Announcements

• Appeals on Q8 based on correct calculation with bad input will be heard

• Appeals will not be successful on the basis of:– Running out of time– Copying the wrong cell– Order of weights on the WMA question

• For next class read Crazy Joey’s p. 77

MGTSC 352Lecture 11: Aggregate Planning

Case 2: Mountain WearSet up and use solver to find minimum cost plan

Air Alberta

Tradeoffs: “So which one of those did you want?” (pg. 50)

Production Inventory Workforce Overtime

Plan 1 Level Changing Level 0

Plan 2 Chase 500 Changing 0

Plan 3 Chase 500 Level Changing

Level and chase:

Mountain Wear …Year 2001Quarter 4 1 2 3 4Demand forecast 7000 3000 1000 10000Units produced 7000 7000 7000 7000Inventory:Beginning-of-quarter 500 500 4500 10500End-of-quarter 500 500 4500 10500 7500

Unit costs Total costsInventory cost $3,000 $15,000 $45,000 $54,000 $6 $117,000Production cost $210,000 $210,000 $210,000 $210,000 $30 $840,000

Number hired 2 0 0 0Number laid off 0 0 0 0Workforce:Beginning-of-quarter 20 22 22 22End-of-quarter 20 22 22 22 22Hours of overtime 0 0 0 0 Unit costs Total costsHiring cost $6,000 $0 $0 $0 $3,000 $6,000Layoff cost $0 $0 $0 $0 $1,500 $0Regular labor cost $220,000 $220,000 $220,000 $220,000 $10,000 $880,000Overtime cost $0 $0 $0 $0 $23 $0

Labor hours: Coefficients

Available 10,560 10,560 10,560 10,560 480 hours per employee, per quarter

Required 10,500 10,500 10,500 10,500 1.5 hours of labor, per unit

Total cost $1,843,000

2002

Production Planning for Mountain Wear

This is "Plan 1" from "Case 2: Mountain Wear."

• Can we find the lowest cost plan with solver?

Active Learning: Formulate Mountain Wear Problem in English • 1 min., in pairs

• Template:– Maximize / minimizes …– By changing …– Subject to …

Extending the Mountain Wear Formulation

• How do we fire 10.625 people

• 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?

More about Integer Constraints

• Problems with integer constraints– Are harder for solver– Can take a long time to find optimal solution

for large problems– By default, solver stops when “within 5% of

optimal”

• What does it mean?

• How can we change the default?

Pg. 74

What does it mean?

0

1

2

3

4

0 1 2 3

x

y

Solution to LP relaxation, profit = 5.1

Best known feasible solution (incumbent solution), profit = 3.8

gap = (5.1 – 3.8)/5.1 = 25%

Solver stops when “gap” is less than “integer tolerance”

Changing the default

Standard Solver

Change to zero

Premium Solver

Options Integer Options Set “integer tolerance” to zero