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Chapter 13: Inventory Management

A stock or store of goods.
Independent-demand item
An item that is ready to be sold or used
Dependent-demand item
Components of finished products, rather than the finished products themselves
Return on investment (ROI)
Profit after taxes divided by total assets.
The different kinds of inventories include the following:
Raw materials and purchased parts.

Partially completed goods, called work-in-process (WIP).

Finished-goods inventories (manufacturing firms) or merchandise (retail stores).

Tools and supplies.

Maintenance and repairs (MRO) inventory.

Goods-in-transit to warehouses, distributors, or customers (pipeline inventory).

Functions of inventory:
1. To meet anticipated customer demand.
2. To smooth production requirements.
3. To decouple operations.
4. To protect against stockouts.
5. To take advantage of order cycles.
6. To hedge against price increases.
7. To permit operations.
8. To take advantage of quantity discounts.
Little’s Law:
The average amount of inventory in a system is equal to the product of the average demand rate and the average time a unit is in the system.
Inventory management has two main concerns:
One is the level of customer service, that is, to have the right goods, in sufficient quantities, in the right place, at the right time. The other is the costs of ordering and carrying inventories.
Inventory turnover:
Ratio of average cost of goods sold to average inventory investment. The turnover ratio indicates how many times a year the inventory is sold. Generally, the higher the ratio, the better, because that implies more efficient use of inventories.
To be effective, management must have the following:
1. A system to keep track of the inventory on hand and on order.

2. A reliable forecast of demand that includes an indication of possible forecast error.

3. Knowledge of lead times and lead time variability.

4. Reasonable estimates of inventory holding costs, ordering costs, and shortage costs.

5. A classification system for inventory items.

Periodic system:
Physical count of items in inventory made at periodic intervals (e.g., weekly, monthly) in order to decide how much to order of each item.
Perpetual inventor system:
(also known as a continual system) System that keeps track of removals from inventory on a continuous basis, so the system can provide information on the current level of inventory for each item.
Two-bin system:
Two containers of inventory; reorder when the first is empty.
Universal product code (UPC):
Bar code printed on a label that has information about the item to which it is attached.
Point-of-sale systems (POS)
Record items at time of sale.
Lead time:
Time interval between ordering and receiving the order.
Purchase cost:
The amount paid to buy the inventory. It is typically the largest of all inventory costs.
Holding, or carrying costs:
Cost to carry an item in inventory – physically, in storage – for a length of time, usually a year. Costs include interest, insurance, taxes (in some states), depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, security). They also include opportunity costs associated with having funds that could be used elsewhere tied up in inventory. Note that it is the variable portion of these costs that is pertinent.
Ordering costs:
The costs of ordering and receiving inventory. Ordering costs are generally expressed as a fixed dollar amount per order, regardless of order size.
Setup costs:
The costs involved in preparing equipment for a job. Are analogous to ordering costs; that is, they are expressed as a fixed charge per production run, regardless of the size of the run.
Shortage costs:
Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit. Shortage costs are sometimes difficult to measure, and they may be subjectively estimated.
A-B-C approach:
Classifying inventory according to some measure of importance, and allocating control efforts accordingly. A (very important), B (moderately important), and C (least important). With three classes of items, A items generally account for about 10 to 20 percent of the number of items in inventory but about 60 to 70 percent of the annual dollar value. At the other end of the scale, C items might account for about 50 to 60 percent of the number of items but only about 10 to 15 percent of the dollar value of an inventory.
Cycle counting:
A physical count of items in inventory.
Radio frequency identification (RFID) tags:
RFID tags transmit product information or other data to network-connected RFID readers via radio waves. Tags attached to pallets, boxes, or individual items can enable a business to identify, track, monitor, or locate any object that is within range of a reader. For example, the tags are used in “speed passes” for toll roads.
Four basic costs are associated with inventories:
Purchase, holding, transaction (ordering), and shortage costs.
Holding costs are stated in either of two ways:
As a percentage of unit price or as a dollar amount per unit.
A-B-C concept.

To solve an A-B-C problem, follow these steps:

1. For each item, multiply annual volume by unit price to get the annual dollar value.

2. Arrange annual dollar values in descending order.

3. The few (10 to 15 percent) with the highest annual dollar value are A items. The most (about 50 percent) with the lowest annual dollar value are C items. Those in between (about 35 percent) are B items.

The key questions concerning cycle counting for management are:
1. How much accuracy is needed?

2. When should cycle counting be performed?

3. Who should do it?

APICS recommends the following guidelines for inventory record accuracy: ± .2 percent for A items, ± 1 percent for B items, and ± 5 percent for C items.
A items are counted frequently, B items are counted less frequently, and C items are counted the least frequently.
Cycle stock:
The amount of inventory needed to meet expected demand.
Safety stock:
Extra inventory carried to reduce the probability of a stockout due to demand and/or lead time variability.
Economic order quantity (EOQ):
The order size that minimizes total annual cost.
EOQ models identify the optimal order quantity by minimizing the sum of certain annual costs that vary with order size and order frequency. Three order size models are described here:
1. The basic economic order quantity model.

2. The economic production quantity model.

3. The quantity discount model.

Assumptions of the basic EOQ model:
1. Only one product is involved
2. Annual demand requirements are known
3. Demand is spread evenly throughout the year so that the demand rate is reasonably constant.
4. Lead time is known and constant
5. Each order is received in a single delivery
6. There are no quantity discounts
The optimal order quantity reflects a balance between carrying costs and ordering costs:
As order size varies, one type of cost will increase while the other decreases.
Average inventory level and number of orders per year are inversely related:
As one increases, the other decreases
Annual carrying cost =
(Q/2) * H
Q = Order quantity in units
H = Holding (carrying) cost per unit per year
Carrying cost is thus a linear function of Q:
Carrying costs increase or decrease in direct proportion to changes in the order quantity Q
In general, the number of orders per year will be D/Q
Where D = Annual demand and Q = Order size
Annual ordering cost is a (constant) function of the number of orders per year and the ordering cost per order:
(D/Q) * S
D = Demand, usually in units per year
S = Ordering cost per order

Because the number of orders per year, D/Q, decreases as Q increases, annual ordering cost is inversely related to order size.

The total annual cost (TC) associated with carrying and ordering inventory when Q units are ordered each time is:
TC = (Q/2) * H + (D/Q) * S
An expression for the optimal order quantity, Q0, can be obtained using calculus:
Q0 = ?(2DS/H)
The length of an order cycle (i.e., the time between orders) is:
The assumptions of the EPQ model are similar to those of the EOQ model, except that instead of orders received in a single delivery, units are received incrementally during production. The assumptions are:
1. Only one item is involved.

2. Annual demand is known.

3. The usage rate is constant.

4. Usage occurs continually, but production occurs periodically.

5. The production rate is constant.

6. Lead time does not vary.

7. There are no quantity discounts.

The number of runs or batches per year is D/Q, and the annual setup cost is equal to the number of runs per year times the setup cost, S, per run: (D/Q)S.
The larger the run size, the fewer the number of runs needed and, hence, the lower the annual setup cost.
The total setup cost is:
TCmin = Carrying cost + Setup cost = (Imax/2) * H + (D/Q) * S
Imax = maximum inventory
The economic run quantity is:
Qp = ?(2DS/H) * ?(p/p-u)
p = Production or delivery rate
u = Usage rate
The cycle time (the time between orders or between the beginnings of runs) for the economic run size model is a function of the run size and usage (demand) rate:
Cycle time = Qp/u
Similarly, the run time (the production phase of the cycle) is a function of the run (lot) size and the production rate:
Run time = Qp/p
The maximum and average inventory levels are:
Imax = Qp/p(p-u) or Qp – (Qp/P) * u


Iaverage = Imax/2

Quantity discounts:
Price reductions for larger orders offered to customers to induce them to buy in large quantities.
The cost of placing an order is a function of order size.
False: The cost of placing an order is typically unrelated to order size.
There are four determinants of the reorder point quantity:
1. The rate of demand (usually based on a forecast).

2. The lead time.

3. The extent of demand and/or lead time variability.

4. The degree of stockout risk acceptable to management.

When carrying costs are constant, all curves have their minimum points at the same quantity.
When carrying costs are stated as a percentage of unit price, the minimum points do not line up.
Single-period model:
Model for ordering of perishables and other items with limited useful lives.
Excess cost:
Difference between purchase cost and salvage value of items left over at the end of a period.
The goal of the single-period model is to
identify the order quantity, or stocking level, that will minimize the long-run excess and shortage costs.
Four classes of models are described: EOQ, ROP, fixed-order-interval, and single-period models.
The first three are appropriate if unused items can be carried over into subsequent periods. The single-period model is appropriate when items cannot be carried over.
Fill rate:
The percentage of demand filled by the stock on hand.
Fixed-order-interval (FOI) model:
Orders are placed at fixed intervals.
Holding, or carrying cost:
Cost to carry an item in inventory for a length of time, usually a year.
Quantity discounts:
Price reductions for larger orders.
Reorder point (ROP):
When the quantity on hand of an item drops to this amount, the item is reordered.
Service level:
Probability that demand will not exceed supply during lead time.
The two basic questions in inventory management are how much to order and when to order.
Using the EOQ model, if an item’s holding cost increases, its order quantity will decrease.
It will decrease because holding cost is in the denominator of the EOQ formula.
Use of the fixed-interval model requires having a perpetual inventory system.
False: A periodic system would be used.
With the A-B-C approach, items which have high unit costs are classified as A items.
False: A-B-C is based on the product of unit cost and annual volume.
When using EOQ ordering, the order quantity must be computed in every order cycle.
False: Unless demand, holding cost, or ordering cost changing, the order quantity will not change.
Inventory might be held to take advantage of order cycles.
True: Using an economic order quantity is an example of this.
The economic order quantity cannot be used when holding costs are a percentage of purchase cost.
False: Refer to Example 3 in the textbook.
Companies that can successfully use the A-B-C approach can avoid using EOQ models.
False: They still need to determine how much to order.
The objective of inventory management is to minimize holding costs.
True: The objective of inventory management is to minimize total cost, which includes ordering costs and sometimes purchase costs (e.g., quantity discount models).
Holding and ordering costs are inversely related to each other.
False: Changes in order quantity will cause one to increase and the other to decrease.
A two-bin system is essentially a simple reorder point system.
True: Reorder when the first bin is empty.
In the basic EOQ model, annual ordering cost and annual ordering cost are equal for the optimal order quantity.
Increasing the order quantity so that it is slightly above the EOQ would not increase the total cost by very much.
True: The total cost curve is flat to the right of the EOQ.
A fixed-interval ordering system would be used for items that have independent demand.
A store that sells daily newspapers could use the single-period model for reordering.
True: The period is one day, and the news in “perishable” beyond one day.
Other things beings equal, an increase in lead time for inventory orders will result in an increase in the:
Order size: Quantity models do not involve lead time.
If average demand for an item is 21 units per day, safety stock is 4 units, and lead time is 2 days, the ROP will be:
46 – ROP = d x LT + SS = 21 x 2 + 4 = 46.
In an A-B-C system, B items typically represent about this percentage of items:
Which model does not take into account the amount of inventory on hand?
ROP: The EOQ factors are demand, ordering costs, and carrying costs.
Which product is usually bought on an ROP basis?
Sugar: Buy more went the quantity on hand gets low.
Which product is usually bought on a fixed interval basis?
Textbooks: Usually bought once a semester.
In the two-bin system, the quantity in the second bin is equal to the:
ROP: The second bin holds the reorder point quantity,
Using the basic EOQ model, if the ordering cost doubles, the order quantity will be:
about 71% of its former value – Because S in under the square root sign, multiplying its value be 2 will increase the EOQ by the square root of 2, which is .707.
If a decrease in unit price causes the average demand rate to increase, which one of these would not increase?
Lead time – Every other choice is a function of demand.
Setup costs are analogous to which one of these costs?
Holding costs – Both setup and ordering costs are in the numerator of the quantity formula; and both are independent of order size.

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