### Chapter 10

### Order Quantities

__Introduction__· Management must establish decision rules to answer: How much should be ordered at one time and when should an order be placed?

· Control is exercised through individual items in a particular inventory called

**stock-keeping units (SKU’s)**.· A

**lot or batch**is defined as a quantity produced together and sharing the same production costs and specifications.· The following are common decision rules for determining what lot size to order at one time: (1) The

**Lot-for-lot****rule says to order exactly what is needed. The order quantity changes whenever requirements change. Since items are ordered only as needed, this system creates no unusual lot-size inventory. Because of this, it is the best method for planning “A” items and is also used in a just-in-time environment. (2)****Fixed-order quantity**rules specify the number of units to be ordered each time an order is placed for an individual item or SKU. The advantage to this rule is that it is easily understood. The disadvantage is that it does not minimize the costs involved. A variation on the fixed-order quantity system is the**min-max system**. In this system, an order is placed when the quantity available falls below the order point. The quantity ordered is the difference between the actual quantity available at the time of order and the maximum. (3) In the**period-order quantity system**, rather than ordering a fixed quantity, we order enough to satisfy future demand for a given period of time.

__Economic-Order Quantity (EOQ)__· The cost of ordering and the cost of carrying inventory both depend on the quantity ordered. The ordering decision rules will minimize the sum of these two costs. The best known system is the

**economic–order quantity (EOQ)**. The assumptions on which the EOQ is based are: (1) Demand is relatively constant and is known. (2) The item is produced or purchased in lots or batches and not continuously. (3) Order preparation costs and inventory-carrying costs are constant and known. (4) Replacement occurs all at once. There are many situations where the assumptions are not valid and the EOQ concept is of no use.·

**Average lot size inventory = order quantity / 2**·

**Number of orders per year = annual demand / order quantity**· The relevant costs are

**annual cost of placing orders**and**annual cost of carrying inventory**. As the order quantity increases, the average inventory and 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 dollars per order,**i**= annual carrying cost rate as a decimal of a percentage,**c**= unit cost in dollars,**Q**= order quantity in units**Annual ordering cost = number of orders x costs per order = (A / Q) x S**

**Annual carrying cost = average inventory x cost of carrying one unit for one year**

**= average inventory x unit cost x carrying cost = (Q / 2) x c x I**

**Total annual costs = annual ordering costs + annual carrying costs**

**= (A / Q) x S + (Q / 2) x c x I**

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).

· Important facts: (1) There is an order quantity in which the sum of the ordering costs and carrying costs is a minimum. (2) This EOQ occurs when the cost or ordering equals the cost of carrying. (3) The total cost varies little for a wide range of lot sizes about the EOQ. It is usually difficult to determine accurately the cost of carrying inventory and cost of ordering. Since the total cost is relatively flat around the EOQ, it is not critical to have exact values. Good approximations are sufficient. Parts are often ordered in convenient packages such as pallet loads, cases, or dozens, and it is adequate to pick the closest package quantity to the EOQ.

· The previous section showed that the EOQ occurred at an order quantity in which the ordering costs equal the carrying costs. If these two costs are equal, the following formula can be derived:

**EOQ = square root of (2AS / ic)**

· 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) and the unit cost (c) increase. The annual demand (A) 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 and 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. Both costs should be as low as possible. 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 manufacturing order. Anything that can be done to reduce these costs reduces the EOQ. Just-in-time manufacturing emphasizes reduction of setup time.

__Variations of the EOQ Model__· The EOQ can be calculated in monetary units rather than physical units. The same EOQ formula given in the preceding can be used, but the annual usage changes from units to dollars. A = annual usage in dollars, S = ordering costs in dollars.

**EOQ = square root of (2A S / i)**

__Quantity Discounts__· Suppliers often give a discount on orders over a certain size. This can be done because larger orders reduce the supplier’s costs; to get larger orders, they are willing to offer volume discounts. The buyer must decide whether to accept the discount, and in doing so, must consider the relevant costs: purchase, ordering and carrying costs.

__Period-Order Quantity (POQ)__· The economic-order quantity 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 material requirements planning, 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 economic-order quantity. It uses the EOQ formula to calculate an economic**time between orders**. This is calculated by dividing the EOQ by the demand rate. This produces 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 economic-order quantity, but the amount ordered each time varies. Thus, the ordering cost is the same but, because the order quantities are determined by the actual demand, the carrying cost is reduced. The calculation is approximate. Precision is not important.**Period-order quantity = EOQ / average weekly usage**

· Practical considerations when using the EOQ:

**Lumpy demand**– The EOQ assume that demand 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 –**It is better to plan a buildup of inventory based on capacity and future demand.**Minimum order**– This minimum may be based on the total order rather than on individual items.**Transportation inventory**– A full load costs less per ton to ship than a part load. This is similar to the price break given by suppliers for larger quantities.**Multiples –**Sometimes, order size is constrained by package size.