Reading Assignment

For after break read:

• Case 6: WestPlast (pg. 104)

• Case 8: Lot Sizing at Altametal (pg. 111)

MGTSC 352

Lecture 12: Aggregate PlanningAir Alberta Example

Aggregate planning in the service sector

Crazy Joey’s ExampleA model that can be linear or nonlinear depending on

how you set it up

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

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. It is the beginning of April. Only 5 attendants have left. What are you going to do now?

In Groups

Recorder is person with most vowels in their name• What happens if we add integer constraints?• What happens if we limit new hires to 15% of

trained attendants?• In which month does Air Alberta have the most

excess attendant hours? • 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?

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

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

Crazy Joey’s (pg. 77)

Crazy Joey's Electronic Liquidation store must determine how to stock its shelves. Joey, being the shrewd (although crazy) character that he is, has come to you with the information that he feels is relevant for the decision. Joey's showroom has 5,000 sq. ft. to display his merchandise. He uses two main suppliers: Double-E Televisions Inc, and The Wavelength Radio Company. Joey is in the enviable position of demand for the TVs and Radios he sells outstripping his capacity to sell them. TVs usually stay for an average of one week on the shelf before being sold, and the same is true of Radios. The relevant data is shown below. Joey’s insurance specifies that he can keep at most $100,000 of capital in the showroom. Joey has a long-standing and positive relationship with Wavelength Radio, and he has agreed to always keep at least 50% of his showroom inventory (measured in sq. ft.) full of Radios.

Go to Excel

Crazy Joey’s (pg. 78)

Joey should keep ________ TVs and ______ radios in the showroom to maximize profit. This will result in a weekly profit of _____________

Joey is considering two strategies to increase his profit even more. Evaluate each of them separately.

1) StellarTech Corp. had come out with a new high definition TV. It offers $65 profit, but it takes up 15 sq. ft., and $215 in capital. If Joey were to start buying from StellarTech as well, how many high definitions TVs should he stock? ______ What will his profit per week be? ________

2) Joey notices that his insurance policy is keeping him from keeping his showroom full of merchandise, and he thinks this is just silly. He can increase his coverage, but he must do so in increments of $50,000 and the premium will increase by $100 per week for every additional $50,000 of coverage. Should he increase his coverage? _____ If yes, then by how much? ____ How much will this increase his profit per week? ____