=Paper=
{{Paper
|id=Vol-3206/paper15
|storemode=property
|title=Robust Optimization on E-commerce Closed-loop Supply Chain with Uncertain Environment
|pdfUrl=https://ceur-ws.org/Vol-3206/paper15.pdf
|volume=Vol-3206
|authors=Haifeng Guo,Shuai Li
}}
==Robust Optimization on E-commerce Closed-loop Supply Chain with Uncertain Environment==
https://ceur-ws.org/Vol-3206/paper15.pdf
Robust Optimization on E-Commerce Closed-Loop Supply Chain
with Uncertain Environment
Haifeng Guo1, Shuai Li1
1
Shenyang Ligong University, No.6, Nanping Middle Road,Hunnan District, Shenyang, 110159,China
Abstract
There are many uncertainty facts exists in e-commerce closed-loop supply chain. Linear
optimization method is difficult to solve this complex network optimization model with
uncertainty. This paper proposes a robust optimization model for handling the uncertainty of
the demands,returns and transportation costs in a E-commerce closed-loop supply chain
network design problem, which determined the best location of the logistics center and
obtained the customer area distribution results by using example simulation; and the
computational results show the robustness of the robust model in dealing with the disturbances
of uncertainty parameters, which verified the feasibility and effectiveness of the model and
method.
Keywords1
E-commerce, closed-loopsupply chain, reverse logistics, uncertainty, robust optimization
1. Introduction
The closed-loop supply chain is delivered through the forward and reverse product recycling,which
convert the open-loop process of “resources,production consumption and waste” into the closed-loop
feedback cycle network of “resources,production,consumption and renewable resources”,its essence is
based on mesh chain in the process of integrating the forward/reverse supply chain[1].
Xuet al.[2]proposed a supply chain operating model which is constructed by using the robust linear
programming method based on scenario analysis;Wang [3]developed a robust optimization model and
algorithm for logistics center location and allocation under uncertain environment; Aryanezhad.et
al.[4]proposed a multi-objective nonlinear robust optimization model for multi-product multi-site
aggregate production planning in a supply chain under uncertainty of cost parameters and demand.
Dong et al.[5]introduced the robust optimization modeland the differential honey badger algorithm
solving the closed loop of fresh food in supply chainnetwork design problems efficiently; Zhang et
al.[6]proposed that the problem of emergency materialallocation under uncertain demand,
comprehensively considering the matching degree of demandand demand time, an interval robust
optimization model with the goal of maximizing the mean valueof comprehensive matching degree is
constructed, and an improved adaptive genetic algorithmbased on random sampling is designed.
This paper proposes a robust optimization model for handling the uncertainty of the demands,returns
and transportation costs, which determined the best location of the logistics center and obtained the
customer area distribution results by using example simulation; and the computational results show the
robustness of the robust model in dealing with the disturbances of uncertainty parameters, which
verified the feasibility and effectiveness of the model and method.
ISCIPT2022@7th International Conference on Computer and Information Processing Technology, August 5-7, 2022, Shenyang, China
EMAIL: ghf_1970@163.com (Haifeng Guo);18940104633@126.com（Shuai Li）
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
99
2. Robust Model with Uncertainties
2.1. Assumptions
To specify the study scope,four assumptions and simplification are postulated as follows.
a. Customer demand for a single type of product.
b. The first level logistics center without inventory capacity constraints.
c. The first level logistics center has adequate product inventory.
d. The first level logistics center can repair all the returns.
2.2. Model formulation
Sets and indices: R set of customer zones, r R ; H set of the second level logistics centers, h H ;
M set of the first level logistics centers, m M ;T set of products suppliers, t T .
Table 1
Parameters
Parameters definition
Fm fixed cost of opening a first level logistics centers at
location m .
Fh fixed cost of opening a second level logistics centers at
location h .
Vm available months of opening a first level logistics
centers at location m .
Vh available months of opening a second level logistics
centers at location h .
Dr new demand at customer zone r .
pr returns demand at customer zone r
Gij unit transportation cost from a location i to j ,
i, j R H M T .
dij distances from a location i to j , i, j R H M T
sm unit distribution processing cost at location m
sh unit distribution processing cost at location h
th unit collection processing cost of returns at location h
xm unit repairing cost of returns at location m .
qij quantity of product shipped from a location i to j ,
i, j R H M T
r returns rates at customer zone r
h inventory capacity at location h
fh unit transverse scheduling transportation cost
between location h
gm unit emergency transportation cost at location m
Qh aggregate processing capacity at location h
100
unit new product processing capacity coefficient at
location h
unit returns processing capacity coefficient at location
h.
Table 2
Variables
Variables definition
km one if location m is opened,zero otherwise
bh one if location h is opened,zero otherwise
g mh , g hm one if location h is assigned to location m for service,zero
otherwise
u hr , u rh one if location r is assigned to location h for service,zero
otherwise
lmr one if the demands can not be satisfied by the all location
h ,zero otherwise.
h one if the demands at location r can not be satisfied by
the location h ,zero otherwise.
d hh distances from a location h to other location h .
2.3. Robust model
E-commerce products are usually returned by the city station which is responsible for collecting and
then back to second level logistics centers(H),and then shipped to first level logistics centers(M) for
returns processing.At the same time,the demand caused by the returns is typically satisfied through a
forward channel,the returned products are classified by the H and then shipped to the M [7].
The amount of returns of customer zones in the city stations(R) depend on the product return
rates,the capacity of each H represent the overall capacity which can stacking new products and
returns.We utilize product-specific coefficients as description for new product unit inventory capacity
and returns unit inventory capacity.
E-commerce closed-loop supply chain network is a two levels’ inventory system which hold
appropriate product inventory for the M and the H.Firstly,it should be satisfied by the H when
customers have a new product demand and returns,which can transverse scheduling the other same
level centers when the H out of stock,and the demand should be transported urgently to the customers
by M when all H is out of stock.
r
m h r
* * *
* * *
* * *
r
m h
r
Figure1:A two levels’ inventory system
Note:forwardflowreverseflowtransversescheduling
The city station should back the returns to H,the returned products are classified by H and then
shipped to M for final processing.
Based on Ben-Tal et al. [8],the uncertain robust linear optimization theory as follows:
In the Constraints(1) of theobjective function,the first two terms represent the fixed costs for m and
h ,the following three terms represent the total cost of transportation and distribution between facilities
point,the sixth term represents the total collection processing cost of returns at location h ,and the
101
following one represents the total transportation from location h to location m and the total repairing
cost of returns at location m ,and the remaining two terms represent the transverse scheduling
transportation cost between location h and emergency transportation cost at location m .
m M
k m Fm / V m + bn Fh / V h + (Gtmdtm qtm + tma )
h H t T m M
+ [(G mhd mhq mh + mh
b
) + s m q mh ]g mh
m M h H
+ [(G hrd hr q hr + hr
c
) + s hq hr ]u hr (1)
h H r R
+ [(G rhd rhq rh + rh
d
) + thq rh ]u rh
r R h H
+ [(G hmd hm q hm + hm
e
) + x m q hm ]g hm
h H m M
+ ( (D r u hr + p r u rh ) − h )fhd hh h
r R
+ ( (D r u hr + p r u rh ) − h )g md mr lmr g mh z
r R h H
Constraints(2) involves uncertainty related to transportation cost;
− tma aGtma qtm tma ，t ,m .
− mh
b
bG mhb q mh mh
b
，m ,h . (2)
− hr
c
cG hr
c
q hr hr
c
，h ,r .
− rh
d
d G rh
d
q rh rh
d
，r ,h .
− hm
e
eG mh
e
q mh hm
e
，h ,m .
Constraint set(3) assure that the location m has adequate product inventory;
qtm − qmh g mh 0，m M
tT hH
(3)
Constraints (4)-(7) involve material flow between facilities.
q g
mM
mh mh − qhr uhr = 0，h H (4)
rR
q D + G ，r R,
hH
hr r v
v
r (5)
h H
q rh pr + w G rw ，r R ,
(6)
qrhurh − qhm g hm = 0，h H
rR mM
(7)
Constraints(8)and (9) enforce the binary on corresponding decision variables.
1, h ( Dr uhr + pr urh )，h H
h = rR (8)
0，else.
1, h ( Dr uhr + pr urh )，r R
lmr = hH rR (9)
0，else.
Constraints(10) and(11) ensure that a customer zone r is assigned to exactly one h for service and a
second level logistics center h is assigned to exactly one m for service respectively.
uhr = urh = 1，r R (10)
hH hH
g
mM
mh = g hm = 1，h H
mM
(11)
Constraint(12) represents that it will have relevant product flow only when the facility is selected,
w is a very large number.
102
qtm wkm ,q mh wkm ,q hr hbh ,q rh hbh，
(12)
q hm hbh，m M ,h H
Constraints (13) and (14) represent the maximum capacity limit.
qmh g mh − hbh 0，h H (13) Dr uhr + pr urh Qhbh，h H
mM rR rR
(14)
Constraint(15) and（16）limit the range of the variables.
g mh , g hm , km , bh , uhr , urh 0,1，r R,
(15)
h H,mM.
tma , mh
b
, hrc , rhd , hm
e
0，t , m, h, r. (16)
Then,the cost minimization model as follows:
min z
s .t . equ .(1) − (16) (17)
3. Computational Experiments
The basic data of example come from vehicle routing problem in the database [8],both the
deterministic and robust models are solved by Lingo optimization software and only considers the
single-cycle closed-loop supply chain problem with single-product. Assuming that the supply chain
network consist of two product suppliers, two alternative first level logistics centers, six alternative
second level logistics centers and 14 city stations customer zone. The coordinate of product suppliers
shown as in Table 3;the basic data of first level logistics centers as shown in Table 4;Table5 and 6 report
the basic data of second level logistics centers and city stations customer zone; the nominal value of unit
transportation between facilities are Gtm = G mh = G rh = G hm =0.051.
Table 3
Coordinate Of Product Suppliers
t Coordinate
1 （30,74）
2 （50,125）
Table 4
Basic Data Of First Level Logistics Centers
m Coordinate Fm sm m Vm
1 （20,30） 500000 0.8 0.5 120
2 （60,50） 600000 0.8 0.5 120
Table 5
Basic Data Of Second Level Logistics Centers s h =0.8, t h =1, s h =0.8, h =1000, Q h =1600, γ=1, β=2
h Coordinate Fh
1 （15,19） 80000
2 （19,75） 100000
3 （31,87） 130000
4 （71,41） 100000
5 （61,83） 110000
6 （59,51） 90000
103
Table 6
Basic data of city stations customer zone
Nominal
Customers Coordinate demand
monthly
1 (1,49) 195
2 (87,25) 195
3 (93,91) 195
4 (29,9) 195
5 (19,47) 195
6 (57,63) 195
7 (5,95) 195
8 (69,1) 195
9 (67,91) 195
10 (21,81) 195
11 (41,23) 195
12 (19,65) 195
13 (25,65) 195
14 (47,95) 195
In addition, r = 0.3 ,unit transverse scheduling transportation cost f h = 0.4 ,unit emergency
transportation cost g m = 0.8 ,the above experiment is solved by Lingo optimization software.
To assess the performance of robust optimization model,the experiments are performed under three
different uncertainty levels (i.e., = 0.3, 0.6, 1 ),the uncertainty levels of the model are assumed to be
equal to (i.e., a = b = c = d = e = v = w ) to analyze the impact of the objective function value,and
five random experiments are generated in the uncertainty set (i.e.,[ nominal value − •G• , nominal value + •G• ])
on the each corresponding uncertainty level to analyze the performance of robust optimization
model,and we use the circumstance of facilities construction and the standard deviation of objective
function values of the robust optimization model to assess the performance of robust optimization
model.
The results under the uncertainty of transportation costs,demand and returns as shown in Table 7; the
standard deviation contrast of objective function values in robust optimization model as shown in Table
8.
Table 7
Experiments results
The The
opening The
opening
Uncerta objective
facilities facilities
inty value in
m
level
in h in
robust
robust robust model
model model
2 2,4,6 31214
2 2,4,6 31262
0.3 2 2,4,6 31244
2 2,4,6 31339
2 2,4,6 31553
2 2,4,6 31955
2 2,4,6 32334
0.6
2 2,4,6 33342
2 2,4,6 32705
104
2 2,4,6 32770
2 2,4,6 33391
2 2,4,6 34024
1 2 2,4,6 34864
2 2,4,6 33820
2 2,4,6 33275
Table 8
Standard deviation of objective function values in robust optimization model
The standard deviation of
Uncertainty
objective value in robust
level
optimization model
0.3 137
0.6 518
1 631
The results showed that the robust model opened the second m facility spot and the second, fourth,
sixth h facility spot under different uncertainty level, it can be seen that robust optimization model has
good stability in dealing with uncertainty circumstances, and the fluctuation of objective function value
is small, and the objective function value in robust model has a small standard deviation, which can
handle the disturbances of uncertainty better and more conductive to the overall stability of the system.
Figure 2 illustrated the wave phenomena of objective function value under the uncertainty level
= 0.6 ,it can be seen that robust optimization model has better stability in dealing with uncertainty
circumstances,and the fluctuation of objective function value is more small than deterministic
model,and the objective function value in robust model has a lower standard deviation,which can
handle the disturbances of uncertainty better and more conductive to the overall stability of the system.
Figure 2:Fluctuations of the objective function value
4. Conclusions
Since there are many uncertainty in e-commerce supply chain network design problems, this paper
based on the recent robust optimization theory proposed an e-commerce closed-loop supply chain
robust optimization model under the uncertainty of transportation costs, demand and returns. Robust
optimization model was designed based on the deterministic model in order to handle the disturbances
of uncertainty parameters of the system, five random experiments are generated under each different
uncertainty levels, and computational results show the superiority of the robust model in dealing with
the disturbances of uncertainty parameters, which also has better robustness. This paper’s work mainly
proposed a e-commerce closed-loop supply chain robust optimization model based on the recent robust
105
optimization theory and applied to the uncertainty supply chain network. However, this paper only
considers a single-product, single-objective problem, and the form of uncertainty set has limitations,
thus the direction of future research work focused on multi-product set, multi-objective and other forms
of uncertainty set robust optimization problems.
5. References
[1] Jr V Guide, R Daniel,V Jayaraman,J D Linton, Building contingency planning for closed-loop
supply chains with product recovery, Journal of Operations Management,2(2),( 2003):35-37, ,.
[2] J W Xu, X Y Huang, H F Guo, Robust optimizations for operating of closed-loop supply chain
with uncertain demands, Systems Engineering and Electronics,30(2),( 2008):283-287.
[3] B H Wang, S W He, Robust Optimization Model and Algorithm for Logistics Center Location and
Allocation under Uncertain Environment, Journal of Transportation Systems Engineering and
Information Technology,9(2),( 2009):69-74,.
[4] S.M.J. Mirzapour Al-e-hashem, H. Malekly, M.B. Aryanezhad, A Multi-objective Robust
Optimization Model for Multi-product Multi-site Aggregate Production Planning In A Supply
Chain Under Uncertainty, Int.J.Production Economics, 34(1),(2011):28-42,.
[5] Dong H, Lin G D,Robust optimization design of fresh closed-loop supply chain network based on,
Application Research of Computers, Vol.39, (2022). doi:10.19734/j.issn.1001-3695.2022.03.0097
[6] zhang X, Zhang H Y, Yuan X M, interval robust optimization of emergency materials allocation
based on matching degree under uncertain demand,Systems
Engineering,( 2022).doi:https://kns.cnki.net/kcms/detail/43.1115.n.20220505.1336.002.html
[7] Gopalakrishan Easwaran, Halit Uster, A closed_loop supply chain network design problem with
integrated forward and reverse channel decisions, IEEE Transactions,5(42)(2010):779-792.
[8] Augerat.CVRP Instances
[DB/OL].(2009).doi:http://osiris.tuwien.ac.at/~wgarn/vehiclerouting/neo/problem%20Instances/
CVRPinstances.html.
106