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MGTSC 352

This case summary discusses the optimization model used by AltaMetal Ltd. for aggregate planning, where 1,000 products are aggregated into 9 groups. The goal is to determine if the demand can be satisfied and how, by creating a production plan based on product groups.

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MGTSC 352

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  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. LINEARINTEGERNONLINEAR“Programming” MODELS A Summary

  8. CLASSIFICATION Decision Variables FunctionsFractionalInteger LinearLPILP NonlinearNLPINLP

  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

  10. 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.

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

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

  13. 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

  14. 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?

  15. 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

  16. 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)

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