MGT 2070 – Assignment #8 Answers
12.9 George Heinrich uses 1,500 per year of a certain subassembly that has an annual
holding cost of $45 per unit. Each order placed costs George $150. He operates 300 days per
year and has found that an order must be placed with his supplier 6 working days before he can
expect to receive the order. For this subassembly, find
a) Economic order quantity
Q
2 DS
2  1,500  150

 100 units
H
45
b) Annual holding cost
Holding cost 
QH 100  45

 $2,250.00
2
2
c) Annual ordering cost
Order cost 
DS 1500  150

 $2,250.00
Q
100
d) Reorder point
Reorder point = demand during lead time 
1,500
units day  6 days  30 units
300
12.23 Larry LaForge Products offers the following discount schedule for its 4-by-8-foot sheets
of quality plywood.
Order
9 sheets or less
10 to 50 sheets
More than 50 sheets
Unit Cost
$18.00
$17.50
$17.25
Home Sweet Home Company orders plywood from LaForge. Home Sweet Home has an ordering
cost of $45. Carrying cost is 20%, and annual demand is 100 sheets. What do you recommend?
(a)
Economic Order Quantity:
Q
2 DS
H
where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit
Order quantity 9 sheets or less, unit price = $18.00
Q
2  100  45
 50 units
0.20  18
Total cost  order cost  holding cost  purchase cost

DS QH
100  45 50  0.20  18

 PD 

 18  100 
Q
2
50
2
 90  90  1,800  $1,980 see note at end of problem re. actual price
(b)
Order quantity 10 to 50 sheets: unit price = $17.50
Q
2  100  45
 50.7 units or 51 units
0.20  17.50
Total cost  order cost  holding cost  purchase cost
DS QH
100  45 51  0.20  17.50

 PD 

 17.50  100 
Q
2
51
2
 88.23  89.25  1750.00  1927.48

(c)
Order quantity more than 50 sheets: unit price = $17.25
Q
2  100  45
 511
. units or 51 units
0.20  17.25
Total cost  order cost  holding cost  purchase cost

DS QH
100  45 51  0.20  17.25

 PD 

 17.25  100 
Q
2
51
2
 88.24  87.98  1,725.00  $1,90122
.
Therefore, order 51 units.
Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number.
13.3 The president of Daves Enterprises, Carla Daves, projects the firm’s aggregate demand
requirements over the next eight months as follows:
Jan
Feb
Mar
Apr
1,400
1,600
1,800
1,800
May
June
July
Aug
2,200
2,200
1,800
1,400
Her operations manager is considering a new plan, which begins in January with 200 units on
hand and ends with zero inventory. Stockout costs of lost sales is $100 per unit. Inventory
holding cost is $20 per unit per month. Ignore any idle-time costs. The plan is called plan A.
Plan A. Vary the workforce level to execute a “chase” strategy by producing the quantity
demanded in the prior month. The December demand and rate of production are both 1,600
units per month. The cost of hiring additional workers is $5,000 per 100 units. The cost of laying
off workers is $7,500 per 100 units. Evaluate this plan.
Month
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Demand
1400
1600
1800
1800
2200
2200
1800
1400
Production
1600
1200
1600
1800
1800
2200
2200
1800
1400
Hire
Fire
Cost
400
$30,000
$20,000
$10,000
$0
$20,000
$0
$30,000
$30,000
$140,000
400
200
400
400
400
Total cost for the plan is $140,000. Note that we do not attempt to include the costs of production
– we assume that production costs are the same between all three plans and can therefore be
cancelled out in any comparison. Also note that in January, we must incur the firing cost to move
from a production level of 1600 to one of 1200.
13.4 Using the information in problem 13.3, develop plan B. Produce at a constant rate of
1,400 units per month, which will meet minimum demands. Then use subcontracting, with
additional units at a premium price of $75 per unit. Evaluate this plan by computing the costs for
January through August.
Month
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Demand
Production
1400
1600
1800
1800
2200
2200
1800
1400
1400
1400
1400
1400
1400
1400
1400
1400
Ending Inv.
200
200
0
0
0
0
0
0
0
Subcontract
Cost
400
400
800
800
400
$4,000
$0
$30,000
$30,000
$60,000
$60,000
$30,000
$0
$214,000
Total cost for the plan is $214,000. Note that the cost for January is to carry over the 200 extra
units in inventory for a month. In February, the inventory is used up.
13.5 Daves is now considering plan C. Beginning inventory, stockout costs, and holding costs
are provided in Problem 13.3.
a)
Plan C. Keep a stable workforce by maintaining a constant production rate equal to the
average requirements and allow varying inventory levels.
The average requirement is found by summing the total demand from January through August,
and dividing the result by 8 months to find 1,775 units per month.
Month
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Demand
Production
1400
1600
1800
1800
2200
2200
1800
1400
1775
1775
1775
1775
1775
1775
1775
1775
Ending Inv.
200
575
750
725
700
275
0
0
375
Stockout
150
25
Cost
$11,500
$15,000
$14,500
$14,000
$5,500
$15,000
$2,500
$7,500
$85,500
Total cost for the plan is $85,500. We would recommend plan C over plan A or B.
b)
Plot the demand with a graph that also shows average requirements. Conduct your
analysis for January through August.
2,200
2,100
2,000
1,900
1,800
1,775
1,700
1,600
1,500
1,400
0
Jan Feb Mar Apr May Jun
Jul Aug