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					   PRODUCTION SCHEDULING
      ALGORITHMS FOR A
 SEMICONDUCTOR TEST FACILITY

  Reha Uzsoy * Louis A. Martin-Vega * Chung-Yee Lee * Paul A. Leonard




Josimar Luna
Justin Zarozny
IEOR E4405 Production Scheduling
April 2011
                        OVERVIEW
• The facility uses automated testing
  equipment to interrogate circuits
  and determine whether or not they
  were operating at the required
  specifications.

• In the test facility product flows
  through the test area in lots. Lots
  vary in size from several individual
  chips to several thousand.
                   OVERVIEW

• There are two main grades of
  product, military and
  commercial.

• The actual sequence of
  operations a lot will go through
  depends on the grade and
  customer specifications
                THE OBJECTIVE

• Job Shop Problem, NP-Hard




• GOAL: Improve customer service
 through better on-time delivery
          SCHEDULING APPRAOCH
1.   Divide job shop into a number of work centers (a work center is defined
     as single machine stations) that have to be scheduled.

2.   Represent the job shop using disjunctive graph.

1.   Sequence each work center whose sequence has not yet been
     determined, and use the objective function to rank the work centers in
     order of criticality. Fix the sequence of the most critical work centers.

2.   Use disjunctive graph representation to capture interactions between
     work centers already scheduled and those not yet scheduled.

3.   Re-sequence those work centers that have already been sequenced
     using precedence information found in 4.
   DISJUNCTIVE GRAPH REPRESENTATION



A disjunctive arc consists of a
pair of arcs having opposite
orientations such that any path
through the graph can contain
at most one of the two. The
example on the right is a shop
with two single machine work
centers and three lots.
USING THE DISJUNCTIVE GRAPH
• When a certain subset of the work centers have been sequenced
 certain constraints are imposed on the sequencing problems of
 the remaining work centers.

• The effectiveness of this approach hinges on the ability to
 efficiently obtain good solutions to the work center sub-
 problems.
   MODELING WORKCENTER PROBLEMS

The approach to scheduling individual work
centers (each work center will consist of only
one tester) will include the use of the following
heuristic scheduling algorithms:

           • Neighborhood Search Algorithm
           • Tabu Search
           • Combination of Neighborhood
             Search Algorithm + Simulated
             Annealing.
   MATLAB & MEASURES OF EFFICIENCY

The Problem: 1 / r, d, prec / Lmax

Initial Base Schedule: EDD

Swaps: change to current best schedule

Considerations: number of evaluations of possible valid
schedules
      NEIGHBORHOOD SEARCH ALGORITHM
Single machine:
   • adjacent pairwise interchange
   • take an arbitrary job in the schedule and insert it in
    another positions
                                     NEIGHBORHOOD SEARCH
   RESULTS:                                Number of       Number of   Cons./sw
                Data Length Solution     Considerations      Swaps        ap
                     10       178              49              4        12.2500
                     10       409              19              1        19.0000
                     50      2254             883             17        51.9412
                     50      1222             685             13        52.6923
                    100      3016             3971            40        99.2750
                    100      3976             4308            43       100.1860
                    200      9351             9579            49       195.4898
                    200      5598            10659            54       197.3889
                         TABU SEARCH
• Tabu-lists contains moves which have been made in the recent past
  but are forbidden for a certain number of iterations.
• Neighborhood: all schedules that can be obtained through adjacent
  pairwise interchanges.
• Tabu-list: pairs of jobs (j, k) that were swapped within the last two
  moves
                                          TABU SEARCH
RESULTS:                                                                Cons./Sw
                Data Length Solution Number of Considerations   Swaps      ap
                    10        178              49                 4     12.2500
                    10        409              19                 1     19.0000
                    50       2261              834               16     52.1250
                    50       1222              685               13     52.6923
                   100       3016             3971               40     99.2750
                   100       3976             4308               43     100.1860
                   200       9351             9579               49     195.4898
                   200       5598             10659              54     197.3889
     NIEGHBORHOOD SEARCH ALGORITHM +
           SIMULATED ANNEALING
Allows moves to inferior solutions in order not to get
stuck in a poor local optimum.
Temperature equation:
RESULTS:
                               SIMULATED ANNEALING
                                                                          Cons./Swa
        Data Length Solution   Number of Considerations   Number of Swaps     p
            10        198                109                    92         1.1770
            10        383                134                   118         1.1282
            50        2327              4529                   3189        1.4203
            50        1370              4011                   2438        1.6453
           100        3502              16511                 13134        1.2571
           100        4123              18144                 13550        1.3390
           200       10494              61022                 45269        1.3480
           200        6362              64728                 42268        1.5314
                         NEIGHBORHOOD SEARCH
Data Length   Solution   Number of Considerations   Number of Swaps   Efficiency
    10          178                 49                    4            12.2500
    10          409                 19                    1            19.0000
    50         2254                883                   17            51.9412
    50         1222                685                   13            52.6923
    100        3016               3971                   40            99.2750
    100        3976               4308                   43           100.1860
    200        9351               9579                   49           195.4898
    200        5598              10659                   54           197.3889
                              TABU SEARCH
Data Length   Solution   Number of Considerations   Number of Swaps   Efficiency
    10          178                 49                    4            12.2500
    10          409                 19                    1            19.0000
    50         2261                834                   16            52.1250
    50         1222                685                   13            52.6923
    100        3016               3971                   40            99.2750
    100        3976               4308                   43           100.1860
    200        9351               9579                   49           195.4898
    200        5598              10659                   54           197.3889
                          SIMULATED ANNEALING
Data Length   Solution   Number of Considerations   Number of Swaps   Efficiency
    10          198                109                    92           1.1770
    10          383                134                   118           1.1282
    50         2327               4529                   3189          1.4203
    50         1370               4011                   2438          1.6453
    100        3502              16511                  13134          1.2571
    100        4123              18144                  13550          1.3390
    200        10494             61022                  45269          1.3480
    200        6362              64728                  42268          1.5314
              RESULTS ANALYSIS
• Neighborhood search and Tabu List algorithm performed
  similarly

• In general Neighborhood Search and Tabu List algorithm
  produce more optimal schedules while utilizing fewer
  iterations (*considerations/swap RATIO*)

• Simulated annealing can outperform Neighborhood Search
  and Tabu List algorithm in instances with low number of jobs

• In the overall job shop scheduling approach it may be
  beneficial to investigate the results of applying all three
  algorithms to individual work centers depending on the
  workload
             RESULTS ANALYSIS
• Benchmarking with optimal results is difficult


• Branch & Bound Approach


• The application of the shifting bottleneck approach to Job
 Shop scheduling has been explored extensively and for
 this particular semiconductor test facility the algorithms in
 place have performed relatively well
    FUTURE RECOMMENDATIONS
• Further investigation is warranted to improve job shop
 scheduling in instances where work centers have multiple
 machines and constraints

• “The ultimate goal of this research is the incorporation of
 the algorithms developed into decision support tools to
 assist shop-floor personnel in real-time decision-making”

             Reha Uzsoy * Louis A. Martin-Vega * Chung-Yee Lee * Paul A.
                                      Leonard
    PRODUCTION SCHEDULING
       ALGORITHMS FOR A
  SEMICONDUCTOR TEST FACILITY




Josimar Luna
Justin Zarozny
IEOR E4405 Production Scheduling
April 2011

				
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