Annotated Bibliography

1. INTRODUCTION The Vehicle Routing Problem with Simultaneous Delivery and Pickup [1] (VRPSDP) is a variant of the traditional VRP. And it is the extension of Vehicle Routing Problem with Backhauls (VRPB) as well. This problem eliminates the service sequence constraint of delivery and pickup requirements. It considers the delivery and pickup process as a whole instead. As a result, it reduces the empty load ratio of vehicles in the transport trip or return trip and improves vehicle transportation efficiency in return. Customers have more and more pickup requirements with the development of E-commerce. They can submit an order of sending express via Internet at any time. Almost all of them hope that express companies can provide faster and better logistics service for them. These companies should make a quick response to the dynamic orders and adjust the existing routes in time when delivering and picking up expresses. This kind of dynamic vehicle routing problem with dynamic demand is so closer to the real world that it has become the research hotspot gradually. An adaptive local search algorithm was studied to solve the dynamic VRPB [2], it adopted the waiting strategies that delivery vehicles can wait in the places where potential customers are likely to occur; In the study [3], mixed vehicle routing problem with dynamic reverse demands and time windows was studied, solving process was divided into static and dynamic phases which were solved by record-to-record travel algorithm respectively. The results demonstrated that integrating dynamic reverse customers

This work is supported by Science and Technology Research Project of

Chongqing Municipal Education Commission of China (Grant No.KJ1603105).

timely in the current solution was more economical than sole arrangement; Considering waiting time and vehicle load, Lv[4] designed a dynamic insertion algorithm to adjust driving routes locally; Liu[5] studied a VRPSDPTW with known delivery demands and random pickup demands; Dynamic Requests Multi-depot Vehicle Routing Problem with replenishment on the way was proposed and it decomposed into a series of static MVRP, decoding method of the most neighboring method combined with greedy rules to control vehicle replenishment along the way was designed, it can reduce the number of used vehicles which can reduce the operating costs of the distribution center [6]; Ninikas[7] investigated a dynamic routing problem that dynamic pickup requests arriving in real time while a predefined plan of serving delivery requests is being executed. They proposed a branch-and-price approach and a novel insertion heuristic which is based on column generation and provided near optimal solutions in an efficient manner; Lin[8] proposed a prototype of a decision support system (DSS) that integrates a hybrid neighborhood search algorithm to solve the offline and online routing problems arising in courier service; For the order whose arrival time is unknown, but its probability distribution is available, Maria [9] proposed an adaptive service policy that aims at estimating the best time period to serve each request within its associated time window in order to reduce distribution costs; Hu[10] investigated a dynamic closed-loop VRP with uncertain pickup and deterministic delivery of incompatible goods, a solution method based on variable neighborhood search (VNS) is developed for solving the VRPSPD; In the study [11] , vehicles can exchange some of their transportation requests, selective requests may be served by the other vehicles while reserved requests will be served by

Delivery Vehicle Routing Problem with Simultaneous Delivery and Pickup in E-commerce Environment

ZHENG Jiajia 1, LIU Guorong2, GU Zhenyu2, BAI Xiaohui2 1. School of Business Administration, Chongqing City Management College, Chongqing 401331

E-mail: [email protected]

2. College of Automation, Chongqing University, Chongqing 400044 E-mail: [email protected]

Abstract: This paper proposes a vehicle routing problem with simultaneous delivery and pickup in E-commerce environment. When receiving a real-time pickup order, it is hard to deal with the contradiction between logistics cost and service timeliness for express company. A dynamic scheduling strategy is developed to allocate real-time requirements utilizing on-delivery vehicle economically and quickly. Firstly, preprocess dynamic pickup orders and determine the scheduling time, which can translate the dynamic demand problem into a series of static problems; Secondly, an improved PFIH algorithm is designed to insert the pickup requirements into existing routes and generate the optimized routes; Finally, with the help of Relocation method and 2-opt method, all unserved pickup requirements are readjusted and re-optimized by the improved PFIH algorithm again. The example shows that the designed algorithm can insert new pickup requirements into the routes of on-delivery vehicles, and re-optimize the optimized routes with new inserted requirements effectively.

Key Words: Simultaneous Delivery and Pickup, scheduling time, PFIH algorithm, Relocation method, 2-opt method

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themselves; customers’ time windows are divided into a plurality of stages, they are classified into customers who can be deferred and customers can’t be delayed according to the demand attributes in each stage[12]. Current studies about DVRPDP are mainly aimed at larger pieces of goods’ delivery, and goods distribution sites are more fixed relatively. With a smaller number of dynamic demands, these company’s demand management and vehicle scheduling is easier relatively in the past. Different from traditional VRPDP, simultaneous delivery and pickup problem of courier vehicles in E-commerce environment is faced with more decentralized and greater number of customers with much more dynamic and random requirements instead of fixed business customers. For these express companies, on the one hand, customers are extremely fragmented, delivery vehicle holds a high empty load ratio and transport capacity resources can’t be used effectively; on the other hand, faced with the new pickup orders, if vehicle utilizing frequency were too high, it would increase the logistics cost; On the contrary, customers would wait for a long time after submitting orders, which will reduce customers’ satisfaction degree. How to solve the contradiction between vehicle utilizing efficiency and timeliness of pickup is becoming an urgent problem for courier companies. In order to solve the problem that delivery vehicles’ transport capacity is wasted and new pickup customer can’t be satisfied in time, this paper proposes a delivery vehicle routing problem with simultaneous delivery and pickup in the E-commerce environment. This paper considers that when the courier vehicles are providing delivery and pickup service for pre-determined customers travelling along the planned routes, distribution center (DC) receives new pickup requirements. After updating all kinds of dynamic information and judging whether to start scheduling, new pickup task will be assigned to on-delivery vehicles. Routes will be optimized and updated in real time.

2. PROBLEM DESCRIPTION VRPSDP proposed in this paper is described as follows A distribution center of express company receives customers’ pickup demands in real time. According to the quantity of received requirements and time interval between two adjacent scheduling programs, the start time of scheduling t (n) would be determined, n is the sequence number of scheduling in this day. Taking locations, time demands of on-delivery vehicles and new pickup customers into account, these requirements are inserted into current routes of on-delivery vehicles under the premise of meeting all customers’ time demands. As for new requirements that can’t be inserted, it would be accepted by vehicles waiting in DC. The goal is to make a quick response to the dynamic requirements, and insert them into delivery vehicles’ routes in real time based on optimal principle. A feasible set of route can be found by minimizing the total delivery and pickup costs. This paper assumes that the locations, time windows of DC and delivery customers are known, and new pickup customers’ are unknown. Weight and volume of expresses are light and small normally, so this paper wouldn’t

consider vehicle weight and volume constraints. The quantity of vehicle departing from DC is limited and vehicles are homogeneous. Notation of the parameters and variables

Set of unfinished requirements of customers Set of new customers Set of virtual customers (on-delivery vehicles Set of on-delivery vehicles when Scheduling starts Set of vehicles in DC when Scheduling starts

K Set of vehicles, Travel cost coefficient of vehicles Departure cost (fixed cost) coefficient of vehicles Punishment coefficient when the vehicle arrives at

customer before Punishment coefficient when the vehicle arrives at

customer behind Earliest allowed start service time of customer Latest allowed start service time of customer Arrival time at customer Waiting time when arriving at customer before

Travel time from to Distance from to

Formula (1) is the objective function, the aim is to minimize the travel cost, fixed cost of vehicles and time penalty cost; constraint (2) and (3) make sure that each customer can only be serviced by one vehicle and be serviced only once. Constraint (4) is the computing method of arrival time and waiting time; Constraint (5) indicates that the number of vehicles departing from DC can’t exceed the total number of vehicles waiting in DC; Constraint (6) is the limit of total

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number of vehicles, respectively, is the number of vehicles waiting in DC, is the number of on-delivery vehicles, is the total number of vehicles; Formula (7) is the decision variable.

3. SOLUTION METHODOLOGY In this paper, this paper adopts a dynamic scheduling strategy involving Dynamic requirements preprocessing, Real-time demand batch insertion and Real-time route re-optimization in order to complete the new pickup requirements with on-delivery delivery vehicles. Firstly, the dynamic order is pre-processed to determine the time of batch scheduling, so as to reduce the cost and ensure the satisfaction degree of customers; secondly, an improved PFIH algorithm is designed to optimize the route in real time, it inserts the pickup demands into current paths and generates optimized routes; finally, all unfinished requirements which have been inserted in the current scheduling period or before the current scheduling period would be re-optimized by the improved PFIH algorithm again.

3.1 Dynamic demand Preprocessing In E-commerce environment, customer's new demands are random and unpredictable. If express enterprises arranged vehicles to collect the expresses instantly after receiving orders in order to improve satisfaction degree of customers, it would increase cost inevitably, frequent route changes are likely to affect the implementation of scheduling plans as well; however, if they waited for orders to reach the economic batch before collection for reducing the costs, it would cause overdue service which would affect satisfaction degree of customers necessarily. How to deal with these randomly new orders quickly and economically and have an advisable balance between satisfaction degree and pickup cost, become the first problem of express companies after receiving orders. Determining suitable scheduling time and preprocessing new orders can avoid waiting for a long time after customers submitting the order, and reduce the pickup cost. According to the quantity of requirements received in real time and time interval between two adjacent scheduling programs, the start time of scheduling would be determined. The planning period (one working day generally) can be divided into different time segments after determining the scheduling time. Each schedule is only directed to orders received before the scheduling time, so the new pickup requirements that need to be assigned are determined for each scheduling period, which translates DVRPSDP into a series of static problems. It is assumed that some requirements are known before start time of the working day, DC receives new pickup requirements at the time the quantity of new pickup requirements received during the time interval is , Q is critical value of new orders’ quantity, is the cumulative quantity of new orders, T is the fixed scheduling time, is the set of time moment whose time interval is T, is the start time of scheduling, n is the scheduling sequence number,

; The scheduling time can be determined according to the following equation as formula (8).

Update vehicles’ positions after determining scheduling time . Locations of vehicles consist of two conditions: distribution center and some spots on the way (including customer points). At current time, start and end points of vehicles waiting in DC are the point of DC, their driving routes are closed loops. But start points of on-delivery vehicles are their current locations instead of DC, and their driving routes are open paths. For on-delivery vehicles, if DC was viewed as a starting point, set of customers served would have to be considered, which could increase the complexity of VRP inevitably in a dynamic environment. In this paper, the concept of virtual customer is introduced to solve the problem. Current locations of on-delivery vehicles are set as virtual customers; these vehicles start from their current locations and must provide service for their virtual customers firstly. Current location of on-delivery vehicle is set as virtual customer , and beginning service time for virtual customer is the arrival time of this point, service time of virtual customer is 0,that is, . It is convenient to distinguish point sets between customers served and customers unserved by virtual customer. This paper uses these virtual customers as the starting points to solve the problem and needn’t to consider the customers served, then this problem can be converted into one mixed vehicle routing problem with closed and open loop, where vehicles start from the distribution center or virtual customers, and finally return to DC in the nth scheduling period.

3.2 Real-time optimization Push Forward Insertion Detection Method was firstly proposed by Solomon, it is one of the most important methods to solve time constraint detection of VRPTW [13]. Solomon [14] took both the distance and time factors into consideration, proposed four heuristic algorithms of VRPTW and three kinds of evaluation functions. It proves that the solution of form 1 is better than form 2 and 3. In addition, he also pointed out that when time window is narrow, it is better to select the unserved customer furthest from the DC as the starting customer of the route. According to the 1st evaluation function form Solomon proposed, this paper designs improved Push Forward Insertion Heuristics (PFIH) Algorithm. The optimized and re-optimized routes are generated by this algorithm. It determines the optimal inserted customer and its optimal insertion position by calculating the insertion cost. It is assumed that feasible route is the route of vehicle , u is the unserved customer to be inserted into the edge between and , is the beginning service time of , is new beginning service time after this route being inserted into u. In order to reflect the increase of beginning service time after the customer point being inserted, the concept of Push Forward (PF) is introduced.

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Calculation method of as formula (9), (10), (11):

The steps of improved PFIH algorithm are as follows

Step 1: Update the new requirements information, unserved customers and on-delivery vehicles information;

Step 2: Select the pickup requirement to be assigned. Calculate the distance between each new point and distribution center , select the point where distance is the largest as the point u who would be assigned successively;

Step 3: Determine the insertion position. Judge whether the point u can be inserted into any customer point pairs in the route ,

Step 3.1: Judge whether the time window of u is satisfied if u were inserted into any customer point pairs , judgment method as formula (12),

Step 3.2: Judge whether the time windows of

follow-up customer are satisfied if u were inserted into any customer point pairs, judgment method as formula (13),

Step 3.3 If these conditions above are satisfied,

calculate the insertion cost inserting u into the feasible position, if not, it is assumed that M is the maximum number and IC=M, calculation method as formula (14),

Step4: Determine the best insertion position. Select feasible position whose IC value is the smallest as the best insertion position;

Step 5: Check if there are more than one points inserting into one route. If so, turn Step 3, if not, turn Step 6;

Step 6: Check if all pickup orders have been assigned in this scheduling program. If so, end; if not, turn Step 7;

Step 7: Check if there is no available vehicle in DC. If so, the unassigned requirements would be moved to next scheduling period; if not, the unassigned requirements would be accepted by vehicles in DC.

It can be found the best insertion position of unallocated requirements by the improved PFIH algorithm. However, it’s hard to guarantee new generated routes are optimal after inserting all unallocated requirements. It is necessary to optimize the route further. Optimization and improvement to initial route can be realized by local search method [15]. The method of local search between the routes and local search in the route are used to optimize initial solution, it proved that optimized route generated by improved

algorithm with reposition method and 2-opt method is the optimal[16]. Because expresses are obviously customized, it must be delivered to specific customer. After these vehicles leaving DC, scheduling center is hard to exchange the delivery tasks belong to different routes. But it is feasible to exchange the pickup tasks. At the real-time re-optimization stage, a customer node is moved from one route to another route using the relocation method (see Figure 1) where remove and reinsert operation is executed; two edges of one route are replaced by two edges belong to another route using 2-opt method (see Figure 2) where exchange operation is executed. Then the improved PFIH algorithm can be used to optimize the routes again.

Fig 1.Relocation method

Fig 2.2-opt method

For those delivery customers, Customers’ adjustment between on-delivery vehicles wouldn’t be carried out after the DC generating the initial routes, it is allowed to change delivery customers’ service sequence by 2-opt method. For those pickup customers, it is permitted to change the service sequence and exchange pickup tasks. Relocation method is used to remove the customer to other routes, 2-opt method is used to change the service sequence of pickup customer.

4. AN ILLUSTRATIVE EXAMPLE This paper selects 100-customers instances of Solomon benchmark instances as illustrative example and selects the problem set r110 randomly from problem sets R1.

4.1 Original routes In the actual distribution process, there are several original delivery routes generating by DC before vehicles leaving from DC. In this paper, this paper selects 10 groups of data from problem set r110 randomly as the new added pickup customers, and the rest are viewed as certain customers. According to the location, time window and requirement, the original routes are generated as shown in Table 1:

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Table1. Original routes

n Route Total cost 1 0-2-41-22-74-73-40-26-54-24-0 140.92 2 0-21-72-75-56-23-39-25-55-4-0 152.46 3 0-27-69-51-9-35-34-78-33-1-0 150.00 4 0-28-76-12-29-81-79-3-77-68-80-0 134.82 5 0-31-11-63-90-10-20-66-65-0 176.19 6 0-52-7-82-18-8-46-48-89-0 187.20 7 0-83-45-84-5-6-94-96-97-13-58-0 127.78 8 0-88-62-19-47-36-49-64-70-0 152.76 9 0-92-98-100-44-16-86-38-14-37-0 134.21 10 0-95-59-99-93-85-87-57-15-43-42-0 130.21 1486.67

It is assumed that DC receives 10 pickup orders continuously. Scheduling time is determined and . The earliest allowed start service time of virtual customer is equal to the current scheduling time , that is , the latest allowed start service time of virtual customer is equal to the latest allowed start service time of the first customer behind this virtual customer in the route of this vehicle, that is , vehicle whose serial number is 0 represents this vehicle is waiting in DC, its location and time window is the same as DC respectively whose location is (35,35) and time window is (0,230). Here are locations and time windows of on-delivery vehicles (see Table 2).

Table2. Location and time windows of vehicles

vehicle 1 2 3 4 5 location (35,29) (38,31) (35,40) (40,36) (34,40)

TW (5,89) (5,96) (5,156) (5,79) (5,85) vehicle 6 7 8 9 10 location (32,39) (30,36) (29,39) (32,31) (31,32)

TW (5,88) (5,97) (5,133) (5,181) (5,83) Pickup customers to be assigned in this scheduling program are as follows: 17, 30, 32, 50, 53, 60, 61, 67, 71, 91 The distribution of new customers, on-delivery vehicles and their routes are as shown in figure 3,

Fig 3.Routes, locations of vehicles and new customers’ distribution

4.2 Real-time optimization Taking the new customer 53 as an example, an improved PFIH algorithm is used to insert the point into some routes.

Possible insertion positions of this point and their insertion costs are as shown in Table 3

Table3. Possible insertion positions of customer 53

IC[i][j] IC[i][j] IC[i][j] [0][0]=41.304382 [2][3]=57.471485 [7][0]=49.321125 [0][1]=38.519165 [3][0]=46.295300 [7][1]=49.911434 [0][2]=43.846031 [3][1]=35.023548 [8][0]=45.488098 [0][3]=40.816109 [3][2]=26.381090 [8][1]=45.894180 [0][6]=12.782240 [4][1]=47.015064 [8][2]=42.258427 [1][0]=29.333740 [5][0]=42.779568 [8][3]=47.274319 [1][1]=30.294168 [5][1]=26.563047 [9][1]=43.771572 [1][3]=45.476616 [6][0]=49.790073 [9][2]=37.733715 [2][0]=51.289654 [6][1]=51.867359 [9][3]=37.478859 [2][1]=44.539963 [6][2]=43.621494 [2][2]=28.589418 [6][4]=27.510660 IC[i][j] shows the insertion cost inserting one new customer into the position between customer and customer in the route . If the new customer point can’t meet their own time requirement or any subsequent customers’ requirements, the IC value would be equal to M whose numerical value is infinitely great. In this example, minimum insertion cost IC[0][6] =12.782240 New customer point 53 would be inserted into the position between the 7th customer and the 8th customer in route 1. The symbol represents the virtual customer’s location of on-delivery vehicle , all customers are assigned using improved PFIH algorithm, and optimized routes inserted into new customers are generated (see Table 4 and Figure 4).

Table4. Optimized routes

n Route Total cost 1 -2-41-22-74-73-40-(53)-26-54-24-0 154.62 2 -21-72-75-56-23-(67)-39-25-55-4-0 170.74 3 -27-69-(30)-51-9-(71)-35-34-78-33-1-0 134.24 4 -28-76-12-29-81-79-3-(50)-77-68-80-0 152.36 5 -31-11-63-90-10-20-66-65-0 175.91 6 -52-7-82-18-8-46-48-(60)-89-0 198.20 7 -83-45-(17)-84-5-6-94-96-97-13-58-0 117.71 8 -88-62-19-47-36-49-64-(32)-70-0 162.94 9 -92-98-100-44-16-86-38-14-37-(91)-0 148.77 10 -95-59-99-93-(61)-85-87-57-15-43-42-0 141.54 1557.03

Fig 4.Optimized routes with new customers

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4.3 Real-time re-optimization Optimized routes are re-optimized by relocation method, 2-opt method and improved PFIH algorithm. It is shown that the route 7,9,10 can be re-optimized (see Figure 5).

Fig 5.Re-optimized routes of route 7,9,10

Customer 58 of route 7 is relocated to terminal position of route 10; customer 93 of route 10 is relocated to the position of route 9; and customer 100 of route 9 is changed the service sequence by 2-opt method. Re-optimized routes plan is slightly better than the optimized routes plan in the respect of total distance and total time, and it's remarkable that the total cost has a 6.5% decline compared to the optimized routes (see Table 5).

Table5. Re-optimized routes of route 7,9,10

n Route Distance Time Cost 7 -83-45-17-84-5-6-94-

96-97-13-0 83.81 208.78 113.75

9 -92-98-44-16-86-38-1 4-37-[100]-91-[93]-0

107.12 232.51 137.89

10 -95-59-99-61-85-87- 57-15-43-42-[58]-0

99.92 224.97 130.01

5. CONCLUSION In e-commerce environment, customers are more scattered and have higher timeliness requirements. It is hard to solve the contradiction between cost of express companies and satisfaction degree of customers. In order to solve the problem that delivery vehicles’ transport capacity is wasted and new pickup demand can’t be satisfied in time, this paper studies vehicle routing problem of delivery vehicles in E-commerce environment. This paper adopts a dynamic scheduling strategy involving Dynamic requirements Preprocessing, Real-time requirements batch insertion and Real-time route re-optimization. Firstly, the dynamic order is pre-processed to determine the time of batch scheduling; Then an improved PFIH algorithm is designed to optimize the route in real time, it inserts the pickup requirements into the current paths and generates optimized routes; finally, all unfinished requirements which have been inserted in current Scheduling period or before the current scheduling period would be re-optimize by the improved PFIH algorithm again. The example shows that the improved algorithm can insert new pickup requirement into the route

of on-delivery vehicle and re-optimize the optimized routes with new inserted requirements effectively.

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