1. MGTSC 352 Lecture 15: Aggregate Planning Altametal Case
Summary of Optimization Modeling

2. AltaMetal Ltd. (Case 8, pg. 111, and pgs. 87 – 92)
Another aggregate planning problem
1,000 products aggregated to 9 groups

3. AltaMetal Ltd. (Case 8, pg. 111, and pgs. 87 – 92)
Is it possible to satisfy demand?
If so, how? (production plan by product group)
Excel …

4. Active Learning Pairs, 1 min. Formulate AltaMetal’s problem in English
What to optimize, by changing what, subject to what constraints …

5. To many change-overs …
The JIT (“just-in-time”) plan we found may require too many changeovers
What if we require a minimum lot size of 30 tons?
Daily capacity = 90 tons
 At most 3 lots per day
Changing cells:
Old: # of tons of product X to produce in month Y
New: # of __ of product X to produce in month Y
Excel …

6. Tired of Waiting for Solver?
Hit Escape key

7. LINEAR INTEGER NONLINEAR “Programming” MODELS
A Summary

8. CLASSIFICATION Decision Variables Functions Fractional Integer
Linear LP ILP
Nonlinear NLP INLP

9. LP SIMPLEX method (linear algebra) Corner point optimality
Move from corner-to-corner, improve obj.
Very efficient
Can solve problems with thousands of variables and constraints

11. ILP Branch & Bound (divide-and-conquer)
Solve the LP, ignoring integer constraints
Select a fractional variable, x6 = 15.7
Create two new problems: x6 ≤ 15, x6  16
Solve the new problems
Continue until all branches exhausted
# of branches is exponential in # of var.

13. NLP Gradient method (uses derivatives) Repeat until convergence
Find an improving direction
Move in the improving direction
Converges to local optimum
Multiple starts recommended

15. INLP Ignore integer constraints, solve the NLP Use Branch & Bound
Solve a series of NLPs
Computationally demanding
No guarantee of optimality
YUCK!

17. Formulating Optimization Models (pg. 93)
Formulate the problem in English
Or French, or Chinese, or Icelandic, … 
Start with data in spreadsheet
Define decision variables – turquoise cells
Express performance measure (profit, or cost, or something else) as function of the decision variables
Express constraints on decision variables
Scarce resources
Physical balances
Policy constraints

18. Solving Optimization Problems
Try simple values of the decision variables to check for obvious errors
Guess at a reasonable solution and see if model is ‘credible’ (sniff test)
Look for missing or violated constraints
Is profit (cost) in ballpark?

19. Optimizing with Solver
Use Simplex LP method (‘assume linear model’) whenever possible
Set Options properly
automatic scaling, assume non-negative
Watch for diagnostic messages – do not ignore! (infeasible, unbounded)
Interpret solution in real-world terms and again check for credibility

20. Things to Remember
The Simplex LP method always correctly solves linear programs
Solver is a slightly imperfect implementation of the Simplex method (but you should generally assume that it is correct)
The biggest source of errors is in the model building process (i.e., the human)