1. © J. Christopher Beck 20051 Lecture 13: Assembly Line Scheduling – The Car Sequencing Problem

2. © J. Christopher Beck 2005 2 Outline Assembly Line Scheduling Car Sequencing to Minimize Setup Cost Car Sequencing with Options Full Car Sequencing Problem

3. © J. Christopher Beck 2005 3 Assembly Lines PaintingSunroofWindshieldWheels

4. © J. Christopher Beck 2005 4 Paced Assembly Lines Line runs at a constant rate Size of work centre proportional to duration of operation It takes longer to install a sunroof than a windshield so the work centre is longer The only thing you can control is the sequence of cars

5. © J. Christopher Beck 2005 5 Car Sequencing to Minimize Setup Cost n cars m paint colors You know the color of each car Every time you change colors it costs you (for cleaning, discarding paint, etc) Setup or transition cost Find a sequence that minimizes setup cost

6. © J. Christopher Beck 2005 6 Car Sequencing to Minimize Setup Cost Pinedo, Appendix D, Example D.4.2 OPL code for this problem You should understand it It would be a good idea to try it out

7. © J. Christopher Beck 2005 7 Car Sequencing with Options See OPL Language Manual and examples (on Pinedo CD) Search index for “car sequencing” Each kind of car requires a certain set of options Sunroof, airconditioning, spoiler, etc. The work centre for each option is capacity constrained

8. © J. Christopher Beck 2005 8 Car Sequencing with Options Painting Sunroof Not enough time to install next sunroof Can only install sunroofs in 1 out of every 3 cars

9. © J. Christopher Beck 2005 9 Car Sequencing with Options Can only install sunroofs in 1 out of every 3 cars But it gets worse Every car requires a set of options Each option has an r/s capacity constraint Now find a sequence!

10. © J. Christopher Beck 2005 10 Car Sequencing with Options From OPL Language Manual, Ch 14 Find a valid sequence Options12345Demand Class 1YYY1 Class 2Y1 Class 3YY2 Class 4YY2 Class 5YY2 Class 6YY2 Capacity1/22/31/32/51/5

11. Options12345Demand Class 1YYY1 Class 2Y1 Class 3YY2 Class 4YY2 Class 5YY2 Class 6YY2 Capacity1/22/31/32/51/5 Class?????????? Option 1 Option 2 Option 3 Option 4 Option 5

12. Options12345Demand Class 1YYY1 Class 2Y1 Class 3YY2 Class 4YY2 Class 5YY2 Class 6YY2 Capacity1/22/31/32/51/5 Class15???????? Option 1XX Option 2 Option 3XX Option 4X Option 5

13. © J. Christopher Beck 2005 13 OPL Model …\examples\opl\car.prj

14. © J. Christopher Beck 2005 14 “Full” Car Sequencing Problem Minimize total setup cost Minimize distance from pre-assigned slot Make-to-order jobs Capacity constraints on options (make the rate of consumption of parts at each station as constant as possible) Constraint or objective?