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Models and Methods for Manufacturing Systems Reengineering
Copyright © IFAC Management and Control of Production and Logistics, Grenoble, France, 2000
MODELS AND METHODS FOR MANUFACTURING SYSTEMS REENGINEERING
Khobotov E.N.
Ministry of Education
Abstract: The problems of modeling of modernization and reengineering processes for manufacturing systems and complexes are considered. It is offered to use the optimization-simulation approach for these purposes. The joint work of optimization and simulation models are used in this approach. The approach allows to solve such design and reengineering problems which cannot be solved with use of the traditional simulation methods. Copyright © 2000 IFAC Keywords: optimization, simulation, design. model, equipment, production, linear programming, manufacturing systems, scheduling algorithms
determine the most favorable appearance for the manufacturing system. It is offered to use for accounts of such models the algorithms constructed on the basis of the optimization-simulation approach. The computing circuit of this approach are described in the papers (Khobotov, 1996a, Khobotov, 1996b, Khobotov, 1996c, Khobotov, 1996d).
1. INfRODUCTION Now the problems of manufacturing systems modernization cause the great interest side by side with problems of designing and management of such systems. These problems arise with mastering of new production and with expansion and perfection of already working manufacturing systems for a maintenance of competitiveness of the making production. It is impossible to create a modem effective working manufacture without the successful decision of such problems. The life cycle of the making production is reduced now. Therefore it should be modernized of the making production or mastered of a new production. That results in turn to a necessity more often to modernize a manufacture used. Besides the same problems arise also when it is demanded to realize the conversion of the defensive enterprises.
2. THE PROBLEM DESCRIPTION It is convenient to consider of static and dynamic statements in the modernization and reengineering problems of manufacturing systems. Let's consider these statements in more detail. It is required in the static statement of these problems to choose the most favorable manufacturing program for the modernized system and to determine the equipment of system which should be replaced, and to choose the new equipment which should be got for the modernizing system. The following information must be known for that task: - the average sizes of workpieces batches from the given workpieces set and prices of the each type workpiece; - the set of technological routes which can be used for processing of the each type workpiece and the
The use of traditional simulation methods for decision of these problems causes great difficulties especially when it is required to determine the most favorable strategy of a replacement of the equipment for the manufacture modernized in view of financial opportunities of the enterprise and waiting profit after the modernization. The principles of creation of static models are considered in the given paper. These models allow to
747
- the transition to the next iteration of modeling is enough complex and can not result in improvement of the characteristics of design systems; - there are complex restrictions on area of change of choosing parameters with design of most of manufacturing systems. Not always it is possible to construct a system with parameters which will be in allowable area; - the simulation methods allow to receive the information about absence of the decision of a designing task not always; - it is difficult to choose the structure of projected systems according to one or several criteria with the help of simulation methods; - it is difficult to interpret the results of simulation of manufacturing systems.
cost of its processing on the appropriate technological route; - the maximal financial means available for modernization of the manufacturing system; - the minimally allowable profit from processing of the chosen production program during in the given time interval; - the equipment types and quantity of the equipment of each type which was in the system before modernization; - the equipment types available for modernization of the system; - the processing time of each type workpiece on all routes of its processing on the all using equipment; the arrange time of the using equipment for processing of the each type workpiece on the all using technological route.
The optimization-simulation approach is based on the joint use of the optimization and simulation models. That approach allows to get rid of above mentioned lacks of simulation methods and to inherit the following advantages of optimization models: - the opportunity to detennine the decision of design tasks quickly if it exists and to receive the information about absence of the decision; - an opportunity to choose the circuits of designing systems according to one or several criteria; - an opportunity to "co-ordinate" a plenty of the initial data and parameters of various nature and to investigate a structure of the system with change of the initial data and criteria.
The production program and equipment replaced and new for the system should be chosen so as to maximize the profit received from the processing of the chosen production program and to minimize expenses for service of the system with the given restrictions for value of the purchased equipment. The decision of a static task allows to determine optimum appearance of the system after its modernization with the given financial restrictions on purchase of the equipment. However the process of modernization of the system in time is not examined in such statement. It is required in the dynamic tasks to determine the quantity and types of the equipment which should be replaced and get for the system and the types of workpieces for the production program of the system modernized, and to detennine the necessary investments for the modernization of the system. All these sizes are required to detennined for each stage of the modernization. The dynamic modernization tasks will not be considered in the given paper.
4.
THE DESCRIPTION OF THE STATIC MODEL
Let's consider the optimization model using in the optimization-simulation approach for the decision of the static modernization task described above. The balance restrictions on use time of the available equipment of the system look like:
3. THE OPTIMIZATION-SIMULATION APPROACH
(1)
The simulation methods are widely used for modeling of manufacturing systems now. The opportunity of experiments realization with models of systems researched under various conditions of work causes their wide application for designing of manufacturing systems and does them practically irreplaceable for a check of serviceability of the systems. However simulation methods have a number of lacks. These lacks complicate their use with designing of complex systems and especially with their modernization.
jEll'
l=l, ...,M j
,
where L is the set of the workpieces types made already, L is the set of the workpieces types which can be made in the system after its modernization in addition, K j is the set of the technological routes for processing of the i -th workpiece, n j is the average size of the i -th workpieces batch (batch of such size is supposed to produce in the system after its modernization), ~ k is the processing time of the i -th
It is necessary to allocate among these lacks the following: - the significant time is required for the decision of majority of tasks of manufacturing systems design with use of simulation methods;
workpiece on the k -th technological route on the j th equipment, 'l' i~ is the arrange time of the j -th
748
equipment for processing of the i -th workpiece on
an interval of time T, f.J. jo is the parameter desig-
the k -th technological route, {jij~
is a variable
nating a load of the additional equipment of the j-th
is a auxiliary parameter, V jl is
type, J 2 is the set of the additional equipment types. Such types were not included into the system earlier, but can be used for modernization of the system. The acquiring equipment can be the same types as the system had before modernization. It may be happened with an expansion of the manufacture of the workpieces made already. Usually the value f.J. jo for
(0 ~ ii;j~ ~ 1),
tu
the resource of using time for the I -th equipment of the j -th type during in the interval of time T , J 1 is the set of the equipment types included into the system before its modernization; M j is the quantity of equipment units of the j -th type, variable type (0,1),
Yjl
is integer
the well made schedule of workpieces processing is equal f.J.jo ::: 0.55 - 0.85.
8;; is the integer variable type
(0,1). The following restrictions should be carried out -k
The following restrictions are carried out for variable
for the variable 0ijl
-k e jjl -k
-k
ejjl-eijl~o,
1=1, ...,M j
i = 1, ...,L, j where
J/
E
(i
j E J1
UJ
2 '
1= 1, ...,M j )
(2)
,
J/, k = 1,..., K
(4)
j ,
is the set of the using equipment types for
manufacturing of the i -th workpiece on the k-th technological route. where The size
= 1,..., L + L- ,
Yjl
o
k i
is equal 1 if the I -th equipment of the
j -th type remains in the system after modernization
Ojk is the integer variable type (0,1). The size
is equal 1 if the i -th workpieces is processed on
the k -th technological route in the system after the modernization, and zero otherwise.
and zero otherwise. The size {jij~ shows the part of the i -th workpieces batch processed on the k-th technological route on the I -th equipment of the
Each batch of the workpieces can be made only on anyone technological route chosen from the set of possible routes. Therefore the following restrictions are included in the model
j -th type. The size ifj~ is equal 1 if the I -th equipment of the j -th type is used for processing of the
K
i -th workpieces on the k -th technological route and
!Ojk ~1, i=1, ... ,L+L,
zero otherwise.
(5)
k=1
The balance restrictions on time of use of the acquiring equipment have the same kind. However the size M j is not known in this case. Therefore the all meaning M
j
Let's consider the substantial sense of these restrictions.
are believed equal zero (M j = 0)
The left part of the restriction (1) represents the sum of three types addendums. The auxiliary parameters
(Khobotov, 1999a) on the first iteration of the model account and the balance restrictions on the time of the additional equipment are entered into the model
~I have physical sense of an idle time of the equip-
ment I of the j -th type. The addendums of the kind
e-
k ijln/ijk
(3)
j=
0,1,2,3..,),
(0 ~ (jjj~ ~ 1 with I
= 0),
ii;;
is
a
a part
ment I of the j -th type and the sum of these addendums designates the common time of processing on the given equipment. The addendums of the kind
if~ 'l'~
ditional equipment acquired for the system moderni(Y
0f
ii;j~ n j of the i -th workpieces batch on the equip-
where Y j is the units quantity of the j -th type adzation
d' .. eSlgnate the processmg time
designate the arrange time of the equipment I
of the j -th type for the subsequent processing of the
variable
i -th workpieces on the k -th technological route, and their sum designates the common arrange time of the equipment I of the j -th type necessary for processing of the production program chosen. Thus the
VjO is the time resource
of use of the j -th type additional equipment during
749
left part of this inequality designates time of processing, arrange and idle of the equipment I of the jth type and cannot exceed the possible temporary resource of work of this equipment
Yjl Vj/
submitted
in the right part of the inequality (1). The equipment owes arranged, as a rule, for processing of the other types of workpieces even in that case, when only one the workpiece will be processed
iJ
on it. The size
tools and technological rigging should not exceed financial means D allocated on modernization of the system,. However the means received from sale of the unnecessary equipment can be used for the modernization of the system. Therefore the following restriction is included in the model MJ
P+C+P-
2, 2,d /(l-Yj/)j
jEll
I~I
can not be equal 0 in the restric-
j;
(8)
-k
tions (1) when 8ij/n j more than O. Therefore the rewhere P is the cost of the equipment acquired for
strictions (2) are included in the model.
modernization of the system, C is the cost of designing of technological rigging and tools for the workpiece mastered again and modernized and for perfection of manufacturing technology of the work-
The substantial sense of restrictions (3) is similar to substantial sense of restrictions (1). The necessity of inclusion in the model of the restrictions (4) is caused by the next demand. The quantity of workpieces of each type processed "parallel" on the same type equipment must be equal in the sum to the size of the appropriate batch of workpieces.
pieces made already, P is the expense for manufacturing of necessary quantity of complete sets of technological rigging and tools, d jl is the price of the possible sale of the I -th equipment of j -th type
The quantity of the additional equipment of the j -th
entered into the system before its modernization,
type Y j can be more than zero only in that case
Yjl
when all
= I (l
= 1,...,M j ,).
d m + 1 is the price of the possible sale of the transport
Therefore the
means.
following restrictions are entered in the model for performance of this condition
The correlation allowing to determine sizes P, C, and P in view of principles of Group Technology are similar to correlation used in (Khobotov, 1999a; Khobotov, 1999b) for determination of analogous sizes in design problems, and consequently here are not considered.
(6)
where
f3
is an enough large constant. But the choice
f3
of the size
The balance restrictions on the accessible time of use of each equipment unit of the system should be included in the model for determination of necessary quantity of complete sets of the technological rigging and tools. The process of calculations of the model must be organized according to the following rule (Khobotov, 1999a; Khobotov, 1999b).
must ensure the reception necessary
meaning for Y j with
Yj/ = 1.
The created system should provide effective processing of the production program chosen. Such efficiency is convenient to estimate by the profit (without the account of the taxes) received during in the given interval of time T from processing of the production program. The size of this profit should not be
The meaning M
below of the given size D. Therefore the following restriction is included in the model
j~1
for the acquiring equipment are
Some meaning
Y j may be more zero in conse-
quence of account of the model. The appropriate
L+L K;
2, 2, nl1
j
supposed equal zero at the first iteration of calculation of the model. Then the model is calculated.
k j
(cj
-
c/) ~ i5,
meanings
(7)
k~l
recalculation of the model is made. Thus the process of increase of dimension of the model always will
where c j is the price of the
i -th workpiece (transfer
c/
is the cost of manufac-
price of the enterprise),
M j are increased on the size Y j and the
result in zero meanings Yj (Khobotov, 1999a). The quantity of places in buffer storage for the again got equipment is determined with use of the same correlation as in (Khobotov, 1999a; Khobotov, 1999b).
turing of i -th workpiece on the k -th technological route with the cost of materials. The acquirement cost of the additional equipment,
750
The simplest variant of the criterion function maximized in this model has a kind L+L
J=a l
m M k Ln;Leik(Ci -ci )-a LLyj,b j K,
J
2
;:1
k:l
j=l /:1
m
-a3 LYjbj ,
(9)
j:l
where a; IS a weight coefficient (a i
;:::
0, i =
1,2,3), b j is a cost of service of the j -th equipment with amortization allocation. The account of model (1) - (9) with constant parameters j / is boiled down to the decision of linear
t
programming task with a part of integer variable (Khobotov,I999b). The quantity and types of the equipment, quantity of transport means and size of buffer storage which it is necessary to include in the modernizing system, quantity of complete sets of tools and technological rigging, the most favorable technological route for processing of each workpiece and the most favorable production program for the system may be determined with the help of the given model. Unfortunately it is impossible to consider the equations and correlation for determination of the quantity of transport means, the size of buffer storage and quantity of necessary complete sets of tools and technological rigging. The size of the paper is limited. Then the schedule of processing of this program on the equipment of the modernizing system is constructed with use of simulation methods. If the time of processing of such program will appear more given time T , that the meanings of auxiliary parameters [,/
are in-
creased by the certain rules. These parameters are equal to zero on the flISt iteration of joint work of the optimization and simulation models. Then the recalculation of the optimization model is made with new meanings [,/ . Such process converges to the decision enough quickly, if it exists. The process of construction of the schedule with use of simulation methods allows also to check up a work of the received circuit of the modernized system. It will be noted that many good scheduling algo-
rithms are developed now. These algorithms allow to construct good schedules for processing of workpieces. But the algorithms work good and quickly when it is known the all workpiece included in the production program of the system and the processing time of each workpiece on the all using equipment on the appropriate technological rout, and the types and quantity of the workpiece processed on the each equipment included into the system. The optimization model in the optimization-simulation approach allows to determin the initial data and parameters un-
751
known for using of scheduling algorithms. Usually these data and parameters are demanded to choose in accordance with one or several criteria and with complex restrictions on an available domain of parameters change. The choice of these data and parameters with help of traditional simulation methods causes the great difficulties. The simulation methods allow to construct a good schedule for processing of the production program in that approach when the all data and parameters demanding for use of scheduling algorithms are know. Therefore the the optimization-simulation approach allows to solve such design and reengineering problems those cannot be solved with use of traditional simulation methods. It is possible to determine with use of model (1) - (9) technical and technological appearance of the system after its modernization with allocation of the certain financial means and with the forecasts about needs of the market for various production, its prices, volumes of consumption, cost of raw material and service of the equipment. Besides the given model allows to estimate production opportunities of the system, its productivity on issue of various workpieces. Such estimations are extremely useful for strategic planning of developments of manufacture and enterprise.
REFERENCES Khobotov, E.N. (l996a). Optimization-Simulation Approach to Modeling of Complex Manfacturing Systems. I. Journal of Computer and System Science (International Journal of Optimization and Control). No 1, .pp. 105-111. Khobotov, E.N. (1996b). Optimization-Simulation Approach to Modeling of Complex Manfacturing Systems. H. Journal of Compute rand System Science (International Journal of Optimization and Control). No 2, .pp. 273-279. Khobotov, E.N. (1996c). Optimization-Simulation Approach to Planning and Choice of Machining Routes. Part I. Automation and Remote Control. Vol. 57, No 1, pp. 98-103 Khobotov, E.N. (1996d). Optimization-Simulation Approach to Planning and Choice of Machining Routes. Part H. Automation and Remote Control. Vol. 57, No 2, pp..272-277. Khobotov, E.N. (I999a). Application of the Otimization-Simulation Approach to Simulation and Design of Production Systems. Part I. Automation and Remote Control. Vol. 60, No 8. pp. 11911200. Khobotov, E.N. (l999b). Application of the Optimization-Simulation Approach to Simulation and Design of Production Systems. Part H. Automation and Remote COlltrol. Vol. 60, No 9. pp. 1341-1346.
MODELS AND METHODS FOR MANUFACTURING SYSTEMS REENGINEERING
Khobotov E.N.
Ministry of Education
Abstract: The problems of modeling of modernization and reengineering processes for manufacturing systems and complexes are considered. It is offered to use the optimization-simulation approach for these purposes. The joint work of optimization and simulation models are used in this approach. The approach allows to solve such design and reengineering problems which cannot be solved with use of the traditional simulation methods. Copyright © 2000 IFAC Keywords: optimization, simulation, design. model, equipment, production, linear programming, manufacturing systems, scheduling algorithms
determine the most favorable appearance for the manufacturing system. It is offered to use for accounts of such models the algorithms constructed on the basis of the optimization-simulation approach. The computing circuit of this approach are described in the papers (Khobotov, 1996a, Khobotov, 1996b, Khobotov, 1996c, Khobotov, 1996d).
1. INfRODUCTION Now the problems of manufacturing systems modernization cause the great interest side by side with problems of designing and management of such systems. These problems arise with mastering of new production and with expansion and perfection of already working manufacturing systems for a maintenance of competitiveness of the making production. It is impossible to create a modem effective working manufacture without the successful decision of such problems. The life cycle of the making production is reduced now. Therefore it should be modernized of the making production or mastered of a new production. That results in turn to a necessity more often to modernize a manufacture used. Besides the same problems arise also when it is demanded to realize the conversion of the defensive enterprises.
2. THE PROBLEM DESCRIPTION It is convenient to consider of static and dynamic statements in the modernization and reengineering problems of manufacturing systems. Let's consider these statements in more detail. It is required in the static statement of these problems to choose the most favorable manufacturing program for the modernized system and to determine the equipment of system which should be replaced, and to choose the new equipment which should be got for the modernizing system. The following information must be known for that task: - the average sizes of workpieces batches from the given workpieces set and prices of the each type workpiece; - the set of technological routes which can be used for processing of the each type workpiece and the
The use of traditional simulation methods for decision of these problems causes great difficulties especially when it is required to determine the most favorable strategy of a replacement of the equipment for the manufacture modernized in view of financial opportunities of the enterprise and waiting profit after the modernization. The principles of creation of static models are considered in the given paper. These models allow to
747
- the transition to the next iteration of modeling is enough complex and can not result in improvement of the characteristics of design systems; - there are complex restrictions on area of change of choosing parameters with design of most of manufacturing systems. Not always it is possible to construct a system with parameters which will be in allowable area; - the simulation methods allow to receive the information about absence of the decision of a designing task not always; - it is difficult to choose the structure of projected systems according to one or several criteria with the help of simulation methods; - it is difficult to interpret the results of simulation of manufacturing systems.
cost of its processing on the appropriate technological route; - the maximal financial means available for modernization of the manufacturing system; - the minimally allowable profit from processing of the chosen production program during in the given time interval; - the equipment types and quantity of the equipment of each type which was in the system before modernization; - the equipment types available for modernization of the system; - the processing time of each type workpiece on all routes of its processing on the all using equipment; the arrange time of the using equipment for processing of the each type workpiece on the all using technological route.
The optimization-simulation approach is based on the joint use of the optimization and simulation models. That approach allows to get rid of above mentioned lacks of simulation methods and to inherit the following advantages of optimization models: - the opportunity to detennine the decision of design tasks quickly if it exists and to receive the information about absence of the decision; - an opportunity to choose the circuits of designing systems according to one or several criteria; - an opportunity to "co-ordinate" a plenty of the initial data and parameters of various nature and to investigate a structure of the system with change of the initial data and criteria.
The production program and equipment replaced and new for the system should be chosen so as to maximize the profit received from the processing of the chosen production program and to minimize expenses for service of the system with the given restrictions for value of the purchased equipment. The decision of a static task allows to determine optimum appearance of the system after its modernization with the given financial restrictions on purchase of the equipment. However the process of modernization of the system in time is not examined in such statement. It is required in the dynamic tasks to determine the quantity and types of the equipment which should be replaced and get for the system and the types of workpieces for the production program of the system modernized, and to detennine the necessary investments for the modernization of the system. All these sizes are required to detennined for each stage of the modernization. The dynamic modernization tasks will not be considered in the given paper.
4.
THE DESCRIPTION OF THE STATIC MODEL
Let's consider the optimization model using in the optimization-simulation approach for the decision of the static modernization task described above. The balance restrictions on use time of the available equipment of the system look like:
3. THE OPTIMIZATION-SIMULATION APPROACH
(1)
The simulation methods are widely used for modeling of manufacturing systems now. The opportunity of experiments realization with models of systems researched under various conditions of work causes their wide application for designing of manufacturing systems and does them practically irreplaceable for a check of serviceability of the systems. However simulation methods have a number of lacks. These lacks complicate their use with designing of complex systems and especially with their modernization.
jEll'
l=l, ...,M j
,
where L is the set of the workpieces types made already, L is the set of the workpieces types which can be made in the system after its modernization in addition, K j is the set of the technological routes for processing of the i -th workpiece, n j is the average size of the i -th workpieces batch (batch of such size is supposed to produce in the system after its modernization), ~ k is the processing time of the i -th
It is necessary to allocate among these lacks the following: - the significant time is required for the decision of majority of tasks of manufacturing systems design with use of simulation methods;
workpiece on the k -th technological route on the j th equipment, 'l' i~ is the arrange time of the j -th
748
equipment for processing of the i -th workpiece on
an interval of time T, f.J. jo is the parameter desig-
the k -th technological route, {jij~
is a variable
nating a load of the additional equipment of the j-th
is a auxiliary parameter, V jl is
type, J 2 is the set of the additional equipment types. Such types were not included into the system earlier, but can be used for modernization of the system. The acquiring equipment can be the same types as the system had before modernization. It may be happened with an expansion of the manufacture of the workpieces made already. Usually the value f.J. jo for
(0 ~ ii;j~ ~ 1),
tu
the resource of using time for the I -th equipment of the j -th type during in the interval of time T , J 1 is the set of the equipment types included into the system before its modernization; M j is the quantity of equipment units of the j -th type, variable type (0,1),
Yjl
is integer
the well made schedule of workpieces processing is equal f.J.jo ::: 0.55 - 0.85.
8;; is the integer variable type
(0,1). The following restrictions should be carried out -k
The following restrictions are carried out for variable
for the variable 0ijl
-k e jjl -k
-k
ejjl-eijl~o,
1=1, ...,M j
i = 1, ...,L, j where
J/
E
(i
j E J1
UJ
2 '
1= 1, ...,M j )
(2)
,
J/, k = 1,..., K
(4)
j ,
is the set of the using equipment types for
manufacturing of the i -th workpiece on the k-th technological route. where The size
= 1,..., L + L- ,
Yjl
o
k i
is equal 1 if the I -th equipment of the
j -th type remains in the system after modernization
Ojk is the integer variable type (0,1). The size
is equal 1 if the i -th workpieces is processed on
the k -th technological route in the system after the modernization, and zero otherwise.
and zero otherwise. The size {jij~ shows the part of the i -th workpieces batch processed on the k-th technological route on the I -th equipment of the
Each batch of the workpieces can be made only on anyone technological route chosen from the set of possible routes. Therefore the following restrictions are included in the model
j -th type. The size ifj~ is equal 1 if the I -th equipment of the j -th type is used for processing of the
K
i -th workpieces on the k -th technological route and
!Ojk ~1, i=1, ... ,L+L,
zero otherwise.
(5)
k=1
The balance restrictions on time of use of the acquiring equipment have the same kind. However the size M j is not known in this case. Therefore the all meaning M
j
Let's consider the substantial sense of these restrictions.
are believed equal zero (M j = 0)
The left part of the restriction (1) represents the sum of three types addendums. The auxiliary parameters
(Khobotov, 1999a) on the first iteration of the model account and the balance restrictions on the time of the additional equipment are entered into the model
~I have physical sense of an idle time of the equip-
ment I of the j -th type. The addendums of the kind
e-
k ijln/ijk
(3)
j=
0,1,2,3..,),
(0 ~ (jjj~ ~ 1 with I
= 0),
ii;;
is
a
a part
ment I of the j -th type and the sum of these addendums designates the common time of processing on the given equipment. The addendums of the kind
if~ 'l'~
ditional equipment acquired for the system moderni(Y
0f
ii;j~ n j of the i -th workpieces batch on the equip-
where Y j is the units quantity of the j -th type adzation
d' .. eSlgnate the processmg time
designate the arrange time of the equipment I
of the j -th type for the subsequent processing of the
variable
i -th workpieces on the k -th technological route, and their sum designates the common arrange time of the equipment I of the j -th type necessary for processing of the production program chosen. Thus the
VjO is the time resource
of use of the j -th type additional equipment during
749
left part of this inequality designates time of processing, arrange and idle of the equipment I of the jth type and cannot exceed the possible temporary resource of work of this equipment
Yjl Vj/
submitted
in the right part of the inequality (1). The equipment owes arranged, as a rule, for processing of the other types of workpieces even in that case, when only one the workpiece will be processed
iJ
on it. The size
tools and technological rigging should not exceed financial means D allocated on modernization of the system,. However the means received from sale of the unnecessary equipment can be used for the modernization of the system. Therefore the following restriction is included in the model MJ
P+C+P-
2, 2,d /(l-Yj/)j
jEll
I~I
can not be equal 0 in the restric-
j;
(8)
-k
tions (1) when 8ij/n j more than O. Therefore the rewhere P is the cost of the equipment acquired for
strictions (2) are included in the model.
modernization of the system, C is the cost of designing of technological rigging and tools for the workpiece mastered again and modernized and for perfection of manufacturing technology of the work-
The substantial sense of restrictions (3) is similar to substantial sense of restrictions (1). The necessity of inclusion in the model of the restrictions (4) is caused by the next demand. The quantity of workpieces of each type processed "parallel" on the same type equipment must be equal in the sum to the size of the appropriate batch of workpieces.
pieces made already, P is the expense for manufacturing of necessary quantity of complete sets of technological rigging and tools, d jl is the price of the possible sale of the I -th equipment of j -th type
The quantity of the additional equipment of the j -th
entered into the system before its modernization,
type Y j can be more than zero only in that case
Yjl
when all
= I (l
= 1,...,M j ,).
d m + 1 is the price of the possible sale of the transport
Therefore the
means.
following restrictions are entered in the model for performance of this condition
The correlation allowing to determine sizes P, C, and P in view of principles of Group Technology are similar to correlation used in (Khobotov, 1999a; Khobotov, 1999b) for determination of analogous sizes in design problems, and consequently here are not considered.
(6)
where
f3
is an enough large constant. But the choice
f3
of the size
The balance restrictions on the accessible time of use of each equipment unit of the system should be included in the model for determination of necessary quantity of complete sets of the technological rigging and tools. The process of calculations of the model must be organized according to the following rule (Khobotov, 1999a; Khobotov, 1999b).
must ensure the reception necessary
meaning for Y j with
Yj/ = 1.
The created system should provide effective processing of the production program chosen. Such efficiency is convenient to estimate by the profit (without the account of the taxes) received during in the given interval of time T from processing of the production program. The size of this profit should not be
The meaning M
below of the given size D. Therefore the following restriction is included in the model
j~1
for the acquiring equipment are
Some meaning
Y j may be more zero in conse-
quence of account of the model. The appropriate
L+L K;
2, 2, nl1
j
supposed equal zero at the first iteration of calculation of the model. Then the model is calculated.
k j
(cj
-
c/) ~ i5,
meanings
(7)
k~l
recalculation of the model is made. Thus the process of increase of dimension of the model always will
where c j is the price of the
i -th workpiece (transfer
c/
is the cost of manufac-
price of the enterprise),
M j are increased on the size Y j and the
result in zero meanings Yj (Khobotov, 1999a). The quantity of places in buffer storage for the again got equipment is determined with use of the same correlation as in (Khobotov, 1999a; Khobotov, 1999b).
turing of i -th workpiece on the k -th technological route with the cost of materials. The acquirement cost of the additional equipment,
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The simplest variant of the criterion function maximized in this model has a kind L+L
J=a l
m M k Ln;Leik(Ci -ci )-a LLyj,b j K,
J
2
;:1
k:l
j=l /:1
m
-a3 LYjbj ,
(9)
j:l
where a; IS a weight coefficient (a i
;:::
0, i =
1,2,3), b j is a cost of service of the j -th equipment with amortization allocation. The account of model (1) - (9) with constant parameters j / is boiled down to the decision of linear
t
programming task with a part of integer variable (Khobotov,I999b). The quantity and types of the equipment, quantity of transport means and size of buffer storage which it is necessary to include in the modernizing system, quantity of complete sets of tools and technological rigging, the most favorable technological route for processing of each workpiece and the most favorable production program for the system may be determined with the help of the given model. Unfortunately it is impossible to consider the equations and correlation for determination of the quantity of transport means, the size of buffer storage and quantity of necessary complete sets of tools and technological rigging. The size of the paper is limited. Then the schedule of processing of this program on the equipment of the modernizing system is constructed with use of simulation methods. If the time of processing of such program will appear more given time T , that the meanings of auxiliary parameters [,/
are in-
creased by the certain rules. These parameters are equal to zero on the flISt iteration of joint work of the optimization and simulation models. Then the recalculation of the optimization model is made with new meanings [,/ . Such process converges to the decision enough quickly, if it exists. The process of construction of the schedule with use of simulation methods allows also to check up a work of the received circuit of the modernized system. It will be noted that many good scheduling algo-
rithms are developed now. These algorithms allow to construct good schedules for processing of workpieces. But the algorithms work good and quickly when it is known the all workpiece included in the production program of the system and the processing time of each workpiece on the all using equipment on the appropriate technological rout, and the types and quantity of the workpiece processed on the each equipment included into the system. The optimization model in the optimization-simulation approach allows to determin the initial data and parameters un-
751
known for using of scheduling algorithms. Usually these data and parameters are demanded to choose in accordance with one or several criteria and with complex restrictions on an available domain of parameters change. The choice of these data and parameters with help of traditional simulation methods causes the great difficulties. The simulation methods allow to construct a good schedule for processing of the production program in that approach when the all data and parameters demanding for use of scheduling algorithms are know. Therefore the the optimization-simulation approach allows to solve such design and reengineering problems those cannot be solved with use of traditional simulation methods. It is possible to determine with use of model (1) - (9) technical and technological appearance of the system after its modernization with allocation of the certain financial means and with the forecasts about needs of the market for various production, its prices, volumes of consumption, cost of raw material and service of the equipment. Besides the given model allows to estimate production opportunities of the system, its productivity on issue of various workpieces. Such estimations are extremely useful for strategic planning of developments of manufacture and enterprise.
REFERENCES Khobotov, E.N. (l996a). Optimization-Simulation Approach to Modeling of Complex Manfacturing Systems. I. Journal of Computer and System Science (International Journal of Optimization and Control). No 1, .pp. 105-111. Khobotov, E.N. (1996b). Optimization-Simulation Approach to Modeling of Complex Manfacturing Systems. H. Journal of Compute rand System Science (International Journal of Optimization and Control). No 2, .pp. 273-279. Khobotov, E.N. (1996c). Optimization-Simulation Approach to Planning and Choice of Machining Routes. Part I. Automation and Remote Control. Vol. 57, No 1, pp. 98-103 Khobotov, E.N. (1996d). Optimization-Simulation Approach to Planning and Choice of Machining Routes. Part H. Automation and Remote Control. Vol. 57, No 2, pp..272-277. Khobotov, E.N. (I999a). Application of the Otimization-Simulation Approach to Simulation and Design of Production Systems. Part I. Automation and Remote Control. Vol. 60, No 8. pp. 11911200. Khobotov, E.N. (l999b). Application of the Optimization-Simulation Approach to Simulation and Design of Production Systems. Part H. Automation and Remote COlltrol. Vol. 60, No 9. pp. 1341-1346.