MGTSC 352Lecture 10: Aggregate Planning

Leduc Control Example:Complete post-optimality analysis

Case 2: Mountain WearSet 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 Learning1 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 Workforce Overtime

Plan 1

Plan 2

Plan 3

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

• 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?