1. MGTSC 352 Lecture 9: Aggregate Planning
Case 2: Mountain Wear Take 2 (there will be one more)
Leduc Control Example:
Possible solver outcomes Linearity
Post-optimality analysis

2. How does Solver Work?
Creates a ‘feasibility space’ which is ‘inside’ all the constraints
If everything is linear then optimum will contain a ‘corner point’ – where two constraints cross
Go around the outside checking all the corners until you can’t get any better
Let’s take a graphical look

3. Possible Solver Outcomes (pg. 63)
Optimization Model
Run Solver
Optimal Solution Found 
Unbounded Problem 
Infeasible Problem 

4. Unbounded Problem How will you know: What it means:
Possible to achieve infinite profit
Either you will become filthy rich, or (more likely) there is something wrong with your model
How to fix it: look for missing constraints

5. Infeasible Problem How will you know: What it means: Possible reasons:
Impossible to satisfy all constraints
Possible reasons:
You need more resources
You over-constrained the problem

6. Unbounded/Infeasible Problem
Means solver cannot solve
The values returned are meaningless
You need to look at your model

7. Post-Optimality Analysis
What if one or more input estimates are off (forecast error)?
Will the optimal solution change?
Solution / plan = values of decision variables
Will the optimal profit change?
Ways to answer such questions:
Graphical analysis
Sensitivity report (pg. 64)
Re-solve (manually, or with Solver Table)
Reformulate
Logic

8. Is the plan still optimal? If not, how will it change? (pg. 65)
Howie realizes that he underestimated the net margin for each AS by $65.
Howie realizes that he overestimated the net margin for each AS by $65.
Howie discovers a new market where he can sell both AS and HLs at a 20% higher net margin than originally estimated.

9. SolverTable (pg. 67) Combines Solver and Data Table
Solves the problem repeatedly and reports all solutions
Free add-in
see COURSE DOCUMENTS > RESOURCES > SOFTWARE on course web

10. More Post-Optimality Analysis
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?
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?
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?

11. 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?

12. Other solvers Survey $1,000 ... $10,000
$1, $10,000
Can solve very large problems (200,000 constraints)
Usually require front-end modeling language (such as AMPL)
Premium solver: $1,

13. Mountain Wear Case
What decisions does Nathan Leung need to make to generate an aggregate plan for Mountain Wear?

14. Active Learning 1 min., in pairs
What constraints (restrictions) must Nathan keep in mind?
Write down as many as you can think of

15. 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

16. Tradeoffs: “So which one of those did you want?” (pg. 50)
Production
Inventory
Workforce
Overtime
Plan 1
Plan 2
Plan 3
Level and chase: