Simulation and Modeling Analysis
Term Project
December 7, 1999
Facilities Planning:
A Simulation Study of a Flow Shop versus a Job-Shop
Manufacturing Layout
Robert Devine
Edmund Foerster
Table of Contents
I. Introduction
II. Problem Formulation and Objectives
a) Description of the products and the manufacturing processes.
b) Proposed material flow and layout of planning charts
III. Model Conceptualization and Translation
a) Flow Shop Model assumptions and structure
b) Job Shop Model assumptions and structure
IV. Data Collection
a)
Determination of standard times for manufacturing operations.
V. Verification
a) Calibration
b) Discrepancies and Problems
VI. Validation
a) Face Validity
b) Validation of model assumptions
c) Comparison of input – output transformations.
VII. Experimental Design
a) Length of the simulation runs
b) Number of replications to be run
VIII.Conclusion
Appendix A: Plant Layout
1.
2
3
4
Figure 1 Flow Shop Layout
Figure 2 Job Shop Layout
Figure 3 Linear Distances (Flow Shop)
Figure 4 Linear Distances (Job Shop)
Appendix B: Flow Shop Documentation and Results
1.
2.
Flow Shop Program Documentation
Output of Flow Shop Model
Appendix C: Job Shop Documentation and Results
1.
2.
Job Shop Program Documentation
Output of Job Shop Model
Appendix D: Presentation Slides
I. Introduction:
The efficient utilization of workers, materials, and machines is critical to a successful organization. Low
cost production can be achieved by assuring proper plant layout. This entails placing the right equipment,
coupled with the right method, in the right location. This in turn, permits the processing of a product in the
most effective manner through the shortest possible distance and in the shortest possible time.
The job shop (or process layout system) and the flow shop (or product layout system) represent two distinct
classical manufacturing systems. The job shop is characterized by the manufacturing of a large variety of
products, which usually results in small manufacturing lot sizes. The layout for a process department is
obtained by grouping like processes together and placing individual process departments relative to one
another based on flow between departments. Production machines are grouped according to the general
type of manufacturing process. For instance, all of the lathes are in one department, the milling machines
in another, and the drill presses are in yet another. “Typically, there exists a high degree of
interdepartmental flow and very little intradepartmental flow”. In addition, workers must have relatively
high skill levels to perform a vast array of work assignments.
The flow shop or product layout is product orientated and is composed mainly of flow lines. They are
characterized by high volume environments where materials typically flow from one workstation directly to
the next adjacent one. With this layout, specialized equipment is dedicated to the manufacture of a
particular product.
II. Problem Formulation and Objectives:
At issue, is the best layout for a proposed plant that will be manufacturing three different types of specialty
parts for the automotive industry (gears, pistons and valves). A job shop with a process layout will be
compared to a flow shop with a product layout. Parameters such as machine utilization, work in process,
personnel and machine requirements, and output and production times will be evaluated to obtain the most
efficient plant layout. The two proposed layouts are pictured in Appendix A, (Figures 1 and 2).
With the flow shop arrangement, parts flow between dedicated workstations. Each part has a direct,
uninterrupted flow path and does not have to compete with other product disciplines for machining time.
With this arrangement, however, there are no provisions for compensating for an over-utilized or underutilized workstation.
With the job shop layout, materials no longer follow straight machining and production line paths, which
can lead to increased transportation times between workstations. In this arrangement, machines are no
longer dedicated to one particular type of part. Instead, if a machine which is normally configured for
producing a certain type of part is lying idle, it can be reconfigured to perform work on a part of a different
discipline.
a) Description of the Products and the Manufacturing Processes:
Gears, pistons and valves comprise the three distinct parts that are to be manufactured. All three parts
come from the foundry and arrive at their respective initial operating stations. The gears will be machined
on a lathe, brought to a surface treatment center, and then coupled with other gears to form a worm gear
assembly. Pistons will be machined on a saw, and then on a lathe. They will then undergo a similar
surface treatment, and will then be joined with a cylinder assembly. The valve, following receipt from the
foundry, will be machined on a saw, a mill and a grinder and will then undergo a heat treatment. All
finished parts and assemblies end up in a dedicated storage area.
b) Proposed material flow and layout of planning charts:
Pictured in Appendix A, (Figures 3 and 4), are the floor plans for the two proposed layouts. Enumerated on
each plan are the approximate dimensions of each workstation and the linear distance between the
midpoints of the workstations. These estimates helped generate the “move logic” parameters for the
computer model. In evaluating the most effective plant layout, one must also consider the material
handling requirements and the excess distance that the products may have to traverse in the different
layouts.
III. Model Conceptualization:
“The first step in model building normally consists of observing the real system and the interactions among
its various components and then subsequently compiling data on its behavior.” Ideally, operators,
technicians, engineers, and supervisors would be consulted to ascertain details about the operation of the
system. Due to a lack of expert knowledge and constrictive time constraints, values of various machining
parameters had to be estimated in lieu of steadfast data. It is recognized that this factor severely limits the
information which can be gleaned from the models. A conceptual model was developed which consisted of
various assumptions concerning the structure of the system as well as hypotheses on values for the input
parameters. These constraints are specified below for both the flow shop and the job shop model. Finally,
two separate simulation models were created to translate the conceptual model into a “computer
recognizable form.” The documentation for these models is contained in Appendices B and C.
a)
In order to abstract the essential features of the problem, the model “Flow Shop” was constructed
based on the following data and structural assumptions.
Data Assumptions: “These assumptions are ideally based on the collection of reliable data and
correct statistical analysis.”
• Arrivals of the unfinished parts arrive from a foundry and have the following arrival and service
time distributions:
Entity
Location
Service Time
Distribution (min)
Gear
Lathe 1
N(4, 0.1)
Boxg (50 gears grouped together)
Surface Treatment 1
N(120, 1)
Gear (ungrouped gears)
Assembly Center 1
N(20, 0.1)
Piston
Saw 1
N(6, 0.1)
Piston
Lathe 2
N(8, 1)
Piston
Surface Treatment 2
N(60, 1)
Piston
Assembly Center 2
N(5, 1)
Valve
Saw 2
N(4, 1)
Valve
Mill
N(90, 1)
Valve
Grinder
N(180, 1)
Valve
Heat treatment
N(120, 1)
Gears: Arrival Rate = t(1.09, 1.2, 1.33)
Valves: Arrival Rate = t(1.36, 1.5, 1.67)
Pistons: Arrival Rate = t(1.82, 2.2, 2.22)
The normal distribution was selected for the service times because it is often used to model the
distribution of a process which can be thought of as the sum of a number of component processes
(i.e. the time to assemble a product is the sum of the times required for each assembly operation).”
•
Parts are assumed to move along linear paths between departments based on estimates of the
proposed plant layout specified in the flow diagram and in the “move logic” of the model.
Structural Assumptions (Flow Shop): “These assumptions involve simplifications and abstractions
from reality”.
• Elements which would be common to both layouts and would not be dependent upon the plant
layout were omitted. Breaks, shift changes and equipment malfunctions would occur regardless of
which plant layout was employed, thus they were not factored into the simulation.
• The plant operates 7 days a week, for three shifts a day.
• Once an item has been machined at a particular location, it waits at that location until a specified
number of similar parts accumulate, the specified parts are then transported to the next location as
one integral unit.
• A machinist is always available to transport the finished parts between stations.
• Machines are considered to be “dedicated”, thus, each workstation is capable of machining only
one type of part.
b) The model “Job Shop “ was constructed based on the following data assumptions:
• Arrivals of the unfinished parts come from a foundry and have the same arrival and service time
distributions as stipulated for the flow shop:
Gears: Arrival Rate = t(1.09, 1.2, 1.33)
Valves: Arrival Rate = t(1.36, 1.5, 1.67)
Pistons: Arrival Rate = t(1.82, 2.2, 2.22)
• Parts are assumed to move along linear paths between departments based on estimates of the
proposed plant layout specified in the flow diagram.
• The time required to convert a machining station over from processing gears to pistons and vice
versa, is to follow a normal distribution, with a mean of 10 minutes and a standard deviation of 2
minutes.
Structural Assumptions (Job Shop):
• The plant operates 7 days a week, for three shifts a day.
• Once an item has been machined at a particular location, it waits at that location until a specified
number of similar parts accumulate, the specified parts are then transported to the next location as
one integral unit.
• Machining stations are no longer considered to be dedicated.
• Pistons have a higher priority than gears. Thus, a shipment of pistons can preempt a shipment of
gears if both products are competing for the same operating station. If a batch of gears (a batch
consists of 50) is in the process of being machined, the pistons will take priority over the gears
only if less than half of the gears have been machined. If more than half of the gears have already
been completed, then the machinist will complete the current set of gears before converting the
workstation over to initiate machining of the pistons.
IV. Data Collection:
A major task in simulation is the collection and analysis of input data. Due to logistics problems and time
constraints, it was not feasible to study an existing manufacturing system. Normally, following data
collection, “the first step in the data analysis process, is to hypothesize a distributional form of the input
data by comparing the shape of the probability density function to a histogram of the data.” Fortunately,
“there are various distributions which have application to instances of incomplete or limited data.” As
stated previously, the normal distribution was selected for the service times because it is often used to
model the distribution of a process which can be thought of as the sum of a number of component
processes. This notion seemed to parallel the manufacturing system model.
The standard time for a given operation, is the time required for an average operator, who is fully qualified
and trained, and who is working at a normal pace, to perform and complete the task at hand. Information
concerning machining times was obtained from Niebel’s “Motion and Time Study, 1972.” This data,
however, was not presented in a readily usable format. For instance, one of our proposed workstations is a
lathe. There are many factors which influence the speed at which this machining is performed. Both the
speed of rotation of the tool and the feed rate of the material are determined by the type of material being
cut, the design of the cutting tool and its material composition. In addition, the type of coolant used for
lubrication, and the method of holding and mounting the subject piece are also salient factors. Similar
complexity problems were encountered for other workstations. A drill press for instance, normally has its
feed rate expressed in terms of thousandths of an inch per revolution and its speeds are documented in
terms of surface feet per minute. Estimation of these parameters would have had to have been made in
order to get a rough order of magnitude service time for each operating station. The information presented
in Neibel’s “Motion and Time Study” was not adapted because the summation of these tolerances would
have exceeded the estimation error which would be introduced by the simple assumption of a normally
distributed processing time with a specified standard deviation.
It is known that certain physical processes give rise to specific distributions. “Scheduled arrivals similar to
airplanes arriving to an airport or manufactured items to a production cell have interarrival times that may
be constant, or constant plus or minus a small random amount to represent early or late arrivals.” With this
in mind, the triangular distribution was chosen to model the interarrival times of the parts from the foundry.
This seemed appropriate in that all three parts should be able to be cast in a relatively constant amount of
time, however there will be variations on both the high end and on the low end. Their arrival rate at the
workstations is dependent on how efficiently the parts are cast at the foundry. Thus the minimum, the
maximum and the modal values for the interarrival times are specified for each part.
V. Verification:
The model building process is an iterative one, for there is a continual comparison of the real system to
both the conceptual model and to the computer model. This comparison or verification is done to assure
that the models accurately reflect the real life system. Some of the model statistics that were used to check
the model output for reasonableness were the percent utilization, the current contents and the total count
output. Based on input parameters, and hand calculations, the numbers generated for these factors were
within reason for some entities and yet were also skewed for others. This eventuality leads us to reject the
current models as they currently stand.
In the flow shop model, there was an appreciable bottleneck in the gear production line. This was
attributed to the relatively long processing times at both the surface treatment center and at the assembly
center. This, coupled with the limited capacity at each of the two centers hindered production and
decreased throughput. Conversely, both the dedicated surface treatment center and the assembly center for
the pistons were relatively underutilized, and spent an appreciable amount of time idle or under capacitated.
It was hoped that these problems could be eradicated with the job shop model.
In the job shop model, the utilization percentage of what was once the pistons dedicated surface treatment
center increased substantially; however, counter-intuitively the assembly station utilization remained
unchanged. If modeled correctly, both of these factors should have increased due to the fact that excess
gears are routed to these workstations if they are currently idle.
Calibration is an iterative process, which involves the use of both subjective tests and objective tests to
evaluate a model. Subjective tests involves the canvassing of people who are intimately knowledgeable
with the operations of the real system and offer insight about the model and its output. Since objective tests
require actual data from the real system, these were not performed as part of the calibration process.
Numerous inconsistencies in output data and improbable operating results led us to believe that there were
problems associated with the logic structure of the models. As a means of troubleshooting the models, each
was broken up into its constituent components or subroutines, and run on a smaller scale. Although this
process greatly facilitated the troubleshooting efforts, it still failed to yield viable outputs for the models.
VI. Validation:
“Validation is the overall process of comparing the model and its behavior with the real system and its
behavior. A three step approach was formulated and consists of the following functions:
1. Structure a model which has “high face validity” by involving the potential users in its development.
2. Validation of model assumptions (data and structural)
3. Comparison of the model input – output transformations with those of the real system”
In an effort to improve the reliability of the output results, multiple replications of the simulation were run.
Using the equations listed in Section VII, the number of replications required to establish a confidence level
of 95% was obtained.
“Validating the input – output transformations requires that at least some version of the system under study
exists, so that system data under at least one set of input conditions can be collected to compare to the
model predictions”. “If the system is in the planning stages and no system operating data can be collected,
complete input-output validation is not possible. Once again we were unable to perform this aspect of the
study in any meaningful way due to our lack of real time input data. When validating data assumptions,
correlation tests are conducted to ensure that the data is random and that no correlation exists. With this
established, the appropriate probability distribution is identified for the input data, the parameters of the
hypothesized distribution are determined, and a goodness of fit test (Chi-square or Kolmogorov - Smirnoff
test) is conducted.
VII. Experimental Design:
The flowshop and jobshop models are classified as non-terminating systems because they are evaluated at
steady-state. “A steady-state simulation is a simulation whose objective is to study long-run, or steadystate, behavior of a non-terminating system. “(DESS, 436) The stopping time (T E) of 336 hours (two
weeks) was chosen to evaluate the system at steady-state. When running the system for one, two, and four
weeks, no change was observed between the two and four week runs for the flowshop model. Since the
flowshop is the baseline, two weeks is the simulation run length for each replication. The models are
assumed to be initially empty and carrying no inventory. The systems could have been approximated by
using a batch method to produce simulated inputs for each batch simulation output. However, the batch
method was not desirable because it would have added more assumptions to the already mounting list.
The following specifications and formulas were used to determine the number of replications that should be
run to establish a 95% confidence interval.
Initial estimate (based on a normalized distribution):
R  [(z/2, R – 1 (S0/n))/]2 :
S0 = sample variance
n = number of initial sample points
 = error criterion
 = 0.05
R = number of replications
To find the number of replications to meet the specifications:
R  [(t/2, R – 1 (S0/n))/]2
The initial number of replications generated (R0) = 5
The number of replications to left to generate the total R (RT) = R - R0
Confidence Interval:
  [(t/2, R – 1 (S0/n)/R]
Since pistons and gears are the entities of concern, the specified 95% confidence interval and the error
criterion () of 0.005 was used to find the initial estimate for R for the two entities. The numbers for the
total time in the system for the piston and gear entities after five replications was chosen to determine the
final R that was needed for the specifications. The minimum R of the two entities will be chosen. This
way it can be “guaranteed” that all numbers will be within the specifications.
First five replications results for average minutes in the system (W).
Entity
Average Minutes
Avg. Standard Deviation ()
Gear
219.002349
0.042178
Piston
110.023395
0.042321
The initial estimates f or Gear and Piston Replications:
Entity
z0.025
Gear
1.96
Piston
1.96
Sample Standard
Deviation (S0)
Number of
Initial Runs (n)
Error Criterion
()
Estimate Total
Replications (R)
0.0422
5
0.005
10.95
0.0423
5
0.005
11.00
Since Gear replications were the minimum, at least eleven replications must be run to fulfill the
specifications. Therefore, the t-distribution will be used to generate the confidence interval for the gear.
The number of replications tested using the t-distribution will be eleven, twelve, and thirteen. Then the
minimum R generated will be used for the total number of replications (R) required.
Tested
Replications (Ri )
t0.025, R - 1
Sample
Standard
Deviation (S0)
Number of
Initial Runs
(n)
Error
Criterion ()
Total
Replications
(R)
11
2.23
0.0422
5
0.005
14.17
12
2.20
0.0422
5
0.005
13.79
13
2.18
0.0422
5
0.005
13.54
Since five replications were already generated, nine additional replications were left to run.
Therefore, the number of replications needed to meet the specifications is fourteen.
VIII. Conclusion:
Presented below are the summary tables for the replications done for both the flow shop and job shop
models. Both models were run for 336 hours (a period of two weeks) and for 14 replications based on the
calculations outlined in the previous section. To facilitate the routing structure, the two models were
structured differently in terms of the grouping of entities. These differing “accounting principles” however,
generated some final numbers which are somewhat misleading on initial review. Regardless, based upon
the numbers generated, it is evident that the two models need further refinement. This however is part of
the iterative process of computer modeling. While it is essential to identify when your models accurately
reflect reality, it is of equal importance to be cognizant of the fact when your models are somewhat flawed
and are in need of further production runs and analysis.
Flow Shop
Model
Gear
Valve


Total
Entries
Avg Min.
per Entry
Avg
Contents
%
Utilized
% Part.
Occup./
Full
% in Move
Logic
% Wait
For Res
ect
% in
operation
8392.5
89.93
37.4
74.8
99.5
.75
12.74
62.08
Surface Treat. 1
167*
119.64
.99***
99.1
99.1
Assembly 1
166*
20.22
.166***
.17
16.65
Saw 1
10013
5.99
2.97
9.93
100.0
3.0
26.55
71.83
Lathe 2
10010
37.16
18.45
20.5
99.97
Surface Treat. 2
333***
59.9
.98***
24.74
98.52
Assembly 2
332***
7.04
.116***
.08
11.60
Saw 2
12719
33.4
21.08
52.72
99.16
.10
68.4
31.5
Mill 1
317**
89.8
1.41***
1.71
99.69
Grinder 1
316**
179.2
2.8***
3.51
99.24
Heat Treat. 1
313**
119.7
1.85***
1.55
98.34
Lathe 1
Piston

Location
* This figure represents the number of boxes of gears processed, to get the number of gears, it must be
multiplied by 50 to get the total figure.
** This figure represents the number of boxes of valves processed and must be multiplied by 40 to get
the total figure.
***Represents 1 Box of the component following grouping (30 pistons per box)
Job Shop
Model
Gear
Piston
Location
Total
Entries
Avg Min.
per Entry
Avg
Contents
%
Utilized
% Part.
Occup./
Full
% in Move
Logic
% Wait
For Res
% in
operation
Lathe 1
15763
33.54
26.2
52.45
98.71
1.38
8.16
90.45
Surface Treat. 1
158*
119.3
.935*
93.5
93.52
2.78
13.12
84.1
.17
68.34
31.49
Alt Surf Treat
N/A
N/A
N/A
N/A
N/A
Assembly 1
313*
20.2
.31*
.31
31.39
Alt Assmbly 2
N/A
N/A
N/A
N/A
N/A
10015
5.99
2.98
9.94
100.0
Saw 1
Lathe 2
10012
37.14
18.4
20.5
99.97
Surf Treat. 2
490***
82.28
1.9***
50.0
99.63
Alt Surf Treat
N/A
N/A
N/A
N/A
N/A
332***
7.05
.116***
.08
11.61
N/A
N/A
N/A
N/A
N/A
Saw 2
12719
33.43
21.08
52.72
99.16
Mill 1
317.2**
89.8
1.43
1.77
99.69
Grinder 1
316**
179.2
2.8
3.51
99.24
Heat Treat. 1
313**
119.7
1.85
1.55
98.34
Assembly 2
Alt Assmbly 1
Valve

N/A = Not Available. It was not possible to track these figures, for it would have necessitated the
creation of additional entities, thus exceeding the capacity of the student version of Pro-Model.
Appendix A: Plant Layout
Appendix B: Flow Shop Documentation and Results
Appendix C: Job Shop Documentation and Results
Appendix D: Presentation Slides