is desirable and the reduction of order quantities is one