OPTIMISATION OF CONTROL GOALS OF FLEXIBLE
MANUFACTURING SYSTEM
Pavol VAŽAN* and Pavol TANUŠKA*
*Department
of Information Technology and Automation
Faculty of Materials Science and Technology, Slovak University of Technology, Trnava, Slovakia
vazan@mtf.stuba.sk, tanuska@ mtf.stuba.sk
Abstract: The paper presents possibilities of using simulation in FMS control. The control goals of
the production are opposite in many cases. The control strategies of FMS have to provide
achievements of different control goals. Simulation method is one of the most effective methods for
the control strategy verification of the production system. The simulation provides a possibility of
optimisation of control goals. The authors have designed solving procedure for optimisation of
control goals. The simulation case study demonstrates optimisation of the cost by simulation way.
The authors have chosen Witness simulator for optimisation of control goals.
Keywords: FMS, control, simulation, optimisation, Witness
1.
INTRODUCTION
The flexible manufacturing system seems to be the key component in all yet defined CIM concepts.
Modern flexible manufacturing systems are complicated, highly automated, computer
controlled integrated systems. Frequent requests on the changes of the types of products,
and distribution problems especially in batch production, incline frequently to change
production strategies. Production strategies have to respect more production goals at the same time.
These production goals are very conflicting, therefore it is very difficult to reach them. The
simulation is the proper method that allows to solve these problems. In case, that the simulation
results can be optimised, there can be find optimal values of the selected production goals for given
the flexible manufacturing system.
2.
PROBLEM FORMULATION
The main goal of the work was to optimise input intervals of parts to the manufacturing system in
such a way, that the production cost will be minimal. But the other production goals have to be
realised. To these production goals belong:
 to maximise capacity utilisation,
 to minimise flow time of manufacturing,
 to maximise the total number of finished parts.
Input interval is the time period between two enter batches into system. It is also known from
practice and from literature (3) that the production goals are opposite, therefore it is impossible to
reach optimal values simultaneously.
The problem defined above we solved on the selected FMS. The foundation of the proper input
intervals of parts requires to provide the number of simulation experiments for different variations of
the input intervals. We decided to use optimising methods, that allow to find the solution without
executing number of simulation experiments.
3.
DEFINITION OF THE FMS MODEL
Each workstation of the FMS is defined as an independent module (see figure 1). All these modules
form the structure of FMS according to the following rules:
 2 compatible machines constitute the Group 1and the Group 2,
 the workstation SRP1 and the workstation SRP2 are the components of the Robotic cell,

the workstation CNC is an independent module.
Figure 1: The model of FMS in simulator Witness.
Each workstation has its own input and output buffers. The transport system consists of four
automated guided vehicles (AGV). In the given FMS a combined storage is used, (main storage is
also system input and system output of the FMS; each workstation as well as FMC has own buffer
and there is one emergency storage). Given manufacturing system has been designed to produce two
kinds of parts at the same time. They are labelled as VD1 and VD2. The parts were produced in
batches. Lot size of every batch contained 5 parts.
There is the following material flow:
VD1: input buffer  Grou2  CNC workstation  Group1  output
VD2: input buffer  SZP1  Robotic cell  Group2  output
4.
SIMULATION TOOLS
The authors used the simulation package Witness of the company Lanner group Ltd., which is at
one’s disposal at the Department of Information Technology and Automation Faculty of Materials
Science and Technology of the Slovak University of Technology, Trnava. WITNESS simulation
software is the most advanced in its field especially for simulation and optimising production
systems. Its plugged in module WITNESS Optimiser significantly reduces the time spent with
experimenting, by automatically finding the optimum solution to satisfy chosen performance criteria.
Using the latest sophisticated mathematical techniques, it offers an easy-to-use interface and the
presentation of optimal results in a selection of useful.
5.
SOLUTION PROCEDURE
The control of FMS influences a lot of factors. All these factors (number of kinds of parts,
processing times, lot size of batches, material flow type and number of workstations) were constant in
all the simulation experiments. The only free parameters (factors) were input intervals of both
batches.
The objective function had to be defined for optimising the production cost. The production cost is
computed according to following function in the realised model.
p
p
i 1
i 1
SumCost   In _ part _ cos t i   Added _ valuei
, in which
In_part_cost is initial cost for every entered parts
Added_value is gained amount in FMS
P is number of entered parts
Total added value is calculated:
p
Sum _ Added _ value   opration _ cos t i  labour _ cos t i  transport _ cos t i
i 1
 storage _ cos t i
where
m
operation _ cos t   t Aj * unit _ cos t1
,where
j 1
m is number of machines
tAj is processing time
unit_cost1 is rate per unit of time
op
labour _ cos t   t Bk * unit _ cos t 2 ,
where
k 1
op is number of set up operations
tBk is set up time
unit_cost2 is rate of unit of labour
top
transport _ cos t   transport _ operation _ cos t l
l 1
top is number of transport operations
NS
storage _ cos t   t Sn * unit _ cos t 3
n 1
NS is number of storages
TSn is time of storage
Unit_cost3 is cost of unit time storage
,where
,where
The function SumCost is growing up with rising of number of finished parts. Therefore it is not
proper to use it as an objective function. The function Unit_Cost was used by the authors. This
function calculates the production cost per finished part.
Unit _ Cost  SumCost no _ out _ parts
, where
no_out_parts are number of finished parts
The production cost were optimised, but other production goals had to reach defined values. The
authors solved the problem of the implementation of the others production goals into the objective
function by adding of constant to the objective function, if the specified values of production goals
were not fulfilled.
The procedure was defined:
IF No_out_parts () < default value of finished parts OR Machine utilisation () < default value of
machine utilisation OR Flow time () > default value of flow time
Unit_Cost = SumCost / No_out_parts + constant1
RETURN Unit_Cost
ELSE
Unit_Cost = SumCost / No_out_parts
RETURN Unit_Cost
ENDIF
Default values of number of finished parts, machine utilisation and flow time were obtained in the
preparatory experiments.
This way was defined as the fundament of optimising scenario. Very important step of solution
procedure is the selection of the optimisation method. A variety of the optimisation methods are
provided, ranging from simply running all combinations through the more complex and intelligent
algorithms. The methods are: (2)
 All combinations, which will run all constrained combinations.
 Min/Mid/Max, which will run all combinations of min, mid and max settings of range
parameters.
 Hill Climb, which is a simple method of searching for improvements. This method iteratively
generates a single neighbour, which is accepted only if it is of the higher quality.
 Random solutions, which generates random combinations and can help indicate how solutions
will vary, by giving a picture of the shape of the entire solution space for a particular scenario.
 Adaptive Thermostatistical Simulated Annealing. The automatic settings for this will
intelligently adjust the algorithm based on the type of results found, working to search for the
best solution for the vast majority of simulation models.
 Six Sigma, which is based on the Simulated Annealing method. With this method you can limit
the level of changes to a model for the purpose of identifying the best options for process
improvement.
The authors have chosen the Adaptive Thermo statistical Simulated Annealing method.
6.
PREPARATORY EXPERIMENTS
The goal of preparatory experiments is (4):
 model functionality verification;
The procedure is identical as the program debugging. It is recommended to use animation. All the
modern simulation tools make the animation possible. Such way enables to focus on the changes of
the system in the time and behaviour of entities.
 setting up of the warm up period,
The warm up period is needed to be set up not to influence the simulation results by the empty
system at the beginning of the simulation. It means that during the warm up period it should be
fulfilled by parts.
 finding the upper and lower lines of system loading,
For finding the system behaviour it is important to change the input intervals of the batches only to
the certain interval. This interval is proper to set up in such way: the system will be overloaded in its
lower line; vice versa in its upper line the system would not be loaded. The best results observed on
the output will be occurred in the selected input values, in this case it will be guaranteed.
 determination of the values for the quantitative rating of the production goals into the objective
function.
Number of finished parts is determined from the overloaded system. The obtained value can be
decreased approximately by 20% according authors.
Machine utilisation is specified on 75-80% according to literature (1).
Flow time is determined from the specific experiment when only one batch is entering to the
system. This procedure is going to be realised for all the types of the batches. The result of the
procedure is the minimal value of the flow time without needless storage. The value of the flow time
is going to be entered into the objective function increased by 20-30%.
The following values were determined for the given FMS by preparatory experiments:
 warm up period=60,
 constraints of the input intervals: VD140,70; VD225,50,
Note:
Accurate setting up of the input intervals markedly reduces the optimization time.
 the measured minimal flow time was 62 time units (average of both batches). The authors chose
the value 80 into the objective function.
7.
RESULTS
Time of the simulation period was set up 2500 time unit (minutes). This time represents
approximately one week of production. Graph 1 presents 25 of the best optimizing results of the input
intervals for the achievement of the minimal unit cost. The other production goals have to be fulfilled
at the same time. The minimum unit cost was found for the value 59 time units for the batch VD1 and
30 time units for the batch VD2 as it can be seen in the Graph 1.This value of the unit cost was
achieved for the following quantitative parameters of the others production goals. They are described
in the Table 1.
Objective function
184
183
Unit Cost
182
181
180
179
178
177
176
30
31
32
30
31
32
30
31
32
30
31
32
30
31
30
31
30
31
30
31
30
30
30
50
50
50
51
51
51
52
52
52
53
53
53
54
54
55
55
56
56
57
57
58
59
60
Input interval of VD1 and VD2
Graph 1: The objective function of the unit cost
The founded minimum Unit cost documents expected results for the values of the input intervals.
It is not proper to insert both batches into the system together. Then the needless waiting in front of
the workstations, processing both batches occurs. In this case they are the Group1 and the Group2.
Longer input interval of batch VD1 is caused by higher operation cost of the batch.
Table1: Quantitative parameters of production goals for optimal unit cost
Production goal
Quantitative Value
Unit cost
178.328 SKK
Total number of finished parts
620
Number of entered batches VD1
215
Number of entered batches VD2
425
Number of batches VD1
210
Number of batches VD2
410
Average machine utilisation
76.122 %
Flow time of VD1
67.63 min.
Flow time of VD2
77.86 min.
Average flow time
72.745 min.
Achievement of high capacity utilisation in the batch production is very complicated because the
operations have different processing time and the machines have different performance. High
performance of the CNC workstation opposite to the others caused that this workstation had low
utilisation (approximately only 50%). Therefore the average machine utilisation above 76% is
considered as a high one. Number of batches in the process is only about 3%. Also this result can be
evaluated as very good.
8.
CONCLUSION
The solution procedure, of the cost minimalization in the dependence from the input intervals of
batches, designed by the authors, led to the successful solution of the optimisation problem, when the
other production goals were fulfilled. The founded solutions, also as the others quantitative
parameters of the production goals are regarded as balanced in conditions of the batch production. No
less important assumption of the successful solution was building up the model of the system in the
Witness environment and the implementation of the complicated control algorithms of FMS. The
procedure of building up the model was not presented because of the short extend of the paper. The
simulation as the fundamental method is very effective tool for problem solving of production system
control.
REFERENCES
1. Gregor, M., Košturiak, J.: Just-in-Time, Výrobná filozofia pre dobrý management, ELITA,
Bratislava 1994, ISBN 80-85323-64-8
2. Lanner Group Ltd.: Witness 2002 on-line help system, UK 2002.
3. Mičieta, B., Král, J: Plánovanie a riadenie výroby, ES ŽU, Žilina 1998
4. Vážan P.: Verifikácia riadenia pružných výrobných systémov simulačnými metódami, Trnava
2001, 162s, Thesis PhD on MtF STU Trnava