Chapter 13 – Inventory Management
38. Given:
Demand can be approximated with a Poisson distribution with a mean of 6 per day. It costs $9 to
prepare each cake. Fresh cakes sell for $12 each. Day-old cakes sell for $9 each. One half of the
day-old cakes are sold and the rest thrown out.
cakes to prepare = 5. The resulting service level will be .446 = 44.6%.
39. Given:
Purchase price = $1.00 per pound. Salvage value = $.80 per pound. Burgers sell for $.60 each.
Four hamburgers can be prepared from each pound of beef. Labor, overhead, meat, buns, and
condiments cost $.50 per burger. Demand is normally distributed with a mean of 400 pounds per
Chapter 13 – Inventory Management
13–52
Education.
40. Given:
Demand for rug cleaning machines is shown in the table below. Machines are rented by the day
only. Profit on rug cleaners = $10/day. Clyde has 4 rug-cleaning machines.
Demand
Frequency
0
.30
1
.20
2
.20
3
.15
4
.10
5
.05
1.00
Demand
Frequency
Cumulative
Frequency
0
.30
.30
1
.20
.50
2
.20
.70
3
.15
.85
4
.10
.95
5
.05
1.00
1.00
a. Determine the implied range of excess cost per machine:
Cs = $10
Ce = unknown
For 4 machines to be optimal, the SL ratio must be ≥ .85 and ≤ .95.
Step 1:
Set SL = .85 and solve for Ce:
Step 2:
Set SL = .95 and solve for Ce:
Chapter 13 – Inventory Management
13–53
Education.
b. If Clyde protests that the answer from part a is too low, does this suggest an increase or a
decrease in the number of machines he stocks?
If the excess cost is supposed to be higher, then the number of machines should be decreased.
When excess cost increases, SL decreases along with the optimum stocking level.
c. Suppose now that excess cost per day = $10 and the shortage cost per day is unknown.
Assuming that the optimal number of machines is 4, what is the implied range of shortage
cost?
Step 1:
Set SL = .85 and solve for Cs:
Step 2:
Set SL = .95 and solve for Cs:
Chapter 13 – Inventory Management
41. Given:
Spares cost $200 each. Unused spares have a salvage value of $50 each. If a part fails and a spare
is not available, 2 days will be needed to obtain a replacement and install it. The cost for idle
equipment is $500/day.
Probability of usage:
Number
0
1
2
3
Probability
.10
.50
.25
.15
a. Use the ratio method to determine the number of spares to order:
# of Spares
Probability of
Demand
Cumulative
Probability
0
.10
.10
1
.50
.60
2
.25
.85
3
.15
1.00
Chapter 13 – Inventory Management
13–55
Education.
42. Given:
Cakes cost $33 each, and they sell for $60 each. Unsold cakes are reduced to half price on
Monday, and typically one-third of those are sold. Any that remain are donated.
Probability of demand:
Number
0
1
2
3
Probability
.15
.35
.30
.20
a. Use the ratio method to determine the number of cakes to prepare to maximize expected
profit:
# of Cakes
Probability of
Demand
Cumulative
Probability
0
.15
.15
1
.35
.50
2
.30
.80
3
.20
1.00
Cs = Selling Price – Unit Cost = $60 – $33 = $27
Ce = Unit Cost – Salvage Value = $33 – [(1/3)(1/2)($60)] = $23
54.
2327
27
es
s
CC
C
SL
Because the service level of .54 falls between the cumulative probabilities of .50 and .80, the
supermarket should stock 2 cases of wedding cakes.
b. Use the ratio method to determine the number of cakes to prepare to maximize expected
payoff.
Stocking
Demand = 0
Demand = 1
Demand = 2
Demand = 3
Expected
Level
Prob. = .15
Prob. = .35
Prob. = .30
Prob. = .20
Payoff
0
[Sell 0, Over 0]
(.15 * 0 * $27) –
(.15 * 0 * $23) =
$0
[Sell 0, Over 0]
(.35 * 0 * $27) –
(.35 * 0 * $23) =
$0
[Sell 0, Over 0]
(.30 * 0 * $27) –
(.30 * 0 * $23) =
$0
[Sell 0, Over 0]
(.20 * 0 * $27) –
(.20 * 0 * $23) =
$0
$0
1
[Sell 0, Over 1]
(.15 * 0 * $27) –
(.15 * 1 * $23) =
-$3.45
[Sell 1, Over 0]
(.35 * 1 * $27) –
(.35 * 0 * $23) =
$9.45
[Sell 1, Over 0]
(.30 * 1 * $27) –
(.30 * 0 * $23) =
$8.10
[Sell 1, Over 0]
(.20 * 1 * $27) –
(.20 * 0 * $23) =
$5.40
$19.50
2
[Sell 0, Over 2]
(.15 * 0 * $27) –
(.15 * 2 * $23) =
-$6.90
[Sell 1, Over 1]
(.35 * 1 * $27) –
(.35 * 1 * $23) =
$1.40
[Sell 2, Over 0]
(.30 * 2 * $27) –
(.30 * 0 * $23) =
$16.20
[Sell 2, Over 0]
(.20 * 2 * $27) –
(.20 * 0 * $23) =
$10.80
$21.50
3
[Sell 0, Over 3]
(.15 * 0 * $27) –
(.15 * 3 * $23) =
-$10.35
[Sell 1, Over 2]
(.35 * 1 * $27) –
(.35 * 2 * $23) =
-$6.65
[Sell 2, Over 1]
(.30 * 2 * $27) –
(.30 * 1 * $23) =
$9.30
[Sell 3, Over 0]
(.20 * 3 * $27) –
(.20 * 0 * $23) =
$16.20
$8.50
Conclusion: The supermarket should stock 2 cases of wedding cakes. This number of cakes
will maximize the expected payoff.
Chapter 13 – Inventory Management
13–56
Education.
43. Given:
On average, 18 ticket holders cancel their reservations, so the company intentionally overbooks
the flight. Cancellations can be described by a normal distribution with a mean equal to 18 and a
standard deviation of 4.55. Profit per passenger = $99. If a passenger is bumped, the company
pays that passenger $200.
Determine the number of tickets to overbook:
Chapter 13 – Inventory Management
Case: UPD Manufacturing
Given:
OI = 6 weeks
S = $32
H = $.08/unit/week
d = 89 units/week
LT = 5 working days = 1 week
1. Students must recognize that without demand variability, the fixed order interval order quantity
equation reduces to:
UPD places an order every 6 weeks and the lead-time is 1 week. Therefore, when the order is
Chapter 13 – Inventory Management
Case: Harvey Industries
To improve the current inventory control system, the new president may want to consider the following:
1. Computerize the inventory control system. Rationale: There are too many parts for the current
2. Currently, no paperwork is used when items are withdrawn from the stockroom when they are
needed on the shop floor. Harvey Industries may either want to establish a procedure for
3. It appears that utilization of A-B-C inventory classification system is needed. Rationale: Harvey
Industries rarely should experience stockouts in those “A” items that account for $220,684 of
$314,673 in annual purchases or for any “A” items for which a stockout leads to significant
downtime costs. ABC analysis will allow Harvey Industries to establish an appropriate degree of
control over items in terms of order quantity and ordering frequency.
Case: Grill Rite
Recommendations:
1. The president’s stance on steady output conflicts with seasonal demand. However, it is unlikely
2. The main problem is inventory management. Therefore, we recommend the following:
a. Having a single, centralized warehouse: This will lower the need for safety stock due to the
canceling effect of random variability in orders from the various regions. Conversely, with
separate warehouses, each warehouse needs a relatively larger safety stock to guard against
Chapter 13 – Inventory Management
Case: Farmers Restaurant
1. Inventory management is crucial not only to Farmers Restaurant, but to businesses in general.
Customer satisfaction and customer return is contingent upon proper inventory management. If
customers visit the Farmers Restaurant and are unable to receive the food they desire due to a
2. A fixed-interval ordering system is appropriate given that the manager reviews inventory and
places orders once a week from the supplier.
3. Given:
SL = 95%
units/week
units/week
Q
45.55 = 46 units (round up) = 23 of the 2-packs.
