Multi-objective Production Planning Considering Partner Selection for
Networked Manufacturing①
Zhi-xiang Chen1 , Li Li2
1
Department of Management Science, Sun Yat-sen University, Guangzhou, China
2
International Business, Sun Yat-sen University, Zhuhai, China
(mnsczx@mail.sysu.edu.cn, Li_whileblue@163.com )
Abstract – This paper studies an integrated optimization
model of production planning with partner selection in a
networked manufacturing system. An integrated multiobjective programming model is proposed and a numerical
example is illustrated. The result shows the effectiveness and
feasibility of the model. The model is suitable for the
decision
of
production
planning
in
networked
manufacturing environment
Keywords – Production planning, partner selection,
multi-objective
programming,
networked
manufacturing
I. INTRODUCTION
Production planning is a core decision problem in a
manufacturing system. Traditional production planning is
assumed that the production resource is limited within a
manufacturer, or relative external resources are
determined. With the globalization and wide application
of information technology, more and more companies are
outsourcing their non-core business to other collaborative
partners. This new economic environment is leading up
to the emergence of collaborative business (Niehaves and
Plattfaut, 2011). Networked manufacturing, or distributed
manufacturing, is one kind of new collaborative business
pattern in the era of IT, which not only changes the
traditional business mode but also changes the business
process. It links the business processes of different
partners (e.g., OEM (Original Equipment Manufacturer),
CM (contact manufacturers) and other partners) together
and forms a strategic alliance to respond to the customer
demand. Under this new business environment, the
production planning decision mechanism is different from
the traditional production planning. Therefore, it is
important to discuss the decision methods of production
planning for networked manufacturing system.
There are some authors have researched the problem
of production planning for distributed and networked
manufacturing. Gnoni et al (2003) deal with lot sizing and
scheduling problem of a multiple-site manufacturing
system with capacity constraints. Similarly, Leung, Wu
and Lai (2003) study the multi-site aggregate production
planning with multi-objective using goal programming
approach. Jolayemi and Oloruniwo (2004) develop a
deterministic model for planning production and
transportation quantities in multi-plant and multiwarehouse environment with extensible capacities. Ling
et al (2006) study the distributed production planning with
supplier selection using Analytical Target Cascading
① This paper is funded by NSFC (70972079)
method. Dudek and Stadtler(2005) study a negotiationbased production planning between supply chains
partners .Boulaksil and Fransoo (2009) study one OEM
manufacturing firm which outsources some of its
production activities to a contract manufacturer. Lin and
Lin (2009) study an interactive meta-goal programming
based decision method of collaborative manufacturing. In
the study, decision participate can interactively make
decision with other partners during the decision, and each
partner can consider his (her) own individual local
objective and preference, finally, a global optimization
result is reached. Chung et al (2010) apply genetic
algorithm (GA) to study the multi-factory production
planning problem. In the model, different factories with
capacity constraints and precedence relationships are
involved, and order completion time, i.e., makespan is
taken as objective of the model. Jung (2011) studies a
fuzzy AHP-GP approach for integrated production
planning considering manufacturing partners. In the
model, decision is made to allocate production tasks to
partners.
In this paper, we study a multi-objective programming
method for networked manufacturing considering partner
selection. The model can concurrently decide the
production lot size and partner selection. This method is
especially suitable for the OEM driven networked
manufacturing system, in which, collaborative partners
are selected when make production planning and allocate
production tasks to different partners.
II. FORMULATION OF THE PROBLEM
A. assumptions and notations
Assumptions
Our model will be formulated based on the production
networked shown in figure 1. In order to formulate the
problem, the following assumptions will be needed.
(1) OEM company acts as the decision maker of the
production planning;
(2) Demand of products in periods is known;
(3) Production planning decision concurrently
considers the supplier or contract manufacturer selection;
(4) All demand in each period should be satisfied and
no shortage and backlog is allowed
(5) Transaction cost is supplier dependent but is not
dependent on variety and quantity of the products.
(6) Holding cost of products is product dependent.
The system of the integrated inventory model is
shown as figure 1.
Contract manufacturers
OEM and products
Customers
CM1
Product 1
CM2
Product 2
┋
┋
Proudct M
CM N
Fig.1 Production network of OEM driven manufacturing
Notations
The following notations will be used in the model.
Indices:
i (=1,…, M) Index of products
j (=1,…, N) Index of contract manufacturers
t (=1, …, T) Index of time periods
Parameters:
Dit Demand of product i in period t. (units/period)
C ij Per unit price of product i supplied by contract
manufacturer j. ($/unit)
H i Holding cost of product i per period and per
unit ($/unit/period)
O j Transaction cost for contract manufacturer i.
( $/per time)
wi Storage space of product i ( m3/per unit)
W Total storage space (m3)
Bt Budget in period t
q ij Quality level of product i offered by contract
manufacturer j
S j Service level of contract manufacturer j
B Model formulation of the problem
In this paper, the problem can be described as: there
is a networked manufacturing system consisting of one
OEM and multiple CMs (contract manufacturers), in
which OEM is responsible for the product sale, market
development and customer service, while CMs are
responsible for the production of products. In order to
meet customer demand, OEM needs concurrently decide
which product will be assigned to which CM to produce,
to maximize the total profit, total product quality level
and customer service level. The three objective functions
are expressed as follows,
Objective functions:
M
Per unit transportation cost of contract
manufacturer j
Decision variables
X ijt The quantity of product i purchased from
contract manufacturer j in period t.
Y jt =1 if contract manufacturer j is selected in
period, 0, otherwise.
Intermediate variable
I it Inventory level of product i in period t
N
i t t 1
M
{
N
T
-
j 1
N
T
 Cij X ijt +  O j Y jt +
i 1 j 1 t 1
M
j 1 t 1
T
t
N
t
  H i ( X ijk   Dik ) +
i 1 t 1
M
N
k 1 j 1
k 1
T
 f
i 1 j 1 t 1
j
X ijt }
Pi ,t Sell price of product i in period t
fj
T
max TP   Pit  X ijt
M
max TQ 
(1)
N
T
 q  X
ij
i 1 j 1
M
N
t 1
ijt
(2)
T
 X
i 1 j 1 t 1
ijt
N
1 T
max TS  
T t 1
S Y
j 1
j
(3)
N
Y
j 1
jt
jt
The first objective is to maximize the total profit; the
second objective is to maximize the total quality level of
all products and the last objective is to maximize the total
service level.
Constraints
t
N
t
I it   X ijk   Dik  0 for all i and t. (4)
k 1 j 1
k 1
 T

  Dik Y jt  X ijt  0
 k t

for all i , j, and t.
(5)
 t N
 t


w
X

i  
ijk    Dik  W for all t. (6)
i 1
 k 1 j 1
 k 1
Because the model is a multi-objective
programming problem, so, in order to solve it, it is
necessary to convert the multi-objective programming
model into single-objective programming model.
There are different methods for converting multiobjective programming model into single-objective
programming model. In this paper, we use the following
method. .
max   P
M
N
i 1 j 1
M
N
ijt
Cij  Bt
T
M
for all t.
i 1 j 1 t 1
T
(8)
i 1 t 1
Y jt ={0,1} for all j and t.
(9)
X ijt  0 for all i ,j, and t
(10)
TQ
TS
 S
TQmax
TS max
(11)
objectives of total profit, total quality and total service
respectively. The TPmax , TQmax and TS max are the
(7)
 X ijt   Dit
TPmax
 Q
s.t. constraints (4)-(10)
In above model,  P , Q , S are the weights of the
M
 X
TP
Constraint of (4) describes that all requirements must
be filled in the period in which they occur and shortage or
backlog is not allowed. Constraint (5) describes that there
is not an order without charging an appropriate
transaction cost. Constraint (6) means that storage space is
limited and constraint (7) means that total purchasing cost
is not exceed the budget. Constraint (8) restricts the total
supply equal to the total demand. The last two constraints
(9) and (10) are variable constraints respectively for
supplier selection and purchasing quantity.
optimal values of TP(total profit), TQ(total quality) and
TS(total service) under their own individual single
objective model without considering other objectives
respectively.
There are different methods can be used for weight
assignment, such as AHP (Analytical Hieratical Process).
For the sake of convenience and saving pages, in this
paper, we first automatically give out the weights of
objectives. The weights are 0.30, 0.40, and 0.30 for total
profit, quality and service respectively.
The solution procedure is described as :
Step 1: Initialization and data setting for the model
Step 2: Solve the three single-objective programming
models of total profit, total quality and total service
respectively to obtain TPmax , TQmax , TS Max .
Step 3: Solve weighted multi-objective programming
model (11) to obtain solution.
Ⅲ NUMERICAL EXAMPLE
In this section we use an example to show the
effectiveness of the model. Data are listed out in table 1
II SOLUTION PROCEDURE
Table 1 parameters of model
Product
Demand/price of OEM
Period 1
Period 2
A
12/100
15/120
B
20/200
21/240
C
20/150
19/170
Transaction cost ($)
Service level
Transportation cost ($/unit)
Price/quality level of CM
Period 3
Period 4
Period 5
17/130
22/210
18/140
20/120
23/240
17/160
13/110
24/210
16/155
CM1
CM2
CM3
C
q
C
q
C
q
30
32
45
110
0.95
6
0.97
0.95
0.98
33
35
43
80
0.90
5
0.95
0.97
0.96
32
30
45
102
0.97
7
0.95
0.97
0.95
Holding
cost
Storage
space
1
2
3
10
40
50
Note: CM=contract manufacturer, total storage space S=200. C=supply price of CM, q=quality level of CM.
Use the data, we first solve each objective
independently using Lingo11, and obtain the maximum
objective value as.
TPmax  35433.07 , TQmax  0.9718051
TS max  0.964
Then we solve model (11), obtain the objective value
The production plan and contract manufacturer
TP= 35334.83, TQ= 0.9658604, TS= 0.9580000
selection result is shown in table 2.
Table 2 solution result t
t=1
t=2
t=3
t=3
t=4
t=5
Xijt Yjt Iit Xijt Yjt Iit Xijt Yjt Iit Xijt Yjt Iit Xijt Yjt Iit Xijt Yjt Iit
A(i=1)
20
13
CM1(j=1)
12
0
0
0
0
0
0
1
15
1
37
1
CM2(j=2)
0
0
0
0
0
0
CM3(j=3) 0
0
0
0
13
0
B(i=2)
1.8
2.2
CM1(j=1)
0
0
19.8
0
0
0
CM2(j=2)
0
0
0
0
0
0
CM3(j=3)
20
1
23.2 1
0
0
24.8
22.3
C(i=3)
CM1(j=1)
0
19
0
18
0
0
CM2(j=2)
20
1
0
0
0
0
0
CM3(j=3) 0
0
0
0
1
1
17
16
From the result we can see that, when use multipleobjective model, the optimal value of each objective in
the integrated mode will be less than the objective value
in single-objective model. This reveals the trade-off
relationship, i.e., when consider multiple objectives in the
decision model, each objective can only be sub-optimal
When there are more objectives, this relationship will be
more significant.
V CONCLUSIONS
The increasing global competition is changing the
business mode. More and more companies are seeking
cooperation with other companies and forming a strategic
alliance to compete with competitors. Under this business
background, production planning decision is different
from that of traditional manufacturing system. This paper
studies an integrated optimization model of production
planning with partner selection in a networked
manufacturing system. An integrated multi-objective
programming model is proposed and a numerical example
is illustrated. The result shows the effectiveness and
feasibility of the model. The model is suitable for the
decision of production planning in networked
manufacturing environment
Further research can be made to extend the work
based on this paper. First, it can be considered multiple
transportation alternatives in the model. Second, it also
can be considered the demand characteristics of
customers, e.g., different customer orders have different
preference for selecting partner. These strategies will
extend the model into a more practical one.
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