Chapter 14 – Independent Demand Inventory
Chapter 14
Independent Demand Inventory
Teaching Notes
Chapter 14 is largely a classical treatment of independent demand inventory problems. In
the first part of the chapter a general rationale for inventory as a buffer stock is provided along
with a discussion of independent and dependent demand. The chapter then develops a rather
standard treatment of inventory costs, EOQ, continuous review systems, periodic review
systems, and how inventory control systems are used in practice. At the end of the chapter,
vendor managed inventory and ABC classification of inventory are discussed.
In teaching this chapter we stress the total cost concept for analyzing inventories with the
EOQ as a special case. In doing this we find it useful to cover price discounts from the
supplement as an alternative cost model to the EOQ. We then point out how the total cost model
can be further generalized to other cases and how the minimum cost can always be found by
enumeration, if all else fails. Next, we deal with the case of uncertain demand through the use of
inventory control systems (continuous or periodic). In this connection ABC and computerized or
manual systems are also reviewed. Finally, we end up with a discussion of turnover and why it
is an inadequate basis for inventory control.
Answers to Questions
1.
Gas Station
No RM or WIP
Finished goods include gas, oil, tires, other car parts plus food and
general store items
Hamburger Stand
RM is meat patty, bun, onions
WIP includes burgers frying or being assembled
FG includes hamburgers on a bun with garnishes
Clothing Store
No RM or WIP
FG are the clothes on the racks
Machine Shop
RM are pieces of unformed steel
WIP includes partly finished orders
FG are completed orders waiting to be shipped to customers
14-2
2. Stockout cost results from loss of current sales and loss of future sales and goodwill. The
profit foregone from loss of current sales can be estimated; lost future sales and goodwill,
however, implies an opportunity loss for which historical data is of little help.
3. A requirements philosophy of inventory management is appropriate when demand is
dependent; a replenishment philosophy is appropriate given independent demand. The
4. Manufacturing has three different types of inventory to manage: raw materials, work in
process, and finished goods. The demand for raw materials and WIP is dependent on the
demand for finished goods. The requirements philosophy is used to avoid shortages in
5. Due to the need to review stock position at fixed intervals, a target level of stock must be
ordered to cover demand until the next review period. This estimated amount is over and
Chapter 14 – Independent Demand Inventory
14-3
6. In a hardware store, the P system might be used for nails or screws in bins, screwdrivers,
hammers, and garden hand tools. This is because these items have a lower unit cost,
7. A decision on customer service level must consider the critical tradeoff between customer
satisfaction and inventory level, i.e., between inventory carrying costs and the cost of lost
sales and goodwill from customer dissatisfaction. The manager might try to evaluate this
8. Contrary to traditional arguments, inventory should not increase directly with sales to
maintain a constant turnover ratio. The EOQ formula is useful in showing that inventory
should increase only with the square root of sales. With very high sales, inventory may
9. Having set an overall company inventory policy including service level standards for
each product group in a store:
Chapter 14 – Independent Demand Inventory
Answers to Problems
______ ______________
1. a. EOQ = 2SD/iC = 2(10)(416)/.2(80) = 22.8 23 cases
b. 23/8 = 2.8 so order every 2.8 weeks
416 cases/year 23 = 18.1 so order 18.1 times per year
c. Annual ordering cost = SD/Q = (10)(416)/23 = $ 180.8
_________________
2. a. EOQ = 2(1200)(300)/.2(25) 379 tables
– combined set-up effect of other products manufactured by GRINELL
___
3. a. EOQ = 2(15)(48)/.3(25) = (note: demand = 48 per year)
14-5
4. a. A 40% increase in demand causes the EOQ to increase by 4 cases from 23 to 27
cases, and total cost to increase by $67 from $365 to $432 per year.
___ ___
5. a. EOQ = 2(1000)(80,000)/.3(100) 2,309 widgets
b. 80,000/2309 = 34.65 lots per year
c. Annual carrying cost = iCQ/2 = .3(100)2309/2 = $34,635
Annual ordering cost = SD/Q = 1000(80000)/2309 = $34,647
Chapter 14 – Independent Demand Inventory
14-6
– seasonal demand or cost trends
__________________
6. a. EOQ = 2(25)(10,800)/.25(50) = 207.85 208 (note: demand = 10,800 per
year)
7. a. R = m + s = 450 + (1.65)250 = 862.5 863 units
b. Number of orders placed per year = 10,800/208 52
1/52 = 0.01923
Chapter 14 – Independent Demand Inventory
8. a. EOQ = 26
NAME:
******************
CHAPTER 14,
PROBLEM 8
SECT:
*********
DATE:
########
INPUT SECTION:
OUTPUT SECTION:
*
*
*
*
*
*
*
ANNUAL SALES:
1440
EOQ =
26
ORDERING COST:
$25
REORDER
POINT=
23.6
CARRYING COST
(%):
35%
z =
1.41
ITEM COST:
$300
ORDER
EVERY:
4.5
DAYS
STANDARD
DEVIATION:
0.2
*
*
*
*
WORKING
DAYS/YEAR:
250
LEAD TIME
(DAYS):
4
SERVICE LEVEL:
92%
*
*
*
c. The Q rule for this item is to place an order for 26 sets whenever stock position
14-8
9. a. P is 4.55 days and T is 50 units.
NAME:
******************
CHAPTER 14
PROBLEM 9
SECT:
******************
DATE:
########
PART A
ANNUAL SALES:
1440
ORDERING COST:
$25
CARRYING COST (%):
35%
INPUT
ITEM COST:
$300
SECTION
STD DEV.
0.2
WORKING DAYS/YEAR:
250
LEAD TIME:
4
SERVICE LEVEL:
92%
DAILY DEMAND:
5.76
OPTIMAL VALUE P
4.55
days
OUTPUT
m’:
49.23
SECTION
sigma’:
0.58
TARGET LEVEL:
50.05
z =
1.41
EOQ =
26.19
b. The P system requires greater investment in inventory than the Q system:
CHAPTER 14, PROBLEM 9, PART B
P
Q
SERVICE
INVENTORY
INVENTORY
LEVEL
INVESTMENT
INVESTMENT
90.0%
4152
4082
92.0%
4175
4097
94.0%
4202
4115
96.0%
4235
4138
98.0%
4289
4175
Chapter 14 – Independent Demand Inventory
14-9
10. a. Q = 14 units (from part 3.a.)
R = m + s
b. P = Q/D = 14/4= 3.5 months
T = m’ +s’
m’ = average demand over P+L period (3.5 + 2 = 5.5 months) = 4 (5.5) = 22 units
c. Pro’s: Using the P system in this case will simplify the record keeping and insure
units for the Q system. The P system will increase the inventory holding costs.
________________
11. a. EOQ = 2(40)(600)/.25(50) 62
Service level Safety stock required (z)
Chapter 14 – Independent Demand Inventory
14–10
Service level $ Inventory Investment
85% 1550 + 104 = $1,654
90% 1550 + 128 = $1,678
12. a. Turnover = sales/investment = $40(600)/investment = $24,000/investment
Annual turnover as a function of service level:
Service level Turnover
b. If sales increase by 50% to 900 and the standard deviation of daily demand is still
1, then:
Chapter 14 – Independent Demand Inventory
14–11
NAME:
******************
CHAPTER 14, PROBLEM 13
SECT:
***********
DATE
########
INPUT SECTION
OUTPUT SECTION
*
*
*
*
*
*
*
ANNUAL SALES
TOTAL ANNUAL DEMAND
FOR 1:
300
IN DOLLARS:
$13,300
FOR 2:
250
OPTIMAL ORDERING
FOR 3:
100
INTERVAL(Yrs):
0.1226
years
FOR 4:
200
ITEM COST
OPTIMAL ORDERING
FOR 1:
$20
INTERVAL(days):
36.8
days
FOR 2:
$18
FOR 3:
$12
ORDERING LOT SIZE
FOR 4:
$8
ORDERING COST:
$20
FOR 1:
37
CARRYING COST
(%):
20%
FOR 2:
31
WORKING DAYS/Yr
300
FOR 3:
12
FOR 4:
25
Chapter 14 – Independent Demand Inventory
14–12
e. Normally A, B or C items refer to items that can be managed by different system.
The A items need tight control, B items medium control and C items looser
14. a. Using the template from problem 13
Type Lot Size
1 300
Chapter 14 – Independent Demand Inventory
14–13
Answers to Supplement Problems
1. a. Yes, Speedy Grocery Store should take the discount, because the total annual cost
NAME :
***************
CHAPTER 14, PROBLEM SP1
SECT :
************
DATE :
18-Dec-02
INPUT SECTION
OUTPUT SECTION
SALES per YEAR :
520
EOQ for 0 to 49 cases
20.82
ORDERING COST :
$10
EOQ with 50 cases or more
21.36
CARRYING CHARGE
per YEAR (%) :
30%
Total Cost for first EOQ
$42,100
ITEM COST
Total Cost for 2nd EOQ
$40,007
0 to 49 CASES:
$80
Total Cost for 50 Cases
$40,194
50 CASES & MORE:
$76
* price applies to the entire order
_____________
2. a. EOQ = 2(20)(50)/.15(25) 23 cases
_____________
b. You could attempt to negotiate for the discount to apply to lower quantities than
30. For example, if the discount of $20 applied at 25 units, the resulting total
annual cost would be:
Chapter 14 – Independent Demand Inventory
14–14
b.
c. The maximum value of inventory is calculated as:
_____________________________
4. a. EOQ = 2(200)(2400)/.24(50)(1 – 200/1000) 316
On-Hand Inventory vs. Time
0
40
80
120
160
200
240
020 40 60 80 100
Weeks
Units in Inventory
Chapter 14 – Independent Demand Inventory
14–15
c.
On-Hand Inventory vs. Time
0
50
100
150
200
250
300
0 5 10 15 20 25 30 35
Days
Units in Inventory