1. No category

Review Problems for Chapter 13
EXAMPLE 1
Planners for a company that makes several models of skateboards are about to prepare the
aggregate plan that will cover six periods. They have assembled the following information:
They now want to evaluate a plan that calls for a steady rate of regular-time output, mainly
using inventory to absorb the uneven demand but allowing some backlog. Overtime and
subcontracting are not used because they want steady output. They intend to start with zero
inventory on hand in the first period. Prepare an aggregate plan and determine its cost using
the preceding information. Assume a level output rate of 300 units (skateboards) per period
with regular time (i.e., 1,800÷6 = 300). Note that the planned ending inventory is zero. There
are 15 workers, and each can produce 20 skateboards per period.
1.
Refer to Example 1. The president of the firm has decided to shut down the plant for
vacation and installation of new equipment in period 4. After installation, the cost per unit
will remain the same, but the output rate for regular time will be 450. Regular output is
the same as in Example 1 for periods 1, 2, and 3; 0 for period 4; and 450 for each of the
remaining periods. Note, though, that the forecast of 400 units in period 4 must be dealt
with. Prepare the aggregate plan, and compute its total cost.
Solution:
From example 1.
Period
1
Forecast
200
Output
Regular
300
Overtime
Subcontract
OutputForecast
100
Inventory
Beginning
0
3
300
4
400
5
500
6
200
Total
1,800
300
300
0
450
450
1,800
100
0
(400)
(50)
250
100
200
200
0
0
Ending
100
200
200
0
0
0
Average
Backlog
50
0
150
0
200
0
100
200
0
250
0
0
500
450
$600
600
600
0
900
900
3,600
50
0
150
0
200
0
100
1,000
0
1,250
0
0
500
2,250
$650
750
800
1,100
2,150
900
6,350
Costs:
Output
Regular
Overtime
Subcontract
Inventory
Backorder @ 5
Total
2.
2
200
Manager T. C. Downs of Plum Engines, a producer of lawn mowers and leaf blowers, must
develop an aggregate plan given the forecast for engine demand shown in the table. The
department has a normal capacity of 130 engines per month. Normal output has a cost of
$60 per engine. The beginning inventory is zero engines. Overtime has a cost of $90 per
engine.
a.
b.
Solution: a.
Develop a chase plan that matches the forecast and compute the total cost of
your plan.
Compare the costs to a level plan that uses inventory to absorb fluctuations.
Inventory carrying cost is $2 per engine per month. Backlog cost is $90 per
engine per month.
Period
Forecast
Output
Regular
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Output
Regular @ 60
Overtime @ 90
Subcontract
Inventory @ 5
Backorder
Total
1
120
2
135
120
130
5
4
120
5
125
6
125
7
140
8
135
Total
1,040
130
10
120
125
125
130
10
130
5
1,010
30
(10)
0
0
0
(10)
$7,200 7,800
450
7,800
900
7,200
7,500
7,500
7,800
900
7,800 $60,600
450
2,700
7,200
8,700
7,200
7,500
7,500
8,700
8,250 $63,300
5
125
6
125
7
140
8
135
Total
1,040
130
130
130
130
1,040
5
5
(10)
5
10
7.5
10
15
12.5
15
5
10
0
(5)
8,250
3
140
(5)
b.
Period
1
2
3
4
Forecast
120
135
140
120
Output
Regular
130
130
130
130
Overtime
Subcontract
Output - Forecast
10
(5)
(10)
10
Inventory
Beginning
0
10
5
0
Ending
10
5
0
5
Average
5
7.5
2.5
2.5
Backlog
5
Costs:
Output
Regular @ 60
$7,800 7,800 7,800 7,800
Overtime
Subcontract @ 50
Inventory @ $2
10
15
5
5
Backorder @ $90
450
Total
$7,810 7,815 8,255 7,805
3.
(5)
5
0
2.5
7,800
7,800
7,800
7,800
$62,400
15
25
20
5
7,815
7,825
7,820
7,805
100
450
$62,950
Nowjuice, Inc., produces bottled pickle juice. A planner has developed an aggregate
forecast for demand (in cases) for the next six months.
Use the following information to develop aggregate plans.
Develop an aggregate plan using each of the following guidelines and compute the
total cost for each plan. Which plan has the lowest total cost?
1.
2.
3.
Use level production. Supplement using overtime as needed.
Use a combination of overtime (500 cases per period maximum), inventory,
and subcontracting (500 cases per period maximum) to handle variations in
demand.
Use overtime up to 750 cases per period and inventory to handle variations in
demand.
Solution:
Period
Forecast
Output
Regular
Overtime
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular @ 10
Overtime @ 16
Inventory @ 1
Back orders @ 10
Total
1. Level production supplemented with overtime as needed.
1
2
3
4
5
6
Total
4,000
4,800
5,600
7,200
6,400
5,000
33,000
5,000
5,000
5,000
1,000
200
–600
1,000
500.0
0
50,000
0
500
0
50,500
1,000
1,200
1,200
600
1,100.0
900.0
0
0
50,000
0
1,100
0
51,100
50,000
0
900
0
50,900
5,000
1,600
–600
600
0
300.0
0
50,000
25,600
300
0
75,900
5,000
1,400
0
0
0
0.0
0
50,000
22,400
0
0
72,400
5,000
0
0
0
0.0
0
50,000
0
0
0
50,000
30,000
3,000
0
2,800
0
300,000
48,000
2,800
0
350,800
2. Combination of overtime, inventory and subcontracting to handle variations in demand.
Max. overtime = 500, max. subcontracting = 500 units.
Period
1
2
3
4
5
6
Total
Forecast
4,000
4,800
5,600
7,200
6,400
5,000
33,000
Output
Regular
5,000
5,000
5,000
5,000
5,000
5,000
30,000
Overtime
500
500
500
500
500
2,500
Subcontract
500
500
Output - Forecast
1,500
700
–100 –1,700
–400
0
0
Inventory
Beginning
1,500
2,200
2,100
400
0
Ending
1,500
2,200
2,100
400
0
0
Average
750.0 1,850.0 2,150.0 1,250.0
200.0
0.0
6,200
Backlog
0
0
0
0
0
0
0
Costs:
Regular @ 10
50,000 50,000 50,000 50,000 50,000 50,000 300,000
Overtime @ 16
8,000
8,000
8,000
8,000
8,000
0
40,000
Subcontract @ 20
0
0
0
0 10,000
0
10,000
Inventory @ 1
750
1,850
2,150
1,250
200
0
6,200
Back orders @ 10
0
0
0
0
0
0
0
Total
58,750 59,850 60,150 59,250 68,200 50,000 356,200
3. Overtime up to 750 units per period maximum to handle variations in demand.
Period
1
2
3
4
5
6
Total
Forecast
4,000
4,800
5,600
7,200
6,400
5,000
33,000
Output
Regular
5,000
5,000
5,000
5,000
5,000
5,000
30,000
Overtime
750
750
750
750
3,000
Output - Forecast
1,000
950
150 –1,450
–650
0
0
Inventory
Beginning
1,000
1,950
2,100
650
0
Ending
1,000
1,950
2,100
650
0
0
Average
500
1,475
2,025
1,375
325
0.0
5,700
Backlog
0
0
0
0
0
0
0
Costs:
Regular @ 10
50,000 50,000 50,000 50,000 50,000 50,000 300,000
Overtime @ 16
0 12,000 12,000 12,000 12,000
0
48,000
Hire/Lay off
0
Inventory @ 1
500
1,475
2,025
1,375
325
0
5,700
Back orders @ 10
0
0
0
0
0
0
0
Total
50,500 63,475 64,025 63,375 62,325 50,000 353,700
We should choose the plan generated in part 1, because $350,800 < 353,700 < 356,200.
4.
Refer to Solved Problem 1 (Refer to textbook, 9th edition, page 626). Prepare an
aggregate plan that uses some combination of laying off ($100 per worker),
subcontracting ($8 per unit, maximum of 20 units per period, must use for three
consecutive periods), and overtime ($9 per unit, maximum of 25 per period, maximum of
60 for the planning horizon). Compute the total cost, and compare it with any of the other
plans you have developed. Which plan has the lowest total cost? Assume you start with 21
workers.
Solution:
Several solutions are possible. Here is one.
Period
Forecast
Output
Regular
Overtime
Subcontract
OutputForecast
Inventory
Beginning
Ending
Average
Backlog
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
210
210
10
20
210
25
20
210
25
20
210
180
180
180
20
180
10
20
1,770
70
100
0
10
40
(50)
0
25
0
12.5
0
0
0
0
0
0
10
5
0
10
50
30
0
50
0
25
0
0
0
0
0
1,260
1,260
225
225
160
160
0
0
0
0
137.5
62.5
0
0
1,782.5 1,707.5
1,260
0
0
0
0
0
0
1,260
1,080
0
0
0
300
25
0
1,405
1,080
0
160
0
0
150
0
1,390
1,080
90
160
0
0
125
0
1,455
1080
0
0
0
0
0
0
1,080
20
10
(5)
0
20
10
0
20
30
25
0
30
25
27.5
0
Costs:
Output
Regular @ 6
$1,260
Overtime @ 9
0
Subcontract @ 8
0
Hiring @ 200
200
Layoff-firing @100
0
Inventory @ 5
50
Backorder @ 10
0
Total
1,510
1,260
90
160
0
0
125
0
1,635
(25)
EXAMPLE 3
Given the following information set up the problem in a transportation table and solve for the
minimum-cost plan:
135
$10,620
$630
$800
$200
$300
$675
$0
$13,225
5.
Refer to Example 3. Suppose that an increase in warehousing costs and other costs brings
inventory carrying costs to $2 per unit per month. All other costs and quantities remain
the same. Determine a revised solution to this transportation problem.
Solution:
–2
1
Period
21
Beg. Inv.
0
2
0
2
100
62
Reg.
82
Over.
0
60
50
80
Sub.
60
Reg.
80
Over.
0
2
5
90
Sub.
58
Reg.
78
Over.
88
3
Demand
10
550
The solution is optimal with a total cost of $124.960.
+34
50
500
0
+14
90
100
750
120
0
80
93
5
700
+2
500
5
96
50
0
60
83
10
Sub.
+12
70
5
86
500
0
92
63
10
+32
0
50
66
120
0
82
90
5
90
0
50
93
50
0
62
80
500
0
+10
30
500
83
+30
94
60
100
0
84
0
0
63
0
64
92
Total
Cap.
+90
0
50
90
5
4
82
0
92
–92
4
0
62
450
1
2
3
50
0
+4
90
100
2,090
6.
Prepare a master schedule like that shown in the above Figure given this information:
The forecast for each week of an eight-week schedule is 50 units. The MPS rule is to
schedule production if the projected on-hand inventory would be negative without it.
Customer orders (committed) are as follows:
Use a production lot size of 75 units and no beginning inventory.
Solution:
Forecast
Customer
Orders
Projected
on-hand
inventory
MPS
ATP
1
50
June
2
3
50 50
4
50
52
35
20
12
23
48
73
23
75
23
75
40
75
43
Week
1
2
3
4
5
6
7
8
7.
5
50
July
6
7
50 50
8
50
48
73
48
75
75
75
75
23
75
75
Net
Projected
Inventory
Inventories
On-Hand
From Previous Wk. Requirements Before MPS (70) MPS Inventory
0
23
48
73
23
48
73
23
52
50
50
50
50
50
50
50
–52
–27
–2
23
–27
–2
23
–27
75
75
75
–
75
75
–
75
23
48
73
23
48
73
23
48
Determine the available-to-promise (ATP) quantities for each period for Problem 6.
Solution: Given above.