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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
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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