1. © J. Christopher Beck 20051 Lecture 14: Assembly Line Scheduling 2

2. © J. Christopher Beck 2005 2 Outline Solving the “Full” Car Sequencing Problem Example 6.3.2 Parallel machines, buffers, & bypass Flexible Flow Line Loading Algorithm

3. 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

4. Options12345Demand Class 1YYY1 Class 2Y1 Class 3YY2 Class 4YY2 Class 5YY2 Class 6YY2 Capacity1/22/31/32/51/5 Class5435462631 Option 1XXXXX Option 2XXXXXX Option 3XXX Option 4XXXX Option 5XX OPL Choice Pts: 39 Failures: 36 Time: 0.07 Vars: 110 Cts: 113

5. © J. Christopher Beck 2005 5 “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?

6. © J. Christopher Beck 2005 6 Solution Ideas Extend CP model Setup costs – easy to add Distance from preassigned slots – easy to add Dispatch rules? IP formulation? Tabu search? Heuristics – Grouping & Spacing (GS) See OPL code in D.4

7. © J. Christopher Beck 2005 7 GS Heuristic Determine total number of jobs Group jobs w.r.t. setup costs Order subgroups w.r.t. shipping dates Sequence jobs within subgroups for capacity constraints

8. © J. Christopher Beck 2005 8 GS Heuristic Determine # jobs / scheduling horizon Group jobs based on setup cost

9. © J. Christopher Beck 2005 9 GS Heuristic Group jobs based on setup cost Order groups w.r.t. shipping/holding cost

10. © J. Christopher Beck 2005 10 GS Heuristic Sequence jobs within groups to account capacity constraints

11. © J. Christopher Beck 2005 11 Example 6.3.2 Single machine, 10 jobs Setup cost (consecutive): c jk = |a j1 – a k1 | If a j2 = a k2 = 1 and spaced l jobs apart the penalty cost is:  2 ( l ) = max(3 – l,0) Tardiness: w j T j Find min cost sequence

12. © J. Christopher Beck 2005 12 Example 6.3.2 c jk = |a j1 – a k1 |  2 ( l ) = max(3 – l,0) w j T j Jobs12345678910 a j1 1113335555 a j2 0110111000 djdj ∞2∞∞∞∞6∞∞∞ wjwj 0400004000 Run GS Heuristic

13. © J. Christopher Beck 2005 13 Flexible Flow Line with Bypass Stage 1 Stage 2 Figure 6.2 ? ? ? ? Maximize throughput Minimize WIP

14. © J. Christopher Beck 2005 14 Flexible Flow Line Loading (FFLL) Three phase (heuristic) algorithm for a flexible flow line with bypass environment Allocate operations to machines Sequence operations Assign release times

15. © J. Christopher Beck 2005 15 Allocate Machines Assume all jobs available at 0 Use Longest Processing Time (LPT) heuristic to (try to) balance load across machines (Later resequencing of jobs does not change machine allocation)

16. © J. Christopher Beck 2005 16 Sequencing What order are the jobs released? Always balance machine use Workload assigned to machine i, pij = 0 for all but one machine Fraction of the total workload of machine i that has entered system just after job k enters Let J k be the set of jobs sequenced up to k (including k)

17. © J. Christopher Beck 2005 17 Sequencing If everything is balanced, machine i has seen the same fraction of its work as all the other machines. So we want: Fraction of the total workload of machine i that has entered system just after job k enters Fraction of the total workload of all machines that has entered system just after job k enters

18. © J. Christopher Beck 2005 18 Sequencing Overload/underload on machine i up to from job k Sum overloads Target workload on machine i Actual workload on machine i Minimize Greedy: Choose as the next job, the one that minimizes

19. © J. Christopher Beck 2005 19 Assign Release Times Let all jobs enter the system as soon as possible Find machine with the largest total processing time (bottleneck) Fix start/end times of operations Move upstream operations as late as possible Move downstream operations as early as possible

20. © J. Christopher Beck 2005 20 Flexible Flow Line with Bypass Stage 1 Stage 2 Figure 6.2 ?? Maximize throughput Minimize WIP