This paper presents a closedloop locationinventoryrouting problem model considering both quality defect returns and nondefect returns in ecommerce supply chain system. The objective is to minimize the total cost produced in both forward and reverse logistics networks. We propose a combined optimization algorithm named hybrid ant colony optimization algorithm (HACO) to address this model that is an NPhard problem. Our experimental results show that the proposed HACO is considerably efficient and effective in solving this model.
According to eMarketer, worldwide businesstoconsumer (B2C) ecommerce sales reached $1.471 trillion in 2014, increasing by nearly 20% over 2013 [
As a classic discrete dynamics problem, the customer service level is determined by three important decisions: facility location decision, inventory decision, and transportation decision [
In the literature, many papers studied the integration and coordination of any two of the above three decisions: locationinventory problem (LIP), locationrouting problem (LRP), and inventoryrouting problem (IRP). For reviews on LIP, readers can refer to Erlebacher and Meller [
There are few researches about the integration optimization of locationinventoryrouting problem (LIRP). Some researchers attempt to carry out research on LIRP [
However, little research has been conducted on the LIRP considering returns. Li et al. [
The above two researches mainly focus on the returns without quality defect but did not consider the MQDR. In this paper, we propose a model of closedloop LIRP with MQDR. To the best of our knowledge, it is the first time to introduce the MQDR into LIRP in ecommerce. An effective hybrid algorithm named hybrid ant colony optimization (HACO) is provided to solve this model. Results of numerical instances indicate that HACO outperforms ant colony optimization (ACO) on optimal solution, iterations, and computing stability.
The remainder of this paper is organized as follows. Section
As we all know, customers’ return in ecommerce is higher than traditional commerce. Because of personal dissatisfaction, or a mistaken purchase of the wrong product, some of the returns are without quality defects. These returns can reenter into the market after a simple repackaging process without being recovered [
In order to meet the needs of MQDR, the merchandise center (MC) is necessary to deliver normal merchandises to the demand points (DPs) of downstream and collect the returned merchandises. MC integrates the functions of distribution center and recycling center and provides quality inspection and repackaging services. Meanwhile the returned merchandises are collected to MCs. Returned merchandises without quality defects become resalable normal items after repackaging treatment at MCs. The plant will recover the returns with quality defects and bring them to the market again.
The operation mode of the system is shown in Figure
Closedloop supply chain for a single product.
The goal of this study is to decide the quantity and location of MCs and arrange the vehicle routes and determine the ordering times on each route. To minimize the total cost of logistics operations, this problem involves the following three decisions: (
To benefit from the risk of MQDR, we take assumptions (
The returned merchandises without quality defect are processed and repackaged at MCs, while others will be shipped back to the plant for reprocessing after a predetermined quantity at the MCs. Assume that the demand at each retailer is known and let
According to the aforementioned assumptions, the inventory levels depend on both demand and the quantity of MQDR. So, during each replenishment cycle, the holding cost of MCs is
In order to exactly describe the logistic distribution costs. Let
So the cost of forward distribution is
We let
The cost of deal with mixed quality defects is
We adopt
In summary, the model is formulated as follows:
It is easy to find that the objective function (
The optimization problem (
The objective function (
Like the VRP, the closedloop LIRP is also an NPhard problem, since it includes the VRP and is more complex than VRP. Generally speaking, there does not exist a complete, efficient, and accurate analytic algorithm to address NPhard problems; ant colony optimization (ACO) has been proved very successful and widely applied to solve the static and dynamic problems as an EC algorithm [
Since the natural number is an efficient coding method for these problems, the sequence of solutions is composed of candidate MCs (
In the HACO, the moving strategy of the ant in node
In order to improve the performance of global searching of our algorithm, the paper applied the scout bee searching phase into the ACO. Scout bees are free bees used for finding a new better solution from the neighbor known solution. As soon as a scout bee finds a new solution, she turns into an employed bee. If there is no improvement in the quality of solution, the bee will abandon that source and continue to search for another new solution.
The searching function of scout bees is as
To meet the requirements for coding sequence type, we described two operations to complete scouts searching process, namely, random array reverse (RAR) and random swap (RS).
Set the initial number of scout bee
Generate two positions randomly named
Get a random probability
Reverse the array between positions
Swap the position of
Calculate the cost of new solution.
Keep the best solution to the next iteration and return to Step
The pseudocodes of ABC are shown in Pseudocode
Procedure: ABC
Input: the initial sequence, the number of scout bee
Output: the better sequence
Begin
Take
while
take
if
Reverse the array between position
else
Swap the position of
Output: the better sequence
End
The global pheromone updating rule is triggered at the end of iteration to reward tours that are in line with the objective of impedance minimization. This strategy is applied to reinforce the pheromone density on the sets of edges belonging to the inspect tour and to increase the likelihood that this tour will also be selected by other ant agents. The rule of global pheromone updating is given by
In addition to the global pheromone trail updating rule, the selected ants will update the local pheromone trail in the process of passing an
Get the formulas for solving
Set the initial parameters for the model: set of candidate MCs
Parameter setting for HACO is as follows: ants number
Using unit matrix
Ant solutions generation module: each ant will generate a feasible solution after traversing the DPs.
Best ant solution module: after calculating each ant’s solution, select the best solution which is known as the iteration best to compare with the global best. Keep the next best solution as the next global best.
Scout bee module: random selection probability
Pheromone updating module: update the information pheromones as follows:
Termination module: if the parent optimal solution and offspring optimal solution are equal during continuous
Output.
The pseudocodes of HACO are shown in Pseudocode
Procedure: HACO for LIRP
Input: coordinates of nodes, demands and returns of DPs, MC parameters, vehicle capacity, HACO parameters
Output: the best solution (include routes, MCs locations, order times and order size)
Begin
Take
while
for 1 to
Foraging Behavior of Ants
Calculate individual total cost Tcost(
end
Tcost_best =
for 1 to
Scout bee searching the neighbor range
make
if
else
exchange(
end
if Tcost(
Tcost_best = Tcost(
end
end
for 1 to
if Tcost(
for 1 to
end
end
end
end
Output: the best solution
End
In this section, numerical simulations are given to illustrate the performance of HACO compared with the traditional ACO. Both algorithms in this paper are compiled by
Parameter values selection is crucial to the efficiency of algorithms. An example named Gaskell 6722 × 5 from the database, which contains the nodes coordinate and the DPs demand, is used to determine the optimal parameter. Gaskell 67 is the instance’s name and 22 × 5 means 5 candidate MCs for 22 DPs. The inventory holding cost
The parameters of algorithm are initialized as follows: ant’s number
We run the program 50 times on the same computer. The performance of ACO and HACO varies with the different values of the parameters, which are shown in Tables
Results with different

Cost  Iterations  

Mean  Std. dev.  C.V.  Mean  Std. dev.  C.V.  
30  ACO  32.4  0.96  0.0295  168.6  30.64  0.1817 
HACO  33.46  1.12  0.0336  125.72  29.02  0.2308  
40  ACO  32.13  0.96  0.03  173.48  32.95  0.1899 
HACO  33.37  0.93  0.0277  117.82  15.4  0.1307  
50  ACO  32.22  0.74  0.0229  157.19  40.58  0.2581 
HACO  32.96  0.96  0.0292  119.26  17.47  0.1465  
60  ACO  32.21  0.67  0.0208  158.12  39.39  0.2491 
HACO  32.72  0.86  0.0263  121.86  17.37  0.1425  
70  ACO  31.96  0.71  0.0223  162.88  32.48  0.1994 
HACO  32.77  1.13  0.0344  121.06  23.7  0.1958 
Results with different

Cost  Iterations  

Mean  Std. dev.  C.V.  Mean  Std. dev.  C.V.  
0.25  ACO  31.92  0.54  0.0168  189.3  73.28  0.3871 
HACO  31.63  0.79  0.025  189.38  69.64  0.3677  
0.5  ACO  31.85  0.78  0.0246  181.86  57.34  0.3153 
HACO  31.52  0.91  0.029  182.24  63.94  0.3509  
1  ACO  32.22  0.74  0.0229  157.19  40.58  0.2581 
HACO  33.06  1.04  0.0315  123.28  14.02  0.1137  
1.25  ACO  32.13  0.79  0.0247  154.24  30.12  0.1953 
HACO  33.11  1.09  0.0331  115.78  11.61  0.1002  
1.5  ACO  32.14  0.9  0.0279  154.96  25.68  0.1658 
HACO  32.97  1.11  0.0335  116.2  10.23  0.0881 
Results with different

Cost  Iterations  

Mean  Std. dev.  C.V.  Mean  Std. dev.  C.V.  
3  ACO  31.91  0.91  0.0286  192.78  42.08  0.2183 
HACO  33.06  1.19  0.0359  148.8  54.84  0.3686  
4  ACO  32.19  0.8  0.0249  170.2  41.89  0.2461 
HACO  33.05  1.14  0.0344  126  42.17  0.3347  
5  ACO  32.22  0.74  0.0229  157.19  40.58  0.2581 
HACO  32.96  0.96  0.0292  119.26  17.47  0.1465  
6  ACO  32.1  0.77  0.0241  159.38  31.99  0.2007 
HACO  33.12  1.19  0.0358  119.86  22.4  0.1869  
7  ACO  32.42  0.84  0.0258  154.69  23.92  0.1546 
HACO  33.25  1.07  0.0322  111.68  8.62  0.0772 
Results with different

Cost  Iterations  

Mean  Std. dev.  C.V.  Mean  Std. dev.  C.V.  
0.1  ACO  32.22  0.74  0.0229  157.19  40.58  0.2581 
HACO  32.12  0.93  0.0289  138.4  21.02  0.1518  
0.2  ACO  32.38  0.87  0.0269  133.27  20.57  0.1543 
HACO  32.7  0.97  0.0296  124.12  13.01  0.1048  
0.3  ACO  32.65  0.94  0.0289  132.8  31.09  0.2341 
HACO  32.75  1.45  0.0443  122.1  13.09  0.1072  
0.4  ACO  33.03  0.94  0.0284  131.86  28.76  0.2181 
HACO  33.31  1.1  0.033  122.98  20.2  0.1643  
0.5  ACO  33.41  0.87  0.0261  157.27  67.72  0.4306 
HACO  33.55  1.08  0.0323  116.24  15.44  0.1328 
Results with different

Cost  Iterations  

Mean  Std. dev.  C.V.  Mean  Std. dev.  C.V.  
50  ACO  31.99  0.72  0.0224  159.72  33.39  0.21 
HACO  33.07  1.22  0.0369  123.7  25.96  0.2098  
100  ACO  31.9  0.67  0.0209  159.8  30.73  0.19 
HACO  32.88  1.09  0.033  121.63  18.91  0.1555  
150  ACO  32.22  0.74  0.0229  157.19  40.58  0.2581 
HACO  33.02  1.05  0.0319  121.14  23.2  0.1915  
200  ACO  32.11  0.8  0.0251  167.66  38.61  0.23 
HACO  32.9  1.12  0.0339  120.8  22.05  0.1825  
250  ACO  32.08  0.87  0.0271  164.08  34.16  0.21 
HACO  33.1  1.09  0.033  121.87  28.95  0.2376 
Results with different

Cost  Iterations  

Mean  Std. dev.  C.V.  Mean  Std. dev.  C.V.  
0.3  33.07  1.22  0.0369  123.70  25.96  0.2098 
0.4  32.88  1.09  0.0330  121.63  18.91  0.1555 
0.5  33.02  1.05  0.0319  121.14  23.20  0.1915 
0.6  32.90  1.12  0.0339  120.80  22.05  0.1825 
0.7  33.10  1.09  0.0330  121.87  28.95  0.2376 
Tables
To get a reliable conclusion, we run another 50 times on the same computer with the best parameter values in Gaskell 6722 × 5. One of the best solutions of objective function in the 50 experiments of HACO is 30.2 million CNY. Table
The solution of Gaskell 6722 × 5.
MC  Routing number  Routing  Order times 

MC1  V1 

17 
V2 

18  
MC2  V3 

37 
MC5  V4 

24 
V5 

18 
Topological structure of the network.
Figure
Trends of objective function value.
The fluctuation curve of optimal objective function value.
ACO
HACO
As shown in Figure
In this section, a series of instances are given to show that HACO is more efficient and stable than classical software and ACO. In order to ensure the demands of DPs are not more than the vehicle capacity, we need to enumerate some instances. In this paper, the daily demands are set as 1/10 of corresponding demands of the database.
As we know, Lingo is a representative classical optimization software tool. Thus we used
Comparisons between HACO and Lingo.
Instance name  Perl 183 
Gaskell 67 
Gaskell 67 


CPU time  Cost  CPU time  Cost  CPU time  Cost  
Lingo  523 s  715392  >1 hour  ∖  >1 hour  ∖ 
HACO  24.5 s  709152  44 s  32691202  99 s  31550446 
Each instance was run 50 times by HACO and ACO with their optimized parameters values, respectively; the results are shown in Tables
Optimal objective function values of two algorithms (CNY).
Instance name  Algorithm  Mean  Std. dev.  C.V. 

Significance test 

Perl 183 
ACO  711347.1  6979.11  0.0098  1.6838  0.048 
HACO  709237.9  5454.48  0.0077  
Gaskell 67 
ACO  31929818.3  627210.66  0.0196  1.7118  0.045 
HACO  31718084.1  609606.04  0.0192  
Gaskell 67 
ACO  3288921.3  43585.25  0.0133  1.6602  0.050 
HACO  3275052  39868.81  0.0122  
Perl 183 
ACO  285145.3  3779.15  0.0133  1.8391  0.034 
HACO  283831.6  3351.00  0.0118  
Christofides 69 
ACO  419695.8  4948.15  0.0118  2.5020  0.007 
HACO  417298.6  4627.32  0.0111  
Perl 183 
ACO  486011.0  4503.39  0.0093  1.8080  0.037 
HACO  484424.1  4270.44  0.0088  
Christofides 69 
ACO  458235.6  6387.00  0.0139  1.6796  0.048 
HACO  456441.6  5317.70  0.0117 
Iterations of two algorithms (times).
Instance name  Algorithm  Mean  Std. dev.  C.V. 

Significance test 

Perl 183 
ACO  193.32  78.70  0.4071  0.6323  0.264 
HACO  183.90  70.04  0.3808  
Gaskell 67 
ACO  191.34  86.36  0.4513  0.7831  0.218 
HACO  180.70  43.32  0.2397  
Gaskell 67 
ACO  254.44  76.84  0.3020  0.2012  0.421 
HACO  251.84  49.42  0.1962  
Perl 183 
ACO  241.74  77.29  0.3197  0.1000  0.460 
HACO  240.46  47.33  0.1968  
Christofides 69 
ACO  245.24  79.10  0.3226  1.2340  0.110 
HACO  229.92  62.30  0.2710  
Perl 183 
ACO  247.18  94.89  0.3839  0.4355  0.332 
HACO  240.80  65.75  0.2730  
Christofides 69 
ACO  248.06  97.18  0.3918  0.2627  0.397 
HACO  244.08  65.48  0.2681 
According to Table
Observe, from Tables
By improving pheromone updates and bee colony searching, we improve the solution quality of the algorithm and make it useful as a guide for the ant searching process. Observed from the results of numerical simulations, HACO can get better result with a fewer number of iterations. Hence, comparing with ACO, HACO is adopted as a better approach in solving this LIRP with MQDR.
With the development of ecommerce, customers’ return keeps a high rate with MQDR, which can be reentered into markets after being repackaged or recovered. In this research, we built a closedloop LIRP model considering both quality defect returns and nondefect returns; we call it MQDR in this paper. We perform an extensive computational study and observe the following interesting results.
Considering MQDR are computationally beneficial for the formulation presented, the MQDR and closedloop pattern with returns are features of the proposed problem in ecommerce, which is never considered in previous work.
Since the evolutionary computation algorithm has been proved successfully in tackling NPhard problem, a hybrid algorithm is proposed by combining ACO algorithm and ABC algorithm to solve the LIRP. HACO integrated the scout bee searching phase into the ACO to improve the global searching ability.
The performance of HACO is evaluated by using the instances in the LRP database, and HACO outperforms ACO on convergence, optimal solution, and computing stability. This numerical study shows the efficiency and effectiveness of the solution method.
However, developing other elements for the LIRP will lead to further research directions. And analyzing the model under the dynamic demand of customs and a timevarying demand can be a valuable subject. The design of experiments and verification by discrete dynamics simulation should be established. Fruit fly optimization algorithm (FOA) as one of the best EC algorithms has attracted the attention of various researchers [
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (nos. 71171093,71471073, and 71571082) and selfdetermined research funds of CCNU from the colleges’ basic research and operation of MOE (nos. CCNU14Z02016 and CCNU15A02046).