A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization
This paper applies a mixed integer linear programming to designing a multi echelon supply chain network (SCN) via optimizing commodity transportation and distribution of a SCN. Proposed model attempts to aim multi objectives of SCN by considering total transportation costs and capacities of all eche...
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| Опубліковано в: : | Системні дослідження та інформаційні технології |
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| Дата: | 2010 |
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Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України
2010
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| Цитувати: | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization / T. Paksoy, E. Özceylan, G.-W. Weber // Систем. дослідж. та інформ. технології. — 2010. — №4. — С. 47-57. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859949406973853696 |
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| author | Paksoy, T. Özceylan, E. Weber, G.-W. |
| author_facet | Paksoy, T. Özceylan, E. Weber, G.-W. |
| citation_txt | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization / T. Paksoy, E. Özceylan, G.-W. Weber // Систем. дослідж. та інформ. технології. — 2010. — №4. — С. 47-57. — Бібліогр.: 26 назв. — англ. |
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| container_title | Системні дослідження та інформаційні технології |
| description | This paper applies a mixed integer linear programming to designing a multi echelon supply chain network (SCN) via optimizing commodity transportation and distribution of a SCN. Proposed model attempts to aim multi objectives of SCN by considering total transportation costs and capacities of all echelons. The model composed of three different objective functions. The first one is minimizing the total transportation costs between all echelons. Second one is minimizing of holding and ordering costs in distribution centers (DCs) and the last objective function is minimizing the unnecessary and unused capacity of plants and DCs.
Застосовується змішане лінійне цілочислове програмування до побудови багатоешелонної мережі поставок (SCN) за допомогою оптимізації перевезень і розподілу в SCN. Запропонована модель дозволяє враховувати багато задач SCN за допомогою розгляду загальних витрат на транспортування і місткості всіх ешелонів. У модель включено три різні цільові функції: перша — мінімізує повні вартості перевезень між усіма ешелонами; друга — мінімізує витрати від збереження і вартості замовлення в центрах розподілу (DCs), а остання цільова функція мінімізує зайву і невикористану потужність заводів і DCs.
Применяется смешанное линейное целочисленное программирование к построению многоэшелонной сети поставок (SCN) посредством оптимизации перевозок и распределения в SCN. Предложенная модель позволяет учесть многие задачи SCN посредством рассмотрения общих затрат на транспортировку и емкостей всех эшелонов. В модель включены три различные целевые функции: первая — минимизирует полные стоимости перевозок между всеми эшелонами; вторая — минимизирует затраты от сохранения и стоимости заказа в центрах распределения (DCs), а последняя целевая функция минимизирует излишнюю и неиспользованную способность заводов и DCs.
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© T. Paksoy, E. Özceylan, G.-W. Weber, 2010
Системні дослідження та інформаційні технології, 2010, № 4 47
УДК 519.854.2
A MULTI-OBJECTIVE MIXED INTEGER PROGRAMMING
MODEL FOR MULTI ECHELON SUPPLY CHAIN NETWORK
DESIGN AND OPTIMIZATION
TURAN PAKSOY, EREN ÖZCEYLAN, GERHARD-WILHELM WEBER
This paper applies a mixed integer linear programming to designing a multi echelon
supply chain network (SCN) via optimizing commodity transportation and distribu-
tion of a SCN. Proposed model attempts to aim multi objectives of SCN by con-
sidering total transportation costs and capacities of all echelons. The model com-
posed of three different objective functions. The first one is minimizing the total
transportation costs between all echelons. Second one is minimizing of holding and
ordering costs in distribution centers (DCs) and the last objective function is mini-
mizing the unnecessary and unused capacity of plants and DCs.
1. INTRODUCTION
Supply chain management has been a hot topic in the management arena in the
recent years. The term «supply chain» conjures up images of products, or sup-
plies, moving from manufacturers to distributors to retailers to customers, along a
chain, in order to fulfill a customer request (Gong et al., 2008).
Supply chain management (SCM) explicitly recognizes interdependencies
and requires effective relationship management between chains. The challenge in
global SCM is the development of decision-making frameworks that accommo-
date diverse concerns of multiple entities across the supply chain. Considerable
efforts have been expended in developing decision models for supply chain prob-
lems (Narasimhan and Mahapatra, 2004).
Enterprises have to satisfy customers with a high service level during stand-
ing high transportation, raw material and distribution costs. In traditional supply
chains, purchasing, production, distribution, planning and other logistics functions
are handled independently by decision makers although supply chains have dif-
ferent objectives. To overcome global risks in related markets, decision makers
are obliged to fix a mechanism which different objective functions (minimizing
transportation/production, backorder, holding, purchasing costs and maximizing
profit and customer service level etc.) can be integrated together. Illustration of a
supply chain network includes suppliers, plants, DCs and customers in Fig. 1
(Syarif et al., 2002).
The design of SC networks is a difficult task because of the intrinsic com-
plexity of the major subsystems of these networks and the many interactions
among these subsystems, as well as external factors such as the considerable multi
objective functions (Gumus et al., 2009). In the past, this complexity has forced
much of the research in this area to focus on individual components of supply
chain networks. Recently, however, attention has increasingly been placed on the
performance, design, and analysis of the supply chain as a whole.
T. Paksoy, E. Özceylan, G.-W. Weber
ISSN 1681–6048 System Research & Information Technologies, 2010, № 4 48
Supply chains performance measures are categorized as qualitative and
quantitative. Customer satisfaction, flexibility, and effective risk management
belong to qualitative performance measures. Quantitative performance measures
are also categorized by: (1) objectives that are based directly on cost or profit
such as cost minimization, sales maximization, profit maximization, etc. and (2)
objectives that are based on some measure of customer responsiveness such as fill
rate maximization, customer response time minimization, lead time minimization,
etc (Altiparmak et al., 2006).
However, the SCM design and planning is usually involving trade-offs
among different goals. In this study, we developed a mixed integer linear pro-
gramming model to design and optimize a supply chain network via providing
multi objective functions mentioned above together. We considered three objec-
tives for SCM problem: (1) minimization of total transportation costs between
suppliers-manufacturers-distribution centers and distribution costs between distri-
bution centers and customers, (2) minimization of holding and ordering costs in
DCs based EOQ (economic order quantity) and (3) providing equity of the capac-
ity utilization ratio of manufacturers and DCs.
In this field, numerous researches are conducted. (Williams, 1981), devel-
oped seven heuristic algorithms to minimize distribution and production costs in
supply chain. (Cohen and Lee, 1989), present a deterministic, mixed integer, non-
linear programming with economic order quantity technique to develop global
supply chain plan. (Pyke and Cohen), 1993, developed a mathematical program-
ming model by using stochastic sub-models to design an integrated supply chain
involves manufacturers, warehouses and retailers. (Özdamar and Yazgaç, 1997),
developed a distribution/production system involves a manufacturer center and its
warehouses. They try to minimize total costs such as inventory; transportation
Fig. 1. Illustration of a Supply Chain Network (Syarif et al. 2002)
A multi-objective mixed integer programming model for multi echelon supply …
Системні дослідження та інформаційні технології, 2010, № 4 49
costs etc under production capacity and inventory equilibrium constraints.
(Petrovic et al., 1999), modeled supply chain behaviors under fuzzy constraints.
Their model showed that, uncertain customer demands and deliveries play a big
role about behaviors. (Syarif et al., 2002), developed a new algorithm based ge-
netic algorithm to design a supply chain distribution network under capacity con-
straints for each echelon. (Yan et al., 2003), tried to contrive a network which in-
volves suppliers, manufacturers, distribution centers and customers via a mixed
integer programming under logic and material requirements constraints. (Yılmaz,
2004), handled a strategic planning problem for three echelon supply chain in-
volves suppliers, manufacturers and distribution centers to minimize transporta-
tion, distribution, production costs. (Chen and Lee, 2004), developed a multi-
product, multi-stage, and multi-period scheduling model to deal with multiple
incommensurable goals for a multi-echelon supply chain network with uncertain
market demands and product prices. The uncertain market demands are modeled
as a number of discrete scenarios with known probabilities, and the fuzzy sets are
used for describing the sellers’ and buyers’ incompatible preference on product
prices. The supply chain scheduling model is constructed as a mixed-integer
nonlinear programming problem to satisfy several conflict objectives, such as fair
profit distribution among all participants, safe inventory levels, maximum cus-
tomer service levels, and robustness of decision to uncertain product demands,
therein the compromised preference levels on product prices from the sellers and
buyers point of view are simultaneously taken into account. (Nagurney and
Toyasaki, 2005), try to balance e-cycling in multi tiered supply chain process.
(Gen and Syarif, 2005), developed a hybrid genetic algorithm for a multi period
multi product supply chain network design. (Paksoy, 2005), developed a mixed
integer linear programming to design a multi echelon supply chain network under
material requirement constraints. (Lin et al., 2007), compared flexible supply
chains and traditional supply chains with a hybrid genetic algorithm and men-
tioned advantages of flexible ones. (Wang, 2007), explained the imbalance be-
tween echelons with peccant supply chain by changing chain’s perfect balanced.
He used ant colony technique to minimize costs in peccant imbalanced supply
chains. (Azaron et al., 2008), developed a multi-objective stochastic programming
approach for supply chain design under uncertainty. Demands, supplies, process-
ing, transportation, shortage and capacity expansion costs are all considered as the
uncertain parameters. Their multi-objective model includes (i) the minimization
of the sum of current investment costs and the expected future processing, trans-
portation, shortage and capacity expansion costs, (ii) the minimization of the vari-
ance of the total cost and (iii) the minimization of the financial risk or the prob-
ability of not meeting a certain budget. (You and Grossmann, 2008), addressed
the optimization of supply chain design and planning under responsive criterion
and economic criterion with the presence of demand uncertainty. By using a
probabilistic model for stock-out, the expected lead time is proposed as the quan-
titative measure of supply chain responsiveness. (Schütz et al., 2008), presented a
supply chain design problem modeled as a sequence of splitting and combining
processes. They formulated the problem as a two-stage stochastic program. The
first-stage decisions are strategic location decisions, whereas the second stage
consists of operational decisions. The objective is to minimize the sum of invest-
T. Paksoy, E. Özceylan, G.-W. Weber
ISSN 1681–6048 System Research & Information Technologies, 2010, № 4 50
ment costs and expected costs of operating the supply chain. (Tuzkaya and Önüt,
2009), developed a model to minimize holding inventory and penalty cost for
suppliers, warehouse and manufacturers based a holononic approach. (Sourirajan
et al., 2009), considered a two-stage supply chain with a production facility that
replenishes a single product at retailers. The objective is to locate distribution cen-
ters in the network such that the sum of facility location, pipeline inventory, and
safety stock costs is minimized. They use genetic algorithms to solve the model
and compare their performance to that of a Lagrangian heuristic developed in ear-
lier work. (Ahumada and Villalobos, 2009), reviewed the main contributions in
the field of production and distribution planning for agri-foods based on agricul-
tural crops. Through their analysis of the current state of the research, they diag-
nosed some of the future requirements for modeling the supply chain of agri-
foods. (Gunasekaran and Ngai, 2009), have developed a unified framework for
modeling and analyzing BTO-SCM and suggest some future research directions.
(Xu and Nozick, 2009), formulated a two-stage stochastic program and a solution
procedure to optimize supplier selection to hedge against disruptions. Their model
allows for the effective quantitative exploration of the trade-off between cost and
risks to support improved decision-making in global supply chain design. (Shin et
al., 2009), provided buying firms with a useful sourcing policy decision tool to
help them determine an optimum set of suppliers when a number of sourcing al-
ternatives exist. They proposed a probabilistic cost model in which suppliers’
quality performance is measured by inconformity of the end product measure-
ments and delivery performance is estimated based on the suppliers’ expected
delivery earliness and tardiness.
After giving the introduction and the relevant literature, At the second sec-
tion, the proposed model which is a multi objective mixed integer linear pro-
gramming model is presented. We tested the novel model with a numerical exam-
ple and discussed the results obtained by LINGO package programmer at the last
section.
2. PROBLEM STATEMENT
Here, the constituted model represents three echelons, multi supplier, multi manu-
facturer, multi DC, and multi customer problem. Decision maker wishes to design
of SC network for the end product, select suppliers, determine the manufacturers
and DCs and design the distribution network strategy that will satisfy all capaci-
ties and demand requirement for the product imposed via customers. The problem
is a single-product, multi-stage SCN design problem. Considering company man-
agers’ objectives, we formulated the SCN design problem as a multi-objective
mixed-integer non-linear programming model. The objectives are minimization of
the total cost of supply chain, minimization holding and ordering costs in DCs,
and maximization of capacity utilization balance for DCs (i.e. equity on utiliza-
tion ratios). The assumptions used in this problem are: (1) the number of custom-
ers and suppliers and their demand and capacities are known, (2) the number of
plants and DCs and their maximum capacities are known, (3) customers are sup-
plied product from a single DC. Fig. 2 presents a simple network of three-stages
in supply chain network.
A multi-objective mixed integer programming model for multi echelon supply …
Системні дослідження та інформаційні технології, 2010, № 4 51
2.1 Model Variables and Parameters.
i is an index for customers ( Ii∈ ),
j is an index for DCs ( Jj∈ ),
k is an index for manufacturing plants ( Kk∈ ), s is an index for suppliers
( Ss∈ ),
skb is the quantity of raw material shipped from supplier s to plant k ,
kjf is the quantity of the product shipped from plant k to DC j , jiq is the
quantity of the product shipped from DC j to customer i ,
⎩
⎨
⎧
=
otherwise, 0,
,customer serves is DC if 1, i
y ji
kD is the capacity of plant k ,
ssup is the capacity of supplier s for raw material, jW is distribution ca-
pacity of DC j , id is the demand for the product at customer i , jic is the unit
transportation cost for the product from DC j to customer i , kja is the unit
transportation cost for the product from plant k to DC j , skt is the unit transpor-
tation and purchasing cost for the raw material from supplier s to plant c, hc is
the holding cost per year at DC j , S is ordering cost to manufacturer k from
each of DCs.
2.2 Objective Function, Constraints.
1f is the total cost of SCN. It includes the variable costs of transportation
raw material from suppliers to manufacturers and the transportation the product
from plants to customers through DCs.
2f is annual holding and ordering cost of products in DCs according to the
economic order quantity (EOQ) model.
Fig. 2. Supply Chain Network of Proposed Model
1
2
3
4
5
1
2
3
4
1
2
3
1
2
3
Customers
T. Paksoy, E. Özceylan, G.-W. Weber
ISSN 1681–6048 System Research & Information Technologies, 2010, № 4 52
3f is the equity of the capacity utilization ratio for manufacturers and DCs,
and it is measured by mean square error (MSE) of capacity utilization ratios. The
smaller value is, the closer the capacity utilization ratio for every manufacturer
and DC is, thus ensuring the demand are fairly distributed among the DCs and
manufacturers, and so it maximizes the capacity utilization balance.
∑∑∑∑∑∑ ++=
j i
jijikj
k j
kj
s k
sksk qcfabtf1Minimize ; (1)
∑
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡ ∑
+
∑
∑
=
j
h
k
kj
h
h
k
kj
k
kj c
fS
c
c
fS
fS
f
2
2
2
Minimize 2 ; (2)
+
−
=
∑
∑ ∑∑ ∑∑
k
DfDf
f k k j k
kkj
j
kkj
2
3
)]/()/[(
Minimize
∑
∑ ∑∑ ∑∑ −
+
j
WqWq
j j i i
iji
i
jji
2)]/()/[(
; (3)
iy
j
ji∑ ∀=1 , (4)
jWyd
j
jjii∑ ∀≤ , (5)
jiydq jiiji ,∀= , (6)
jqf
i
ji
k
kj ∀==∑∑ , (7)
kb
k
ssk∑ ∀≤ sup , (8)
kbf
j s
skkj∑ ∑ ∀≤ , (9)
kDf
j
kkj∑ ∀≤ , (10)
jiy ji ,}1,0{ ∀= , (11)
skjiqfb jikjsk ,,,0 ∀≥ . (12)
The model is composed of three objective functions (Eq. 1–3). The first ob-
jective function (Eq. 1) defines minimizing shipment costs between suppliers,
manufacturers, DCs and customers. The second objective function is minimizing
A multi-objective mixed integer programming model for multi echelon supply …
Системні дослідження та інформаційні технології, 2010, № 4 53
holding and ordering costs in DCs using economic order quantity model (Eq. 2).
Equation 3 (third objective) minimizes equity of the capacity utilization ratio of
manufacturers and DCs.
Constraint (Eq. 4) represents the unique assignment of a DC to a customer,
(Eq. 5) is the capacity constraint for DCs, (Eq. 6) and (Eq. 7) gives the satisfac-
tion of customer and DCs demands for the product, (Eq. 8) gives the supplier ca-
pacity constraint, (Eq. 9) describes the raw material supply restriction, (Eq. 10) is
the manufacturer production capacity constraint. Finally, constraints (Eq. 11) and
(Eq. 12) are integrality constraints.
3. NUMERICAL EXAMPLE
In this section we present a numerical example to illustrate the proposed model
mentioned in previous section. The application of the model is performed for a
logical data which was inspired from related cases in the real world. The consid-
ered supply chain network includes five suppliers which are located different
places, three manufacturers, three distribution centers and four customers (Fig. 2).
The network is structured to supply raw materials and transport products from
suppliers to end-users is constituted from multi echelon and capacitated elements
of network considering minimizing the total transportation costs between all eche-
lons (suppliers, manufacturers, distribution centers (DCs) and customers, holding
and ordering costs in DCs and unnecessary and unused capacity of plants and
DCs via decreasing variance of transported amounts between echelons. Numerical
data used in example are given below, respectively. Table 1 and 2 gives the pri-
orities of objectives obtained by Expert Choice 11.5 program to find rate of pur-
poses according to AHP methodology.
T a b l e 1 . Relatives of Objective Functions (AHP)
1f 2f 3f
1f 1 2 3
2f 1/2 1 3/2
3f 1/3 2/3 1
Sum 1.83 3.67 5.5
T a b l e 2 . Normalized AHP Matrix
1f 2f 3f
1f 0.545 0.545 0.545
2f 0.273 0.273 0.273
3f 0.182 0.182 0.182
According to Table 2, weight of each objective function is 0.542, 0.273 and
0.182 respectively. Because of matrix consistency < 0.1, this matrix will be ac-
cepted. Parameters: Number of Total Suppliers: 5; Number of Total Customers: 4;
Number of Total Manufacturers: 3; Number of Total Distribution Centers: 3;
S 20 tl; hC 1,5 tl.
T. Paksoy, E. Özceylan, G.-W. Weber
ISSN 1681–6048 System Research & Information Technologies, 2010, № 4 54
T a b l e 3 . Unit transportation costs values between suppliers and manufactur-
ers (TL)
Suppliers Manufacturers
1 2 3 4 5
1 0.5 0.3 0.4 0.4 0.5
2 0.6 0.4 0.5 0.6 0.6
3 0.5 0.5 0.6 0.6 0.4
T a b l e 4 . Unit transportation costs values between manufacturers and DCs (TL)
Manufacturers DCs
1 2 3
1 1.4 1.1 1.1
2 1.1 1.2 0.8
3 1.3 1.4 0.9
T a b l e 5 . Unit transportation costs values between DCs and Customers (TL)
DCs Customers
1 2 3
1 0.9 0.9 0.7
2 0.7 0.6 0.6
3 0.8 0.5 0.7
4 0.6 0.9 0.8
T a b l e 6 . Capacities of Suppliers, Manufacturers, DCs and Demands of Cus-
tomers (unit)
Suppliers Manufacturers DCs Customers
1 5000 7000 6300 3100
2 5500 6500 6700 3100
3 5250 6500 6000 3100
4 4750 – – 3100
5 4500 – – –
T a b l e 7 . The results obtained by LINGO package program
Decision Value Decision Value
X1,3 2000 Y3,2 3400
X2,1 2400 Y3,3 3100
X2,2 3100 Z1,4 3100
X3,1 400 Z2,2 3100
X5,3 4500 Z2,3 3100
Y1,2 2800 Z3,1 3100
Y2,1 3100 Objective (tl) 13678
According to data obtained LINGO package program, results are given
above table 7. Under capacity constraint and transportation costs, decision maker
A multi-objective mixed integer programming model for multi echelon supply …
Системні дослідження та інформаційні технології, 2010, № 4 55
purchased raw materials from all suppliers except fourth. 2000 units from first
suppliers, 5500 units from second supplier, 400 units from third and 4500 units
from fifth supplier, are transported to manufacturers. 2800 units which come from
second and third supplier are shipped to second DC from first manufacturer. Also
3100 units of product are transported from second manufacturer to first DC. 3400
units to second DC and 3100 units to third DC totally 4460 units of product
shipped from third manufacturer. Supporting equation 4 constraint, each customer
provided their demand only one DC via providing a better balanced distribution.
All customers’ demand is supplied from DCs as 3100, 6200 and 3100 units re-
spectively (Fig. 3). At three echelons, all transportation costs and hold-
ing/ordering costs in DCs (first and second objective functions) calculated about
13678tl. Providing the third objective, the unnecessary and unused capacity of
plants and DCs are minimized via decreasing variance of transported amounts
between second and third echelons. When we examined the second and third
echelons’ distribution, it’s seen that the transportation between manufacturers-
DCs-customers come and go from 2800 units to 3400 units considering balancing
distribution.
4. CONCLUSION
In this study, a mixed integer non-linear programming model is developed to de-
sign a supply chain network by combining three different objectives. Considered
three objectives: (1) minimization of total transportation cost of plants and distri-
bution centers (DCs), inbound and outbound distribution costs, (2) minimization
of holding and ordering costs via EOQ method (3) maximization of capacity utili-
zation balance for DCs (i.e. equity on utilization ratios). We used the developed
model to determine from which suppliers, manufacturers, DCs and how much
amounts will be transported to answer customers demand. We developed binary
variables to provide a DC for a customer. So we have prevented unbalanced dis-
tributions between DCs and customers.
Fig. 3. Raw Material and Product flow
1
2
3
4
5
1
2
3
4
1
2
3
1
2
3
2400
3100
2800
3100
3100
3100
3100
3100
2000
4500
400
3400
3100
Customers Suppliers Manufacturers
Distibution
Centers
T. Paksoy, E. Özceylan, G.-W. Weber
ISSN 1681–6048 System Research & Information Technologies, 2010, № 4 56
In future, new solution methodology based on tabu search or heuristic meth-
ods can be developed to obtain new optimal solutions for the multi-objective SCN
design problem, and the effectiveness of the solution methodology can be investi-
gated. Additionally, uncertainty of costs and demands can be considered in the
model and new solution methodologies including uncertainty can be developed
via fuzzy models.
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Received 27.10.2009
From the Editorial Board: the article corresponds completely to submitted manu-
script.
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| id | nasplib_isofts_kiev_ua-123456789-50068 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1681–6048 |
| language | English |
| last_indexed | 2025-12-07T16:16:03Z |
| publishDate | 2010 |
| publisher | Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України |
| record_format | dspace |
| spelling | Paksoy, T. Özceylan, E. Weber, G.-W. 2013-10-04T14:52:58Z 2013-10-04T14:52:58Z 2010 A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization / T. Paksoy, E. Özceylan, G.-W. Weber // Систем. дослідж. та інформ. технології. — 2010. — №4. — С. 47-57. — Бібліогр.: 26 назв. — англ. 1681–6048 https://nasplib.isofts.kiev.ua/handle/123456789/50068 519.854.2 This paper applies a mixed integer linear programming to designing a multi echelon supply chain network (SCN) via optimizing commodity transportation and distribution of a SCN. Proposed model attempts to aim multi objectives of SCN by considering total transportation costs and capacities of all echelons. The model composed of three different objective functions. The first one is minimizing the total transportation costs between all echelons. Second one is minimizing of holding and ordering costs in distribution centers (DCs) and the last objective function is minimizing the unnecessary and unused capacity of plants and DCs. Застосовується змішане лінійне цілочислове програмування до побудови багатоешелонної мережі поставок (SCN) за допомогою оптимізації перевезень і розподілу в SCN. Запропонована модель дозволяє враховувати багато задач SCN за допомогою розгляду загальних витрат на транспортування і місткості всіх ешелонів. У модель включено три різні цільові функції: перша — мінімізує повні вартості перевезень між усіма ешелонами; друга — мінімізує витрати від збереження і вартості замовлення в центрах розподілу (DCs), а остання цільова функція мінімізує зайву і невикористану потужність заводів і DCs. Применяется смешанное линейное целочисленное программирование к построению многоэшелонной сети поставок (SCN) посредством оптимизации перевозок и распределения в SCN. Предложенная модель позволяет учесть многие задачи SCN посредством рассмотрения общих затрат на транспортировку и емкостей всех эшелонов. В модель включены три различные целевые функции: первая — минимизирует полные стоимости перевозок между всеми эшелонами; вторая — минимизирует затраты от сохранения и стоимости заказа в центрах распределения (DCs), а последняя целевая функция минимизирует излишнюю и неиспользованную способность заводов и DCs. en Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України Системні дослідження та інформаційні технології Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization Багатоцільова модель змішаного цілочислового програмування для побудови і оптимізації багатоешелонної мережі поставок Многоцелевая модель смешанного целочисленного программирования для построения и оптимизации многоэшелонной сети постановок Article published earlier |
| spellingShingle | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization Paksoy, T. Özceylan, E. Weber, G.-W. Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи |
| title | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization |
| title_alt | Багатоцільова модель змішаного цілочислового програмування для побудови і оптимізації багатоешелонної мережі поставок Многоцелевая модель смешанного целочисленного программирования для построения и оптимизации многоэшелонной сети постановок |
| title_full | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization |
| title_fullStr | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization |
| title_full_unstemmed | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization |
| title_short | A multi-objective mixed integer programming model for multi echelon supply chain network design and optimization |
| title_sort | multi-objective mixed integer programming model for multi echelon supply chain network design and optimization |
| topic | Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи |
| topic_facet | Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/50068 |
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