NVENTORY
DECISIONS
SUPPLEMENT
A: INVENTORY DECISIONS
Inventory planning and control decisions are an important aspect of the management of
many organizations. Inventory levels are not left to chance but rather are carefully
planned. Major questions to be answered are: How does the manager know what inventory level is right for the firm? Won’t the level that is right vary from organization to
organization?
Specifically, inventory decisions involve how much to order, the so-called economic
order quantity, when to order, the reorder point issue combined with the safety stock
quantity, and finally, the special questions associated with perishable products. Cost factors, uncertainty, and revenues all contribute to the decision analysis.
The purpose of this supplement is to examine the inventory control methods available
to the manager to answer these questions, and the relevant costs for these decisions.
LEARNING OBJECTIVE 1
Compute the optimum
inventory level and order size.
Costs Associated with Inventory
Three groups of costs are associated with inventory. The first group, known as inventory
ordering costs, consists of costs associated with the acquisition of inventory. Examples
include:
1. Clerical costs.
2. Transportation costs.
The second group, known as inventory carrying costs, consists of costs that arise
from having inventory on hand. Examples include:
1.
2.
3.
4.
5.
6.
Storage space costs.
Handling costs.
Property taxes.
Insurance.
Obsolescence losses.
Interest on capital invested in inventory.
The third group, known as costs of not carrying sufficient inventory, consists of
costs that result from not having enough inventory on hand to meet customers’ needs.
Costs in this group are more difficult to identify than costs in the other two groups, but
nevertheless they can include items that are very significant to a firm. Examples of costs
in this group are:
1.
2.
3.
4.
5.
6.
Customer ill will.
Quantity discounts forgone.
Erratic production (expediting of goods, extra set-up, etc.).
Inefficiency of production runs.
Added transportation charges.
Lost sales.
Inventory ordering costs
Those costs associated with the
acquisition of inventory, such as
clerical costs and transportation
costs.
Inventory carrying costs
Those costs associated with the
storage of inventory, such as
rental or storage space, handling
costs, property taxes, insurance,
and interest on funds.
Costs of not carrying sufficient
inventory
Those costs that result from not
having enough inventory on hand
to meet customers’ needs; such
costs would include customer ill
will, quantity discounts forgone,
erratic production, added
transportation charges, and lost
sales.
In a broad conceptual sense, the right level of inventory to carry is the level that minimizes the total of these three groups of costs. Such a minimization is difficult to achieve,
however, because certain of the costs involved are in direct conflict with one another.
Notice, for example, that as inventory levels increase, the costs of carrying inventory also
increase, but the costs of not carrying sufficient inventory decrease. In working toward total
cost minimization, therefore, the manager must balance off the three groups of costs
against one another. The problem really has two dimensions—how much to order (or how
much to produce in a production run) and how often to do it.
Economic order quantity (EOQ)
Computing the Economic Order Quantity
The how-much-to-order question is commonly referred to as the economic order quantity (EOQ). It is the order size that results in a minimization of the first two groups of costs
The order size for materials that
results in a minimization of the
costs of ordering inventory and
carrying inventory.
SA-2
Supplement A Inventory Decisions
just described. Careful thought about order quantity will suggest that order quantity will be
one of the determinants of inventory control levels. We consider two approaches to computing the economic order quantity—the tabular approach and the formula approach.
The Tabular Approach
Given a certain annual consumption of an item, a firm might place a few large-quantity
orders each year, or it might place many small-quantity orders. Placing only a few orders
will result in low inventory ordering costs but in high inventory carrying costs, as the average inventory level would be very large. On the other hand, placing many orders would
result in high inventory ordering costs but in low inventory carrying costs; in this case, the
average inventory level would be quite small.
As stated earlier, the economic order quantity seeks the order size that balances off
these two groups of costs. To show how it is computed, assume that a manufacturer used
3,000 subassemblies (manufactured parts inserted in other manufactured items) in the
manufacturing process each year. The subassemblies are purchased from a supplier at a
cost of $20 each. Other cost data are given below:
Inventory carrying costs, per unit, per year . . . . . . . . . . . . . . . . . $ 0.80
Cost of replacing a purchase order . . . . . . . . . . . . . . . . . . . . . . . 10.00
Exhibit SA–1 contains a tabulation of the total costs associated with various order
sizes for the subassemblies. Notice the total annual cost is lowest (and is equal) at the 250and 300-unit order sizes. The economic order quantity lies somewhere between these two
points. We could locate it precisely by adding more columns to the tabulation, and we
would in time zero in on 274 units as being the exact economic order quantity.
The cost relationships from this tabulation are presented graphically in Exhibit SA–2. Notice from the graph that total annual cost is minimized at that point when
annual carrying costs and annual purchase order costs are equal. The same point identifies the economic order quantity, because the purpose of the computation is to find the
point of exact trade-off between these two classes of costs.
Observe from the graph that total cost shows a tendency to flatten out between 200
and 400 units. Most firms look for this minimum cost range and choose an order size that
falls within it, rather than choosing the exact economic order quantity. The primary reason is that suppliers will often ship goods only in round-lot sizes.
EXHIBIT SA–1 Tabulation of Costs Associated with Various Order Sizes
Order Size in Units
Symbol*
E/2
Q/E
C(E/2)
P(Q/E)
T
25
Average inventory in units . . . . .
Number of purchase orders . . . .
Annual carrying cost
at $0.80 per unit . . . . . . . . . .
Annual purchase order cost
at $10 per order . . . . . . . . . .
Total annual cost . . . . . . . .
50
100
200
250
300
400
1,000
3,000
12.5
120
25
60
50
30
100
15
125
12
150
10
200
7.5
500
3
1,500
1
10
$ 20
$ 40
$ 80
$100
$120
$160
$400
$1,200
1,200
600
300
150
120
100
75
30
10
$1,210
$620
$340
$230
$220
$220
$235
$430
$1,210
$
*Symbols:
E Order size in units (see headings above).
Q Annual quantity used in units (3,000 in this example).
C Annual cost of carrying one unit in stock.
P Cost of placing one order.
T Total annual cost P(Q/E) C(E/2)
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SA-3
Supplement A Inventory Decisions
EXHIBIT SA–2 Graphic
Solution to Economic Order Size
$500
400
Cost
Total cost
300
Annual carrying cost
at $0.80 per unit
200
Annual ordering cost
at $10 per order
100
0
0
200
400
600
800
1,000
Order size (units)
Economic order
quantity
The table in Exhibit SA–1 is based on the formula:
T P(Q/E) C(E/2)
where P is a constant cost per order, and C is a unit cost of carrying a unit of inventory for
the period of time under consideration. If quantity discounts can be obtained for orders of
a certain size, another term representing the purchase costs of the particular lot size
should be added to the formula or another line to the table. Other complications arise
where annual or period demand is not known, lead times vary, or multiple deliveries are
necessary for each order.
The Formula Approach
The economic order quantity can also be found by means of a formula. The formula is
derived by solving the minimization of T P(Q/E) C(E/2) for E using calculus. The
result is:
2 QP
E C
where:
E order size in units.
Q annual quantity used in units.
P cost of placing one order.
C annual cost of carrying one unit in stock.
Substituting with the data used in our preceding example, we have:
Q $3,000 subassemblies used per year.
P $10 cost to place one order.
C $0.80 cost to carry one subassembly in stock for one year.
E
5,0
00
7
$0.8
0 $0
.80
2(3,000)($10)
$60,000
E 274 (the economic order quantity)
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SA-4
Supplement A Inventory Decisions
Although data can be obtained very quickly using the formula approach, it has the
drawback of not providing as great a range of information as the method discussed previously, and it cannot be used where changes in purchase prices occur with changes in lot
sizes.
Observation of the table shown in Exhibit SA–1 can lead to the question of why
inventory orders are based on yearly needs. Yearly needs combined with order sizes determine the number of orders placed and the ordering costs. The reasoning underlying the
use of annual quantity Q is the availability of annual carrying costs. If carrying costs were
expressed for a shorter time, then Q could be for a shorter time.
JIT and the Economic Order Quantity
The EOQ will decrease under either of these circumstances:
1. The cost of placing an order decreases.
2. The cost of carrying inventory in stock increases.
Managers who advocate JIT purchasing argue that the cost of carrying inventory in
stock is much greater than generally realized because of the waste and inefficiency that
inventories create. These managers argue that this fact, combined with the fact that JIT
purchasing dramatically reduces the cost of placing an order, is solid evidence that companies should purchase more frequently in smaller amounts. Assume, for example, that a
company has used the following data to compute its EOQ:
Q 1,000 units needed each year.
P $60 cost to place one order.
C $3 cost to carry one unit in stock for one year.
Given these data, the EOQ would be:
E
4
0,0
00
C $
3
2QP
2(1,000)($60)
E 200 units
Now assume that as a result of JIT purchasing, the company is able to decrease the
cost of placing an order to only $10. Also assume that because of the waste and inefficiency caused by inventories, the true cost of carrying a unit in stock is $8 per year. The
revised EOQ would be:
E
2
,5
00
C $
8
2QP
2(1,000)($10)
E 50 units
Under JIT purchasing, the company would not necessarily order in 50-unit lots since purchases would be geared to current demand. This example shows quite dramatically, however, the economics behind the JIT concept as far as the purchasing of goods is concerned.
Economic production
lot size
The number of units produced in
a production lot that results in a
minimization of set-up costs and
the costs of carrying inventory.
Set-up costs
Labour and other costs involved
in getting facilities ready for a run
of a different production item.
Production Lot Size
The economic order quantity concept can also be applied to the problem of determining the
economic production lot size. Deciding when to start and when to stop production runs is
a problem that has plagued manufacturers for years. The problem can be solved quite easily by inserting the set-up cost for a new production lot into the economic order quantity
formula in place of the purchase order cost. The set-up cost includes the labour and other
costs involved in making facilities ready for a run of a different production item.
To illustrate, assume that Chittenden Company has determined that the following
costs are associated with one of its product lines:
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Supplement A Inventory Decisions
Q 15,000 units produced each year.
P $150 set-up costs to change production from one product to another.
C $2 to carry one unit in stock for one year.
Managers involved in the theory of constraints would go even further in reducing lot
sizes. When a particular work centre is not a constraint, the only significant cost involved
in set-ups is typically direct labour wages. However, since direct labour wages are considered to be a fixed cost rather than a variable cost in the theory of constraints, the incremental cost of set-ups is considered to be zero. Therefore, at work centres that are not a
constraint, the economic lot size in the theory of constraints is as small as a single unit. At
the constraint itself, set-up time is very costly, since each minute spent setting up is a
minute taken away from producing output that could be sold. Therefore, set-up reduction
efforts should be focused on the constraint and lot sizes should be larger at the constraint
than at other work centres.
Managers should be extremely cautious when applying the results of activity-based
costing (ABC) analyses to computation of the economic lot size. Typically, one of the
results of an ABC analysis is a dramatic increase in the apparent costs of set-ups. The reason for this is that under conventional costing systems, many of the costs that might be
attributed to switching over from one product to another are lumped into the general manufacturing overhead cost pool and distributed to products based on direct labour-hours or
some other measure of volume. When an ABC analysis is done, these costs are separately
identified as set-up costs. As a consequence, set-up costs appear to increase, and this
would seem to imply that the economic lot size should be increased. However, a close
examination of the costs attributed to set-ups in the ABC analysis will usually reveal that
most of the costs cannot actually be avoided by reducing the number of set-ups. For
example, machinery depreciation may be included in set-up costs. However, reducing the
number of set-ups may have no impact at all on the amount of machinery depreciation
actually incurred.
What is the optimal production lot size for this product line? It can be determined by
using the same formula used to compute the economic order quantity:
O
2
,2
50,0
00
$
2 $2
2(15,000)($150)
$4,500,000
O 1,500 (economic production lot size in units)
The Chittenden Company will minimize its overall costs by producing in lots of
1,500 units each. Tabular analysis can be used to provide a more flexible model for the
planning of production lot sizes.
JIT systems are being touted as a total manufacturing system for repetitive manufacturing environments such as those used to produce food and beverages, electrical products, textiles, and automobiles. Small lot production and flexible manufacturing are key
elements to the system. Distances in Canada may pose a problem for some industries but
not necessarily for all. The seasonal nature of some businesses may preclude the use of
JIT because additional production capacity is simply too costly to permit production only
when the need is evident in the form of customer orders. However, the potential improvements in productivity and quality, together with the reduction in needed investment in
inventory, make JIT production an option to be seriously investigated for manufacturers
and processors.
JIT production philosophy, when it was originated, examined carefully the assumptions in economic production lot size analysis. The typical analysis as presented earlier
assumes that set-up time is a known fixed cost, for example, $150 per set-up in the preceding example. JIT approached this production lot size problem by attempting to reduce
set-up costs to zero. If set-up costs in the Chittenden Company example were $0.0, the
economic production lot size in units would be one, a JIT production approach. The
less the set-up cost, the smaller the production lots. Production approaches have been
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SA-5
SA-6
Supplement A Inventory Decisions
redesigned in some operations so that many different products can be manufactured at little or no set-up cost. For example, a world-class automobile manufacturer has been noted
as being able to change from one model to another in 2.5 minutes, a complete retooling
operation.
Reorder Point and Safety Stock
Reorder point
The point in time when an order
must be placed to replenish
depleted stocks; it is determined
by multiplying the lead time by
the average daily or weekly
usage.
Lead time
The interval between the time that
an order is placed and the time
that the order is finally received
from the supplier.
We stated earlier that the inventory problem has two dimensions—how much to order and
how often to do it. How often to do it involves what are commonly termed the reorder
point and the safety stock, and seeks to find the optimal trade-off between the second two
groups of inventory costs outlined earlier (the costs of carrying inventory and the costs of
not carrying sufficient inventory). First, we will discuss the reorder point and the factors
involved in its computation. Then, we discuss the circumstances under which a safety
stock must be maintained.
The reorder point tells the manager when to place an order or when to initiate production to replenish depleted stocks. It is dependent on three factors—the economic order
quantity (or economic production lot size), the lead time, and the rate of usage during the
lead time. The lead time can be defined as the interval between the time that an order is
placed and the time that the order is finally received from the supplier or from the production line.
Constant Usage during the Lead Time If the rate of usage during the lead time is
known with certainty, the reorder point can be determined by the following formula:
Reorder point Lead time Average daily or weekly usage
To illustrate the formula’s use, assume that a company’s economic order quantity is
500 units, that the lead time is 3 weeks, and that the average weekly usage is 50 units.
Reorder point 3 weeks 50 units per week 150 units
The reorder point would be 150 units. That is, the company automatically places a new
order for 500 units when inventory stock drops to a level of 150 units, or three weeks’
supply, left on hand.
Variable Usage during the Lead Time
Safety stock
The difference between average
usage of materials and maximum
usage of materials that can
reasonably be expected during
the lead time.
The previous example assumed that the 50
units per week usage rate was constant and was known with certainty. Although some
firms enjoy the luxury of certainty, the more common situation is to find considerable
variation in the rate of usage of inventory items from period to period. If usage varies
from period to period, the firm that reorders in the way computed earlier may soon find
itself out of stock. A sudden spurt in demand, a delay in delivery, or a snag in processing
an order may cause inventory levels to be depleted before a new shipment arrives.
Companies that experience problems in demand, delivery, or processing of orders
have found that they need some type of buffer to guard against stockouts. Such a buffer
is usually called a safety stock. A safety stock serves as insurance against greater-thanusual demand and against problems in the ordering and delivery of goods. Its size is
determined by deducting average usage from the maximum usage that can reasonably be
expected during a period. For example, if the firm in the preceding example was faced
with a situation of variable demand for its product, it would compute a safety stock as
follows:
Maximum expected usage per week . . . . . . . . .
Average usage per week . . . . . . . . . . . . . . . . .
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lead time . . . . . . . . . . . . . . . . . . . . . . . . . . .
Safety stock . . . . . . . . . . . . . . . . . . . . . . . . . .
73.3
50
23.3
3
70
units
units
weeks
units
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SA-7
Supplement A Inventory Decisions
The reorder point is then determined by adding the safety stock to the average usage
during the lead time. In formula form, the reorder point will be:
Reorder point (Lead time Average daily or weekly usage) Safety stock
Computation of the reorder point by this approach is shown both numerically and graphically in Exhibit SA–3. As shown in the exhibit, the company places a new order for
500 units when inventory stocks drop to a level of 220 units left on hand.
If management does not wish to assume the worst-case situation by using the maximum expected usage per week, then a slightly more complex calculation of the safety
stock is necessary as shown in Exhibit SA–4 and based on the data that follow. Assume
that management makes the following estimates for a yearly period:
Carrying cost per year, $1 per unit
Stockout cost per unit, $0.60
Average usage per week, 50
Orders placed per year. 12
Demand
Probabilities
80
120
140
150
160
180
220
0.05
0.06
0.20
0.38
0.20
0.06
0.05
1.00
These estimates reflect the uncertainty experienced by management when it faces the various demand possibilities. The table of demand levels and corresponding probabilities
presents how management has described the uncertainty it faces. This description will, as
we shall see, be incorporated in the safety stock calculation.
The calculation of the optimal safety stock begins by computing the various inventory
quantities that the demand probabilities indicate could be satisfied by the safety stock.
These, quantities are the demand quantities in excess of the expected demand during the
Inventory (units)
EXHIBIT SA–3 Determining the Reorder Point—Variable Usage
570
Reorder point
Safety stock
Average usage
Maximum
expected
usage
220
70
0
5 weeks
Economic order quantity. . . . 500.units
Lead time. . . . . . . . . . . . . . . 3.weeks
Average weekly usage. . . . . 50.units
Maximum weekly usage. . . . 77.3.units
Safety stock . . . . . . . . . . . . . . 70.units
10 weeks
15 weeks
Lead
time
3 weeks
Reorder point = (3 weeks ⴛ 50 units per week) + 70 units = 220 units
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Economic
order
quantity
20 weeks
SA-8
Supplement A Inventory Decisions
lead time period. Calculation (a) in Exhibit SA–4 illustrates the amounts. Each unit of
safety stock inventory will be on hand for the year (the typical time period used), so the
carrying costs per unit of inventory per year is used to determine the first cost element: the
total carrying cost and the safety stock per year.
The second set of calculations computes the stockout costs caused because demand
exceeds the safety stock quantity. Column (b) in Exhibit SA–4 reflects the excess demand
possibilities above the safety stock and the average demand during the lead time; in other
words, the stockout quantity. The stockout in units is multiplied by the stockout cost per
unit of 60 cents to give the stockout cost for each time an order is placed. Knowledge of
the average inventory usage per year and the order size is used to determine the number
of times orders are placed in a year. To determine the stockout total costs, the stockout
cost per order is multiplied by the number of orders per year by the probability of each
possible demand level to yield column (d). The sum of the total carrying cost for the
safety stock and the expected stockout costs give the cost for each safety stock level.
The lowest expected total costs provide the optimal level of safety stock. Notice that
Exhibit SA–4 suggests that 10 is the optimal level, with a total cost of carrying the safety
stock of $40.24. The conservative maximum safety stock level of 70 suggested earlier had
an annual cost of $70 in this illustration.
Perishable Products
Inventory problems for perishable products or services such as hotel rooms pose an interesting and somewhat different inventory problem. Basically, if too much or too many are
ordered, the cost of the inventory is similar to a carrying cost, while ordering too few has
the cost of contribution forgone from the lost sale. A firm cannot sell what it does not
have, while it loses what it purchased but did not sell.
Assume the following:
Purchase cost, $3 per unit.
Selling price, $5 per unit.
EXHIBIT SA–4 Safety Stock Level
(a)
Safety
Stock
Level
in Units
Total
Carrying
Cost per
Year
–0–
$–0–
10
10
30
70
30
70
(b)
(c)
Stockout
in
Units
Stockout
Cost per
Order Time
Number of
Times Orders
Placed
Probability
of
Stockout
10
30
70
20
60
40
0
$ 6.00
18.00
42.00
12.00
36.00
24.00
0.00
12
12
12
12
12
12
12
0.20
0.06
0.05
0.06
0.05
0.05
0.00
(d)
Expected
Stockout
Cost per
Year
$14.40
12.96
25.20
8.64
21.60
14.40
0.00
(e)
Total
Cost
per
Year
$52.56
40.24
44.40
70.00
(a) Safety stock level is possible demand minus expected demand (e.g., 180 150 30). Carrying cost of safety stock is units times
cost per unit to carry (e.g., 30 $1 $30).
(b) Stockout in units is possible demand minus expected demand minus safety stocks (e.g., 220 150 10 60; 180 150 10 20).
(c) Stockout cost per order time is stockout in unit times stockout cost per unit (e.g., 30 $0.60 $18.00; 40 $0.60 $24.00).
(d) Expected stockout cost per year is stockout cost per time the order is placed, times the number of orders placed per year, times the
probability of a stockout each time (e.g., $6 12 0.20 $14.40; $12 12 0.06 $8.64). The probability of a stockout is
obtained from the data for various demand levels in excess of the expected amount of 150 plus the safety stock.
(e) Total cost per year is the carrying cost of the safety stock plus the expected stockout cost per year for the appropriate demand levels
(e.g., $0.0 $14.40 $12.96 $25.20 $52.56; $30 $14.40 $44.40).
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SA-9
Supplement A Inventory Decisions
Remember:
You cannot sell what you do not have.
What you buy but cannot sell is lost.
Carefully review the calculations in Exhibit SA–5 to see how the information can be combined to select the optimum inventory level.
For perishable products, each unsold unit of inventory generally is lost; at best, it may
receive a rebate from the inventory supplier. Comparison of the total revenue based on
demand quantities time selling prices, with the purchase cost of the inventory adjusted for
any rebates or returns, determines the cell profit or loss for each combination of demand
and inventory shown in Exhibit SA–5. Because the demand levels are uncertain, each possible net income before income taxes for the particular inventory level is multiplied by the
probability of the demand level to yield the expected profits. The maximum expected
profit is considered to be the indicator of the optimum inventory level.
EXHIBIT SA–5 Calculation of
Profitability of Order/Demand Combinations
and Probability/Demand
Optimal Inventory
0.10
0.15
0.05
0.40
0.30
Inventory
1
2
3
4
5
Expected Profit
1
2
3
4
5
$2
1
4
7
10
$2
4
1
2
5
$2
4
6
3
–0–
$2
4
6
8
5
$2
4
6
8
10
$2.00
3.50
4.25
4.75
3.25*
.........
.........
.........
.........
.........
Note: Four units is the optimum level of inventory because it has the greatest profit, $4.75.
*Profit probability; for example, [0.10(10) 0.15(5) 0.05(0) 0.40(5) 0.30(10)] $3.25
QUESTIONS
SA-1
What three classes of costs are balanced by a company’s inventory policy?
SA-2
What trade-offs in costs are involved in computing the EOQ (economic order quantity)?
SA-3
Define lead time and safety stock.
SA-4
List at least three costs associated with a company’s inventory policy that do not appear
as an expense on the income statement.
SA-5
“Managers are more interested in a minimum cost range than they are in a minimum cost
point.” Explain.
SA-6
What implications exist when management can reduce set-up costs?
SA-7
What modifications are necessary to the economic order quantity calculations when
purchase discounts are possible?
SA-8
What are the inventory costs associated with perishable products?
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QUESTIONS
SA-10
Supplement A Inventory Decisions
EXERCISES
EXERCISES
EXERCISE SA–1 Vancouver Company uses 5,400 units of part X-7 each year. The cost of
placing one order for part X-7 is estimated to be about $10. Other costs associated with carrying
part X-7 in inventory are:
Annual Cost
per Part
Insurance . . . . . . . . . . . . . . . . . . . . . . .
Property taxes . . . . . . . . . . . . . . . . . . . .
Interest on funds invested . . . . . . . . . . .
Other . . . . . . . . . . . . . . . . . . . . . . . . . .
$0.12
0.05
0.10
0.03
Total cost . . . . . . . . . . . . . . . . . . . . . .
$0.30
Required:
1. Compute the economic order quantity (EOQ) for part X-7.
2. Assume that the company has been able to reduce the cost of placing an order to only $1. Also
assume that when the waste and inefficiency caused by inventories is considered, the cost to
carry a part in inventory jumps to $1.20 per unit. Under these conditions, what would be the
EOQ?
EXERCISE SA–2 Joseph Wong of Hong Kong, China, distributes medical supplies throughout
Germany. Selected information relating to a quick-developing X-ray film carried by the company
is given below:
Economic order quantity (EOQ) . . . . . . . . 700 units
Maximum weekly usage . . . . . . . . . . . . . . . 84 units
Lead time . . . . . . . . . . . . . . . . . . . . . . . . .
4 weeks
Average weekly usage . . . . . . . . . . . . . . . . 70 units
Management is trying to determine the proper safety stock to carry on this inventory item and to
determine the proper reorder point.
Required:
1. Assume that no safety stock is to be carried. What is the reorder point?
2. Assume that a full safety stock is to be carried.
a. What would be the size of the safety stock in units?
b. What would be the reorder point?
EXERCISE SA–3 Flint Company uses 12,000 units of part AK-4 each year. To get better control
over its inventories, the company is anxious to determine the economic order quantity (EOQ) for
this part.
Required:
1. The company has determined that the cost to place an order for the part is $30, and it has
determined that the cost to carry one part in inventory for one year is $1.50. Compute the EOQ
for the part.
2. Assume that the cost to place an order increases from $30 to $40 per order. What will be the
effect on the EOQ? Show computations.
3. Assume that the cost to carry a part in inventory increases from $1.50 to $2.00 per part.
(Ordering costs remain unchanged at $30 per order.) What will be the effect on the EOQ? Show
computations.
4. In (2) and (3) above, why does an increase in cost cause the EOQ to go up in one case and to
go down in the other?
EXERCISE SA–4 Classify the following as either (a) costs of carrying inventory or (b) costs of
not carrying sufficient inventory:
1. Airfreight on a rush order of a critical part needed in production.
2. Interest paid on investment funds.
3. Municipal taxes on inventory.
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Supplement A Inventory Decisions
4.
5.
6.
7.
8.
9.
10.
SA-11
Spoilage of perishable goods.
Excessive set-up costs.
Customers lost through inability of the company to make prompt delivery.
Quantity discounts lost as a result of purchasing in small lots.
Fire insurance on inventory.
Loss sustained when a competitor comes out with a less expensive, more efficient product.
A general feeling of ill will among customers, due to broken delivery promises.
PROBLEMS
PROBLEM SA–5 Economic Order Quantity, Safety Stock, and JIT Purchasing Impact
Myron Metal Works, Inc., uses a small casting in one of its finished products. The castings are
purchased from a foundry located in another province. In total, Myron Metal Works, Inc.,
purchases 54,000 castings per year at a cost of $8 per casting.
The castings are used evenly throughout the year in the production process on a 360-day-peryear basis. The company estimates that it costs $90 to place a single purchase order and about $3.00
to carry one part in inventory for a year.
Delivery from the supplier generally takes 6 days, but it can take as much as 10 days. The days
of delivery time and the percentage of their occurence are shown in the following tabulation:
Delivery Time
(Days)
Percentage
of Occurence
6 ............................
75
7 ............................
10
8 ............................
5
9 ............................
5
10 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
.............................
100
Required:
1. Compute the ECQ.
2. Assume that the company is willing to assume an 15% risk of being out of stock. What would
be the safety stock? The reorder point?
3. Assume that the company is willing to assume only a 5% risk of being out of stock. What
would be the safety stock? The reorder point?
4. Assume a 5% stockout risk as stated in (3) above. What would be the total cost of ordering and
carrying inventory for one year?
5. Refer to the original data. Assume that the company decides to adopt JIT purchasing policies.
This change allows the company to reduce its cost of placing a purchase order to only $6.
Also, the company estimates that when the waste and inefficiency caused by inventories are
considered, the true cost of carrying a unit in stock is $7.20 per year.
a. Compute the EOQ.
b. How frequently would the company be placing an order, as compared to the old
purchasing policy?
PROBLEM SA–6 Tabulation Approach; Economic Order Quantity (EOQ); Reorder Point
You have been engaged to install an inventory control system for Dexter Company. Among the
inventory control features that Dexter desires are indicators of “how much” to order “when.” The
following information is furnished for one item, called a duosonic, that is carried in inventory:
a. Duosonics are sold by the gross (12 dozen) at a list price of $800 per gross, FOB shipper.
Dexter receives a 40% trade discount off list price on purchases in gross lots.
b. Freight cost is $20 per gross from the shipping point to Dexter’s plant.
c. Dexter uses about 5,000 duosonics during a 259-day production year but must purchase a total
of 36 gross per year to allow for normal breakage. Minimum and maximum usages are 12 and
28 duosonics per day, respectively.
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PROBLEMS
SA-12
Supplement A Inventory Decisions
d. Normal delivery time to receive an order is 20 working days from the date that a purchase
request is initiated. A stockout (complete exhaustion of the inventory) of duosonics would stop
production, and Dexter would purchase duosonics locally at list price rather than shut down.
e. The cost of placing an order is $30.
f. Space storage cost is $24 per year per average gross in storage.
g. Insurance and taxes are approximately 12% of the net delivered cost of average inventory, and
Dexter expects a return of at least 8% on its average investment. (Ignore ordering costs and
carrying costs in making these computations.)
Required:
1. Prepare a schedule computing the total annual cost of duosonics based on uniform order lot
sizes of one, two, three, four, and five gross of duosonics. (The schedule should show the total
annual cost according to each lot size.) Indicate the EOQ.
2. Prepare a schedule computing the minimum stock reorder point for duosonics. This is the point
below which reordering is necessary to guard against a stockout. Factors to be considered
include average lead period usage and safety stock requirements.
(CPA, adapted)
PROBLEM SA–7 Economic Order Quantity, Safety Stock, and JIT Purchasing Impact
Stoffer Manufacturing Company uses 7,200 units of material X each year. The material is used
evenly throughout the year in the company’s production process. A recent cost study indicates that
it costs $3.20 to carry one unit in inventory for a year. The company estimates that the cost of
placing an order for material X is $180.
On the average, it takes 7 days to receive an order from the supplier. Sometimes, orders do not
arrive for 10 days, and at rare intervals (about 2% of the time) they do not arrive for 12 days. Each
unit of material X costs the company $15. Stoffer works an average of 360 days per year.
Required:
1. Compute the EOQ.
2. What size safety stock would you recommend for material X? Why?
3. What is the reorder point for material X in units?
4. Compute the total cost associated with ordering and carrying material X in inventory for a year.
(Do not include the $15 purchase cost in this computation.)
5. Refer to the original data. Assume that as a result of adopting JIT purchasing policies, the
company is able to reduce the cost of placing a purchase order to only $5. Also assume that
after considering the waste and inefficiency caused by inventories, the actual cost of carrying
one unit of material X in inventory for a year is $18.
a. Compute the new EOQ.
b. How frequently would the company be placing a purchase order, as compared to the old
purchasing policy?
PROBLEM SA–8 Integration of Purchases Budget, Reorder Point, and Safety Stock
The Press Company manufactures and sells industrial components. The Whitmore Plant is
responsible for producing two components, AD-5 and FX-3. Plastic, brass, and aluminum are used
in the production of these two products.
Press Company has adopted a 13-period reporting cycle in all of its plants for budgeting
purposes. Each period is four weeks long and has 20 working days. The projected inventory levels
for AD-5 and FX-3 at the end of the current (seventh) period and the projected sales for these two
products for the next three four-week periods are as follows:
Component
Projected Inventory
Level (in Units)
End of 7th Period
AD-5 . . . . . . . . . . .
FX-3 . . . . . . . . . . .
3,000
2,800
Projected Sales (in Units)
8th
Period
9th
Period
10th
Period
7,500
7,000
8,750
4,500
9,500
4,000
Past experience has shown that adequate inventory levels for AD-5 and FX-3 can be maintained if
40% of the next period’s projected sales are on hand at the end of a reporting period. Based on this
experience and the projected sales, the Whitmore Plant has budgeted production of 8,000 units of
AD-5 and 6,000 units of FX-3 in the eighth period. Production is assumed to be uniform for both
products within each four-week period.
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Supplement A Inventory Decisions
The raw material specifications for AD-5 and FX-3 are as follows:
AD-5
(Kilograms)
FX-3
(Kilograms)
2.0
0.5
—
1.0
—
1.5
Plastic . . . . . . .
Brass . . . . . . . .
Aluminum . . . . .
Data relating to the purchase of raw materials are:
Plastic . . . . .
Brass . . . . .
Aluminum . .
Purchase
Price per
Kilogram
Standard
Purchase
Lot
(Kilograms)
Reorder
Point
(Kilograms)
$0.40
0.95
0.55
15,000
5,000
10,000
12,000
7,500
10,000
Projected
Inventory
Status at the
End of the
7th Period
(Kilograms)
On
Hand
On
Order
Lead
Time in
Working
Days
16,000
9,000
14,000
15,000
—
10,000
10
30
20
The sales of AD-5 and FX-3 do not vary significantly from month to month. Consequently, the
safety stock incorporated into the reorder point for each of the raw materials is adequate to
compensate for variations in the sales of the finished products.
Raw material orders are placed the day the quantity on hand falls below the reorder point.
Whitmore Plant’s suppliers are very dependable so that the given lead times are reliable. The
outstanding orders for aluminum and plastic are due to arrive on the 4th and 10th working days of
the eighth period, respectively. Payments for all raw material orders are remitted in the month of
delivery.
Required:
Whitmore Plant is required to submit a report to corporate headquarters of Press Company summarizing the projected raw materials activities before each period commences. The data for the
eighth-period report are being assembled. Determine the following items for plastic, brass, and
aluminum for inclusion in the eighth-period report:
1. Project quantities (in kilograms) of each raw material to be issued to Production.
2. Projected quantities (in kilograms) of each raw material ordered and the date (in terms of
working days) the order is to be placed.
3. The projected inventory balance (in kilograms) of each raw material at the end of the period.
4. The payments for purchases of each raw material.
(CMA, adapted)
PROBLEM SA–9 EOQ Computations Sporting Goods Ltd. buys baseballs at $20 per dozen
from its wholesaler. All purchase orders are authorized by the respective department managers,
who are paid weekly salaries of $600 to work 40 hours. On average, it takes a manager about 15
minutes to gather the information required to issue the purchase order. When not engaged in
administrative duties, such as placing orders, hiring and scheduling staff, and attending meetings,
the managers spend their time selling.
Once the purchase order information is gathered, it is typed onto a purchase order by a parttime employee hired on an hourly basis, at $12 per hour, to do typing. It takes this person 10 minutes to type the order. The order form costs $0.25 and mailing costs are $1.25.
When the order arrives, it is unloaded from the truck and placed in the stockroom by the stock
supervisor, who is paid $12 per hour. It takes 20 minutes to unload and store each order. Rent,
insurance, and taxes for each dozen baseballs in inventory amounts to $0.40 per year.
Sporting will sell about 36,000 dozen baseballs evenly throughout the year in its busy store
where each salesperson generates weekly sales with a contribution margin of $2,000. In fact, the
store is so busy that part-time staff, which is paid $10 per hour, is constantly used to help with sales.
Sporting desires a 10% return on any investment that it makes.
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SA-13
SA-14
Supplement A Inventory Decisions
Required:
1. What is the economic order quantity in dozens?
2. Assuming that Sporting Goods ordered in order sizes of 800 dozen evenly throughout the year,
what would be the total annual inventory expenses to sell 36,000 dozen baseballs?
3. Suppose that by streamlining its relationship with its supplier, Sporting Goods can lower its
total cost of placing each order to $1. What are the consequences of this reduction in orderplacing costs compared with the order size in (2)?
(CGA-Canada, adapted)
PROBLEM SA–10 Economic Order Quantity and Safety Stock The Daffodil Co. Ltd. has
obtained the following costs and other data pertaining to one of its raw materials:
Working days per year, 250 days
Normal use per day, 400 units
Maximum use per day, 600 units
Minimum use per day, 100 units
Lead time, 8 days
Cost of placing one order, $20.00
Carrying cost per unit per year, $0.30
You may need to use the following formula
2QCP
Required:
Compute the following:
1. Economic order quantity.
2. Safety stock.
3. Reorder point.
4. Normal maximum inventory.
5. Absolute minimum inventory.
6. Average inventory.
7. Assume use per day can occur with the following levels of chance:
Daily
Demand
Probability
400
450
500
550
600
0.40
0.30
0.20
0.05
0.05
.............
.............
.............
.............
.............
Stockout costs are estimated to be $0.05 per unit. Determine the safety stock amount that minimizes the expected costs involved.
(CGA-Canada, adapted)
PROBLEM SA–11 Inventory of Perishable Products A newsstand receives its weekly order
of Glimpse magazine on Monday and cannot reorder during the week. Each copy costs $0.90 and
sells for $1.50. Unsold copies may be returned the following week for a $0.60 rebate. When the
newsstand runs out of copies, the owner knows from past experience that customers will purchase
Glimpse magazine elsewhere for an average of two weeks; therefore, the estimated goodwill loss
for stockouts is $1.20 per unsatisfied customer. Demand has been remarkably constant, ranging
from 7 to 10 copies per week, as shown below:
Demand (in copies)
7
8
9
10
Probability of time
0.03
0.04
0.20
0.10
Required:
1. Determine the optimal number of copies to stock and the expected profit.
2. What is the expected opportunity loss from stocking seven copies?
(CMA-Canada, adapted)
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Supplement A Inventory Decisions
SA-15
PROBLEM SA–12 Inventory of Perishable Products Bruno’s Bakery stocks fresh-baked
doughnuts that sell for $6 per dozen and cost $4 per dozen to produce. Unsold day-old doughnuts
are reduced in price to $3 per dozen and are always completely sold without affecting the current
day’s demand for fresh doughnuts. Bruno, the owner of the bakery, estimates daily demand
characteristics for fresh doughnuts as follows:
(Dozens)
Demand
Probability
30
32
34
36
38
0.1
0.2
0.3
0.3
0.1
.............
.............
.............
.............
.............
Required:
How many dozens of doughnuts should Bruno’s Bakery produce each morning to maximize net
income? Support your decision by preparing an appropriate payoff table.
(CMA-Canada, adapted)
CASE
CASE SA–13 Economic Order Quantity Computations Pierce Company is a regional
distributor of automobile window glass. With the introduction of the new subcompact car models
and the expected high level of consumer demand, management recognizes a need to determine the
total inventory cost associated with maintaining an optimal supply of replacement windshields for
the new subcompact cars introduced by each of the three manufacturers. Pierce is expecting a daily
demand for 50 windshields. The purchase price of each windshield is $70.
Other costs associated with ordering and maintaining an inventory of these windshields are as
follows:
a.
b.
c.
d.
e.
f.
g.
The historical ordering costs incurred in the purchase order department for placing and processing orders are shown below:
Year
Orders Placed and Processed
Total Ordering Costs
2004
2005
2006
28
77
140
$17,220
17,465
17,780
Management expects the order costs to increase 16% over the amounts and rates experienced
during the last three years.
The windshield manufacturer charges Pierce a $80 shipping fee per order.
A clerk in the receiving department receives, inspects, and secures the windshields as they
arrive from the manufacturer. This activity requires eight hours per order received. This clerk
has no other responsibilities and is paid at the rate of $12.50 per hour. Related variable overhead costs in this department are applied at the rate of $2.50 per hour.
Additional warehouse space will have to be rented to store the new windshields. Space can be
rented as needed in a public warehouse at an estimated cost of $2,500 per year plus $5.35 per
windshield.
Breakage cost is estimated to be 6% of the cost per windshield.
Taxes and fire insurance on the inventory are $1.15 per windshield.
The desired rate of return on the investment in inventory is 18% of the purchase price.
Six working days are required from the time an order is placed with the manufacturer until it is
received. Pierce uses a 300-day workyear when making economic order quantity computations.
Required:
Calculate the following values for Pierce Company:
1. Value for ordering cost that should be used in the EOQ formula.
2. Value for storage cost that should be used in the EOQ formula.
3. Economic order quantity.
4. Minimum annual cost as the economic order quantity point.
5. Reorder point in units.
(CMA, adapted)
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