GOAL PROGRAMMING Serhat  ÖKSÜZ Ahmet  TATIŞ Mehmet YILMAZ
THE VIEW OF THE PRESENTATION <ul><li>●   Introduction </li></ul><ul><li>●   System approach to concurrent engineering   </...
INTRODUCTION <ul><li>●   Life-Cycle Costing (LCC) ; </li></ul><ul><li>● Time-Based Competition (TBC) ; </li></ul><ul><li>●...
Concurrent Engineering <ul><li>Is the collaboration among   functional areas; </li></ul><ul><li>Product design ,design for...
 
GOAL PROGRAMMING <ul><li>Introduced by Charnes and Cooper in 1960’s </li></ul><ul><li>Provides a method of dealing with a ...
Goal Programming Versus Linear Programming <ul><li>Multiple Goals (instead of one goal) </li></ul><ul><li>Deviational Vari...
APPLICATION AREAS <ul><li>Accounting  </li></ul><ul><li>Agriculture  </li></ul><ul><li>Economics  </li></ul><ul><li>Engine...
Types Of Goal Programming <ul><li>􀂅 Weights method: the single objective </li></ul><ul><li>function is the weighted sum of...
CASE STUDY AND THE EXAMPLE <ul><li>COMPANY PROFILE </li></ul><ul><li>▪   Medical manufacturing company  </li></ul><ul><li>...
Aim of the study <ul><li>Minimized  life cycle cost and time </li></ul><ul><li>Timely introduction of products to market <...
CE TEAM <ul><li>Product designer </li></ul><ul><li>Manufacturing engineer </li></ul><ul><li>Quality control manager </li><...
STRATEGIC GOALS (P 1 ) COST OF PRODUDUCTS TO MARKET (P 11 ) TIME OF PRODUDUCTS TO MARKET (P 12 ) ▪ Products research and  ...
INTERMEDIATE GOALS (P 2 ) THROUGHPUT COST (P 21 ) THROUGHPUT   TIME (P 22 ) ▪ Procurement cost   ▪ Non-recurring manufactu...
TACTICAL  GOALS (P 3 ) OPERATIONAL AND MATERIAL COST (P 31 ) DELIVERY   TIMES (P 32 ) ▪ Operations cost  ▪ Maintenance  co...
 
THE GOALS OF THE COMPANY  <ul><li>For products X 1  and X 2  ; </li></ul><ul><li>STRATEGIC GOALS </li></ul><ul><li>▪   Eng...
Strategic Goal   Engineering Design Cost   <ul><li>Total  EDC : 2  x 1  +  4 x 2 </li></ul><ul><li>Upper Resource Limit : ...
Strategic Goal   Cost of Quality <ul><li>Total  COQ :   1  x 1  +  2 x 2 </li></ul><ul><li>Upper Resource Limit :   130 </...
Strategic Goal   Value Added to Product <ul><li>Total  VAP :   4 x 1  +  5 x 2 </li></ul><ul><li>Upper Resource Limit :   ...
I ntermediate Goal   Recurring Manufacturing Cost <ul><li>Total  RMC :   4 x 1  +  3 x 2 </li></ul><ul><li>Upper Resource ...
I ntermediate Goal   Set-Up Time <ul><li>Total  SUT  :   3 x 1  +  4 x 2 </li></ul><ul><li>Upper Resource Limit :   60 </l...
Tactical Goal   Delivery Reliability <ul><li>Total  DR  :   3 x 1  +  4 x 2 </li></ul><ul><li>Upper Resource Limit :   22 ...
Tactical Goal   Operations Cost <ul><li>Total  OC  :   3 x 1  +  4 x 2 </li></ul><ul><li>Upper Resource Limit :   45 </li>...
The Model
The Model  <ul><li>The strategic goal  : </li></ul><ul><li>Min d 1 +  + d 2 +  +   d 3 -  ; </li></ul><ul><li>{   Min  w 1...
The solution <ul><li>Let the solution be: </li></ul><ul><li>x 1   =  80  ,   x 2   = 0   ,  </li></ul><ul><li>d 1 +  =0   ...
The Model  <ul><li>The intermediate goal  : </li></ul><ul><li>Min d 4 +  + d 5 +  ; </li></ul><ul><li>2 x 1  +  4 x 2   + ...
The solution <ul><li>Let the solution be: </li></ul><ul><li>x 1   =  13.33  ,   x 2   =  53.33  ,  </li></ul><ul><li>d 4 +...
The Model  <ul><li>The  tactical goal  : </li></ul><ul><li>Min d 6 -  + d 7 +  ; </li></ul><ul><li>2 x 1  +  4 x 2   +  d ...
The solution <ul><li>Let the solution be: </li></ul><ul><li>x 1   =  13.33  ,   x 2   =  53.33  ,  </li></ul><ul><li>(EDC)...
The solution <ul><li>Let the solution be: </li></ul><ul><li>This means: </li></ul><ul><li>EDC  =  2 x 1  +  4 x 2   +  d 1...
Min d 1 + + d 2 + + d 3 -  2 x 1  + 4 x 2  + d 1 -   - d 1 +  = 240 1 x 1  + 2 x 2  + d 2 -   - d 2 +  = 130 4 x 1  + 5 x ...
X 1  = 80;  X 2  = 0; d 1 +   = 0 ;  d 2 + = 0 ; d 3 - = 0
Min d 4 + + d 5 +   2 x 1  + 4 x 2  + d 1 -   - d 1 +  = 240 1 x 1  + 2 x 2  + d 2 -   - d 2 +  = 130 4 x 1  + 5 x 2  + d ...
X 1  = 13.33;  X 2  = 53.33; d 4 +  = 43.33 ;  d 5 +  = 193.33;
Min d 6 -  + d 7 +   2 x 1  + 4 x 2  + d 1 -   - d 1 +  = 240 1 x 1  + 2 x 2  + d 2 -   - d 2 +  = 130 4 x 1  + 5 x 2  + d...
X 1  = 13.33;  X 2  = 53.33; d 6 -  = 0.00 ;  d 7 + = 195.0;
CONCLUSION <ul><li>PGP is particularly appropriate where there is a hierarchy of priority levels for the goals, as is the ...
<ul><li>THANKS </li></ul>
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Goal Programming

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Goal Programming

  1. 1. GOAL PROGRAMMING Serhat ÖKSÜZ Ahmet TATIŞ Mehmet YILMAZ
  2. 2. THE VIEW OF THE PRESENTATION <ul><li>● Introduction </li></ul><ul><li>● System approach to concurrent engineering </li></ul><ul><li>● Goal Programming </li></ul><ul><li>● Application Areas </li></ul><ul><li>● Weighting Method and Preemptive Method </li></ul><ul><li>● The Case Study and The Example </li></ul><ul><li>● Demonstration of The Model By Using Sets </li></ul><ul><li>● Managerial implications for the company </li></ul><ul><li>● Conclusions and assessment </li></ul>
  3. 3. INTRODUCTION <ul><li>● Life-Cycle Costing (LCC) ; </li></ul><ul><li>● Time-Based Competition (TBC) ; </li></ul><ul><li>● T he three planning-horizon levels ; </li></ul><ul><li>▪ S trategic, </li></ul><ul><li>▪ I ntermediate , </li></ul><ul><li>▪ T actical , </li></ul>
  4. 4. Concurrent Engineering <ul><li>Is the collaboration among functional areas; </li></ul><ul><li>Product design ,design for quality ,process design, design for manufacturing and planning ,logistic design etc. </li></ul><ul><li>In the early phases of product design </li></ul><ul><li>CE requires : </li></ul><ul><li>▪ fast adaptation </li></ul><ul><li>▪ product innovation </li></ul><ul><li>▪ short product delivery time to market </li></ul><ul><li>for a firm to remain competitive . </li></ul>▪
  5. 6. GOAL PROGRAMMING <ul><li>Introduced by Charnes and Cooper in 1960’s </li></ul><ul><li>Provides a method of dealing with a </li></ul><ul><li>collection of goals, rather than an explicit </li></ul><ul><li>objective function. </li></ul><ul><li>Objective is to minimize the deviation from each of the goals that have been established. </li></ul><ul><li>Constraints are “soft” in that you may </li></ul><ul><li>violate one (i.e. not meet one goal) if it </li></ul><ul><li>means you can make better progress </li></ul><ul><li>toward one of the other goals. </li></ul>
  6. 7. Goal Programming Versus Linear Programming <ul><li>Multiple Goals (instead of one goal) </li></ul><ul><li>Deviational Variables Minimized (instead of maximizing profit or minimizing cost of LP) </li></ul><ul><li>“ Satisficing ” (instead of optimizing) </li></ul>
  7. 8. APPLICATION AREAS <ul><li>Accounting </li></ul><ul><li>Agriculture </li></ul><ul><li>Economics </li></ul><ul><li>Engineering </li></ul><ul><li>Finance </li></ul><ul><li>Government </li></ul><ul><li>I nternational Context </li></ul><ul><li>Management </li></ul><ul><li>Marketing </li></ul>
  8. 9. Types Of Goal Programming <ul><li>􀂅 Weights method: the single objective </li></ul><ul><li>function is the weighted sum of the of the functions representing the goals of the problem. </li></ul><ul><li>MIN Z= w 1 d 1 +w 2 d 2 +…+w n d n </li></ul><ul><li>􀂅 Preemptive method: prioritizes the goals in </li></ul><ul><li>order of importance, then optimizes one goal at a time. </li></ul>
  9. 10. CASE STUDY AND THE EXAMPLE <ul><li>COMPANY PROFILE </li></ul><ul><li>▪ Medical manufacturing company </li></ul><ul><li>producing skin prepping applicators </li></ul><ul><li>▪ 10 years in the Industry </li></ul><ul><li>▪ Hospitals, first aid users and indust rial </li></ul><ul><li>companies are the customers </li></ul><ul><li>▪ 125 employees </li></ul><ul><li>▪ 17 million $ annual sales </li></ul>
  10. 11. Aim of the study <ul><li>Minimized life cycle cost and time </li></ul><ul><li>Timely introduction of products to market </li></ul><ul><li>Increased deliver reliability </li></ul><ul><li>Measurable improvement in supplier performance </li></ul><ul><li>Improvements in changeover and setup technologies </li></ul>
  11. 12. CE TEAM <ul><li>Product designer </li></ul><ul><li>Manufacturing engineer </li></ul><ul><li>Quality control manager </li></ul><ul><li>Marketing manager </li></ul><ul><li>Purchasing manager </li></ul><ul><li>Product design activities and practices are coordinated and accomplished concurrently. </li></ul><ul><li>Suppliers inputs and assistance is in terms of part and product is taken into consideration. </li></ul>
  12. 13. STRATEGIC GOALS (P 1 ) COST OF PRODUDUCTS TO MARKET (P 11 ) TIME OF PRODUDUCTS TO MARKET (P 12 ) ▪ Products research and development cost ▪ Engineering design cost ▪ Product investment cost ▪ Product investment and developing cost ▪ Cost of quality ▪ Speed of response to customers ▪ Product time to market ▪ Design lead time ▪ Order-to-delivery cycle ▪ Total product delivery time
  13. 14. INTERMEDIATE GOALS (P 2 ) THROUGHPUT COST (P 21 ) THROUGHPUT TIME (P 22 ) ▪ Procurement cost ▪ Non-recurring manufacturing costs ▪ Recurring manufacturing costs ▪ Facilities cost ▪ Initial logistics/support costs ▪ Cost of quality ▪ Manufacturing lead time ▪ Set-up time ▪ Producrtion cycle time ▪ Changeover time ▪ Delay time ▪ Distribution lead time ▪ Manufacturing response time ▪ Procurement lead time
  14. 15. TACTICAL GOALS (P 3 ) OPERATIONAL AND MATERIAL COST (P 31 ) DELIVERY TIMES (P 32 ) ▪ Operations cost ▪ Maintenance cost ▪ Product modification cost ▪ Facilities cost ▪ Product phase-out and disposal cost ▪ Delivery reliability ▪ Delivery speed
  15. 17. THE GOALS OF THE COMPANY <ul><li>For products X 1 and X 2 ; </li></ul><ul><li>STRATEGIC GOALS </li></ul><ul><li>▪ Engineering Des i gn Cost under 240 $ </li></ul><ul><li>▪ Cost Of Quality under 130 $ </li></ul><ul><li>▪ Minimum Value Added to Product 320 $ </li></ul><ul><li>INTERMED I ATE GOALS </li></ul><ul><li>▪ Recurring manufacturing cost under 170 $ </li></ul><ul><li>▪ Set up Time under 60 min </li></ul><ul><li>TACTICAL GOALS </li></ul><ul><li>▪ Delivery Reliability over 22 </li></ul><ul><li>▪ Operation Cost under 45 $ </li></ul>
  16. 18. Strategic Goal Engineering Design Cost <ul><li>Total EDC : 2 x 1 + 4 x 2 </li></ul><ul><li>Upper Resource Limit : 240 </li></ul><ul><li>2 x 1 + 4 x 2 = 240 + d 1 + - d 1 - </li></ul><ul><li>2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 </li></ul><ul><li>{ 2 x 1 + 4 x 2 < = 240 } </li></ul><ul><li>d 1 + indicates the EDC over 240 while d 1 - </li></ul><ul><li>indicates the EDC under the goal . </li></ul><ul><li>The objective is to minimize d 1 + </li></ul>
  17. 19. Strategic Goal Cost of Quality <ul><li>Total COQ : 1 x 1 + 2 x 2 </li></ul><ul><li>Upper Resource Limit : 130 </li></ul><ul><li>1 x 1 + 2 x 2 = 130 + d 2 + - d 2 - </li></ul><ul><li>1 x 1 + 2 x 2 + d 2 - - d 2 + = 130 </li></ul><ul><li>{ 1 x 1 + 2 x 2 < = 130 } </li></ul><ul><li>d 2 + indicates the COQ over 130 while d 2 - </li></ul><ul><li>indicates the COQ under the goal . </li></ul><ul><li>The objective is to minimize d 2 + </li></ul>
  18. 20. Strategic Goal Value Added to Product <ul><li>Total VAP : 4 x 1 + 5 x 2 </li></ul><ul><li>Upper Resource Limit : 320 </li></ul><ul><li>4 x 1 + 5 x 2 = 320 + d 3 + - d 3 - </li></ul><ul><li>4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 </li></ul><ul><li>{ 4 x 1 + 5 x 2 > = 320 } </li></ul><ul><li>d 3 + indicates the VAP over 320 while d 3 - </li></ul><ul><li>indicates the VAP under the goal . </li></ul><ul><li>The objective is to minimize d 3 - </li></ul>
  19. 21. I ntermediate Goal Recurring Manufacturing Cost <ul><li>Total RMC : 4 x 1 + 3 x 2 </li></ul><ul><li>Upper Resource Limit : 170 </li></ul><ul><li>4 x 1 + 3 x 2 = 170 + d 4 + - d 4 - </li></ul><ul><li>4 x 1 + 3 x 2 + d 4 - - d 4 + = 170 </li></ul><ul><li>{ 4 x 1 + 3 x 2 < = 170 } </li></ul><ul><li>d 4 + indicates the RMC over 170 while d 4 - </li></ul><ul><li>indicates the RMC under the goal . </li></ul><ul><li>The objective is to minimize d 4 + </li></ul>
  20. 22. I ntermediate Goal Set-Up Time <ul><li>Total SUT : 3 x 1 + 4 x 2 </li></ul><ul><li>Upper Resource Limit : 60 </li></ul><ul><li>3 x 1 + 4 x 2 = 60 + d 5 + - d 5 - </li></ul><ul><li>3 x 1 + 4 x 2 + d 5 - - d 5 + = 60 </li></ul><ul><li>{ 3 x 1 + 4 x 2 < = 60 } </li></ul><ul><li>d 5 + indicates the SUT over 60 while d 5 - </li></ul><ul><li>indicates the SUT under the goal . </li></ul><ul><li>The objective is to minimize d 5 + </li></ul>
  21. 23. Tactical Goal Delivery Reliability <ul><li>Total DR : 3 x 1 + 4 x 2 </li></ul><ul><li>Upper Resource Limit : 22 </li></ul><ul><li>4 x 1 + 5 x 2 = 22 + d 6 + - d 6 - </li></ul><ul><li>4 x 1 + 5 x 2 + d 6 - - d 6 + = 22 </li></ul><ul><li>{ 4 x 1 + 5 x 2 > = 22 } </li></ul><ul><li>d 6 + indicates the DR over 22 while d 6 - </li></ul><ul><li>indicates the DR under the goal . </li></ul><ul><li>The objective is to minimize d 6 - </li></ul>
  22. 24. Tactical Goal Operations Cost <ul><li>Total OC : 3 x 1 + 4 x 2 </li></ul><ul><li>Upper Resource Limit : 45 </li></ul><ul><li>6 x 1 + 3 x 2 = 45 + d 7 + - d 7 - </li></ul><ul><li>6 x 1 + 3 x 2 + d 7 - - d 7 + = 45 </li></ul><ul><li>{ 6 x 1 + 3 x 2 < = 45 } </li></ul><ul><li>d 7 + indicates the OC over 45 while d 7 - </li></ul><ul><li>indicates the OC under the goal . </li></ul><ul><li>The objective is to minimize d 7 + </li></ul>
  23. 25. The Model
  24. 26. The Model <ul><li>The strategic goal : </li></ul><ul><li>Min d 1 + + d 2 + + d 3 - ; </li></ul><ul><li>{ Min w 1 d 1 + +w 1 d 2 + +w 1 d 3 - + w 2 d 4 + +w 2 d 5 + + w 3 d 6 - + w 3 d 7 + } </li></ul><ul><li>2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 ; </li></ul><ul><li>1 x 1 + 2 x 2 + d 2 - - d 2 + = 130 ; </li></ul><ul><li>4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 ; </li></ul><ul><li>4 x 1 + 3 x 2 + d 4 - - d 4 + = 170 ; </li></ul><ul><li>3 x 1 + 4 x 2 + d 5 - - d 5 + = 60 ; </li></ul><ul><li>4 x 1 + 5 x 2 + d 6 - - d 6 + = 22 ; </li></ul><ul><li>6 x 1 + 3 x 2 + d 7 - - d 7 + = 45 ; </li></ul><ul><li>x 1 , x 2 , d i + , d i -  0 </li></ul>
  25. 27. The solution <ul><li>Let the solution be: </li></ul><ul><li>x 1 = 80 , x 2 = 0 , </li></ul><ul><li>d 1 + =0 , d 2 + = 0 , d 3 - =0 </li></ul>
  26. 28. The Model <ul><li>The intermediate goal : </li></ul><ul><li>Min d 4 + + d 5 + ; </li></ul><ul><li>2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 ; </li></ul><ul><li>1 x 1 + 2 x 2 + d 2 - - d 2 + = 130 ; </li></ul><ul><li>4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 ; </li></ul><ul><li>4 x 1 + 3 x 2 + d 4 - - d 4 + = 170 ; </li></ul><ul><li>3 x 1 + 4 x 2 + d 5 - - d 5 + = 60 ; </li></ul><ul><li>4 x 1 + 5 x 2 + d 6 - - d 6 + = 22 ; </li></ul><ul><li>6 x 1 + 3 x 2 + d 7 - - d 7 + = 45 ; </li></ul><ul><li>d 1 + =0 ; d 2 + = 0 ; d 3 - = 0 ; </li></ul>
  27. 29. The solution <ul><li>Let the solution be: </li></ul><ul><li>x 1 = 13.33 , x 2 = 53.33 , </li></ul><ul><li>d 4 + = 43.33 , d 5 + = 193.33 </li></ul>
  28. 30. The Model <ul><li>The tactical goal : </li></ul><ul><li>Min d 6 - + d 7 + ; </li></ul><ul><li>2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 ; </li></ul><ul><li>1 x 1 + 2 x 2 + d 2 - - d 2 + = 130 ; </li></ul><ul><li>4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 ; </li></ul><ul><li>4 x 1 + 3 x 2 + d 4 - - d 4 + = 170 ; </li></ul><ul><li>3 x 1 + 4 x 2 + d 5 - - d 5 + = 60 ; </li></ul><ul><li>4 x 1 + 5 x 2 + d 6 - - d 6 + = 22 ; </li></ul><ul><li>6 x 1 + 3 x 2 + d 7 - - d 7 + = 45 ; </li></ul><ul><li>d 1 + =0 ; d 2 + = 0 ; d 3 - = 0 ; </li></ul><ul><li>d 4 + = 43.33 ; d 5 + = 193.33 ; </li></ul>
  29. 31. The solution <ul><li>Let the solution be: </li></ul><ul><li>x 1 = 13.33 , x 2 = 53.33 , </li></ul><ul><li>(EDC) d 1 + = 0 & d 1 - = 0 , </li></ul><ul><li>(COQ) d 2 + = 0 & d 2 - = 10 , </li></ul><ul><li>(VAP) d 3 + = 0 & d 3 - =0 , </li></ul><ul><li>(RMC) d 4 + = 43.3 & d 4 - =0 , </li></ul><ul><li>(SUT) d 5 + = 193.3 & d 5 - =0 , </li></ul><ul><li>(DR) d 6 + = 298 & d 6 - = 0 , </li></ul><ul><li>(OC) d 7 + = 195 & d 7 - =0 . </li></ul>
  30. 32. The solution <ul><li>Let the solution be: </li></ul><ul><li>This means: </li></ul><ul><li>EDC = 2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 ; </li></ul><ul><li>COQ = 1 x 1 + 2 x 2 - d 2 + = 130 – 10 = 120 ; </li></ul><ul><li>VAP = 4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 ; </li></ul><ul><li>RMC = 4 x 1 + 3 x 2 + d 4 - = 170 + 43.3 = 213.3 ; </li></ul><ul><li>SUT = 3 x 1 + 4 x 2 + d 5 - = 60 +193.33 = 253.33 ; </li></ul><ul><li>DR = 4 x 1 + 5 x 2 + d 6 - = 22 + 298 = 320 ; </li></ul><ul><li>OC = 6 x 1 + 3 x 2 + d 7 - = 45 + 195 = 240 . </li></ul>
  31. 33. Min d 1 + + d 2 + + d 3 - 2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 1 x 1 + 2 x 2 + d 2 - - d 2 + = 130 4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 4 x 1 + 3 x 2 + d 4 - - d 4 + = 170 3 x 1 + 4 x 2 + d 5 - - d 5 + = 60 4 x 1 + 5 x 2 + d 6 - - d 6 + = 22 6 x 1 + 3 x 2 + d 7 - - d 7 + = 45
  32. 34. X 1 = 80; X 2 = 0; d 1 + = 0 ; d 2 + = 0 ; d 3 - = 0
  33. 35. Min d 4 + + d 5 + 2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 1 x 1 + 2 x 2 + d 2 - - d 2 + = 130 4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 4 x 1 + 3 x 2 + d 4 - - d 4 + = 170 3 x 1 + 4 x 2 + d 5 - - d 5 + = 60 4 x 1 + 5 x 2 + d 6 - - d 6 + = 22 6 x 1 + 3 x 2 + d 7 - - d 7 + = 45 d 1 + + d 2 + + d 3 - = 0
  34. 36. X 1 = 13.33; X 2 = 53.33; d 4 + = 43.33 ; d 5 + = 193.33;
  35. 37. Min d 6 - + d 7 + 2 x 1 + 4 x 2 + d 1 - - d 1 + = 240 1 x 1 + 2 x 2 + d 2 - - d 2 + = 130 4 x 1 + 5 x 2 + d 3 - - d 3 + = 320 4 x 1 + 3 x 2 + d 4 - - d 4 + = 170 3 x 1 + 4 x 2 + d 5 - - d 5 + = 60 4 x 1 + 5 x 2 + d 6 - - d 6 + = 22 6 x 1 + 3 x 2 + d 7 - - d 7 + = 45 d 1 + + d 2 + + d 3 - = 0 d 4 + +d 5 + = 236.667;
  36. 38. X 1 = 13.33; X 2 = 53.33; d 6 - = 0.00 ; d 7 + = 195.0;
  37. 39. CONCLUSION <ul><li>PGP is particularly appropriate where there is a hierarchy of priority levels for the goals, as is the case in this paper </li></ul><ul><li>The most important decisions with regard to time and cost of products are made at the product design stage </li></ul><ul><li>Using CE optimises the LCC and TBC in order to be competitive </li></ul>
  38. 40. <ul><li>THANKS </li></ul>

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