MGTSC 352
Lecture 10: Aggregate Planning
Leduc Control Example:
Complete post-optimality analysis
Case 2: Mountain Wear
Set up and use solver to find minimum cost plan
Announcements
• HW 3 grading
• For next week read
– Air Alberta p. 72
– Crazy Joey’s p. 77
More Post-Optimality Analysis
4.
Another semiconductor supplier offers Howie 5 more PsoCs for a
premium of $150 each (above and beyond the going rate of $720
per unit). Should Howie buy these PSoCs?
5.
Howie sometimes helps out with programming the LCDs, thereby
increasing the amount of available programming time. Should he
help out in this cycle? If so, how long should he help out?
6.
Howie’s nephew offers to work in assembly for a premium rate of
$12 per hour (above and beyond the going rate of $20 per hour).
Should Howie hire his nephew? For how many hours?
One More
• Howie notices that with the currently
optimal production plan, 168 of the
available programming hours are not
used. Howie wonders whether he could
increase production and profits by training
the programmers to help out with
assembly. What would the optimal total net
margin be if all programmers were also
trained to do assembly?
Other solvers
• Survey
– http://lionhrtpub.com/orms/surveys/LP/LP-survey.html
• $1,000 ... $10,000
• Can solve very large problems (200,000 constraints)
• Usually require front-end modeling language
(such as AMPL)
• Premium solver: $1,000 http://www.solver.com/
Active Learning
1 min., in pairs
Mountain Wear
• What decisions does Nathan Leung need
to make to generate an aggregate plan for
Mountain Wear?
• What constraints (restrictions) must
Nathan keep in mind?
• Write down as many as you can think of
Mountain Wear Case
• What decisions does Nathan Leung need
to make to generate an aggregate plan for
Mountain Wear?
Mountain Wear Case
• What constraints (restrictions) must
Nathan keep in mind?
Summary of Data (pg. 49)
•
•
•
•
•
•
•
•
•
•
•
Materials cost:
per unit
Labour requirements:
hrs/unit
Labour availability:
hours/employee/quarter
# of workers at beginning of year:
Labour cost:
employee/quarter
Overtime labour cost:
per hour
Hiring cost:
Layoff cost:
Inventory holding cost:
per unit/quarter
Inventory at beginning of year:
Required safety stock:
Look at Nathan’s plans in Excel
Tradeoffs: “So which one of those
did you want?” (pg. 50)
Production Inventory
Plan 1
Plan 2
Plan 3
Level and chase:
Workforce
Overtime
Mountain Wear …
• Can we
find the
lowest
cost plan
with
solver?
P ro d u c tio n P la n n in g fo r M o u n ta in W e a r
Y ear
Q uarter
2001
4
2002
T h is is "P la n 1" fro m
1
2
3
4
D em and forec as t
7000
3000
1000
10000
U nits produc ed
7000
7000
7000
7000
500
500
4500
10500
500
4500
10500
7500
"C a se 2: M o u n ta in W e a r."
Inventory :
B eginning-of-quarter
E nd-of-quarter
500
U nit c os ts
Inventory c os t
P roduc tion c os t
Total c os ts
$3,000
$15,000
$45,000
$54,000
$6
$117,000
$210,000
$210,000
$210,000
$210,000
$30
$840,000
N um ber hired
2
0
0
0
N um ber laid off
0
0
0
0
20
22
22
22
22
22
22
22
W ork forc e:
B eginning-of-quarter
E nd-of-quarter
H ours of overtim e
H iring c os t
Lay off c os t
R egular labor c os t
O vertim e c os t
20
0
$6,000
0
$0
0
$0
0 U nit c os ts
$0
Total c os ts
$3,000
$6,000
$0
$0
$0
$0
$1,500
$0
$220,000
$220,000
$220,000
$220,000
$10,000
$880,000
$0
$0
$0
$0
$23
$0
Labor hours :
C oeffic ients
hours per em ploy ee,
A vailable
10,560
10,560
10,560
10,560
480 per quarter
R equired
10,500
10,500
10,500
10,500
1.5 unit
hours of labor, per
Total c os t
$1,843,000
Active Learning: Formulate
Mountain Wear Problem in English
• 1 min., in pairs
• Template:
– Maximize / minimizes …
– By changing …
– Subject to …
Extending the
Mountain Wear Formulation
• Should we include additional constraints?
– Limit on overtime?
– Limit on hirings / firings?
–?
• How do the additional constraints impact
cost?
Air Alberta (pg. 72)
Air Alberta is doing aggregate planning of flight attendant staffing for
the next 6 months. They have forecast the number of flight attendant
hours needed per month for March to August, based on scheduled
flights, and wish to determine how many new attendants to hire each
month. Each trained attendant on staff supplies 150 hours per month.
A newly hired attendant is called a trainee during the first month, and
each trainee’s net contribution is negative (-100 hours) because (s)he
requires supervision, which detracts from the productivity of other
attendants. Each trained attendant costs $1500 in salary and benefits
per month while each trainee costs $700 per month. Normal attrition
(resignations and dismissals) in this occupation is high, 10% per
month, so Air Alberta never has any planned layoffs. Trainees are
hired on the first day of each month and become attendants on the
first day of the next month (with no attrition). As of March 1, Air Alberta
has 60 trained attendants.
Go to Excel
What do you mean hire 1.413
attendants?
• You can’t do that, right?
– Right.
– But: sometimes it’s better to ignore such
details
– Especially if the numbers are large:
• Not much difference between hiring 123 and 124
people, so might as well allow fractional values
Integer Constraints:
Include or leave out?
For
• More realistic
Against
• No sensitivity report
• May take longer to
solve
• Not that important if
numbers are big
Air Alberta (pg. 73)
1. Solver settings to find a least cost staffing plan:
2. The least cost staffing plan:
3. The total cost of this plan is $
4. In which month does Air Alberta have the most
excess attendant hours?
5. Air Alberta is considering running extra charter
flights requiring 1000 flight attendant hours in
either June or July. Which month would you
choose to minimize total staffing costs? Why?
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