Problem definition and Analysis

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Problem definitionand Analysis
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Scope
Define what to study (and what not). Too much
wasted work!
Key object classes (order, delivery, ...) and
actions. Actions cause state change of
objects. Necessary for understanding and modeling.
Performance indicators (system time, resource
occupation, cost, ...)
Problems to be addressed
Solution alternatives
Account for expected future developments
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Objects and actions
Objects have a life cycle, consisting of
states. For example, for the passport
case, citizen and civil servant objects do matter.
A citizen can be in various states e.g. not
involved, entered, being judged, being
instructed, away for 2nd photo, back, being
helped, finished.
Servant's states idle, judging, instructing,
processing.
Passport actions?
Ferry objects and actions?
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Performance indicators
Passport case average lead time, standard
deviation. maximum queue size (facilities). occupa
tion rate of civil servant.
Ferry case?
Average lead time and standard deviation for A to
B and for B to A cars.
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Problems and solutions
Passport case Long queues (possibly, depending
on demand)
Solutions approve more, skip judgement,
appointment system
Ferry case?
Which new ferry to buy
Consider future developments extrapolate
trends beware special circumstances!
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Analysis
Parameters - maximal capacity of key
resource(s) - r arrival intensity divided by
capacity (both measured in nr of cases per time
unit)
Capacity and intensity can be estimated or
assumed.
Analyze extreme cases - small r - r almost 1
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Passport problem
case citizen needing document resource civil
servant
performance measured by system time (wait time
service time).
Problem long queues.
Proposed solutions - less strict judgement -
oblige photo from preferred shop
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Passport analysis
Analyze extreme cases.
Passport/photo example accept ratio a, with 0 lt
a lt 1 average time to instruct photo remake
t average time to create document u Average
resource time needed for client u a.t (
waiting time in absence of queues) Average influx
r clients per u a.t time units. r 1 not
enough resource capacity infinite waiting time.
Assuming M/M/1 queue (appendix F), we obtain an
average service time of (u a.t) / (1-r).
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M/M/1 passport queue
time / (u a.t )
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Passport case
Simulation needed?
Can you think of additional constraints that
preclude the problem's analysis?
Proposed solutions - less strict judgement -
oblige photo from preferred shop - introduce an
appointment system
Give comment on proposals
Beware of tunnel vision!
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Ferry problem
case car needing to cross resource ferry
performance measured by system time (wait time
service time).
Problem new ferry needed
Proposed alternatives - faster, less cars -
slower, more cars
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Ferry analysis
Ferry example cycle time c up to n10 places
per cycle (batch size) capacity n/c cars per
time unit
Input r (n/c) cars per time unit r lt1. Minimum
average waiting time c/2. Processing fixed time
c/2. Low influx (e.g. r 0.3) negligible
probability of more than n waiting cars. average
system time c e.
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Ferry queue
time / c
r
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Two ferries are proposed. For ferry 1, cycle time
c equals 6 minutes, n equals 10. For ferry 2, c
equals 8 minutes and n equals 15.
systime ferry 2
systime ferry 1
system time (minutes)
intensity (cars per minute)
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Standard deviation important for traffic studies.
measured times 5,11,13, 7,14 average 10
measured times 8,11,10, 9,12 average 10
How do the two ferries compare w.r.t. stdev?
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Ferry case
Simulation needed?
M/D/1 queue with batches extra time for getting
on/off
Give essential characteristics.
Choice between alternatives depends on traffic
intensity. Increase expected? Decision based on
mean throughput time m and standard deviation
s. For only plm. 15 of cases, throughput time
exceeds m s.
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Classwork/Homework
Classwork Exercises on page 6 and 10 of lecture
notes. Analyze DCT case, pose additional
questions, propose strategies.
Homework Study chapter 3 and appendix F of
lecture notes. Special attention to Little's
formula and M/M/1. Assignment (individual,
discussions encouraged) Write DCT report (2 pags
A4), defining concepts pertaining to the
case. Indicate a few promising solution
strategies.
(give evidence by analysis)
Mail to m.voorhoeve_at_tue.nl