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Using Binary Integer Programming to Deal with Yes-or-No Decisions

Using Binary Integer Programming to Deal with Yes-or-No Decisions. Chapter 7: Hillier and Hillier. Agenda. Case Study: California Manufacturing Company Wyndor Case Revisited Variation of Wyndor’s Problem. Applications of Binary Variables. Binary variables only allow two choices

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Using Binary Integer Programming to Deal with Yes-or-No Decisions

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  1. Using Binary Integer Programming to Deal with Yes-or-No Decisions Chapter 7: Hillier and Hillier

  2. Agenda • Case Study: California Manufacturing Company • Wyndor Case Revisited • Variation of Wyndor’s Problem

  3. Applications of Binary Variables • Binary variables only allow two choices • This makes them suited for problems that are characterized by variables that can take on only two possibilities. • Examples: • Do a project or not do a project? • To hire or not to hire? • To build or not to build? • To Sell or not to sell?

  4. Case Study: California Manufacturing Company (CMC) • The California Manufacturing Company is a company with factories and warehouses throughout California. • It is currently considering whether to build a new factory in Los Angeles and/or San Francisco. • Management is also considering building one new warehouse where a new factory has been recently built. • Should the CMC build factories and/or warehouses in Los Angeles and/or San Francisco?

  5. Case Study: CMC Cont.

  6. Case Study: CMC Cont. • FLA, FSF, WLA,WSF are all binary variables which take on the value of 1 if the specific item is done and zero if it is not done. • We also need to make sure that at most one warehouse is built and it is built where a factory is built.

  7. Mathematical Model for CMC

  8. Wyndor Case Revisited • Two new products have been developed: • An 8-foot glass door • A 4x6 foot glass window • Wyndor has three production plants • Production of the door utilizes Plants 1 and 3 • Production of the window utilizes Plants 2 and 3 • Objective is to find the optimal mix of these two new products.

  9. Wyndor Case Revisited Cont.

  10. Wyndor Case Revisited Cont.

  11. Changing Wyndor to Account for Setup Costs • Suppose that two changes are made to the original Wyndor problem: • If Wyndor chooses to produce doors, it must pay a one time set-up cost of $700, while if Wyndor produces windows it must pay a set-up cost of $1,300. • We want to restrict the doors and windows to be integer values.

  12. Graphical Solution to Original Wyndor Problem

  13. Feasible Solutions for Wyndor with Setup Costs

  14. Wyndor’s Mathematical Model With Set-Up Costs

  15. Changing Wyndor to Account for Mutually Exclusive Products • Suppose Wyndor decides that it only wants to produce doors or windows rather than both. • This implies that either doors have to be zero or windows have to be zero.

  16. Wyndor’s Mathematical Model With Mutually Exclusive Products

  17. Changing Wyndor to Account for Either-Or Constraints • Suppose the company is trying to decide whether to build a new up-to-date plant that will be used to replace plant 3. • This implies that Wyndor wants to examine the profitably of using plant 4 versus plant 3.

  18. Wyndor’s Data with Either/Or Constraint

  19. Graphical Solution with Plant 3 or Plant 4

  20. Wyndor’s Mathematical Model With Either/Or Constraint

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