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21
15) Eagle Fabrication has the following aggregate demand requirements and other data for the upcoming
four quarters.
Quarter
Demand
Previous quarter's output
1500 units
1
1300
Beginning inventory
200 units
2
1400
Stockout cost
$50 per unit
3
1500
Inventory holding cost
$10 per unit at end of quarter
4
1300
Hiring workers
$4 per unit
Laying off workers
$8 per unit
Unit cost
$30 per unit
Overtime
$10 extra per unit
Which of the following production plans is better: Plan A—chase demand by hiring and layoffs; or
Plan B—produce at a constant rate of 1200 and obtain the remainder from overtime?
16) Osprey Fabrication has the following aggregate demand requirements and other data for the
upcoming four quarters.
Quarter
Demand
Previous quarter's output
1300 units
1
1400
Beginning inventory
0 units
2
1200
Stockout cost
$50 per unit
3
1600
Inventory holding cost
$10 per unit at end of quarter
4
1500
Hiring workers
$40 per unit
Laying off workers
$80 per unit
Subcontracting cost
$60 per unit
Unit cost
$30 per unit
Overtime
$15 extra per unit
Which of the following production plans is better: Plan A — chase demand by hiring and layoffs;
Plan B— pure level strategy, or Plan C — 1350 level with the remainder by subcontracting?
17) A manufacturer of industrial seafood processing equipment wants you to develop an aggregate plan
for the four quarters of the upcoming year using the following data on demand and capacity.
Quarter
Units
Regular
Time
Over-
time
Sub-
contract
Initial inventory
Regular time cost
250 units $1.25/unit
1
200
400
80
100
Overtime cost
$1.50/unit
2
750
400
80
100
Subcontracting cost
2.00/unit
3
1200
800
160
100
Carrying cost
$0.50/unit/quarter
4
450
400
80
100
No back ordering is
allowed
a. Find the optimal plan using the transportation method.
b. What is the cost of the plan?
c. Does any regular time capacity go unused? How much in what periods?
d. What capacity went unused in this solution? (List in detail.)
18) Washington Laundry Products, Inc., makes commercial and industrial laundry machines (the kinds
hotels use), and has these aggregate demand requirements for the next six months. The firm has regular
capacity for 200 units, and overtime capacity for 40 more. Currently, subcontracting can supply up to 100
units per month, but the subcontracting firm may soon be unavailable.
Month
Demand
Costs and other data
1
220
Previous output level
150 units
2
160
Beginning inventory
100 units
3
200
Stockout cost
$250 per unit
4
210
Inventory holding cost
$100 per unit at end of month
5
200
Unit Cost, regular time
$1,200 per unit
6
190
Subcontracting
$2,000 per unit
Unit Cost, overtime
$1,500 per unit
Hiring workers
$200 per unit
Laying off workers
$500 per unit
Which is cheaper: to produce level, incurring back orders and inventory charges; or to produce a base
quantity of 120, using first, overtime, then subcontracting, to meet demand?
19) Reddick's Specialty Electronics makes weatherproof surveillance systems for parking lots. Demand
estimates for the next four quarters are 25, 9, 13, and 17 units. The firm is preparing an aggregate plan
that uses inventory, regular time and overtime and back orders. Subcontracting is not allowed. Regular
time capacity is 15 units for quarters 1 and 2, 18 units for quarters 3 and 4. Overtime capacity is 3 units
per quarter. Regular time cost is $2000 per unit, while overtime cost is $3000 per unit. Back order cost is
$300 per unit per quarter; inventory holding cost is $100 per unit per quarter. Beginning inventory is zero.
The data inputs for this problem, and the optimal solution, generated by microcomputer software, appear
below. Answer the following questions based on the scenario and the solution.
a. How many total units will be produced in quarter 1 for delivery in quarter 1?
b. How many units in total will be used to fill back orders over the four quarters?
c. What is the cost to produce one unit in Quarter 4 using overtime to deliver in quarter 1 (filling a back
order)?
d. At the end of quarter 3, what is the ending inventory of finished systems?
e. What is the total cost of the solution?
f. What is the average cost per unit?
Reddick's Specialty Electronics
Period 1
Period 2
Period 3
Period 4
Supply
RT 1
2,000
2,100
2,200
2,300
15
OT 1
3,000
3,100
3,200
3,300
3
RT 2
2,300
2,000
2,100
2,200
15
OT 2
3,300
3,000
3,100
3,200
3
RT 3
2,600
2,300
2,000
2,100
18
OT 3
3,600
3,300
3,000
3,100
3
RT 4
2,900
2,600
2,300
2,000
18
OT 4
3,900
3,600
3,300
3,000
3
Demand
25
9
13
17
Reddick's Specialty Electronics Solution
Optimal cost =
$132,200
Period 1
Period 2
Period 3
Period 4
Dummy
RT 1
15.
OT 1
3.
RT 2
6.
9.
OT 2
3.
RT 3
4.
13.
1.
OT 3
3.
RT 4
17.
1.
OT 4
3.
20) Osprey Machine Works has the following demand requirements and other data for the upcoming four
quarters.
Quarter
Demand
Previous quarter's output
2500 units
1
2300
Beginning inventory
200 units
2
2400
Stockout (backorder) cost
$50 per unit
3
2600
Inventory holding cost
$10 per unit at end of quarter
4
2100
Hiring workers
$4 per unit
Laying off workers
$8 per unit
Unit cost
$30 per unit
Overtime
$10 extra per unit
What is the total cost of pursuing a level aggregate plan over the coming year?
21) Golden Eagle Machine Works has the following demand requirements and other data for the
upcoming four quarters.
Quarter
Demand
Previous quarter's output
2500 units
1
2300
Beginning inventory
200 units
2
2400
Stockout (backorder) cost
$50 per unit
3
2600
Inventory holding cost
$10 per unit at end of quarter
4
2100
Hiring workers
$4 per unit
Laying off workers
$8 per unit
Unit cost
$30 per unit
What is the total cost of pursuing a chase aggregate plan over the coming year?
22) An electronics manufacturer makes video security systems for parking lots. Demand estimates for the
next four quarters are 15, 9, 23, and 17 units. The company is preparing an aggregate plan that uses
inventory, regular time, overtime, and back orders. Subcontracting is not allowed. Regular time capacity
is 12 units for quarters 1 and 2, 15 units for quarters 3 and 4. Overtime capacity is 6 units per quarter.
Regular time cost is $20,000 per system, while overtime cost is $30,000 per unit. Back order cost is $2000
per system per quarter; inventory holding cost is $500 per unit per quarter. Beginning inventory is zero.
Complete the table of data inputs for solving this aggregate planning problem with the transportation
method. Specifically, how many sources are there, and how many destinations? What is the supply from
each source, and the demand of each destination? What is the cost of each source-destination pair?
