ProblemSolving Tools

1
Chapter 2

• Problem-Solving Tools

2
Exploratory Tools

• Pareto Analysis
• Fish Diagrams
• Gantt Chart
• PERT Chart
• Job / Worksite Analysis Guide

3
Pareto Analysis

• Items identified and ordered on common scale in
  decreasing frequency, creating a cumulative
  distribution
• 80/20 Rule 20 of the items account for 80 of
  the problems
• Allows the company to concentrate resources on
  the jobs with the most problems

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Pareto Analysis
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Fish-bone Diagrams

• Cause-and-effect diagrams
• Identified problem or undesirable result is the
  head
• Contributing factors are the bones
• Typical categories include Human, machine,
  methods, materials, environment, and
  administrative
• Estimates associated probabilities

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Fish-bone Diagrams
7
Gantt Chart

• Used for planning of complex projects
• Shows expected start and completion times, also
  duration of events
• Similarly, major events can be broken into
  smaller sub-tasks
• Shade the bars to show actual completion time

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Gantt Chart

• Example Diagram

9
PERT Chart

• Program Evaluation and Review Technique (PERT) is
  a planning and control tool
• Also known as Network Diagram or Critical Path
• Graphically portrays the optimum way to obtain a
  desired objective with respects to time
• Optimistic, average, and pessimistic time
  estimates utilized

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Critical Path Method

• Critical path the longest path
• A job (i,j) is non-critical if (LCj-ESi)gtDij
• Forward path calculate ESi maxESiDij, ?i
• Backward path LCi minLCj-Dij, ? j
• Where Dij is job(i,j) duration ES0
  Earliest start time at the beginning node (node
  0) LCnESn, latest completion time at the
  end node n
• An activity (i,j) lies on the critical path
  if ESiLCi ESjLCj ESj-ESiLCj-L
  CiDij

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Example of PERT Chart
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Illustrative Calculations

• Forward calculations
• ES1 0
• ES2 maxES1 D1,2 max044
• ES3 maxES1 D1,3 max022
• ES4 maxES1 D1,4 max033
• ES5 maxES2 D2,5 ES3 D3,5 max41257
• ..
• ES12 LC12 27
• Backward calculations
• LC11 min LC12 D11,12 min 27 -2 25
• LC10 min LC11 D10,11 min 25 -1 24
• LC9 min LC12 D9,12 LC10 D9,10 min 27
  -4 24-4 20
• .
• LC1 0
• Critical jobs identification
• Job A ES1 LC1 0 (satisfied)
• ES2 ? LC2 (not satisfied) ? job A is
  non-critical job
• Job B ES1 LC1 0 (satisfied)
• ES3 ? LC3 (not satisfied) ? job B is
  non-critical job

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Job / Worksite Analysis Guide

• Identify problems within a particular area,
  department, worksite
• Perform a walkthrough observing the area, worker,
  task, environment, administrative constraints,
  etcbefore collecting data
• Develop an overall perspective of the situation
• Particularly useful in workstation redesign

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Job / Worksite Analysis Guide

• Example Guide

15
Recording and Analysis Tools

• Operation Process Chart
• Flow Process Chart
• Flow Diagram
• Worker and Machine Process Charts
• Gang Process Charts

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Operation Process Chart

• of all operations,
  inspections, time allowances, materials
• Depicts of all
  components and sub-assemblies and products
• Provides information on the
  , required for jobs and
  inspections
• Construction
• Circle operation
• Square inspection
• Vertical lines processes horizontal lines
  material
• Parts enter vertical lines ? assembly leave ?
  disassembly
• Materials left horizontal lines ? assembly
  right? disassembly
• Time values ? operations, inspections

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Operation Process Chart

• Example Diagram

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Flow Process Chart

• More detailed, fit for closer observation of
  components or assemblies
• Shows all (distances) and storage
  (times) for product movement in plant
• Aids in the of hidden costs
• Can be beneficial for
  suggestions
• Types product/material, operative/person
• Construction
• Symbol ? step move
• Start, end store
• Numbers ? symbols
• Diagonal lines join the symbols ? flow
• Additional column additional information
• The summary section at the top of the form

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Flow Process Chart

• Example Diagram

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Flow Diagram

• Pictorial representation of the
• Good supplement to the Flow Process Chart
• Construction
• The symbols/numbers activity ?corresponding to
  those appearing on the flow process chart
• The flow ? charted ? movement of a single object
  is being followed

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Flow Diagram

• Example Diagram

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Worker and Machine Process Charts

• Used to study, analyze, and improve
  workstation
• operator serve machines
• Shows the time relationship between working cycle
  of and the operating cycle of the
• Reveals for both machines and workers

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Worker and Machine Process Charts

• Example Diagram

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Gang Process Chart

• An adaptation of Worker and Machine chart
• workers serve machine
• Shows and of machine and
  workers ? reduce idle operator time and idle
  machine time

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Gang Process Chart

• Example Diagram

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Gang Process Chart
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Quantitative Tools

• Three types of a worker and machine relationship
• Synchronous servicing
• Completely random servicing
• Combinations of random and synchronous servicing
• Line balancing

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Synchronous Servicing

• Assigning more than one machine to an operator
• Where
• N number of machines assigned to operator
• l service time per machine (load and unload)
• m machine running time

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Synchronous Servicing
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Synchronous Servicing

• When N is not an integer number ? round up idle
  machine, round down idle worker ? justify ? ?
  use the of the product as a guideline
• Estimate the number of machines assigned to the
  operator
• Where w total worker time (not directly
  interacting with the machine, e.g. walking time
  to the next machine)
• Calculate total expected cost of production per
  cycle from one machine
• Where K1 operator rate (/unit time)
• K2 cost of machine (/unit time)
• N N1 ? cycle_time (l m)
• N N2 ? cycle_time N2(l w)

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Machine Idle Time and Worker Idle Time
W M1 M2 M3
W M1 M2 M3 M4
w l
w l
Cycle_time l m
m
Cycle time N2(lw)
m
Worker idle time
Machine idle time
N N2
N N1
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Synchronous Servicing Example

• It takes an operator 1 to service a machine and
  0.1 to walk to the next machine. Each machine
  runs automatically for 3, the operator earns
  10/h and the machine cost 20/h to run. How many
  machines can the operator service?

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Synchronous Servicing Example

• It takes an operator 1 to service a machine and
  0.1 to walk to the next machine. Each machine
  runs automatically for 3, the operator earns
  10/h and the machine cost 20/h to run. How many
  machines can the operator service?
• Solution
• Estimate the number of machines assigned to the
  operator N (lm)/(lw) 3.6 ?N1 3 and N2
  4
• With N1 3 TEC1 (lm)(K1 N1K2)/N1
  (13)/60( )/3
  1.556/unit
• With N2 4 TEC2 (lw)(K1 N2K2)
  
  (10.1)(10 x20)/60 1.65/unit

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An Alternative Solution

• With N1 3
• The production rate per hour
  45units/hr
• The expected cost TEC1 (K1 N1K2)/R
  
  (103x20)/45 1.556/unit
• With N2 4
• The production rate per hour
  54.54 units/hr
• The expected cost TEC2 (K1 N2K2)/R
  
  (104x20)/54.54 1.65/unit
• If l 0.9 (10 decrease in loading /unloading
  time), what will the result be affected?
• R increase 10 (from 54.54 to 60 units/hr)
• TEC decrease 3.6 (from 1.556 to 1.5/unit)
• A reduction of idle time from 0.7 min for the
  operator
• Check?

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Random Servicing

• The case when
• Do not know when the machine needs to be serviced
• How long the service takes ?
• The probability of M (out of N) machines down
• Total expected cost
• Where K1 hourly rate of operator
• K2 hourly rate of machine
• N number of machines assigned
• R rate of production (units from N
  machine/hour)

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Random Servicing
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Random Servicing Example

• An operator is assigned to service 3 machines
  that have an expected downtime of 40. When
  running, each machine can produce 60 units/h. The
  operator is paid 10/h, and a machine costs 60/h
  to run. Is it worth hiring another operator to
  keep the machines running?
• Solution
• One operator
• machine down (n) probability machine hour
  lost/8-hr day
• 0 0.216
  0
• 1 0.432 0
• 2 0.288 0.288x8 2.304
• 3 0.064 0.064x16 1.024
• 
  Total 3.328
• Total production time
  - 3.328 20.672 (hours)
• Total number of products to be produced 20.672
  x60 12430.3 units.
• Average rate 1240.3/(8) 155.04 ?TEC
  1.23/unit

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Solution

• two operators
• machine down (n) probability machine hour
  lost/8-hr day
• 0 0.216 0
• 1 0.432 0
• 2 0.288 0
• 3 0.064 0.064x8 0.512
• 
  Total 0.512
• Total production time - 0.512
  23.448(hrs)
• Number of products to be produced 23.448x60
  1409.28units
• Average rate 1409.28/( ) 1176.16 ?TEC
  1.14/unit
• Three operators TEC (3x103x60)/180
  1.17/unit

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Combinations of random and synchronous servicing

• When
• Servicing time constant
• The machines are serviced randomly
• Breakdowns follow a certain distribution
• Approaches
• N 6 Use the empirical curves
• N gt 6 Wrights formula
• If TBF ? exponential distribution Ashcrofts
  method
• Calculate k l/m ?using table A3-13 ?machine
  interference
• and c m l i
• Where k service ratio, c total cycle time
• l servicing time, i machine
  interference time
• ( )
• I inference ( mean servicing time)
• X mean machine running time/mean
  machine servicing time,
• N number of machines/operator

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Example
In a quilling production, an operator is
assigned 60 spindles. The mean machine running
time/ package determined by stopwatch study, is
150. The standard mean servicing time/package is
3. Calculate the machine interference using the
Wrights formula and the Ashcrofts method?
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Solution

• Wrights formula
• Thus, we would have
• machine running time 150.0 min
• servicing time 3.0 min
• machine interference time 11.6 x 3 34.8 min
• Ashcrofts method
• From Table A3-13, Appendix 3, with exponential
  service time and k l/m 3/150 0.02 N 60,
  we have a machine interference time 16.8 of the
  cycle time. i 0.168c
• c m l i 150 3 0.168c ? 0.832c 153
• ?c 184 min
• i 0.168c 30.9 min

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Line Balancing

• Helps to determine the ideal number of workers to
  be assigned to a production line
• Computer software is available to eliminate the
  calculations

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Line Balancing Problem 1

• Given
• Operation times
• Cycle time
• Requirement determine number of operators needed
  for each operation
• The rate of production is dependent on the
  slowest operator
• Where E efficiency
• S.M. standard time per operation
• A.M allowed standard time per
  operation
• Idle100 - E

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Line Balancing Problem 1

• Procedure
• Calculate total number of operators required
• Where N number of operator needed in the line
  R Desired rate of production
• Find time required for producing one unit
• Number of operators needed for each operation
  (standard time of operation/allowed time to
  produce one unit)
• Find the slowest operation operation time
  (standard time/number of operators in the
  operation)

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Example

• Assume that we have a new design for which we
  are establishing an assembly line. 8 distinct
  operations are involved. The line must produce
  700units/day (or 700/4801.458 units/min), and
  since it is desirable to minimize storage, we do
  not want to produce many more than 700units/day.
  The 8 operations involve the following standard
  minutes based on existing standard data 1.25
  min, 1.38 min, 2.58 min, 3.84 min, 1.27 min, 1.29
  min, 2.48min, 1.28 min. To plan this assembly
  line for the most economical setup, we estimate
  the number of operators required for a given
  level of efficiency say, 95 .

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Solution

• total number of operators required at 100
  efficiency N 1.458(1.25 1.381.28)/1 22.4
• total number of operators required at
  95efficiency
• 22.4/0.95 23.6 24 (operators)
• time required for producing one unit
  480/7000.685 minutes
• Number of operators need on each operation
• Operation standard minutes no. of operators
• Operation1 1.25 1.25/0.685 2
• Operation2 1.38 1.38/0.685 2
• Operation3 2.58 2.58/0.685 4
• Operation4 3.84 3.84/0.685 6
• Operation5 1.27 1.27/0.685 2
• Operation6 1.29 1.29/0.685 2
• Operation7 2.48 2.48/0.685 4
• Operation8 1.28 1.28/0.685 2
• Total 15.37 24

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Solution

• Slowest operation
• Operation Time
• Operation1 1.25/2 0.625
• Operation2 1.38/2 0.690
• Operation3 2.58/4 0.645
• Operation4 3.84/6 0.640
• Operation5 1.27/2 0.635
• Operation6 1.29/2 0.645
• Operation7 2.48/4 0.620
• Operation8 1.28/2 0.640
• Output of the line 2 operators x 60 min/ 1.38
  87 pieces/hour or 696 piecs/day

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Line Balancing Problem 2

• Given
• Maximum allowable cycle time
• Maximum allowable number of workstations
• Precedence constraint
• Processing time for each job
• Requirement how to assign jobs to
  workstation?minimize number of workstations

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Line Balancing Problem 2

• Procedure
• Step1 Calculate positional weight for each job
  sum of processing time of that job and the
  processing time of jobs that follow the
  considered job.
• Step 2 Sort positional weight in decreasing
  order. Set W1
• Step 3 Assign job Jk to workstations according
  to
• Its positional weight
• Processing time tW tk C, assign job Jk to
  workstation W if not W W1
• Precedence constraint
• Step 4 repeat step 3 until all jobs are assigned
• Where tW total assigned time at work station W

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Line Balancing Example

• Assume that the required production per
  450-minute shift is 300 units. The cycle time of
  the system is 450/300 1.5 minutes

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Solution

• Positional weights
• Sorted jobs positional weight
  Immediate predecessors
• 0 0.460.250.221.10.870.280.721.320.49
  0.556.26 -
• 1 4.75 -
• 3 4.40 0,1
• 4 4.18 3
• 2 3.76 0
• 5 3.51 2
• 6 2.64 5
• 8 2.36 4,6
• 7 1.76 4
• 9 1.04 7,8
• 10 0.55 9

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Solution