The model of dynamic managment system of manufactoring

Transkrypt

THE MODEL OF DYNAMIC MANAGMENT SYSTEM OF MANUFACTORING
COMPANY ON THE BASIS OF THE PROBABLISTIC MODEL
TOMASZ WOŁOWIEC, JANUSZ SOBOē
Summary
In the paper a design of the probabilistic model of reserves is discussed. The objective was an elaboration of the optimal strategy of materials reserves management
in the series manufacturing. The authors discuss the probabilistic model of reserves
aiming at the elaboration of the best management of primary material in industrial
company. The model has been verified as far as it was feasible using numerical data
concerning various wood products including furniture of series production. The presented probabilistic model of reserves allows the formation12 of optimum strategy of
the (R, Z) type of primary materials management with due consideration to profits
coming from low cost components in working and furniture industrial company. This
paper also describes the model of dynamic management system of manufacturing
company and presents arguments for changing processes inside a company in the
light of change in the stream of incoming orders for finished products. The results of
computer simulation of designed model, show some dynamic characteristics across
divisions of manufacturing company during production process. In the model of production facility, different departments were taken into account. The departments are
involved in activities related to flow of information, orders, materials and prefabricates, production processes as well as finished products storage and shipment
Keywords: model of dynamic management system
1. Introduction
Cleverness and effective management of the entire manufacturing company, requires a system
capable of performing dynamic analysis of managing operation. This activity is determined by
a need to adjust operation of facility to constantly changing demands of market34. The analysis of
information flow in manufacturing facility, and subsequent flow of decisions, materials and
1
Jagas, J. (2004): Produktywno pracy. Opole: Uniwersytet Opolski. ISBN 978-83-7641-056-2.
Farlow, S.J. - Haggard, G.M. (1987): Applied mathematics for Management, Life Science and Social Sciences. New York:
RANDOM HOUSE. ISBN 0-397-35160-6.
3
4
2
254
Tomasz Wołowiec, Janusz Sobo
The model of dynamic managment system of manufactoring company
on the basis of the probablistic model
products is one of the most important aspects of entrepreneurial activity56. The management
method presented in this paper is used to expose weak links in organisation structure that influence
efficiency of the entire manufacturing company789. The weak links can be also identified on lower
level of organisational structure, for example, in the process of product manufacturing. On such
level, inputs may include consumable tooling, machining fluids, scrap and chips headed for recycling, etc.101112. The analysis takes into account the interactions between streams of accepted
orders, materials, production orders, production processes, finished products, money and personnel
within a company. Instrument for simulation of the interactions is model that reflects the specific
characteristics of entire system. The goal of this study was to build the dynamic model of manufacturing company managing operation, and analyze the reasons for changing processes inside
a company due to changes in the stream of incoming orders for finished products. The departments
taken into account in the model are involved in flow of information, orders, materials and prefabricates, production as well as finished products storage and shipment.
2. Description of the model
The analogue symbolic diagram of model (Fig. 1) represents general structure of manufacturing company, and reflects principle managerial activities. In the symbolic description of
production facility model the following departments were included: orders department (ZF),
supply department (ZM), store of materials (MM), production department (P) and stock of finished products (MP). The assumptions of company operations are as follows:
The volume of production should be high enough to maintain stock of finished products at the
level of K (i.e. three) times higher than the average of orders (ZS) for products. That demand is
achieved by shift from production orders (ZP) to production preparation. The production orders
(ZP), as amount, can be represented by the following equation:
(1)
ZP = S1+ ZS
S1 – auxiliary variable representing the difference between required and actual levels of
stock of finished products, ZS – average amount of received orders.
5
Hilier, F.S. - Lieberman, G.J. (1998): Introduction to stochastic models in operations research. New York: McGraw-Hill,
Inc. ISBN 0-03-894995-7.
6
Wołowiec T.: ZOZ a wybrane aspekty zarzdzania zapasami w warunkach sezonowoci sprzeday usług medycznych.
„Antidotum zarzdzanie w opiece zdrowotnej 2002 nr 10. ISSN 1230-0969, s. 13–30.
7
Hilier, F.S. - Lieberman, G.J. (1997): Introduction to operations research. New York: McGraw-Hill, Inc. ISBN 0-07028908-5.
8
Wołowiec T. Suseł A.: Conception of the optimal and safe strategy of material reserves management on the basis of the
probabilistic model. /in/ JASEK R. (red.) Internet, Competititiveness and Organizational Security. lin: Tomas Bata
University in Zlin 2010. ISBN: 978-83-61645-16-0. s. 467–472.
9
ukowski, P. (2009): Managing Model of the Storing Material in an Economic Organization, Foundry Journal - Science
and Practice, vol. 59, No. 7-8, p. 414–419.
10
probabilistic model. /in/ JASEK R. (red.) Internet, Competititiveness and Organizational Security. lin: Tomas Bata
11
Wołowiec T. Suseł A. Uwarunkowania płodnoci imigrantek oraz nie-imigrantek w USA, Acta Universitatis Lodziensis,
„Folia Oeconomica”, 2009, nr 231. ISSN 0208-6018. s. 447–467.
12
ukowski, P. (2009): Koncepcja optymalnej strategii zarzdzania zapasami materiałów w przedsibiorstwie przemysłowym, (in) Uwarunkowania rozwoju systemów zarzdzania, (ed.). H. Hawanie, W. Iwaszkiewicz. Bielsko-Biała:
Akademia Humanistyczno-Ekonomiczna. ISBN 978-83-9332397-0-3.
255
Studies & Proceedings of Polish Association for Knowledge Management
No. 41, 2011
The needed level of product is the average volume of orders (ZS) and multiple by the
amplification coefficient K. The coefficient K is a number of weeks during which the required level of stock of finished products would be sufficient for shipment of products with
speed equal to the average speed of received orders. Auxiliary variable S1 is defined by the
following formula:
(2)
S1 = K ⋅ ZS – MP
K – amplification coefficient, ZS – average amount of received orders,
MP – actual amount (level) of stock of finished products.
1) In case when the level of store of materials (MM) falling below the level defined (S2) by
amount of received orders (ZF), incoming orders should be temporarily stopped (ZZF).
If the level of store of materials (MM) is below (S3) than defined minimum value (Min),
transfer of production orders (ZR) to production department (P) lines should be stopped as
well.
S3 = MM – Min
(3)
2) The stream of amount of orders for purchase of materials (ZZM) shifted to supply department
equals the stream of amount of orders for finished products (R) in manufacturing company.
Information processing ability of office are also taken into account.
This ability is defined as the average times of transition for: averaging of orders – TZS, supply –
TZM, production – TP, distribution – TZF. Then, the condition 1 – TMP is met.
P(x)
S2
Delivery orders
materials and
prefabricated
elements
ZZF
ZZF
R
2
Orders
portfolio
ZF
3
ZZM
11
Supply
ZM
department 13
R
Averaging ZS
of orders
5
TZS
2
TZF
K
Market of
manufaktures
products
S1
4
4
Z 1(T)
Min
T
Z
M
1
S3
Create of
production
orders
TMP
P(x)
Finished
products
stock
orders
ZR
WP
T
P
8
x
ZR
MP
10
information
materials
P
9
ZP
ZP
7
Production
department
12
Materi als MM
store
14
ZMP
Archive of
executive
an orders
MZM
ZZF = ZR
6
6
Figure 1. Analogue-symbolic model of manufacturing company
Source: Own work.
256
3. Building of the management model
Two streams of information come from market through sales department (Fig. 1). The first
information carries orders about the specific types of products, whereas the second one about the
volume of these orders.
In the first decision making point, R, amount of stream of incoming orders for finished products is described. The orders are coming in batches. This amount is assumed to be represented by
the step function and shown in the equation:
(4)
R = R0 + Z · 1 (T)
The second decision making point can be represented by the function P*:
1, if MM ≥ ZF
P* = 0, if MM < ZF
(5)
hence:
ZZF = P* · R
(6)
The third decision making point, ZF, presents amount of received orders for products. The
amount of orders portfolio ZF can be described as:
ZF = ZF0 + DT (ZZF – ZMP)
(7)
The fourth decision making point, ZMP, regulates:
- amount of products taken from production taken from stock of finished products (MP)
- amount of completed orders transmitted from orders portfolio to archive.
The fourth decision making point can be represented by the equation:
ZMP = ZF/TZF
(8)
The fifth decision making point, ZS, describes the average value of incoming orders stream,
R, (with influence of the second decision station, ZZF). The fifth decision making point is represented by the equation:
(9)
ZS = ZS0 + DT (ZZF – ZS0)
The sixth decision making point, ZP, determines (S1):
- amount of orders transmitted to production,
- amount of materials transmitted to production.
The amount of production orders ZP is described by the equation:
ZP = ZS + S1/TP
(10)
The process of transmission of orders to production is stopped when the level of stock of materials is minimal. This decision is taken at the seventh decision making point, ZP. It makes certain
of fulfiling the assumption 2. This point can be presented by the function F*:
1, if S 3 ≥ 0
F* = 0, if S 3 < 0
and
(11)
257
No. 41, 2011
ZR = F* · ZP
(12)
The eighth decision making point, WP, defines time for production. The time of transmission,
P, is considered as permanent and accumulating element of manufacturing company abilities
which seems to be equaled amount of production orders. The influence of the eighth decision
making point can be presented by the equation:
WP = P/TP
(13)
The ninth decision making point defines current amount of production orders portfolio and is
defined as:
(14)
P = P0 + DT (ZR – WP)
The tenth decision making point, MP, defines the level of finished products. Its input is the
stream of production WP, and output is the stream of finished products delivering a market. The
difference between these two streams remains as stock of finished products. The influence of the
tenth decision making point:
MP = MP0 + DT (WP – ZMP)
(15)
The eleventh decision making point, ZZM, defines the value of stream of orders for purchase
of materials through supply department. In accordance with the condition 3, it equals the stream
of orders for products. It is expressed by the equation:
ZZM = R
(16)
The twelfth decision making point, MZM, presents the stream of materials transfering to materials store in a supply department. The amount of this stream is regulated based on the
information about orders number accumulated in the supply department. This point can be presented as the equation:
MZM = ZM/TZM
(17)
The thirteenth decision making point, ZM, accumulates the difference between incoming
stream of orders for purchase of materials, ZZM, and the stream of completed orders. This is equal
to the stream of purchased materials, MZM, transfering to store of materials through the supply
department.
(18)
ZM = ZM0+ DT (ZZM – MZM)
The fourteenth decision making point, MM, gathers the difference between the stream of purchased materials, MZM, and the stream of their transmission to production ZP. The influence of
this decision point presents the equation:
MM = MM0 + DT (MZM – ZP)
(19)
where:
R – stream of orders for products, R0 – initial amount of orders, Z – amount of incoming orders, ZF – new amount of received orders portfolio, ZF0 – former amount of incoming orders, ZS
– average amount of incoming orders, ZS0 – former amount of orders, P – amount of production
orders, P0 – former value of production orders portfolio, MM – level of store of materials, MM0 –
former amount (level) of store of materials, ZM – amount of orders of the supply department, ZM0
– former amount of orders of the supply department, MP – finished products stock, MP0 – former
amount (level) of stock of finished products, ZZF – amount of incoming orders, ZMP – amount of
completed orders, ZR – transmission of orders to production, WP – transmission of orders from
production equal to production value – amount of production stream, ZZM – stream of orders for
258
purchase of materials, MZM – stream of materials, DT – time period, TZF – orders realisation
lead time (assumed to be a constant), TP – time of transmission of company production abilities,
TZM – time of materials purchase.
4. Results of simulation
The simulation results of the above described two cases are illustrated in Fig. 2 and Fig. 3.
The figures show that with the increase of product orders to the level of 20 units/week, disruptions
in the company operation appear. That results in the fluctuations in production level and as well as
in the stream of materials required for production. These fluctuations cease at about 16th weeks
after the increase of orders for products.
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ϭϬϬ ϮϬϬ
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Figure 2. Simulation results for level of materials in store while increase of orders 40 units/week
and initial level of materials 270 units
Source: Own studies.
When the increase of product orders to the level of 40 units/week was simulated, disruptions
in the company operation can be observed even in 25th week, but the amplitude of fluctuations is
within 10% of average value as well.
This graph shows also the reason of disruptions in the company operation at very long period
of time. The intersection of lines MM and ZF (in accordance with the assumption 2) is the graphical presentation of periodic suspending of acceptance of orders. This effect is proportional to
market demand fluctuations and causes additional disruptions in the company operation1314.
13
ukowski, P. (2009): Managing Model of the Storing Material in an Economic Organization, Foundry Journal - Science
and Practice, vol. 59, No. 7-8, p. 414-419.
14
[9] ukowski, P. (2009): Koncepcja optymalnej strategii zarzdzania zapasami materiałów w przedsibiorstwie przemysłowym, (in) Uwarunkowania rozwoju systemów zarzdzania, (ed.). H. Hawanie, W. Iwaszkiewicz. Bielsko-Biała:
259
No. 41, 2011
5. Conclusions
The investigation of the dynamic model of manufacturing company management was conducted using data from the study of manufacturing company. The result of simulation show that,
with the increase of product orders, disruptions in a company appear. The disruptions result in the
fluctuations in the level of production and stream of materials and prefabricates required for
production. These fluctuations cease after various periods of time. The length of periods of time
depends on the increase of orders and operating settings that are internal to the operation of manufacturing facility.
6. Case model – introduction
In order to ensure the production continuity, the reserves of different kinds of based material
are generated and maintained. In the furniture industry, wide range and community of decisions, as
well as, economic influence of wrong decisions concerning material reserves are of such importance, that they prove a need of overworking an optimal strategy of based material reserves
management on the basis of the probabilistic model with an application of computer techniques15.
Z
Z
Z
L
Cycle 1
L
Cycle 2
Time
Figure 3. Change in the level of material reserves in a store: Z – value of order of special kind of
material, R – value of safety reserve, L – period of delivery
Source: Base on [1].
The level of wood material reserves in a store of furniture industry's differs during time, depending on input and output of these materials. Input of these materials depends on the amount of
supplied material and time between deliveries, whereas output depends on the level of production
consumption (Fig. 1). A period of time between subsequent material deliveries (delivery cycle)
fluctuates, as well as production consumption of different kinds of materials. The problem of
based material management could be a source of opposite tendencies in a factory. There are groups
of different factors (technical, organizational, economical, financial etc.) which influence high or
low levels of material reserves. High levels of material reserves are concerned with the great costs
15
260
of storage, but low levels influence costs as well, because of the lack of production consumption
ensuing (the continuity not ensured). The level of based material reserves is maintained on certain
rigidly determined levels. Keeping of high or low levels of materials in a store is a source of
additional costs1617. The main objective of reserves management optimization should focus on
analysis of costs of these materials, while criterion of optimization should be the minimization of
value of expected medium costs of buying, storing and lack of production consumption ensuring
of based materials. As a result of main (criterion) function optimization there is to ensure the levels
of based materials needed for the regular production program realization, with the lowest level of
costs181920.
7. Constructing of the probabilistic model
In order to construct the probabilistic model of reserves management such symbols are introduced:
D – mean production consumption for special kind of material in certain time (e.g. medium
years consumption),
Z
– value of order of special kind of material,
D/Z – mean number of orders of special kind of material in certain time (e.g. during one year),
R – value of safety reserve (for special kind of material),
K – constant costs of orders,
h
– single cost of storing,
p
– single cost in case of lack of needed level of reserve for special kind of material in a store,
L
– period (time) of delivery (time for order realisation),
v
– production consumption for special kind of material in period of delivery,
E(v) – wanted value of production consumption for special kind of material in period of delivery,
g(v) – probability distribution of production consumption for special kind of material in period
of delivery (function, of random variable density probability),
b
– mean level of lacking stores in period of delivery,
B – mean level of lacking stores for special material in certain investigation time,
E(B) – expected value of mean level of lacking stores for special material in certain time,
A – uniform distribution – upper limit of function,
E
– operator of expected value,
F(Z,R)– main function of model with decisive variables Z and R.
16
Farlow, S.J. - Haggard, G.M. (1987): Applied mathematics for Management, Life Science and Social Sciences. New
York: Random House. ISBN 0-397-35160-6.
17
Hilier, F.S. - Lieberman, G.J. (1998): Introduction to stochastic models in operations research. New York: McGrawHill, Inc. ISBN 0-03-894995-7.
18
Wołowiec T.: ZOZ a wybrane aspekty zarzdzania zapasami w warunkach sezonowoci sprzeday usług medycznych.
„Antidotum zarzdzanie w opiece zdrowotnej 2002 nr 10. ISSN 1230-0969, s. 13–30.
19
probabilistic model. /in/ Jasek R. (red.) Internet, Competititiveness and Organizational Security. lin: Tomas Bata
20
Wołowiec T. Suseł A. Uwarunkowania płodnoci imigrantek oraz nie-imigrantek w USA, Acta Universitatis Lodziensis,
„Folia Oeconomica”, 2009, nr 231. ISSN 0208-6018. s. 447–467.
261
No. 41, 2011
It should be noted, that by the end of delivery cycle expected level of reserve of certain
based material in a store is R–E(v) but when a particular order is completed (on the beginning of
cycle) such level is Z+R–E(v). Expected medium level of reserves for certain kind material in the
cycle (if v R) is equal to:
(Z
+ R − E
(v )) + (R
− E
(v ))
2
If,
calculated:
v > R
Z
= 2
+ R − E
(v )
(1)
, then medium level of lacking reserve of certain based material (b) in a store is
∞
b =
(v
− R
) g (v ) dv
(2)
R
Expected in a certain time (e.g. during one year) medium level of lacking stocks special
based material (B) in a store is obtained by the equation:
(B ) =
D
Z
(3)
Having calculated the certain levels of special material reserves, we can calculate appropriate costs, multiplicating appropriate single costs h and p by the expressions (1) and (3).
E
b ⋅
Thus, the main function of optimisation in the probabilistic model of material reserve management at a certain time can be expressed by the formula:
E
[F (Z
, R
)] =
K
D
Z
Z
+ h 2
+ R − E
(v )
+
p
D
Z
b →
min
(4)
The first component of sum represents mean cost of constants, the second one is mean cost of
storing reserves, whereas the third component means cost in case of lack kind of certain reserve.
Changes in the level of quantities of basic values (Z and R ) in the main function will be minimal
when Z and R are optimal2122. Then, the dependencies should determined from which optimal
values Zo and Ro could be calculated. It is necessary, the first partial derivatives ofthe function (1)
in a comparison with Z and R values will be zero.
21
Hilier, F.S. - Lieberman, G.J. (1998): Introduction to stochastic models in operations research. New York: McGrawHill, Inc. ISBN 0-03-894995-7.
22
Hilier, F.S. - Lieberman, G.J. (1997): Introduction to operations research. New York: McGraw-Hill, Inc. ISBN 0-07028908-5.
262
R
E
R
R
R
R
q u
a t i o n
5
1
E
q u
a t i o n
6
2
3
o
o
Z
=
1
Z
Z
r
Z3
2
Z
Z
o
m
Z
w
Figure 4. Scheme of iteration researches Z0 and R0
Optimal values of order and store level R expressions could be found:
Z
0
2 D
=
(K
+ pb
)
(5)
h
hZ
∞
g (v )dv
=
(6)
pD
Should be underlined that the expressions (5) and (6) can not be used for direct calculating of
optimal values (Zo, Ro). (Fig. 2.). Thus, an iterative method (process) of seeking Zo and Ro values
in the finite number of steps was elaborated2324. The conditions of required convergence of the
iterative method (existence of the solution of problem) satisfies the inequality as follows:
0
Ro
pD
h
i. e.
23
2 D [K + pE
h
>
Z
w
> Z
m
(v )]
(7)
(Fig. 4).
Farlow, S.J. - Haggard, G.M. (1987): Applied mathematics for Management, Life Science and Social Sciences. New
York: Random House. ISBN 0-397-35160-6.
24
ukowski, P. (2009): Koncepcja optymalnej strategii zarzdzania zapasami materiałów w przedsibiorstwie przemysłowym, (in) Uwarunkowania rozwoju systemów zarzdzania, (ed.). H. Hawanie, W. Iwaszkiewicz. Bielsko-Biała:
263
No. 41, 2011
8. Algorithm of setting the optimal values
Beginning the iterative process with the first probable meaning of Z value equals
2 DK / h , with the increase of iteration numbers the value of Zi increases, when Ri value decreases. Hence, the iterative process is quickly convergent.
It is recommended to use computer techniques to calculate the R0 and Z0 ( R 0 = lim R i )
i→ ∞
. For this purpose the computer software of operative scheme of R0 and Z0 was written. This
program does calculations until the difference Ri+1 – Ri values is adequately low (e.g. 0,00001). It
means, that two calculated values are similar. For the optimal value R0 we use then Ri+1 value,
because R0 ≅ Ri+1. The optimal value of Z0 were estimated on the basis of R0(Ri+1) (Fig. 3, Fig. 4).
It should be noted, that in case when there is even distribution of probability of production consumption of bases materials, the expressions (5) and (6) should be solved directly, i. e.
optimal values of R0 and Z0 could be presented as follows:
R
0
=
A 1 −
Z
− 1
p
0
D
=
D
2 K h
− A h h ( D
(8)
2 K
− A h )
(9)
The formulas (8), (9) are based on case of even probability of production consumption of materials:
g ( v ) =
0 ,
1
,
A
if
v ∉ ]0 , A [
if
v ∈ ]0 , A [
(10)
The integral in the expression (6) can be presented by using elementary functions. In general case, the presented simplification is not possible and iterative process of estimation R0 and Z0
should be then employed.
9. Empirical verification of the model (on real data)
The constructed probabilistic model is under empirical verification. The practical verification
of the constructed model was performed for every main kind of based material used during serial
production of furniture (kitchen sets, combined set, chairs, armchairs). In the calculations numerical data was used from the 6-year periods of production activities of furniture factories in Poland.
The verification showed, that worked out the iterative method of solving the model of reserves
leads to estimation of optimal values of reserves R0 and order Z0 with minimal costs, and in this
way leads to determination of optimal (R, Z) type strategy of based material reserves management
in a factory25.
25
Hilier, F.S. – Lieberman, G.J. (1997): Introduction to operations research. New York: McGraw-Hill, Inc. ISBN 0-07028908-5.
264
Start
Data input
D, K, h, p, ε Α
Start
Z
=
w
Data input
D, K, h, p, ε Α
2 D( K + p
Values determination
Zw ; Zm
Zm =
Zw < Zm
R(1) = 0
h
R1 := 0
No
solution
Zi =
Determination of the values
of the matrix elements
R0 (I + 1) Z0 (I + 1)
Printing of the matrix
elements values
R 0(I +1) Z0(I + 1)
No
solution
i := 1
Values determination Z0(1)
I = I + 1
A
)
2
Zw < Zm
I = 1
R0(I + 1) - R0 (I) < ε
pD
h
2DK
h
hZ i Ri +1 = A
1 − pD bi =
Z i +1 =
Ri2+1
A
− Ri +1 +
2A
2
2 D( K + pbi )
h
i := i + 1
Ri +1 − Ri < ε
Stop
Printing:
Ri +1 , Z i +1
Stop
Figure 6. R0 and Z0 optimal values searching block diagram with uniform distributio
10. Optimal strategy formation
The main rule of optimal strategy of reserves management is: when the level of reserves of
special based material in a store reaches value R0, the order should be equal to the value of Z0, so
that mean costs concerned with reserves with time under consideration will be minimal.
The constructed probabilistic model of wood reserves management has methodological value
because it shows the method of working out an optimal strategy of basal reserves of based material
management in the conditions of serial and polyassortment production of furniture and other based
products in special conditions of economical practice in the furniture industry.
265
No. 41, 2011
11. Conclusions
The model has been verified at an attainable scale using the numerical data concerning different assortment of materials in the serial production of furniture. The proposed probabilistic model
makes it possible to elaborate the optimal strategy of type R, Z in the management of reserves of
based materials of the manufacturing company with large-lot production. The strategy is based on
minimal expenses connected with a supply of materials. Computer modeling provide sets of
information on the optimal strategy of material reserves as well as cut the costs of production.
%LEOLRJUDSK\
[1] Jagas, J. (2004): ProduktywnoĞü pracy. Opole: Uniwersytet Opolski. ISBN 978-83-7641-0562. [2] Farlow, S.J.- Haggard, G.M. (1987): Applied mathematics for Management, Life Science
and Social Sciences. New York: Random House. ISBN 0-397-35160-6.
[3] Hilier, F.S. - Lieberman, G.J. (1998): Introduction to stochastic models in operations research.
New York: McGraw-Hill, Inc. ISBN 0-03-894995-7.
[4] Hilier, F.S. - Lieberman, G.J. (1997): Introduction to operations research. New York: McGrawHill, Inc. ISBN 0-07-028908-5.
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266
MODEL DYNAMICZNEGO SYSTEMU ZARZĄDZANIA W FIRMIE PRODUKCYJNEJ
W WYKORZYSTANIEM MODELI PROPABLIUSTYCZNYCH
Streszczenie
W artykule zaprezentowano propablistyczny model rezerw. Konstrukcja modelu
podporzdkowana była budowie optymalnej strategii rezerw materiałowych w produkcji seryjnej. Model zweryfikowano przy uyciu danych liczbowych dotyczcych
rónych produktów z drewna, w tym meble z produkcji seryjnej. W artykule przedstawiono równie model dynamicznego systemu zarzdzania firm produkcyjn.
Słowa kluczowe: zarządzanie zapasami, modele propablistyczne
Tomasz Wołowiec
Wyzsza Szkola Biznesu — National-Louis University (WSB-NLU)
ul. Zielona 27, 33-300 Nowy Sacz, Poland
e-mail: [email protected]
Janusz SoboĔ
WyĪsza Szkola Biznesu — National-Louis University (WSB-NLU)
ul. Zielona 27, 33-300 Nowy Sącz, Poland
PaĔstwowa WyĪsza Szkoła Zawodowa w Gorzowie Wlkp.
ul. Teatralna 25, 66-400 Gorzów Wlkp.
e-mail: [email protected]

The model of dynamic managment system of manufactoring

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