# 14. Simulation and Factory Physics

Document Sample

```					   14. Simulation and Factory Physics
1. @Risk: Harriet Hotel and Overbooking Problems

2. Introduction to Simulation
–   Methods of modeling uncertainty
–   Monte Carlo simulation

3. Managing production lines without variability

4. Managing production lines with variability
–   Throughput rate, flow time and inventory levels
–   Line balancing
–   Single machine stations vs. parallel machines

1
Overbooking Problem
• Common practice in

• Difference between overbooking problems and newsvendor
problems

2
Harriet Hotel

100           Note:
125            HarrietHotel.xls is
30             available on
0.95           CourseInfo
200
=B2-B3
try different values
=RiskBinomial(B7, B4)
=MIN(B1,B8)
=B8-B9
=RiskOutput() +B6*B9-B5*B10
1. First, start @Risk. Excel will start automatically.
2. Make “Actual Arrivals" a Binomial Random Variable:
4.   Set Iterations & Sampling: Menu: @Risk, Simulation, Settings
5.   Run the Simulation: Menu: @Risk, Simulation, Start
3
6.   Analyze the Results: Results Window: Results, Results Settings or Quick Report
@Risk Simulation Settings. Menu: @Risk, Simulation, Settings
Number of times the simulation is
repeated for each scenario.
Number of Scenarios.
• use 1 if you enter a single value
for “Number of Reservations
Accepted", or
• use 7 if use RiskSimTable with
seven different values.

“Monte Carlo” causes @Risk to
show randomly generated values
when you press function key F9.

A "fixed seed" causes @Risk to
use the same random numbers
every time a run is repeated.
This means that all simulations
will face the same “Actual
Arrivals”.
4
@Risk Report Settings
Results Window: Results, Report Settings

Specify the reports you are interested in.

For example, you can put these

Generate the selective reposts.
5
Using the @Risk Simulation Add-in for Excel
1.   Open @Risk. (Excel will be opened for you.)
–   Performance measures (output cells)
–   Decision variables (under your control)
–   Random variables (input cells)
3.   Use probability functions to represent your random variables
–   Go to Insert | Function and select @Risk Distribution, or
–   go to @Risk | Model | Define Distributions
4.   Identify the performance measures you wish to gather data on
–   Go to @Risk | Add Output, or simply type in Riskoutput()
–   You can see the list of your input and output cells by going to
@Risk | Model | List of Outputs and Inputs
5.   Specify simulation settings: @Risk | Simulation | Settings
–   Iterations: # iterations and # simulations
–   sampling
6.   Start the simulation (@Risk | Simulation | Start)
7.   Analyze results                                                       6
Selecting a Distribution (p. 550)
• Quantifying Uncertainty                           You can also go to @Risk |
– Mean and Standard Deviation                   Model | Define Distributions,
– Shape (skewness)
among the different probability
– Min, mostlikely, max                          distributions.

• Discrete Probability Distributions:
–   RiskIntUniform (x,y)
–   RiskDuniform({x1,x2,…,xn})
–   RiskDiscrete ({x1,x2,…,xn}, {p1,p2,…,pn})
–   RiskBinomial(n,p)

• Continuous Probability Distributions:
–   RiskUniform(x,y)
–   RiskNormal(m,s)
–   RiskLogNorm(m,s)
–   RiskTriang(min, most likely, max)
7
Analyzing Simulation Results
• After the simulation runs, the Results Window will automatically open,
showing summary statistics for
– the output cells and
– the input cells if you’ve chosen to collect them in the Sampling tab of
Simulation Settings
• You can move back and forth between the results and your
spreadsheet through the “Show Excel Window” button and the “Show
Result Window” button (or through @Risk | Results).
• From the Results Window:
– Copy the simulation results to an Excel worksheet for further analysis and
safekeeping by going to Results | Report Setting or Quick Report
– To generate a graph, right-click on an output (or input) cell and then
choose the type of graph you want (histogram or cumulative). Right-click
on any graph to change its format or to copy it into a standard Excel
graph.
• To simulate for different values of a decision variable (One variable at
a time!):
– Use RiskSimTable({x1,x2,…xn}); x1, x2, … xn can be cells or numbers.
– type n in “# of simulations” under @Risk | Simulation | Settings
• Reports: mean, std, percentiles                                               8
Some Tips
• @Risk will run all the models that are open. If you are only
interested in results from one model, close all other models.
• @Risk can handle multiple random variables.

Year             Return
1998             =Riskuniform(0.07,0.15)
1999             =Riskuniform(0.03,0.10)

• @Risk allows formulas such as: B1*(1+RiskNormal(10,9))+B3
• @Risk can handle multiple output cells
Annual profit         RiskOutput()+formula
Service level         RiskOutput()+formula
Inventory cost        RiskOutput()+formula

9
Introduction to Simulation
• Approaches to analyzing uncertainty:

• Monte Carlo simulation using computers

• Why important?

10
Factory Physics
•   Managing production lines without variability

•   Managing production lines with variability
–   Throughput rate, flow time and inventory levels
–   Line balancing
–   Single machine stations vs. parallel machines
–   Sources of variability

11
The Penny Fab

punch press     stamps         places a     cleans
cuts penny     Lincoln’s      rim on the   away any
blanks          face          penny       burrs

A production line that makes giant one-cent pieces. The line
consists of four machines in sequence. Capacity of each
machine is one penny every two hours. (A balanced line with
no variability.)

• Theoretical flow time (hours) T0 =
• Bottleneck rate per hour R0 =
• To achieve R0 , Inventory needed is: I0 =

12
Penny Fab One

2 hrs    2 hrs   2 hrs   2 hrs

T = Flow
Time for
each Penny      I        T      R       RxT
1                        1
R=
2                        2
Throughput
Critical       3                        3       Rate for
WIP level I0    4                        4        System
5                        5
6                        6
7                        7
8                        8
9                        9
13
Throughput and Flow Time vs. Inventory

.5                                  20
Throughput (Jobs/hr)

Flow time (Hours)
.4                                  16

.3                                  12

.2                                      8

.1                                      4

0                                       0
0   2   4   6   8   10   12   14
Inventory (jobs)
To achieve the Theoretical Throughput Rate R0 = 0.5 jobs per hour
The minimum Inventory needed is I0 = 4.0 jobs
14
Station 1

2 hr
Station 2

5 hr

Station 3

10 hr
3 hr

Station 4
Penny Fab Two

15
Penny Fab Two
Station      c         Tp      Capacity
1          1         2 hr
2          2         5 hr
3          6        10 hr
4          2         3 hr

R0 =               T0 = _______________ I0 = ________________

Station 1       Station 2    Station 3   Station 4
# of jobs
Utilization

16
Line Balancing

5 jobs/shift

2.5 jobs/shift
on each machine
=> Extra capacity at the first station!

• Processing rate at station 1: 1 job/shift 50% of the time, 4
jobs/shift 50% of the time; avg 2.5 jobs/shift
• Processing rate at station 2: 2 jobs/shift 50% of the time,
8 jobs/shift 50% of the time; avg 5 jobs/shift
17
Line Balancing (cont.)
Potential Production         Actual
Station 1        Station 2    Output
M1       M2      M3       M1
1   1         1       1        2            2
2   1         1       4        2            2
3   1         4       1        2            2
4   1         4       4        2            2
5   4         1       1        2            2
6   4         1       4        2            2
7   4         4       1        2            2
8   4         4       4        2            2
9   1         1       1        8            3
10   1         1       4        8            6
11   1         4       1        8            6
12   1         4       4        8            8
13   4         1       1        8            6
14   4         1       4        8            8
15   4         4       1        8            8
16   4         4       4        8            8
69

The expected output rate =              jobs/shift   18
Line Balancing (cont.)
• If we shut down one of the machines at station 1, the expected
output rate              jobs/shift.

Potential Production
Station 1        Station 2   Actual Output
M1       M2          M1
1    1         1           2            2
2    1         4           2            2
3    4         1           2            2
4    4         4           2            2
5    1         1           8            2
6    1         4           8            5
7    4         1           8            5
8    4        4            8            8
28

What is the capacity of a line with variability?

19
Penny Fab Two Throughput Rate
0.5

without variability
0.4
Throughput Rate, R

0.3
with variability

0.2

0.1

0
2   4   6   8   10    12     14   16   18   20   22   24   26
Inventory, I
With                           • Simulation is the tool to find R(I) and T(I) !!
variability                      • To get close to the bottleneck rate R0 you might
need a huge inventory!!                         20
Penny Fab Two Flow Time

80

70

60
Flow Time, T

50

T             40

30
without variability
20

10

0
0   2   4   6   8   10 12   14 16 18 20 22 24 26
Inventory, I
21
Penny Fab One
• Single Machine Stations

c=1           c=1     c=1             c=1

2 hrs         2 hrs   2 hrs           2 hrs

• Parallel Machines

c=1           c=1             c=2

2 hrs         2 hrs

4 hrs

22
Internal Benchmarking Example
Large Panel Line:
Process                    Rate (p/hr)   Time (hr)
Treater                      191.5          1.2
Machining                    186.2          5.9
Circuitize                   150.5          6.9
Optical Test/Repair          157.8          5.6
Drilling                     185.9         10.0
Copper Plate                 136.4          1.5
Procoat                      146.2          2.2
Sizing                       126.5          2.4
EOL Test                     169.5          1.8
Bottleneck rate,             126.5         33.1
theoretical process time
23
Internal Benchmarking
• Best inventory level without variability = 126.5  33.1 = 4,187

• Actual Values:                    • Benchmark:
– T = 34 days = 816 hours          – Theoretical FT = 33.1 hours
– I = 37,400 panels                – “best inv level” = 4,187 panels
– R = 45.8 panels/hour             – Bottleneck rate = 126.5 panels/hr

• Conclusions:
– Throughput is 36% of capacity
– WIP is 8.9 times the “best inventory level”
– Flow Time is 24.6 times theoretical flow time

• Why?
24
Takeaways
1. @Risk

–   Spreadsheet model: performance measures, decision
variables, random variables
–   Probability functions for representing random variables,
e.g., RiskNormal(m,s)
–   Decision variables: RiskSimTable (one variable at a time!)
–   Output cells for performance measures (Riskoutput)
–   Simulation settings (run length, desired reports)
–   Reports (mean, std., percentiles)

2. Simulation
–   Methods of modeling uncertainty
–   Monte Carlo simulation: random number generation

25
Takeaways
3. Managing production lines without variability
– There exists an optimal Inventory level =
bottleneck rate  theoretical flow time
– Managing production lines with variability

4. Throughput rate increases as inventory
increases
– Throughput rate < bottleneck rate
– Unbalance Lines
– Single machine stations vs. parallel machines

26

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 79 posted: 5/1/2012 language: English pages: 26
How are you planning on using Docstoc?