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Parcel Delivery by Collaborative Use of Truck Fleets and Bus-Transit Vehicles.

Abstract

City express delivery demand is characterized by large quantities, small parcel sizes, dense batch frequency, and timeliness. To meet demand and control costs and C[O.sub.2] emissions from parcel delivery, a collaborative delivery mode using bus vehicles and a truck fleet is proposed. A model is built to optimize delivery schemes based on a bus-road mixed network and thus minimize the fixed cost, the delivery cost, the compensation cost for the emitted C[O.sub.2], and the unpunctuality penalty cost. An ant-colony algorithm is designed to solve the model. Delivery schemes for the 97 demand sites in a Chinese city are calculated under collaborative mode and truck-only mode. The advantages of a collaborative mode are verified by comparing the two types of delivery schemes.

Keywords

City logistics, collaborative delivery, transit network, two-echelon vehicle routing problem, ant-colony algorithm

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Due to the rapid tempo of modern life and advancements in e-commerce, consumers have grown accustomed to purchasing goods on the Internet. As a consequence, there has been a substantial increase in parcel deliveries. Due to the nature of e-commerce, city delivery is characterized by large quantities (e.g., 179,700 parcels per day in Dalian city), small parcel sizes, dense batch frequency, and timeliness (Savelsbergh and Van Woensel 20i6). Thus, delivery companies are faced with increasingly complex issues regarding vehicle scheduling, link planning, and truck stowage, and designing delivery schemes is difficult for a given fleet of trucks and drivers (Faugere and Montreuil 2016). To address this problem, most delivery companies increase capacity and extend detour distances and working hours. However, the result is more truck usage, longer travel times, and greater traffic loads. Finally, more delivery trucks and longer traveled mileage have aggravated the traffic congestion. On the city level, to control and manage freight transport, trucks are banned during rush hours, and delivery typically takes place during off-peak hours (Holguin-Veras and Polimeni 2006), which may be beneficial for the environment. However, these measures may reduce the timeliness and efficiency of parcel delivery.

Meantime, urban passenger transport also causes traffic congestion. As car ownership has increased, more personal trips are taken by cars. The increment in personal car trips has led to serious traffic congestion and pollution (Wang and Zhou 2015). In response, large cities are undertaking efforts to alleviate traffic congestion and reduce traffic emissions. For example, substantial investments are being made in road and urban railway systems. As a result, a large number of bus terminals and depots are being put to use, many new bus routes are being opened or extended, and bus operating frequencies are increasing. In large Chinese cities, the time headways of buses have fallen to 3-5 minutes during rush hour. All large cities have a dense bus-transit network, which is convenient for travelers.

In passenger transport systems, enhancing public transit and vehicle sharing are two key measures to reduce congestion. This inspired us to apply the same principles to parcel delivery. The accessibility, dense frequency, and stowage space offered by bus transit are well matched to the attributes of express parcel delivery, that is, large quantities, small parcels, dense batch frequency, and timeliness. We propose using buses as a supplementary delivery mode in conjunction with trucks. When some parcels are delivered by buses instead of trucks, truck travel will decrease, and bus travel will not increase. Therefore, the delivery cost and C[O.sub.2] emissions may decrease, while bus utilization will increase. Moreover, buses can transport parcels during rush hours in central areas (i.e., areas where trucks are usually banned during rush hours), which may extend the delivery time and increase the delivery timeliness and efficiency.

The integration of passenger and freight transport has already been adopted in long-haul freight transport. For example, in air transport, passenger planes carry cargo in the belly of the aircraft (Yu, Yang, and Yu 2017). In maritime transport, passenger ships, such as ro-ro ships, carry trucks in the lower cabins. In highway transport, intercity coaches carry cargo in the lower cabins (Yang et al. 2013). Urban areas also offer examples. In Zurich tramway lines are used to collect large and heavy rubbish and electrical items. In Dresden supplies to the Volkswagen factory are delivered by tram. In both cases, the utilization of passenger transport vehicles is improved, thereby reducing the number of truck trips. These collaborative transports are adopted by a single company to deliver single types of cargoes. The simplicity of the freights' origins and destinations makes the delivery easy to accomplish. However, the destinations and time windows of e-commerce parcels are much more complicated, and matching parcels with bus vehicles is difficult and cannot be achieved on instinct alone. Instead, a programming model should be used to assign parcels to bus vehicles and connect the bus vehicles with the trip-end trucks for relay deliveries.

The existing literature considers collaborative transport as a type of vehicle routing problem (VRP) and build corresponding models (Masson et al. 2017). In these models, some unrealistic assumptions, which may simplify the problem, have been made (Savelsbergh and Van Woensel 2016). Examples include assuming that the details of passenger travel demand and cargo transport demand are known at the beginning of a day (Ghilas, Demir, and Van Woensel 2013, 2016) and assuming that the costs of modifying bus vehicles, transshipment between buses and trucks, and bus delivery can be neglected (Masson et al. 2017). Moreover, some adoptions of bus service may affect the service level or timeliness of bus transit. That is, bus routes may be adjusted for parcel delivery (Ghilas, Demir, and Van Woensel 2013, 2016), and parcels can be loaded and unloaded on any bus stops (Masson et al. 2017; Trentini et al. 2010). These assumptions and adoptions may be reasonable if the volumes of passengers and parcels are small. However, in the case of greater volume, they may induce some unrealistic delivery schemes.

Given the above context, this article proposes an advanced collaborative delivery mode based on the joint use of buses and trucks and establishes a model to design vehicle routing and cargo delivery (including parcel batch composition, departure times, and the vehicle link for each batch) schemes that minimize the total cost of parcel delivery. In our collaborative delivery mode, (1) the costs of bus vehicle modification, bus delivery, and transshipment between buses and trucks are taken into account; (2) parcels can be loaded and unloaded only at terminal bus stops; and (3) bus routes are fixed and trip-end deliveries are still done by trucks.

According to Ghilas, Demir, and Van Woensel (2013), a good collaborative transport scheme should take into account both the spatial consolidation of delivery routes and the time coordination of two types of vehicles. The main aim of consolidation is to make the whole scheme more efficient, while the coordination is to make each delivery behavior precise, well timed and well organized, and realize an accurate vehicle connection. Therefore, the delivery scheme should include the delivery routes and the times when parcels reach each node. To realize this, a bus route is abstracted as a dummy node (as shown in fig. 1, where BS denotes the terminal bus stops, B denotes the dummy node, DC denotes the distribution center and circles denote the demand sites). Then, a route that is based on collaborative delivery of truck and bus can be represented by a set of real nodes (DCs and demand sites) and a dummy node, in which the links in front of and behind the dummy node are served by trucks, and delivery to the dummy node is performed by buses. In this case, the problem can be considered as a two-echelon vehicle routing problem (2E-VRP). In 2E-VRP, two levels of VRP are considered. The first level is the delivery from the DC to the satellite facilities, and the second level is the delivery from the satellites to the demand sites. In our problem, the dummy node works as a satellite, and in the first level, parcels can be delivered not only to satellites but also to demand sites. Thus, we define this problem as a two-echelon vehicle routing problem with fixed scheduled lines (2EVRP-FSL).

The contributions of this article are as follows: (1) in the condition of without changing the routes, dispatching frequencies, and stop locations of bus transit in a city, we build a mixed-integer model to design the collaborative delivery schemes and illustrate the feasibilities and efficiencies of the collaborative parcel delivery by jointly using trucks and bus vehicles; (2) we propose a method to solve the 2E-VRP as a VRP by converting the research subject from vehicles to parcels; (3) we design an advanced ant-colony algorithm, which can solve large scale problem in the real case; and (4) we offer some suggestions for collaborative delivery based on the impacts of the unit bus delivery price and unit penalty cost for delivery delay on the total cost and C[O.sub.2] emissions.

The remainder of the article is structured as follows. The next section provides a review of existing works. Then, we give a detailed description of the problem. Section Model Construction introduces the mixed-integer formulation for this particular problem. Section Solution Algorithm provides the algorithm for the model. Section Case Study reports the results obtained from computational experiments, compares different results in truck-only mode and collaborative mode, and performs sensitivity analysis. Conclusions are stated in last section.

Literature Review on Relevant Problems

Limited literature on integrating passenger transport and freight transport is available. To the best of our knowledge, Trentini and Malhene (2010) first conducted a survey on sharing transport between passengers and freight and provided relevant concepts and solutions to improve urban mobility. The solutions indicate the possibilities of combining passenger and freight transport (e.g., using a tram for freight transport). Ghilas, Demir, and Van Woensel (2013) studied parcel delivery by public transit, and an arc-based mixed-integer programming model was built to optimize passenger and parcel routes simultaneously. In several instances, he clarified the benefits of integrated passenger and freight transport. Li et al. (2014) investigated the share-a-ride problem of taxies. They studied the problem of parcel delivery by taxi and proposed a large neighborhood search heuristic. In France Gonguet et al. (2014) proposed a new service for rural areas that integrates mixed transport in a network with regular lines and demand-responsive vehicles. Masson et al. (2017) investigated the management of urban transport flows by combining passenger and freight transport. The main concept of their study was to use the spare capacity of city buses to carry goods into central business districts. The idea emerged in the context of B2B parcel delivery by near-zero emissions vehicles. The goal of the study was to provide useful insights into the feasibility and operating costs of deploying freight transport within the system. Ghilas, Demir, and Van Woensel (2016) studied the possibility of taking advantage of available public transit as a part of the freight journey. They view this specific transport problem as a "pickup and delivery problem with fixed scheduled lines" (PDP-FSL). An adaptive large neighborhood search heuristic is proposed to solve the problem.

Although efforts have been made in the theoretical research and in practice to address the collaborative transport of freight and passengers, according to Ghilas, Demir, and Van Woensel (2016), a sufficient integrated transport solution to short-haul transport has never been realized. In fact, in short-haul transport, passengers and freight rarely share modes, although for the most part they share the same infrastructure, highlighting the potential efficiency gains from an integrated approach (Lindholm and Behrends 2012). Table 1 provides an overview of the related literature.

Problem Description

In a collaborative delivery system, there are two types of vehicles for parcel delivery: trucks and buses. In the service of passengers, buses cannot remain at stops for a long time, and parcels can be handled only at the terminal stops. Thus, trucks are also needed to transport parcels from the terminal stops to their destinations. A parcel can be delivered in two ways: (1) delivery to the destination by truck; (2) delivery from the distribution center to a terminal stop (called a start terminal stop) by truck first, transfer by buses to the terminal stop on the opposite side of the same bus route (referred to as an end terminal stop), and finally, delivery by another truck to the destination. To avoid reductions in passenger capacity, parcels should not occupy vehicle space that is dedicated for passengers, and it should be recognized that the parcel holding capacity of buses is far less than that of trucks. A single batch of parcels delivered by a truck at one time may require the service of multiple buses (called a bus group).

To determine the delivery routes of parcels, two conversions are necessary. First, the object of study should be the batches of parcels rather than the vehicles. Assuming that parcels in a batch are packed in a box, then making a delivery scheme for the boxes is similar to determining a vehicle dispatch scheme in a normal VRP. With the box delivery scheme, the delivery plans of trucks and transport plans of buses can be obtained. Second, bus routes are set as dummy nodes, B. Because the bus routes are given, and bus vehicles always transport parcels from the start terminal stops to the end terminal stops, the dummy nodes, B, can be seen as a type of demand site. In this case, in a route with a dummy node, parcels with destinations after the dummy node are transported by bus first and then delivered by truck. Thus, we convert the integrated route in figure 1 into a simple route, shown in figure 2, which consists of a truck route (the solid arrow) and dummy node B. The delivery route for one batch of parcels may contain two circles due to the existence of B rather than one circle, as in a general VRP.

In the bus and truck integrated network, one batch of parcels canbe delivered to both dummy nodes and demand sites, unlike the situation in 2E-VRP. Indeed, in 2E-VRP, the parcels will be delivered to satellites first and then to the demand sites. Therefore, the problem considered here differs from the general 2E-VRP, and the method of dividing a 2E-VRP into 1+n VRPs cannot be used. Thus, we must find a new method to solve the 2E-VRP as a single VRP.

If we delete the links from the final demand site to B and from B to the origin (the dotted lines in fig. 3) and add a dummy link from the final demand site to the origin (the dashed line in fig. 3), the two-circle route to deliver one batch of parcels becomes a one-circle route. From the delivery scheme optimized based on this discussion, after adding links from B to the origin and from the final demand site to B and deleting the link from the final demand site to the origin, we obtain the delivery scheme of the original problem and the value of the objective function. In this way, the 2E-VRP can be solved as one VRP, and the spatial consolidation of delivery routes is realized.

Because buses are dispatched based on fixed frequencies, the connection time of trucks and buses is a key issue in temporal coordination. Figure 4 shows issue and how delivery occurs from site 1 to site 2 by bus route B and trucks. To illustrate the whole process, we further divide dummy node B into nodes [B.sub.1], [B.sub.2], [B.sub.3], and [B.sub.4] to represent the start times of different periods. [B.sub.1] indicates the time when parcels are unloaded from a truck at a start bus terminal stop. Node [B.sub.2] indicates the time when parcels are loaded onto buses and wait for delivery. Node [B.sub.3] indicates the time when parcels arrive at the end bus terminal stop and wait for unloading. Node [B.sub.4] indicates the time when parcels are loaded onto another truck from a bus to await delivery.

Moreover, node [B.sub.2] is further divided into n subnodes based on bus departure times. After being unloaded from a truck, a parcel reaches node [B.sub.1] and then moves to the first unoccupied subnode ([B.sup.t2.sub.2] in fig. 4) between [B.sup.t1.sub.2] and [B.sup.tn.sub.2]. Through [B.sup.t2.sub.2], the parcels reach node [B.sub.3] and wait for a truck to relay delivery to [B.sub.4]. They finally reach site 2 by truck. The solid arrow lines in Figure 4 show the delivery route. In this way, we are able to know the time when parcels arrive at dummy nodes and demand sites; in addition, the time coordination of the two types of vehicles is demonstrated.

Here, we may use a small example to clarify how the delivery scheme of the trucks and bus vehicles can be obtained. As shown in figure 5, rectangles and rhombuses represent the distribution center and the bus route at different time points, respectively, and the circles in one row represent a demand site at different times. The time windows of the demand sites are displayed on the left. Solid black lines represent the route of a truck departing from the distribution center. The three solid lines on the right side represent the route of a truck departing from the end terminal stop. Solid lines between rhombuses represent the bus route in a delivery route. The dotted lines represent the wait time of parcels at terminal stops.

Here, the route of a box is D-1-B-2-3-B-D, which indicates that parcels to demand sites 2 and 3 are transshipped by bus route B. Because demand sites 1 are located on the route from D to B, it is clear that the truck on this route delivers the parcels to both the start terminal stop and the demand site. Here, the route of the truck starting from center D is D-i-B-D. The route of the truck starting from the end terminal stop is B-2-3-B. The parcels being delivered to demand sites 2,3 are transshipped by bus. In this way, the problem of box delivery is similar to the vehicle dispatching problem in the general VRP. In the next section the model for this problem is constructed.

Model Construction

For modeling, the following assumptions are made:

A1: The speed of vehicles and the period of service time are known beforehand and remain unchanged during a planning horizon. This assumption is also used by previous studies (see, e.g., Ghilas, Demir, and Van Woensel 2013).

A2: Each bus terminal stop is considered as a transfer point for packages (e.g., DHL-Packstation, http://www.dhl.de/en/ paket/pakete-empfangen/packstation.html). Packages can be stored until their departure time at these terminal stops (e.g., Ghilas, Demir, and Van Woensel 2013).

A3: Parcels can use some space that is not used by passengers without impacting the passenger flow (Masson et al. 2017).

A4: A bus route is abstracted as several nodes based on the departure frequency.

Sets in the model:

O - set of distribution centers

B - set of dummy nodes, which represent bus routes

K - set of trucks that depart from the distribution center

P - set of delivery batches

N - set of nodes, such as distribution center, demand sites and dummy nodes of bus routes

[N.sup.c] - set of demand sites

The decision variables of the model are the following:

[t.sub.ikp] - the time when truck k, carrying batch p, departs from the center, [for all]i [member of] O; [for all]k, p

[mathematical expression not reproducible]

[mathematical expression not reproducible]

The intermediate variables of the model are as follows:

[mathematical expression not reproducible]

[mathematical expression not reproducible]

[mathematical expression not reproducible]

The parameters used in the model are the following:

[c.sup.e] - unit compensation cost for CO emissions

[c.sup.b1] - fixed cost of a bus vehicle

[c.sup.t1] - fixed cost of a truck

[c.sup.t2] - unit truck delivery cost

[c.sup.b2] - unit price paid by the delivery company to the bus operator

[c.sup.h] - unit transshipment cost

[c.sup.p] - unit penalty cost for unpunctual time

[E.sub.c] - CO emissions factor of trucks

[D.sub.ij] - distance from node i to node j

[D.sup.j] - distance between start terminal stop and end terminal stop of bus route j

[q.sub.i] - weight of parcels for demand site i

[t.sup.truck.sub.ij] - transport time between node i and node j

[t.sup.d.sub.j] - the departure time of the first bus in bus route j

[t.sup.s.sub.j] - service time at node j, including the loading and unloading time; if node j is a dummy node, the time that parcels spend on-board the bus vehicle is also included.

[t.sup.l.sub.j] - loading time at dummy node j

[t.sup.s.sub.t], [t.sup.e.sub.i] - start and end time of the time window of node i

[W.sup.k] - total loading weight of truck k

[W.sup.b] - total loading weight of a bus group

[T.sub.s] - time that trucks and buses start working

[T.sub.e] - time of trucks and buses ending work

The model is as follows:

Min [C.sub.f] + [C.sub.d] + [C.sub.t] + [C.sub.e] (1)

[mathematical expression not reproducible] (2)

[mathematical expression not reproducible] (3)

[mathematical expression not reproducible] (4)

[mathematical expression not reproducible] (5)

[mathematical expression not reproducible] (6)

[mathematical expression not reproducible] (7)

The objective (eq. 1) is to minimize the total cost, which includes the fixed cost (eq. 2), the delivery cost and the transshipment cost (eq. 3), the penalty cost for unpunctual time (eq. 4) and the compensation cost for C[O.sub.2] emissions (eq. 5). Equation 6 means that if truck k is in use, [x.sup.truck.sub.k] = 1; otherwise, [x.sup.truck.sub.k = 0. Equation 7 means that if bus route j is in use, [y.sup.bus.sub.j] = 1; otherwise, [y.sup.bus.sub.j = 0.

[mathematical expression not reproducible] (8)

[mathematical expression not reproducible] (9)

[mathematical expression not reproducible] (10)

[mathematical expression not reproducible] (11)

[mathematical expression not reproducible] (12)

Equation 8 means that if parcels to demand site j are delivered in batch p, [g.sub.jp] = 1; otherwise, [g.sub.jp] = 0. Equation g ensures that if one batch is delivered collaboratively, then the truck should connect to the terminal stop. Equation 10 shows the method to calculate the time that batch p departs from node j. Equation 11 guarantees that if bus route j is used to deliver batch p, then the parcels in batch p should be loaded on the buses before the bus departure time. Equation 12 calculates the earlier or later arrival time of parcels at demand sites.

[mathematical expression not reproducible] (13)

[mathematical expression not reproducible] (14)

[mathematical expression not reproducible] (15)

[mathematical expression not reproducible] (16)

[mathematical expression not reproducible] (17)

Equations 13 and 14 are the truck and bus vehicle capacity constraints. Equation 15 guarantees that each node must be served only once. Equation 16 guarantees that the trucks must return to the centers they departed from. Equation 17 guarantees that the service time of trucks and bus vehicles is within the operation time period.

[mathematical expression not reproducible] (18)

[mathematical expression not reproducible] (19)

[mathematical expression not reproducible] (20)

[x.sub.ijkp] = 0; [for all]j [member of] O; [for all]I [member of] B; [for all]k [member of] K; [for all]p [member of P (21)

[x.sub.ijkp] = {0,1} [for all]i, j [member of] N; [for all]k [member of] K; [for all][ [member of] P (22)

[mathematical expression not reproducible] (23)

[[summation].sub.j [member of] N] [[summation].sub.k [member of] K] [x.sub.ijp] [less than or equal to] 1; [for all]I [member of] O; [for all]p [member of] P (24)

Equation 18 calculates the time when a truck returns to the distribution center and prepares for its next departure. Equation 19 guarantees that the times at which trucks depart from the distribution center will not conflict with each other. Equation 20 guarantees that each delivery batch can be transferred only by a bus route once or less. Equation 21 indicates that the chosen bus routes must transport parcels. Equation 22 indicates that [x.sub.ijkp] is a 0-1 variate. Flow conservation is considered in equation 23. Equation 24 ensures that each batch leaves the depot at most once.

Solution Algorithm

To solve the above problem, we refer to three evolutions of VRP: the heterogeneous fleet vehicle routing problem (HFVRP), the vehicle routing problem with a private fleet and common carrier (VRPPC) and the two-echelon VRP (2E-VRP).

The HFVRP is a variant of the VRP in which the vehicles may have different capacities, fixed costs and variable unit costs. Golden et al. (1984) were among the first to tackle this problem using a constant unit variable cost. They developed algorithms and two implementations of the giant tour-based algorithm. Different algorithms were subsequently proposed to solve this problem, such as the tabu search heuristic (Gendreau et al. 1999), the backtracking adaptive threshold accepting algorithm (Tarantilis, Kiranoudis, and Vassiliadis 2004), adaptations of the variable neighborhood search (VNS) (Imran, Salhi, and Wassan 2009), two memetic algorithms (Prins 2009) and the iterated local search heuristic (Penna, Subramanian, and Ochi 2013). Many extensions of HFVRP have been proposed to solve more practical problems, such as the multidepot HFVRP with time windows (Dondo and Cerda 2007; Paraskevopoulos et al. 2008; Prieto et al. 2011), the HFVRP with time windows and multiple products (De la Cruz et al., 2013), the HFVRP with time windows and split deliveries (Belfiore and Yoshida Yoshizaki 2009; Campos, Yoshizaki, and Belfiore 2006), and the HFVRP considering carbon emissions (Kwon, Choi, and Lee 2013). In general, in these studies heterogeneous fleet vehicles are used to deliver parcels, and all vehicles in the fleet can determine delivery routes and departure times freely.

In VRPPC, due to low capacity or profit maximization, an operator deputes some work to external collaborative companies with payment (Hou et al. 2014). Volgenant and Jonker (1987) proposed the VRPPC in the case of one vehicle. Diaby and Ramesh (1995) solved the model of a case study with 200 customers by the branch and bound method. The solution of the VRPPC in the case of multiple vehicles was first proposed by Chu (2005), who solved the problem heuristically through a savings-based construction procedure. Bolduc et al. (2008) later proposed a set of benchmark instances of different types of vehicles. Cote and Potvin (2009) proposed a tabu search algorithm for the VRPPC. In the studies concerning VRPPC, the links of the trucks must be replanned after a new task is received, and the delivery links of different vehicles are planned by the carriers.

Meanwhile, many studies and algorithms have attempted to solve 2E-VRP. According to Feliu et al. (2007), in a 2E-VRP demands are first delivered from the distribution center to the satellites and then from the satellites to customers. Jepsen, Spoorendonk, and Ropke (2013) proposed an edge flow model and a branch-and-cut algorithm. Baldacci, Mingozzi, and Roberti. (2011) introduced a new route relaxation called ng-route for VRP. Baldacci et al. (2013) subsequently proposed an exact method that decomposes the 2E-CVRP into a limited set of multi-depot capacitated VRPs with side constraints. Because 2E-VRP is NP-hard, a large number of heuristic algorithms are employed (Grangier et al. 2016; Hemmelmayr, Cordeau, and Crainic 2012). For the solution, 2E-VRP is often divided into two VRPs, where the first-echelon VRP is solved to determine the delivery links from the distribution centers to the satellites and the second-echelon VRP is solved to determine the delivery links from the corresponding satellites to the demand sites. Our model is an extension of the 2E-VRP with a time window constraint. It is clearly an NP-Hard problem. For practical applications, it needs to be solved by a heuristic algorithm (Labadi, Prins, and Reghioui 2008).

Ant-colony optimization (ACO), which is inspired by the behavior of ants seeking food in the real world, is a probabilistic technique and has been used for solving combinatorial optimization problems, such as traveling salesman (Dorigo 1996), vehicle routing (Bell and McMullen 2004; Yu and Yang 2011; Yu, Yang, and Yao 2009;), quadratic assignment (Gambardella, Taillard, and Dorigo 1997), and job-shop scheduling (Colorni et al. 1994). However, Doerner, Focke, and Gutjahr (2007) found that ACO can be outperformed when solving VRPs. As mentioned before, to solve our problem we changed the study object from the vehicles to the batches of parcels; thus, the route design is similar to the food-searching process of ants. When searching for food, ants first choose foods and, step by step, the intermediate nodes form a loop with their nest as the start and ending points. Here, we can take the DC as the nest, the demand sites as food, and the dummy nodes as intermediate nodes. Then, ACO can be used to solve the model. The detailed solution steps are as follows:

Step 1: Initialization. The initial attractions of all links are assumed to be the same. Each link is given an initial weight [[bar.[tau]] = C, where C is set by trial test. The number of ants is set as the number of demand sites. All ants will depart from the distribution center.

Step 2: Determine the expected value of links. Let [[eta].sub.ij] represent the expected value of choosing a link (i, j). It is set as the reciprocal of the delivery cost and the penalty cost for unpunctual time and C[O.sub.2] emissions on link (i, j). If the dummy box has been transferred previously, the bus delivery cost for the new node j will be added, and the time limitation of trucks departed from this end terminal stop will be considered. If the time chosen for this dummy box has been chosen before, a large number will be added to the total cost to prevent this scheme from being executed.

Step 3: Calculate the next feasible node. Each demand site must be visited by an ant only one time; thus, the feasible nodes include only the unvisited points and the start terminal stops when the current node is a demand site. When the current node is a start terminal stop, the feasible node must be the final terminal stop at the same bus route. To select the next node from the set of feasible nodes, we need to know the rule for choosing the next node. For its calculation, first the selection probabilities of all feasible nodes are obtained, and then the next node is searched by roulette wheel selection. The details are as follows.

Based on the pheromone density and the expected value, the probability of ant at node i choosing node j as the next node is:

[mathematical expression not reproducible] (25)

Here, [[tau].sub.ij] means the amount of pheromones on link (i, j). [[eta].sub.ij] is the expected value of choosing link (i, j). [alpha] , [beta] are the heuristic factors of the link pheromone and visibility, tabu is the set of infeasible nodes.

Then, the next node is chosen by roulette-wheel selection; first, all feasible nodes are ordered with the original label sequence to obtain temporary label j'. For instance, if the original labels are 5,12, 23, 67, and 89, the temporary labels are 1, 2, 3, 4, and 5. Obtaining a random number [epsilon], [epsilon] [member of] (0, 1) (i.e., [member of] = 0.8); according to the order, the [p.sub.ij]s of the feasible nodes accumulate until they are greater than or equal to [epsilon]. Then, the last node will be the next visiting one. For instance, if the [p.sub.ij]s of the feasible nodes are [p.sub.i1=] 0.2, [p.sub.i2] = 0.3, [p.sub.i3] = 0.1, [p.sub.i4] = 0.2, and [p.sub.i5] = 0.2, the accumulated [p.sub.ij]s of nodes 1-4 is 0.2 + 0.3 + 0.1 + 0.2 = 0.8; thus, the feasible node will be 4, and its original label is 67. Repeat steps 2 and 3 until the quality of parcels in this dummy box reaches the quality limitation of buses or trucks.

Step 4: Update the pheromone. After one round of calculation, the pheromone density on the link that was passed by ants should be updated as:

[[tau].sup.new.sub.ij] = [rho] x [[tau].sup.old.sub.ij] + [[summation].sup.k.sub.k=1] [DELTA][[tau].sup.k.sub.ij], [rho] [member of] (0, 1) (26)

Here, [[tau].sup.old.sub.ij], [[tau].sup.new.sub.ij] are the old and updated pheromone amounts on link (i.j), respectively. [[summation].sup.K.sub.k=1] [DELTA][t.sup.k.sub.ij] is the added pheromone on link (i,j), which is the quotient of the total amount of pheromone Q and the value of the objective function on link k, where k is the serial number of the kth link in the delivery scheme and K is the total number of links in the delivery scheme. Because a bus route may be chosen repeatedly, if the pheromone on the bus route is added for every time of usage, the choice probability of the route may rise substantially to affect the correctness of the solution. Thus, the pheromone on a bus route can be accumulated only once when the route is chosen more than one time.

Before addressing the large-scale actual case, we test the model and heuristic using 12 small examples (parameters of them are shown in table 2). We use VBA in Microsoft Office Excel2016 to program the ant-colony algorithm and compared its solution with the commercial solver (Lingo) using a computer with i3-4160 CPU and 4.00-GB memory. The results obtained by the commercial solver (Lingo) and our heuristic are shown in table 3. The second, third, and fourth columns in table 3 provide the number of demand sites (NDS), number of bus routes (NBR), and number of trucks (NT). The calculating times and the values of the objective function of our heuristic and the commercial solver are provided in the fifth and eighth columns. The last column shows the relative difference between the optimal solutions solved separately by the commercial solver and our heuristic. Table 3 shows that although our heuristic cannot obtain the optimal solution, the gaps are always less than 5 percent. Furthermore, the commercial solver is unable to produce the calculation results in an acceptable time for instances 11 and 12, whereas our heuristic can solve the large-scale case. Therefore, we believe that our heuristic should be considered a feasible algorithm.

Case Study

Here we choose Dalian City as an example to analyze the advantages of the collaborative mode and its performance in different situations, the details of data are shown in the next section. In the introduction, we mentioned the advantages of the collaborative mode, such as cost saving, truck travel distance, and environmental load reduction. Here we compare the collaborative mode and the truck-only mode by one case to prove the correctness of our theoretical analysis. Moreover, we will focus on the sensitivity analysis of the unit bus delivery price and the unit penalty cost for unpunctual time because the bus delivery price and the sensitivity of customers to time have a great impact on the total cost of the collaborative transport.

Data Used

Data of Dalian City (China) are used for the case study. Figure 6 shows the demand sites (DP), the distribution center (DC), the bus routes (BR), the start bus terminal stops (SBS), the end bus terminal stops (EBS), and the urban road network (RN). The location of the demand sites is from YUNDA Express Co., Ltd. The delivery amounts in the DPs are fitted based on the delivery volumes of S. F. Express Co., Ltd and the regional population. The delivery time windows for the demand sites (sliced by one hour) are randomly generated.

Figure 7 shows the delivery amounts needed in the demand sites and the time window constraints, where the size of the upper half circle shows the amount, and the size of the lower half circle illustrates the start time of the time window. The smaller the lower half, the earlier the time window is. The delivery service is assumed to accept orders before 11:00 and deliver parcels between 11:00 and 20:00 by the collaborative use of trucks and bus vehicles.

Furthermore, six bus routes are selected for parcels delivery (see fig. 6). In these bus routes, 10.5m and 12m long (mainly 12m long) bus vehicles are used. For loading the parcels, the "Delivery Boxes" may be installed in the space under the roof and in the top of the chairs along both sides within the vehicles (see fig. 8). By discussing with the bus company, the maximum capacity of the "Delivery Boxes" in a bus is set to be 500 kg. The remaining parameters are set as in table 2 above, and the parameters in the ant-colony algorithm are [alpha] = 1, [beta] = 2, [rho] = 0.8, Q = 100.

Results and Analyses

We have tried to solve the model for this actual case using the commercial solver but failed to obtain results after a week of calculation. Obviously, the scale of the real case is too large for the commercial solver. Then, we solved the model with the self-designed heuristic and obtained the results in 30 minutes. Table 4 shows the departure times and travel links of the dummy boxes in the output delivery scheme, where 1 represents the distribution center, 2-7 represent bus routes, 8-104 represent the demand sites, and the rows represent the delivery links of parcel batches. For example, in the fifth batch, the demand sites are 39, 22,19 and 26, and the parcels leave the distribution center for the start terminal stop of bus route 5 at 13:28. Then, they are transported to the end terminal stop of bus route 5 by bus, and finally, they are delivered by truck to the demand sites 39,22,19, and 26 from the end terminal stop.

To test the effect of collaborative delivery, we compared the delivery schemes of the collaborative mode and truck-only mode. The result of truck-only mode is calculated by setting the decision variable [y.sup.bus.sub.j] to zero in our model. It is found that the total costs are 2,940 yuan and 3,247 yuan, respectively. Collaborative mode may decrease the total cost by 9.5 percent.

Figure 9 shows part of the collaborative delivery links. Because transporting the parcels by bus does not induce extra bus travel, collaborative delivery may reduce the traveling distance of trucks by 12.6 percent; as a result, the emitted C[O.sub.2] will also decrease at the same rate, from 0.159 ton to 0.139 ton. In figure 9 it can be seen that the parcels shipped to demand sites far from the distribution center (more than 5 km) are mainly transported by bus vehicles first and then delivered by trucks, while the parcels shipped to demand sites near the distribution center are delivered by truck directly. In addition, the number of demand sites with delayed deliveries is reduced by 26.2 percent, and the total time of unpunctual deliveries may decrease by 57.7 percent. The on-time delivery rate increased significantly.

Sensitivity Analysis

Sensitivity Analysis of the Unit Penalty Cost for Unpunctual Time

The unit penalty cost for unpunctual time cp influences the delivery method and the delivery links and further affects the total cost, the punctuality, and the energy saving effects. The delivery price of buses is calculated according to the cargos carried and distances traveled; thus, delivering parcels in small amounts and multiple batches by buses not only meets the punctuality requirement but also does not increase the delivery cost. At the same time, delivering parcels by buses will not increase the traveling distance, so the environmental load does not increase. Hence, if [c.sup.p] is in a suitable range, the collaborative mode will be more energy saving and environmentally friendly.

To test the suitable range of [c.sup.p], we conduct a sensitivity analysis and obtain the total unpunctual time of the deliveries and the C[O.sub.2] emissions as shown in figure 10, where the line respects the unpunctual time of deliveries and the columns show the C[O.sub.2] emissions. When [c.sup.p] is 0.1 yuan/minute, the unpunctual time is much longer, and the bus delivery is less, the delivery timeliness is poor, and the collaborative delivery does not function well. When cp is 0.2-0.4 yuan/minute, the unpunctual time is shorter, the C[O.sub.2] emissions are less, and the proportion of bus delivery is higher. The collaborative delivery functions well. When cp increases to 0.5 yuan/minute, the unpunctual time is much shorter, but C[O.sub.2] emissions increase significantly. However, the amount of delivery shows no obvious changes, while the detour distance for trucks increases greatly. Although timeliness is improved, the environmental load increases, and as a result the merits of collaborative delivery are weakened. Therefore, it can be said that when [c.sup.p] is 0.2-0.4 yuan/minute, collaborative delivery functions best. In this situation, the delivery companies and bus company should vigorously cooperate to promote collaborative delivery.

Sensitivity Analysis of the Unit Bus Delivery Cost

The bus delivery cost [c.sup.b2] in the model is not the actual cost but rather the fee that the delivery company pays to the bus company, which is a negotiated result and determines the willingness to collaborate. By conducting a sensitivity analysis in terms of [c.sup.b2], we obtained figure 11, where the line represents the C[O.sub.2] emissions, and the columns illustrate the total cost. As shown, the C[O.sub.2] emissions and total costs increase as the bus delivery price increases. When [c.sup.b2] is 1.3-1.5 yuan/ton/km, the C[O.sub.2] emissions do not change markedly (0.131-0.139 tons), and the total cost increases slowly. In this case, due to the lower price, the delivery company allocates many parcels to buses. When [c.sup.b2] increases from 1.5 to 1.6 yuan/ton/km, the C[O.sub.2] emissions and total cost increase significantly, potentially because the delivery company is not willing to use buses due to the high price.

As [c.sup.b2] changes from 1.6 to 1.7 yuan/ton/km, the C[O.sub.2] emissions increase significantly, but the total cost shows a lower degree of change. This finding may be due to the following: although the bus delivery price increases by 0.1 yuan/ton/km, the bus-transported volume decreases to offset to total cost, and this decrease in the bus-transported volumes may increase the C[O.sub.2] emission. In terms of total cost and CO emissions, we can state that 1.4 yuan/ton/km is a reasonable price for bus delivery.

When [c.sup.b2] is 1.8 yuan/ton/km, buses will not be used, and thus, the collaborative mode cannot reduce the total cost. In this case, the collaborative mode may not be feasible.

Conclusion

We proposed a collaborative parcel delivery mode that jointly uses buses and trucks, in which the bus routes are fixed; the costs of bus vehicle modification, bus delivery, and transshipment between buses and trucks are taken into account; parcels can be loaded and unloaded only at terminal bus stops; and trip-end deliveries are still performed by trucks. We defined the collaborative delivery as a 2EVRP-FSL and considered the 2E-VRP as one VRP to solve this problem. Testing the collaborative and truck-only modes in the case study revealed that the collaborative mode has remarkable advantages in economical, environmentally friendly, and timely delivery. Indeed, by utilizing the collaborative mode, the total cost may decrease by 9.5 percent, the unpunctual time may decrease by 57.7 percent, and C[O.sub.2] emissions may decrease by 12.6 percent. We further analyzed the optimal delivery schemes corresponding to different penalty costs and bus delivery prices, which may serve as references for decision-making in different scenarios.

From the above results, it can be seen that: (1) for the bus operators, the collaborative mode can provide them additional income without increasing the cost; (2) for the delivery company, the collaborative mode can reduce their delivery cost and improve the timeliness of delivery; (3) for urban residents, the collaborative mode can reduce transport environment load, ease traffic congestion and provide more timely express-delivery services. Therefore, the collaborative mode can reach a tripartite win situation of bus operators, delivery companies, and urban residents.

Although the collaborative delivery mode offers great advantages, there are still some unsolved issues in practice. First, although the range of the bus delivery price is provided by sensitivity analyses, the exact operating price is still undetermined. Second, the placing position and size of the delivery boxes on bus vehicles should be studied further. Third, the parcels can be loaded/unloaded only at terminal stops. Therefore, collaborative delivery will not affect the service level of bus transit. However, the role and efficiency of bus delivery are limited. Therefore, how to handle parcels at middle stops and how to use loop bus routes should be studied further. Fourth, because two companies are involved in collaborative delivery, their operation and management structures should be reorganized. Finally, in this article we have only tackled the collaborative delivery based on the exiting bus system with the aim to reduce congestion and help delivery companies to save cost. This kind of collaborative delivery can avoid the negative impacts of parcel delivery on passenger travels; however, it may limit the advantages of the collaborative delivery. In fact, depending on the cost-benefit, bus operator may enlarge delivery service by increasing bus routes, bus vehicles, or operation frequency. This may the good topic for our future study.

In future research, we will analyze the incentives of bus-transit operators and determine the equilibrium bus delivery price for cooperatives between bus-transit companies and parcel delivery companies. We will also work with a bus-transit company to determine optimal storage areas and box sizes based on the layout of various bus vehicles.

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Yunzhu He

Dalian Maritime University

Zhongzhen Yang

Corresponding Author

1 Dalian Maritime University

2 Ningbo University

yangzz@dlmu.edu.cn

yangzhongzhen@nbu.edu.cn

Caption: Figure 1: Description of a bus-truck collaborative delivery route

Caption: Figure 2 Bus and truck delivery routes

Caption: Figure 3 Bus and truck delivery routes using our new method

Caption: Figure 4 Temporal connections of buses and trucks

Caption: Figure 5 Link of a single batch of parcels

Caption: Figure 6 Demand sites, DC, bus routes and road network in the study area

Caption: Figure 7 Delivery demand and time window in the study area

Caption: Figure 8 The site of the "Delivery Boxes" in a bus

Caption: Figure 9 Links in the collaborative delivery

Caption: Figure 10 Sensitivity analysis of unit time penalty cost

Caption: Figure 11 Changes in total costs and C[O.sub.2] emissions as the bus delivery price Changes
Table 1/Overview of the Literature Related to Integrated Transport
with Bus Routes

Paper                Hetero-   Cost Related
                     geneous   to Passenger
                               Transport
                               Vehicles
                     fleet        1         2         3
Trentini and         [check]   [check]   [check]   [check]
Malhene 2010
Ghilas, Demir, and   [check]      -      [check]      -
Van Woensel 2013
Ghilas, Demir, and   [check]      -      [check]      -
Van Woensel 2016
Masson et al. 2017   [check]      -         -         -
Our research         [check]   [check]   [check]   [check]

Paper                Transfers to    Impacts on    Large-scale
                     Fixed Lines     Passengers'   Real Case
                                     Travel Time   Analysis

                      4       5
Trentini and          -       -        [check]          -
Malhene 2010
Chilas, Demir, and    -                [check]          -
Van Woensel 2013
Ghilas, Demir, and    -    [check]     [check]       [check]
Van Woensel 2016
Masson et al. 2017    -    [check]     [check]       [check]
Our research          -                   -          [check]

Notes: Here we give an updated table of table 1 in Ghilas et al.
2013. 1 = Transshipment cost is considered; 2 = Added cost for
parcel delivery of passenger vehicles is considered; 3 = Modification
cost of passenger transport vehicles is considered; 4 = No schedule
of the fixed lines is considered; 5 = Schedule of the fixed lines
is considered; [check] = The aspect is considered; - = the aspect is
not considered.

Table 2/Values of Parameters

Coefficients/parameters                     Variable      Value
Unit compensation cost                      [C.sup.e]   187.59 (d)
Fixed cost of a bus vehicle                 [C.sup.b1]   0.4 (f)
Fixed cost of a truck                       [C.sup.t1]   325 (a)
Unit truck delivery cost                    [C.sup.t2]   0.9 (b)
Unit price paid by the delivery company     [C.sup.b2]   1.5 (g)
to the bus operator
Unit transshipment cost                     [C.sup.h]       20
Unit penalty cost for unpunctual time       [C.sup.p]      0.2
C02 emissions factor of trucks              [E.sub.c]    0.17 (e)
Total loading weight of truck k             [W.sup.k]       2
Total loading weight of a bus group         [W.sup.b]    0.5 (c)

Coefficients/parameters                     Unit
Unit compensation cost                      Yuan/ton
Fixed cost of a bus vehicle                 Yuan/day
Fixed cost of a truck                       Yuan/day
Unit truck delivery cost                    Yuan/km
Unit price paid by the delivery company     Yuan/ton/km
to the bus operator
Unit transshipment cost                     Yuan/ton
Unit penalty cost for unpunctual time       Yuan/min
C02 emissions factor of trucks              Kg/km
Total loading weight of truck k             Ton
Total loading weight of a bus group         Ton

(a) The price of a truck is 150,000 yuan; the truck's life span is
8 years, and it will be in operation 250 days each year. The daily
salary of a driver is 250 yuan; thus, [C.sup.t1] = 150000/8/250 +
250 [approximately equal to] 325 yuan/day.

(b) The diesel consumption of a truck traveling 100 kilometres is
15 L. The price of diesel is 6 yuan/L, and [C.sup.t2] = 0.9
yuan/km.

(c) The time headway of bus vehicles on the six routes is 5
minutes, and four buses compose a bus team. The loading capacity of
a bus is 0.5 tons.

(d) The unit compensation cost C (e) = 187.59 yuan/ton, which is
the C[O.sub.2] tax rate in Japan (Wang et al. 2014).

(e) The C[O.sub.2] ([E.sub.c]) emitted by trucks can be calculated
by [E.sub.c] = [f.sub.c] .[U.sub.c] = 0.17 kg/km (Taniguchi et al.
2001), where the fuel consumption ([f.sub.c]) of a truck is 0.0549
kg/km, and the emission factor of C[O.sub.2] ([U.sub.c]) from
diesel is 3.16 kg/kg.

(f) The cost to modify a bus cabinet for loading parcels is 1,000
yuan, and its life span is 10 years with 250 days of use annually.
Thus, [C.sup.b1] = 0.4 yuan/day.

(g) The delivery cost of bus vehicles is the fee paid by the
express companies to bus operators. Based on the truck delivery
cost, (C.sup.b2] = 1.5 yuan/ton/km.

Table 3/Comparison of the Results
                                             Values of the
                           CPU Time        Objective Function

ID   NDS   NBR   NT   Heuristic   Lingo    Heuristic   Lingo
1     5     1    1       <1         19       458.8     455.1
2     5     2    1       <1         34       456.0     455.1
3     5     1    2       <1        211       462.9     455.1
4     5     2    2       <1        281       459.6     455.1
5    10     1    1        3        1593      635.0     623.7
6    10     2    1        6        2853      647.7     623.7
7    10     1    2        8       37678      654.2     623.7
8    10     2    2       12       50805      636.4     623.7
9    15     1    1       21       254800     826.9     794.0
10   15     2    1       27       510872     8050      794.0
11   15     1    2       56         -        742.1       -
12   15     2    2       88         -        726.8       -

ID    Heuristic vs. Lingo
      Values of Objective
         Functions:
      Heuristic vs. Lingo

1            0.83%
2            0.21%
3            1.73%
4            0.99%
5            1.81%
6            3.85%
7            4.89%
8            2.04%
9            4.14%
10           1.39%
11             -
12             -

Table 4/Collaborative Delivery Schemes

Batch   Dept.      Delivery Route
        Time (a)
1       415        1-32-30-51-68-84-93-103-90-97-100-85-1
2       207        1-3-94-96-78-79-81-95-88-77-11-104-86-3-1
3       80         1-5-13-18-42-41-35-40-44-45-23-5-1
4       330        1-5-24-36-43-38-25-20-5-1
5       148        1-5-39-22-19-26-5-1
6       85         1-3-102-89-92-72-71-74-87-9-12-3-1
7       327        1-3-98-91-75-101-14-80-73-3-1
8       267        1-3-99-70-21-16-17-3-1
9       174        1-3-15-10-8-37-52-46-47-3-1
10      53         1-3-31-59-50-62-64-49-63-57-3-1
11      380        1-5-27-55-53-34-33-29-82-67-61-5-1
12      234        1-3-69-66-65-48-58-54-60-76-3-1
13      193        1-5-28-56-83-5-1

(a) Departure time. The number indicates the minutes from the
open time to the departure time. If the open time is 11:00 and
the departure time is 17:55, then the number should be 415.
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Author:He, Yunzhu; Yang, Zhongzhen
Publication:Transportation Journal
Geographic Code:7IRAN
Date:Sep 22, 2018
Words:10224
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