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Chapter 15

Chapter 15. Goal Programming – Part 2. Goal Programming Priorities. Different levels for goals that give relative importance to the various goals (in addition to weights) P1 Represents highest priority

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Chapter 15

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  1. Chapter 15 Goal Programming – Part 2

  2. Goal Programming Priorities • Different levels for goals that give relative importance to the various goals (in addition to weights) • P1 Represents highest priority • P2 Represents next highest priority; satisfied next as long as there is no reduction in the achievement of P1 goal

  3. Goal Programming with Priorities • Minimize Z = P1 d1- + P2 d2- • Subject to: • 2X1 + 3X2 <= 640 • X1 + d1- - d1+ = 200 • X2 + d2- - d2+ = 120 • X1, X2 => 0 • d1+, d1-, d2+, d2- => 0 Now the objective function includes priorities

  4. GP with Priorities • We are a textile company and have the following constraints: ALL OF WHICH ARE GOAL CONSTRAINTS • X1 + X2 + d1- - d1+ = 80 hrs. Prod. Capacity • X1 + d2- - d2+ = 70 hrs. Upholstery • X2 + d3- - d3+ = 45 hrs. Dress material • X1 + X2 + d4- - d4+ = 90 hrs. Overtime

  5. GP with Priorities • Objective Function: • Min. Z = P1 d1- + P2 d4+ + P3 d2- + P3 d3- + P4 d1+ (with priorities – but no weights) • Min. Z = P1 d1- + P2 d4+ + 5P3 d2- + 3P3 d3- + P4 d1+ (with priorities AND weights)

  6. GP with Priorities • Where do weights 5 and 3 come from? • 1 yard of upholstery material contributes $2.50 to profit • 1 yard of dress material contributes $1.50 to profit 2.50 = 5 so we use 5:3 ratio as weights 1.50 3

  7. GP with Priorities • Min. Z = P1 d1- + P2 d4+ + 5P3 d2- + 3P3 d3- + P4 d1+ • Subject To Goal Constraints: • X1 + X2 + d1- - d1+ = 80 hrs. Prod. Capac. • X1 + d2- - d2+ = 70 hrs. Upholstery • X2 + d3- - d3+ = 45 hrs. Dress material • X1 + X2 + d4- - d4+ = 90 hrs. Overtime

  8. Graphical Solution Upholstery X1 90 80 70 d1+ d2- d1- d4+ d4- d3- X2 45 80 90 Dress

  9. Min. Z = P1 d1- + P2 d4+ + 5P3 d2- + 3P3 d3- + P4 d1+ Upholstery X1 90 80 70 d1+ d2- d1- d4+ d4- d3- X2 45 80 90 Dress

  10. Min. Z = P1 d1- + P2 d4+ + 5P3 d2- + 3P3 d3- + P4 d1+ Upholstery X1 90 80 70 d1+ d2- d1- d4+ d4- d3- X2 45 80 90 Dress

  11. Min. Z = P1 d1- + P2 d4+ + 5P3 d2- + 3P3 d3- + P4 d1+ Upholstery X1 90 80 70 d1+ d2- d1- d4+ d4- d3- X2 45 80 90 Dress

  12. Min. Z = P1 d1- + P2 d4+ + 5P3 d2- + 3P3 d3- + P4 d1+ Upholstery X1 90 80 70 d1+ d2- d1- d4+ d4- d3- X2 45 80 90 Dress

  13. GP with Priorities Solution • X1 = 70 Upholstery • X2 = 20 Dress • d1- = 0 Regular production • d4+ = 0 Overtime production • d2- = 0 • d3- = 25 • d1+ = 10 Regular production Sales goals

  14. Min. Z = P1 d1- + P2 d4+ + 5P3 d2- + 3P3 d3- + P4 d1+ Upholstery X1 90 80 70 d1+ d2- d1- d4+ d4- d3- X2 45 80 90 Dress

  15. For Next Class • Complete reading Goal Programming pages (thru 727) • Do Goal Programming HWs

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