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 15, PROBLEM 9, PART B
INVENTORY
INVENTORY
INVESTMENT
INVESTMENT
m’ = average demand over P+L period (3.5 + 2 = 5.5 months) = 4 (5.5) = 22 units
s’ = safety stock = z’
’= (4.0)5.5 = 9.38
z = 1.65 (for a service level of 95%)
s’ = 1.65 * 9.38 = 15.48 15 units
T = 22 + 15 = 37 units
11. a. EOQ = 2(40)(600)/.25(50) 62
_
b. Under Q system: = (1)4 = 2
Service level Safety stock required (z)
85% 1.04(2) = 2.08 tires
90% 1.28(2) = 2.56
95% 1.65(2) = 3.30
97% 1.88(2) = 3.76
99% 2.33(2) = 4.66
c. I = Q/2(C) + Cs (note: C = $50)
Service level $ Inventory Investment
85% 1550 + 104 = $1,654
90% 1550 + 128 = $1,678
95% 1550 + 165 = $1,715
97% 1550 + 188 = $1,738
99% 1550 + 233 = $1,783
d. A service level of 95% might be established with the argument that the investment
tied up in inventories increases steeply for each percentage point increase in service
level beyond that point.
12. a. Turnover = sales/investment = $40(600)/investment = $24,000/investment
Annual turnover as a function of service level:
Service level Turnover
85% 24,000/1654 = 14.5
90% 24,000/1678 = 14.3
95% 24,000/1715 = 14.0
97% 24,000/1738 = 13.8
99% 24,000/1783 = 13.5
b. If sales increase by 50% to 900 and the standard deviation of daily demand is still
1, then:
________________
EOQ = 2(40)(900)/.25(50) = 76
Average inventory at the 95% service level =
76/2 + 1.65(2) = 38 + 3.3 = 41.3
Inventory turnover becomes 600/41.3 = 14.5. Turnover increases from 14.0 to 14.5
times per year.
13. a. The optimal ordering interval is 36.8 days.
b. The amount of each type of carpet ordered in the combined order would be 37 yards
of type 1, 31 yards of type 2, and 12 yards of type 3 and 25 yards of type 4.
NAME:
******************
CHAPTER 15, 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
14. a. Using the template from problem 13
Type Lot Size
1 300
2 250
3 100
4 200
b. – Give Easyfoot a discount making it worthwhile to order larger lot sizes.
– Reduce the supplier’s set-up costs.
– Negotiate a blanket contract with Easyfoot that in effect assures continued demand
and permits larger lot sizes.
1. a. Yes, Speedy Grocery Store should take the discount, because the total annual cost
of purchasing 50 or more cases at a time is lower than the cost of not taking the
discount.
NAME :
***************
CHAPTER 15, 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
b. The grocery store is indifferent when the discount is $.39 per case.
______________
2. a. EOQ = 2(20)(50)/.15(25) 23 cases
______________
EOQDiscount = 2(20)(50)/.15(20) = 25.8 cases
Since 30 cases are required to receive the discount, the EOQDiscount is infeasible.
30. For example, if the discount of $20 applied at 25 units, the resulting total annual
cost would be:
TC25 = (50/25)(20) + .15(20)(25/2) + 50(20) = 1077.5
Since this only saves you about $1 per year, it is not worth too much negotiating
3. a. EOQ = 2(1200)(300)/.2(25)(1 – 300/500) = 600
b.
c. The maximum value of inventory is calculated as:
4. a. EOQ = 2(200)(2400)/.24(50)(1 – 200/1000) 316
_________________
b. EOQ = 2(200)(2400)/.24(50) 283
TC283 = (200)(2400/283) + .24(50)(283/2) + 2400(50)
= 1696 + 1698 + 120,000 = 123,394
2400(50)
= 1519 + 1517 + 120,000 = 123,036
The cost to the company of the smaller lot size is
0
40
80
120
160
200
240
020 40 60 80 100 120
Units in Inventory
Weeks
On-Hand Inventory vs. Time
On-Hand Inventory vs. Time
11. a. EOQ = 2(40)(600)/.25(50) 62
_
b. Under Q system: = (1)4 = 2
Service level Safety stock required (z)
85% 1.04(2) = 2.08 tires
90% 1.28(2) = 2.56
95% 1.65(2) = 3.30
97% 1.88(2) = 3.76
99% 2.33(2) = 4.66
c. I = Q/2(C) + Cs (note: C = $50)
Service level $ Inventory Investment
85% 1550 + 104 = $1,654
90% 1550 + 128 = $1,678
95% 1550 + 165 = $1,715
97% 1550 + 188 = $1,738
99% 1550 + 233 = $1,783
d. A service level of 95% might be established with the argument that the investment
tied up in inventories increases steeply for each percentage point increase in service
level beyond that point.
12. a. Turnover = sales/investment = $40(600)/investment = $24,000/investment
Annual turnover as a function of service level:
Service level Turnover
85% 24,000/1654 = 14.5
90% 24,000/1678 = 14.3
95% 24,000/1715 = 14.0
97% 24,000/1738 = 13.8
99% 24,000/1783 = 13.5
b. If sales increase by 50% to 900 and the standard deviation of daily demand is still
1, then:
________________
EOQ = 2(40)(900)/.25(50) = 76
Average inventory at the 95% service level =
76/2 + 1.65(2) = 38 + 3.3 = 41.3
Inventory turnover becomes 600/41.3 = 14.5. Turnover increases from 14.0 to 14.5
times per year.
13. a. The optimal ordering interval is 36.8 days.
b. The amount of each type of carpet ordered in the combined order would be 37 yards
of type 1, 31 yards of type 2, and 12 yards of type 3 and 25 yards of type 4.
NAME:
******************
CHAPTER 15, 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
14. a. Using the template from problem 13
Type Lot Size
1 300
2 250
3 100
4 200
b. – Give Easyfoot a discount making it worthwhile to order larger lot sizes.
– Reduce the supplier’s set-up costs.
– Negotiate a blanket contract with Easyfoot that in effect assures continued demand
and permits larger lot sizes.
1. a. Yes, Speedy Grocery Store should take the discount, because the total annual cost
of purchasing 50 or more cases at a time is lower than the cost of not taking the
discount.
NAME :
***************
CHAPTER 15, 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
b. The grocery store is indifferent when the discount is $.39 per case.
______________
2. a. EOQ = 2(20)(50)/.15(25) 23 cases
______________
EOQDiscount = 2(20)(50)/.15(20) = 25.8 cases
Since 30 cases are required to receive the discount, the EOQDiscount is infeasible.
30. For example, if the discount of $20 applied at 25 units, the resulting total annual
cost would be:
TC25 = (50/25)(20) + .15(20)(25/2) + 50(20) = 1077.5
Since this only saves you about $1 per year, it is not worth too much negotiating
3. a. EOQ = 2(1200)(300)/.2(25)(1 – 300/500) = 600
b.
c. The maximum value of inventory is calculated as:
4. a. EOQ = 2(200)(2400)/.24(50)(1 – 200/1000) 316
_________________
b. EOQ = 2(200)(2400)/.24(50) 283
TC283 = (200)(2400/283) + .24(50)(283/2) + 2400(50)
= 1696 + 1698 + 120,000 = 123,394
2400(50)
= 1519 + 1517 + 120,000 = 123,036
The cost to the company of the smaller lot size is
0
40
80
120
160
200
240
020 40 60 80 100 120
Units in Inventory
Weeks
On-Hand Inventory vs. Time
On-Hand Inventory vs. Time