CHAPTER 13 AG G R EG A T E PL A N N I N G 205
(c) The accounting business, as everyone recognizes, has
one extremely busy season (during March and April
tax preparation time), and several less hectic but still
very active months (such as when quarterly payments
Reg. Time
Overtime
Month
CPAs
Jan
660
800
0
$0
Feb
550
800
0
$0
Apr
1,320
800
$25,000
May
715
800
0
$0
June
649
800
0
$0
206 CHAPTER 13 AG G R EG A T E PLANNING
13.23 The intent of the authors is that this problem be solved
using the transportation problem format. Assuming that back
orders are not permitted, the solution is:
Total cost = $20,400
13.24 Assuming that back orders are not permitted, the solution is:
Total cost = $874,320
CHAPTER 13 AG G R E G A T E PL A N N I N G 207
Total cost = $308,125
Note: Ending inventory of 3 units held to period 5 each
require the additional carrying cost of $200. You may
wish to convey this hint to students when assigning the
problem.
13.26
December work force 8
Labor hours per refrigerator 4 hrs
Costs (per refrigerator)
Reg time
=
$48 = 4 hr $12/hr.
Overtime
=
72 = 4 hr $18/hr.
Subcontract
=
80
Holding
=
8
Forecast
Demand
Jan
400
Feb
500
Mar
550
Apr
700
Initial inventory
250
Units demanded last period
320
13.25 Even though back orders are permitted, note they are not
used. One of the multiple optimal solutions is:
Stockout
=
0
Hiring
=
40 per refrigerator
May
800
June
Stockout
=
0
Hiring
=
40 per refrigerator
May
800
June
208 CHAPTER 13 AG G R EG A T E PLANNING
(b) Each employee produces 2 units
2 10 employees 20 days = 400 units
per period
All plants operating
1 & 3 operating, 2 closed
Feb
500
400
150
0
0
0
Mar
550
400
0
0
0
0
Apr
700
400
0
300
0
0
May
800
400
0
400
0
0
June
700
400
0
300
0
0
Total
Cost
All plants operating
1 & 3 operating, 2 closed
Feb
500
400
150
0
0
0
Mar
550
400
0
0
0
0
Apr
700
400
0
300
0
0
May
800
400
0
400
0
0
June
700
400
0
300
0
0
Total
Cost
capacity) or 5,000 in 3 (20% of capacity). The idled capacity
versus unemployment question is an interesting, nonquantitative
aspect of the case and could lead to discussion of the forecasts for
the housing market and thus the plant’s product.
The optimum producing and shipping pattern is:
From
From
There are three alternative optimal producing and shipping
Getting the solution manually should not be attempted.
It will take eight tableaux to do the “All Plants” configuration,
with degeneracy appearing in the seventh tableau; the “1 & 2”
configuration takes five tableaux, etc. It is strongly suggested that
POM for Windows, Excel, or other software be used.
3. Frequent price changes can frustrate airline passengers
and may do the same to basketball fans. The approach
may encourage delayed purchases if the perception is
that prices may go down (or, of course, the opposite may
occur). Dynamic pricing is time-consuming and possibly
Forecast
Reg Time
UNITS
Period
Demand
Production
Inventory
Holding
Shortage
Change
Increase
Decrease
Jan
400
400
250
250
0
80
80
0
210 CHAPTER 13 AG G R EG A T E PLANNING
Aggregate Planning
Time Periods 52
Shortages: Back orders—Carry shortages from period to period
2nd shift
3rd shift
1st shift
2nd shift
2nd shift
3rd shift
1st shift
2nd shift
1. Which variations in demand for police services should be con-
sidered in an aggregate plan for resources? Which variations
2. Evaluate the current staffing plan. What does it cost? Are
26 officers sufficient to handle the normal workload?
Salaries:
Salaries:
26 officers $28,000 per year
= $728,000
Overtime:
2,400 hours per year $18 per hour
= $43,200
Subcontractors:
40 officers 9 hours $18 per hour
5 football games per year
= $32,400
25 part-timers 9 hours $9 per hour
5 football games per year
= $10,125
$813,725
Overtime: No additional cost, as subcontracting and over–
time costs are the same.
4. How much does it currently cost the university to provide
police services for football games? What would be the pros
and cons of subcontracting this work completely to outside
18 officers work 8 hours overtime @ $18/hr
8 officers work 16 hours overtime @ $18/hr
40 outside officers work 9 hours @ $18/hr
25 part-timers work 9 hours @ $9/hr
5 football games per year
Cost [(18 8 18) (8 16 18) (40 9 18)
(25 9 9)] 5
[2,592 2,304 6,480 2,025] 5
= + +
+
= + + +
212 CHAPTER 13 AG G R EG A T E PLANNING
5. Can you propose any other alternatives?Many of the
innovative suggestions for handling the variability in demand
for services involve using part–time workers. Police officers
require extensive training, so this alternative usually means
hiring off-duty police officers from other agencies. Under
206 CHAPTER 13 AG G R EG A T E PLANNING
13.23 The intent of the authors is that this problem be solved
using the transportation problem format. Assuming that back
orders are not permitted, the solution is:
Total cost = $20,400
13.24 Assuming that back orders are not permitted, the solution is:
Total cost = $874,320
CHAPTER 13 AG G R E G A T E PL A N N I N G 207
Total cost = $308,125
Note: Ending inventory of 3 units held to period 5 each
require the additional carrying cost of $200. You may
wish to convey this hint to students when assigning the
problem.
13.26
December work force 8
Labor hours per refrigerator 4 hrs
Costs (per refrigerator)
Reg time
=
$48 = 4 hr $12/hr.
Overtime
=
72 = 4 hr $18/hr.
Subcontract
=
80
Holding
=
8
Forecast
Demand
Jan
400
Feb
500
Mar
550
Apr
700
Initial inventory
250
Units demanded last period
320
13.25 Even though back orders are permitted, note they are not
used. One of the multiple optimal solutions is:
208 CHAPTER 13 AG G R EG A T E PLANNING
(b) Each employee produces 2 units
2 10 employees 20 days = 400 units
per period
capacity) or 5,000 in 3 (20% of capacity). The idled capacity
versus unemployment question is an interesting, nonquantitative
aspect of the case and could lead to discussion of the forecasts for
the housing market and thus the plant’s product.
The optimum producing and shipping pattern is:
There are three alternative optimal producing and shipping
Getting the solution manually should not be attempted.
It will take eight tableaux to do the “All Plants” configuration,
with degeneracy appearing in the seventh tableau; the “1 & 2”
configuration takes five tableaux, etc. It is strongly suggested that
POM for Windows, Excel, or other software be used.
3. Frequent price changes can frustrate airline passengers
and may do the same to basketball fans. The approach
may encourage delayed purchases if the perception is
that prices may go down (or, of course, the opposite may
occur). Dynamic pricing is time-consuming and possibly
Forecast
Reg Time
UNITS
Period
Demand
Production
Inventory
Holding
Shortage
Change
Increase
Decrease
Jan
400
400
250
250
0
80
80
0
210 CHAPTER 13 AG G R EG A T E PLANNING
Aggregate Planning
Time Periods 52
Shortages: Back orders—Carry shortages from period to period
1. Which variations in demand for police services should be con-
sidered in an aggregate plan for resources? Which variations
2. Evaluate the current staffing plan. What does it cost? Are
26 officers sufficient to handle the normal workload?
26 officers $28,000 per year
= $728,000
Overtime:
2,400 hours per year $18 per hour
= $43,200
Subcontractors:
40 officers 9 hours $18 per hour
5 football games per year
= $32,400
25 part-timers 9 hours $9 per hour
5 football games per year
= $10,125
$813,725
Overtime: No additional cost, as subcontracting and over–
time costs are the same.
4. How much does it currently cost the university to provide
police services for football games? What would be the pros
and cons of subcontracting this work completely to outside
18 officers work 8 hours overtime @ $18/hr
8 officers work 16 hours overtime @ $18/hr
40 outside officers work 9 hours @ $18/hr
25 part-timers work 9 hours @ $9/hr
5 football games per year
Cost [(18 8 18) (8 16 18) (40 9 18)
(25 9 9)] 5
[2,592 2,304 6,480 2,025] 5
= + +
+
= + + +
212 CHAPTER 13 AG G R EG A T E PLANNING
5. Can you propose any other alternatives?Many of the
innovative suggestions for handling the variability in demand
for services involve using part–time workers. Police officers
require extensive training, so this alternative usually means
hiring off-duty police officers from other agencies. Under