Discrete Optimization for Dynamic Systems of Operations Management in DataDriven Society
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Simulation Optimization of Discrete Logistics Processes: A Case Study on Logistics of an ECommerce Enterprise in Shanghai
Abstract
With the rapid development of online shopping in recent years, logistics distribution has received much attention from enterprises and online consumers. Logistics distribution involves many factors and complex processes; conventional qualitative methods are unable to provide an effective analysis. Thus, this paper sets a framework to solve the above problem. A case study of an Ecommerce enterprise in Shanghai on logistics distribution is proposed to discretize the whole process and minimize the total costs. Then the AnyLogic software is used to simulate and optimize the system from three aspects, including routes selection, warehouses quantity, and warehouses layout. Finally, this paper analyzes the simulation results, which would provide some valuable references for practical logistics.
1. Introduction
In recent years, Ecommerce industry has developed rapidly. Online shopping is almost necessary to everyone. Logistics distribution is the last link of online shopping whose importance is rising as society demand increases. Whether goods can be delivered to consumers in time affects the consumers satisfaction of this shopping directly. Especially in the annual “Double Eleven” shopping festival, parcel quantities in various regions have increased rapidly and many delivery points have exploded. As shown in Figure 1, the logistics orders of Double Eleven in 2018 have set a new record. Logistics industry has also transformed into the rapid development stage. It is estimated that distribution costs account for over 50% of the total operational costs. This problem needs to be solved urgently. Besides, logistics distribution as one of the three major contents (distribution, storage, and management) in the logistics field includes scheduling management, distribution tools, distribution routes, delivery time, natural environment, human resources, and so on. More are getting to the importance of logistics distribution. Therefore, in this paper, much attention is paid to optimize and analyze the logistics distribution, shorten the delivery time, improve the distribution efficiency, and reduce the distribution costs. The distribution tools are necessary in the whole process which occupy considerable resources under demands uncertainty. To lower the logistics costs dramatically, reducing this consumption is significant through optimization [1]. Hence this paper considers the vehicle as the breakthrough point to analyze the costs optimization in system.
Meanwhile, the research on vehicle is not a theoretical problem in logistics distribution process. Lots of factors are contained including vehicles quantity, distribution terminal, delivery time, unloading time, and demand changes. Conventional qualitative methods are not insufficient to solve it. In recent years, computational technology including hardware and software has developed rapidly. This technology characterizes reflecting on complicated processes or behaviors to solve problems through simulation. Simulation is a new subject that has gradually formed with the development of computer technology. It was firstly proposed in the early 20th century and was mainly utilized in water conservancy research. Simulation is the process of experimental research on the system by establishing and using the real system model. Similar to the application of algorithm on theoretical issues, simulation has significant effects on practical problems, particularly the complex and practical problems like logistics distribution. By discretizing and dividing the whole process into different parts, an integrated model is established and analyzed for every part to obtain the system data. According to the obtained data, optimal results are calculated [2]. The methods have more practical value than the theoretical algorithm. Better simulation methods have been presented in recent years as the computer technology develops. Simulation on the application of logistics distribution will have broader prospects.
This paper studies the discrete logistics processes which include many stochastic variables and factors. The method of mathematical modeling is not suitable. Therefore, the simulation is used to optimize the logistics distribution system and get the practical results.
For the simulation research of logistics distribution problems, the GPSS language (The General Purpose Systems Simulator) was firstly presented by American Geoffrey Gordon in 1961, which is a solution to discrete events, particularly the queuing phenomenon [3]. Considering the combination of continuous system and discrete system, simulation language of hybrid system occurred after the 1970s, for instance, SLAM language (Simulation Language for Alternative Modeling), which translates the program into FORTRAN language and then compiles it into machine codes with high execution rate. The language can be used in discrete systems, continuous systems, and hybrid systems consisting of both [4]. KV has established an interactive model to support the logistics planning on container operations, which can provide the evaluation of the ports performance, optimize the utilization rate of ports, and shorten the turnaround time of ships [5]. Ila et al. proposed an eightstep simulation model development process (SMDP) to the design, implementation, and evaluation of logistics and supply chain study by adopting discrete events [6]. Meng et al. modeled the problem of free delivery in Ecommerce companies with uncertain demands and discussed the influence of uncertain factors on the optimal solution [7]. Geng et al. established a selforganized elastic supply chain model based on MAS and designed the local fitness function, neighbor structure, and community interaction rules with the enterprises as agent. The results indicate that the system has an aggregation effect and its evolution can be controlled by MAS parameters [8]. Cui et al. transformed one step of RUL estimate of simulation model in discrete events logistics system into two steps. An instance validated the effectiveness and testified the performance of the twostep RUL estimation which is better than the onestep estimation [9]. Li et al. established a nonlinear model for vehicle routing planning problems subject to time windows which considered the influence of road irregularities on fresh fruits and vegetables. Compared to the results with the conventional models, the new model is superior to the prior one [10]. Lin et al. constructed a method of using transit signals first in the case of emergency evacuation among a sudden disaster without a specializedtransit channel. The bus signal priority dominated by four factors which could evacuate personnel and lessen time as much as possible. Paramics is utilized to simulate this method which is better than the other methods [11]. Thies et al. studied the effects of resources sharing on potential savings in logistics industry through a model of discrete instances and the resource utilization in installation stage of offshore wind energy generator based on Agent. The simulation results show that weather has a significant influence on the installation time, use time, and resources utilization rate. Meanwhile, the resources sharing has a potential saving on the installation of offshore wind energy generator [12]. Li et al. adopted the method of dynamic traffic network analysis and discussed the optimization of regional traffic organization. Then they simulated it with selfdeveloped software and proposed the optimized model and algorithm to prove the method on availability and feasibility [13]. Wei et al. identified that, in a discretetime VMI supply chain system composing of one retailer and one manufacturer, production fluctuations can be interestingly stable even if the retailer subsystem is fluctuant. Simulation experiments are used to verify the theoretical results on inventory and production fluctuation [14]. Teodor Gabriel et al. proposed an innovative classification method for the use of simulation in a complicated system of multimodal transportation with multiparticipant. This method identifies the main findings, trends, and future routes in multidimension of multimodal transportation [15]. Mandi et al. presented a grouping formula based on the branch pricing to study the opportunityconstrained vehicle routing problem with stochastic demands and enhanced the solution quality by simulation experiments and sensitivity analysis [16]. Hu et al. proposed an urban traffic model (AUTM) for predicting and avoiding the traffic congestion. This model is used to the simulation of largescale practical cases in different cities under different congestion conditions and has satisfactory results [17]. In response to the increasingly complicated logistics systems studies on discrete or continuous process, the number of simulation software arises with the rapid development of computer technology in related fields [18], which has developed a tendency to visualization, modularity, and intelligence. Modeling speed is accelerated and simulation effect is improved through prefabrication of various components. Many simulation platforms in this area are commonly seen on the market, for instance, Arean, Witness, Flexsim, Promodel, Automod, and so on.
This paper considers adopting a simulation tool, Anylogic software, which is developed early in this century to visualize modeling with a wide application scope. Complicated logistics distribution problems are discretized and simulated from the perspective of different processes. Moreover, one Ecommerce enterprise in Shanghai is studied as a case. This paper starts with continuous changes of warehouse quantities and demands and optimizes the route selection, warehouses quantity, and warehouses layout. Ultimately, some optimization suggestions are raised based on simulation results of the software.
2. Application of AnyLogic Simulation Platform in Logistics Distribution Field
AnyLogic, a commercial simulation software released in 2000 by the AnyLogic Company, is a powerful simulation platform which can be applied in a wide range of fields, including logistics simulation, supply chain simulation, virus pervasion, road traffic, pedestrian evacuation, military simulation, and so on. This platform can also be used in discrete events modeling, agentbased modeling, and dynamics system modeling. This paper combines the AnyLogic technology with a case of an Ecommerce enterprise in Shanghai on logistics distribution to propose the optimization suggestions.
The detailed introduction on the distribution case of an Ecommerce enterprise in Shanghai is shown as follows.
Ecommerce enterprises usually distribute goods to customers in two steps: (1) deliver goods from largescale warehouses to distribution stations; (2) deliver goods from distribution station to customers with numerous manpower and material resources. Thus, twopart costs occur. The second costs are much more than the first one due to the large number of involving personnel. Moreover, higher risks of traffic accidents and loss of goods are generated. Hence, to save costs and reduce risks, the Ecommerce company in Shanghai has established commodity selfraising points in various regions. The company only dispatches vehicles transferring goods to the distribution points and customers pick up the goods themselves so that the costs of the second part can be completely saved. At the same time, the injury of the delivery personnel and the loss of the goods are dramatically reduced.
According to statistics, 51 selfraising points have been established in the main urban area of Puxi by the Ecommerce company. The distribution map is obtained through the AnyLogic platform as follows in Figure 2.
Firstly, one largescale warehouse is considered to construct in Northwest of Shanghai outside the main urban area, which is responsible for goods distribution to selfraising points in main urban area of Puxi. The location is shown in Figure 3.
The AnyLogic simulation is used to model and calculate the cost and the time requirement of completing 51 selfraising points on vehicles, which are salient criterion for assessing the solution.
Many practical factors need to be considered before starting the simulation. For instance, the time requirements for delivery beyond the limits are causing the compensation to the customer called tardiness cost which increases the total costs. Besides, the number of goods from every selfraising point affects the total delivery time and some timesensitive delivery requirements for subsequent points.
Because of the different situations every day, the above two factors of every selfraising point can generate the orders quantity and the delivery time requirement through a random function as the fundamentals of the simulation. Thus, the following four items are included in every selfraising point: (1) name; (2) location; (3) goods quantity; (4) time limits.
While largescale warehouses only involve delivery, only the following two items need to be considered: (1) name; (2) location.
Two solutions are considered in this paper for route planning: (1) the shortest route solution, which calculates the shortest route between two locations as the real path for vehicles travelling; (2) the timelimited precedence solution, which considers firstly to deliver the goods with timesensitive requirements and then the shortest route solution is adopted. Solution one can reduce the vehicles travelling costs and increase the tardiness costs while solution two is completely the opposite. Ultimately, the simulation results are used to compare the two solutions on the total costs and the total time.
Setting up three agents for the simulation of this problem, they are as follows: (1) selfraising point agent; (2) warehouse agent, (3) distribution vehicle agent.
The distribution vehicle agent is the main activity target, including controlling the vehicle from the warehouse, searching for the closest selfraising point and unloading the goods, continuously searching for a new point, and returning to the warehouse until all goods are unloaded.
The time to accomplish the delivery of the selfraising points is calculated to compute the travelling costs. The time span consists of the vehicle travelling time from one point to another and the unloading time at the terminal.
The calculation formula of total costs is as follows:
where
Meanwhile, the total time of entire system is calculated to judge if the delivery solution meets the criterion.
The calculation formula is
where
The logical structure to implement the functions of the distribution vehicle agents is composed of four states, six transitions, and one selection structure, as shown in Figure 4.
The following operation interface can be obtained through the above analysis and modeling, which is shown in Figure 5.
Simulation to the selfraising points of the Ecommerce enterprise vehicle distribution can be performed by selecting the route planning mode and clicking the running button. Relevant data is obtained.
3. Simulation Performance and Optimization Analysis
This paper considers the logistics distribution settings under single warehouse, double warehouses, and three warehouses. The raw data of these three settings are all in Table 1. In a sharp increase of orders for special events like “Double Eleven”, we have increased the order number by ten times on the basis of the original data, which makes the research more realistic. Finally, we compare the results of simulation and provide suggestions for improvements.

3.1. Comparison of Two Solutions in Single Warehouse Mode
Only one delivery at all distribution points is accomplished in this mode. Assuming the shortest route solution is selected to the next point, the following results are obtained by running the AnyLogic:
TotalRunCost:41657.899;
TotalDelayCost:1074320.791;
TotalCost:1115978.69.
Meanwhile, some critical data on the sequence of every distribution point, time nodes, and time length during distribution processes are shown in Table 2.

According to Table 2, obviously the total time accomplishing the whole process (among vehicle departing and returning to the warehouse) is 1541.58 virtual time with single warehouse (the shortest route solution).
As shown in Table 2, some goods have timerestricted requirements that must be delivered before time limits, or tardiness costs occurred. The timelimited precedence solution is utilized to minimize the tardiness costs when the next station route needs to be selected. In other words, the goods with time requirements should be delivered first and then the shortest route solution is adopted to deliver goods without time requirements.
Through AnyLogic platform, the results of distribution costs in single warehouse (timelimited precedence solution) are as follows:
TotalRunCost:49796.137;
TotalDelayCost:59418.424;
TotalCost:109214.56.
Meanwhile, 1622.96 virtual times are required to accomplish the entire distribution procedure.
Comparisons of the results on the shortest route solution and the timelimited precedence solution in single warehouse mode are shown in Table 3.

As presented in Table 3, the timelimited precedence solution causes the increments in total traveling costs by 19.54% and the abatements in total tardiness costs by 94.47%. The total costs are also reduced by 90.21%, because this solution can reduce the tardiness costs of the selfraising points with time limits effectively. Nevertheless, without adopting the shortest route solution, the vehicle travelling costs are raised and the total distribution time also increases by 5.28%. Because the amount of cost reduction is far larger than the increments, the total costs are reduced. In summary, under the circumstances of generating order number randomly, to the selfraising points with timerestricted requirements, the timelimited precedence solution has lower tardiness costs and total costs, but the traveling costs and distribution time increased merely.
Moreover, the total time span to complete the distribution is long whatever the two solutions are. In practice, reducing the delivery time to the customers significantly is an important problem the Ecommerce companies face. This paper considers adding one warehouse, that is, double warehouses mode to solve this problem.
3.2. Simulation Comparison of Double Warehouses Mode and Single Warehouse Mode
The distribution in double warehouses mode is delivering goods to all the selfraising points simultaneously with two warehouses. According to the warehouse layout of the Ecommerce enterprise, the distribution warehouse is added to the west of Shanghai interplaying with the original one. The distribution of double warehouses and selfraising points is shown in Figure 6.
The simulation consequences of double warehouses in the shortest route solution by AnyLogic are shown as follows:
TotalRunCost:42067.155;
TotalDelayCost:377939.599;
TotalCost:420006.754.
It takes 848.60 virtual time to accomplish the entire distribution process.
Similarly, following consequences of double warehouses can be obtained in the timelimited precedence solution:
TotalRunCost:51287.608;
TotalDelayCost:45760.399;
TotalCost:97048.007.
It takes 890.88 virtual time to accomplish.
The consequences of two solutions are compared in Table 4.

As shown in the Table 4, in double warehouses mode with the timelimited precedence solution, the total traveling costs and delivery time increase by 21.92% and 4.98%, the total tardiness costs and the total costs reduce by 87.89% and 76.89%. The reasons are the same as the single warehouse mode that without adopting the shortest route solution results in an increase in the travelling costs and entire delivery time. Nevertheless, the tardiness costs are significantly reduced so that the total costs are reduced.
In order to comprehend the influence of the warehouse quantity on the distribution costs and the delivery time, above results are compared to gain Tables 5 and 6.


By comparing Tables 5 and 6, the double warehouses model can significantly reduce the total time compared to the single warehouse model in the two solutions. Particularly under the circumstances of the shortest route solution, the tardiness costs and the total costs are reduced dramatically, because the two warehouses distribute goods simultaneously to different selfraising points which reduces the time. In the shortest route solution, the delay time is so long that reducing delivery time can have great effects, while, in the timelimited precedence solution, the delay time is tiny without evident efficiency. In conclusion, the double warehouses mode has more effects than the single one in tardiness costs and total costs in the shortest route solution.
Moreover, in special shopping festivals, for instance, 11.11, 618, and so on, goods quantities increase dramatically on every selfraising point of the Ecommerce companies. Therefore, this article will enlarge ten times of the order number for each point to study this problem with AnyLogic.
Simulation results of double warehouses in the shortest route solution are shown (the order number is magnified by ten times):
TotalRunCost:42067.155;
TotalDelayCost:8148314.73;
TotalCost:8190381.884.
Meanwhile, the overall distribution time is 6428.60 virtual time.
Simulation time of double warehouses in the timelimited precedence solution is as follows (the order number is magnified by ten times):
TotalRunCost:51287.608;
TotalDelayCost:2758085.139;
TotalCost:2809372.747.
Meanwhile, the overall distribution time is 6470.88 virtual time.
Compared with the normal order number, two tables are obtained as in Tables 7 and 8.


As shown in Tables 7 and 8, the tardiness costs, the total costs, and the time requirements are many times larger than the normal one during the special shopping festival. The double warehouses model is completely incapable of meeting the practical demands. Therefore, this paper considers adding another warehouse to reduce the time and costs in three warehouses mode.
3.3. ThreeWarehouse Mode and the Influence of Distribution Area Adjustment on the Simulation Results
Three warehouses are utilized to be distributed simultaneously in threewarehouse mode which is also the fundament for multiple warehouse distribution research. In this paper, the warehouse location of the Ecommerce enterprise in Shanghai is taken as example. We expand the double one to threewarehouse model. The distribution of warehouses and selfraising points are shown in Figure 7.
The simulation consequences of three warehouses in the shortest route solution can be obtained by AnyLogic as follows:
TotalRunCost:45398.807;
TotalDelayCost:132487.919;
TotalCost:177886.726.
Meanwhile, the overall distribution time is 641.76 virtual time.
Similarly, the simulation consequences of three warehouses in the timelimited precedence solution are obtained as follows:
TotalRunCost:52468.394;
TotalDelayCost:15795.939;
TotalCost:68264.333.
Meanwhile, the overall distribution time is 676.48 virtual time.
Comparing the mentioned consequences with the two warehouses in two solutions, a significant improvement has occurred. However, by observing the three warehouses and distribution sites in Figure 7, the new warehouse WareHouseC is close to the WareHouseB. Therefore, the location of WareHouseC is adjusted to the southwest of Shanghai so that the nearby selfraising points have a relatively close warehouse to save the delivery time and total costs. The distribution of the adjusted warehouse and selfraising points are shown in Figure 8.
As shown in Figure 8, the WareHouseC is located in the southwest of Shanghai and these three warehouses are distributed evenly after adjustment of the location.
With the AnyLogic, the simulation consequences of three warehouses (adjusted location) in the shortest route solution can be obtained:
TotalRunCost:42057.032;
TotalDelayCost:49689.094;
TotalCost:91746.126.
Meanwhile, the overall distribution time is 697.08 virtual time.
Similarly, the simulation consequences of three warehouses (adjusted location) in the timelimited precedence solution can be obtained:
TotalRunCost:49418.701;
TotalDelayCost:0;
TotalCost:49418.701.
Meanwhile, the overall distribution time is 747.00 virtual time.
Comparison of the simulation results in three warehouses mode without adjusting, Tables 9 and 10, is obtained.


As shown in Tables 9 and 10, after the adjustment of warehouse location, the traveling costs, the tardiness costs, and the total costs are reduced, particularly in the timelimited precedence solution. All the time requirements in initialization data are met as the warehouse location adjusts and the tardiness costs are not generated. In this paper, the overall distribution time increases, which is primarily due to comprehensive conditions of selfraising points. If differences are shown, then the overall distribution time may be decreased.
4. Conclusions
This paper uses AnyLogic simulation software to model and simulate the vehicle distribution process. Then the results are analyzed and optimized on three factors including routes selection, warehouses quantity, and warehouses layout. As shown in the simulation consequences, the timelimited precedence solution can dramatically reduce the tardiness costs and the total costs; increasing the warehouses quantity can significantly lessen the overall delivery time; vehicle travelling costs, tardiness costs, and total costs can also be reduced by distribution of warehouse locations reasonably, which also have an influence on the overall delivery time. What can also be observed from the results is that the method studying logistics distribution by AnyLogic is feasible, which can visualize complicated problems and improve operability effectively. More optimal methods and algorithms like heuristic can be used in future research. The optimization module also can be contained.
Data Availability
All the data used to support the findings of this study are included in our manuscript and are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
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Copyright
Copyright © 2019 Xiang Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.