A green multi-objective open vehicle routing problem for reverse logistics with consolidation points and dual time windows

Planning delivery and collection routes is a critical operational task in logistics and supply chain management (Dutta et al., 2022; Singhtaun and Piyapornthana, 2022). Each day, goods are transported across cities and regions to serve customers, stores, and drop-off points. Effective route planning reduces transportation costs, saves time, and improves service quality and reliability (Dasdemir et al., 2022), while operating under constraints such as limited fleet capacity, fuel costs, service-time preferences, and emission regulations (Heidari et al., 2023). In this context, the Vehicle Routing Problem (VRP), first introduced by Dantzig and Ramser (1959), serves as the classical optimization framework. In its basic form, vehicles depart from a central depot, visit customers, and return to the depot (see also Niu et al., 2022; Peng et al., 2024). Since then, numerous VRP variants have been developed to capture real-world complexities (e.g. Shao et al., 2023; Singhtaun and Piyapornthana, 2022). Comprehensive overviews of these variants are provided by Shao et al. (2023), and Archetti et al. (2025).

An important extension of the classical VRP is the Open Vehicle Routing Problem (OVRP), which has received increasing attention in recent years. In the OVRP, vehicles are not required to return to the depot after completing their routes; instead, each route may terminate at the last customer served (Sánchez-Oro et al., 2020; Soto-Mendoza et al., 2020). This open-route structure is particularly relevant in settings involving third-party logistics (3PL) providers, rental fleets, or contract-based carriers, where eliminating return trips can significantly reduce travel time, fuel consumption, and operating costs (Cao et al., 2025; Ren, 2011). The concept was first introduced informally by Schrage (1981) and later formalized by Sariklis and Powell (2000). Recent modeling advances and applications of the OVRP are discussed by, among others, Xiao et al. (2024) and Zhang et al. (2024).

The OVRP has been widely applied in reverse logistics, where used products are collected from geographically dispersed customers (Sánchez-Oro et al., 2020; Tonbul et al., 2024). In such settings, customer availability is often restricted to specific time windows, making service-time coordination essential. Incorporating time-window constraints yields the Open Vehicle Routing Problem with Time Windows (OVRPTW), which more accurately reflects operational scheduling requirements (Niu et al., 2022). In practice, planners must also account for heterogeneous vehicle capacities and maximum route durations (Ruiz et al., 2019). At the same time, companies seek to minimize costs while responding to increasing environmental pressures and service-quality expectations. These concerns have motivated the development of green vehicle routing models aimed at reducing fuel consumption and greenhouse gas emissions (Dutta et al., 2022; Heidari et al., 2023; Niu et al., 2018a), while maintaining high customer satisfaction, as delays or missed collections can negatively affect service perception (Cota et al., 2022; Sun et al., 2021).

While previous studies have examined trade-offs between cost and either environmental impact or service quality (e.g. Sánchez-Oro et al., 2020; Zheng et al., 2023), to the best of our knowledge, no study has jointly addressed cost, CO₂ emissions, and customer satisfaction within the OVRP framework. Some works integrate environmental considerations by embedding fuel consumption or emissions into a single cost-based objective (e.g. Niu et al., 2018b; Zhang and Wang, 2013), while others incorporate service quality through time-window penalties, without modeling customer satisfaction as a separate objective (e.g. Xia and Fu, 2019). Moreover, although consolidation mechanisms (e.g. Atefi et al., 2018; Rostami et al., 2025) and dual time-window structures (e.g. Rahmani, 2021) have been studied in OVRP variants, these features are typically considered in bi-objective or cost-focused settings, without explicitly capturing their interaction with environmental and customer-oriented objectives.

Motivated by these gaps, this study proposes a novel extension of the OVRP that jointly considers cost, CO₂ emissions, and customer satisfaction, and incorporates two additional features to better reflect real-world reverse logistics operations:

1. Local consolidation points: Certain customers may temporarily act as intermediate collection points for nearby returns. Multiple vehicles can deliver to these nodes, after which another vehicle continues the route depending on capacity. This mechanism enables chained open routes, reduces redundant trips, and improves routing efficiency while supporting economic and environmental objectives (Atefi et al., 2018; Rostami et al., 2025).

2. Dual time windows: The problem distinguishes between operationally acceptable service intervals and preferred customer time slots. The former provides scheduling flexibility, while the latter is treated as a soft constraint capturing customer satisfaction. This structure is particularly relevant in reverse logistics, where coordination with individual customer availability is critical (Rahmani, 2021).

The proposed model, which is formulated as a mixed-integer linear program (MILP), addresses logistical challenges that are increasingly relevant in sectors such as e-commerce, retail, consumer electronics, and drugstore chains (e.g. Amazon, H&M, IKEA, MediaMarkt, Rossmann), which often manage high volumes of returns from geographically dispersed customers. These activities are frequently outsourced to 3PL providers to improve efficiency and competitiveness (Ren et al., 2024). In such settings, vehicles are not necessarily required to return to a central depot, making open routing particularly suitable (Brito et al., 2016; Niu et al., 2018b). In dense urban environments, customer-based consolidation points can further enhance routing efficiency by aggregating returns, while dual time windows support flexible scheduling that accounts for both operational constraints and customer preferences. By jointly considering cost, CO₂ emissions, and customer satisfaction, the proposed model offers strong practical potential for modern reverse logistics operations.

The remainder of the paper is organized as follows. Section 2 introduces the problem and notation. Section 3 presents the proposed mathematical model. Detailed linearization of the nonlinear constraints is provided in Supplementary Material 1. Section 4 presents an illustrative case study, and Section 5 concludes the paper.

This study considers a green open vehicle routing problem for reverse logistics in which a geographically distributed set of customers is served by a heterogeneous fleet of non-returning vehicles. Routes start at customer nodes and may terminate at either another customer or the central depot, eliminating mandatory return trips and thereby reducing travel distance, fuel consumption, and emissions. The choice of route termination points directly affects feasibility, load transfers, and cost optimization, distinguishing the proposed formulation from the classical OVRP.

Figure 1 schematically compares the classical OVRP with the proposed variant. In the classical OVRP (left panel), vehicles start at customer nodes and terminate at the depot, whereas the proposed structure (right panel) incorporates customer-based consolidation points and dual time windows.

The transportation network is modeled as a complete directed graph $G=(L,A)$⁠, where $L={0,1,2,...,n}$ includes the depot (node 0) and customer nodes $CN={1,...,n}$⁠. The arc set $A$ consists of directed arcs $(i,l)$ with travel durations $tilv$⁠, distances $dil$⁠, and costs $cilv$⁠, which may vary by vehicle type $v∈V$⁠. Owing to urban asymmetries such as one-way streets or traffic conditions, the triangle inequality may not hold. Model notation is summarized in Table 1.

Note that transportation cost $cilv$​ for traveling from node $i$ to node $l$ using vehicle $v$ is determined as $cilv=dcv.dil+tcv.tilv$​, where the first term represents the distance and the second, the time component.

Using the notation above, the main modeling features are incorporated as follows.

Each customer node $i∈CN$ is characterized by a demand $qi$⁠, a fixed service time $si$⁠, and two service intervals that implement the model's dual time window structure:

1. A soft time window $[eis,lis]$⁠, within which service is preferred.

2. A hard time window $[eih,lih]$⁠, within which service is permitted.

To capture deviations from preferred service times, both lateness and earliness dissatisfaction are modeled. If service at customer i $∈CN$ starts after the soft latest time $lis$​, lateness is defined as $li=max⁡(0,a‾i−(lis−si))$⁠. The corresponding normalized lateness dissatisfaction $δil$​ is calculated as $li/(lih−lis)$​, scaling lateness by the interval between soft and hard times, $lih−lis$​. This is then weighted by the customer-specific lateness coefficient $wδil$​, demand $qi$⁠, and priority weight $γi$​, emphasizing punctuality for high-priority customers.

Similarly, if service starts before the soft earliest time $eis$​, an earliness variable $εjiv=max(0,−M(1−xjiv)+eis−ajiv−τjiv)$ is defined for each vehicle $v$ arriving at node $i$ from node $j$⁠. The maximum earliness at node $i$⁠, $εimax=max(εjiv)$⁠, is used to compute the normalized earliness dissatisfaction $δie=εimax/(eis−eih)$⁠. This is then weighted by the earliness weight $wδie$​, demand $qi$⁠, and priority level $γi$​, capturing the negative impact of early service on customer satisfaction.

In addition to service timing, the model incorporates load transfers between routes. Customer nodes $i$ may serve as temporary consolidation points when they receive two or more incoming routes, as indicated by binary variable $xicp$​. At these nodes, a vehicle may continue the collection by taking over the aggregated load from preceding routes. This mechanism operates alongside standard vehicle capacity constraints. If the load departing from any node exceeds the volumetric capacity $CvV$​ or the weight capacity $CvW$​ ​of the assigned vehicle, a new vehicle with sufficient capacity must continue the route.

The problem is formulated as a MILP that minimizes transportation cost and CO₂ emissions while maximizing customer satisfaction, subject to operational and routing constraints. The complete formulation is presented below and explained in detail thereafter.

Subject to

Objective (1) minimizes the total transportation cost, which comprises three components:

Routing costs: The term $cilvxilv$​ represents the cost of traveling from node $i$ to node $l$ using vehicle type $v$⁠.

1. Service-related bonuses: The term $ξvslxilv$ accounts for the additional payment to drivers of vehicle type $v$ for the service time $sl$​ at node $l$⁠.

2. Idle-time bonuses: The term $ξvτijv$​ captures compensation for drivers who arrive at customer $j$ before the start of the hard time window and must wait (idle) before beginning service.

Objective (2) minimizes total CO₂ emissions through three elements:

1. Distance- and load-dependent emissions: The term $efvdil(ρ0vxilv+αvwboxyilv)$ models emissions from traveling between nodes $i$ and $l$ using vehicle type $v$⁠. Here, $efv$​ is the emission factor, $dil$ is the distance, $ρ0v$​ is the emission rate of an empty vehicle, and $αvwboxyilv$ captures the load-dependent emissions.

2. Idle emissions due to early arrival: The term $λvτijv$ represents emissions from vehicles idling while waiting before the start of a customer's hard time window.

3. Idle emissions during service: The term $λvslxilv$ accounts for emissions during service activities (e.g. loading or unloading) at node $l$⁠.

Objective (3) maximizes customer satisfaction by minimizing total weighted dissatisfaction across all customer nodes and includes the following key elements:

1. Normalized dissatisfaction levels: The lateness dissatisfaction $δil$ and earliness dissatisfaction $δie$ capture deviations from the soft time windows for each customer $i$⁠.

2. Weighting coefficient: These are scaled by customer-specific weights $wδil$ and $wδie$​, reflecting the relative importance of avoiding lateness versus earliness. To ensure a normalized outcome in the range [0, 1], the weights are constrained such that $wδil+wδie=1.$

3. Aggregation and normalization: The dissatisfaction values are aggregated across customers and normalized by the total weighted demand $∑i∈CNγiqi$⁠, where $γi$ reflects the customer's importance and $qi$ their demand.

This normalization has two purposes:

1. It constrains the satisfaction level $Z3$​ within the range [0,1], allowing its interpretation as a satisfaction ratio (from 0% to 100%).

2. It ensures comparability across instances of different sizes, such as networks with varying numbers of customers or total demand, by expressing satisfaction as a relative rather than absolute performance indicator.

Constraint (4) ensures that customer $i$ is served by at most one vehicle of any type $v$⁠, meaning that no more than one outgoing arc $(i→l)$ is allowed from node $i$⁠.

Constraint (5) designates node $j$ as a consolidation point (⁠$xjcp=1$⁠) if and only if at least two vehicles arrive at this node (i.e. $∑i∈CN,i≠j∑v∈Vxijv≥2$⁠); otherwise $xjcp=0$⁠.

Constraint (6) enforces the vehicle's volume capacity limit, ensuring that the total volume of goods $vboxyilv$ transported on any arc $(i→l)$ does not exceed the volumetric capacity $CvV$ of the assigned vehicle. If the arc is not used (⁠$xilv=0)$⁠, the transported volume must be zero.

Constraint (7) ensures that the load shipped out of node $j$ equals the load shipped into node $j$ plus its own demand $qj$⁠.

Constraint (8) enforces the weight capacity of each vehicle, ensuring that the total weight of the items $wboxyilv$ transported on a given arc $(i→l)$ does not exceed the vehicle's weight capacity $CvW$⁠. If the arc is not used (⁠$xilv=0)$⁠, the transported weight must be zero.

Constraint (9) ensures proper arrival time sequencing by enforcing that the actual service start time $a‾j$ at customer node $j$ is no earlier than the sum of the vehicle's arrival time $atijv$ and its waiting time $τijv$⁠. This accounts for situations where vehicles arrive before the customer's time window $ejh$ begins and must wait before starting service.

Constraint (10) links the arrival time $atjlv$​ at a destination node $l$ to the service start time $a‾j$ at origin node $j$ plus service time $sj$ and travel time $tjlv$⁠, activated only if the arc is used $xjlv=1$⁠.

Constraint (11) ensures timely delivery to the depot node $o$ by requiring that the vehicle arrives at the depot $atiov$ before the latest allowable delivery time $dtmax$⁠, taking into account the service time $so$​ required at the depot.

Constraint (12) limits incoming arcs at customer $i$ depending on whether it is designated as a consolidation point (⁠$xicp=1)$ or has positive demand (⁠$qi>0)$⁠.

Constraint (13) defines lateness $lj$ at node $j$ as the positive delay beyond the soft latest start time, computed as $max⁡(0,a‾j−(ljs−sj))$⁠.

Constraint (14) models service earliness at customer node $i∈CN$⁠. For each incoming arc $(j,i)$ and vehicle type $v∈V$⁠, the earliness variable $εjiv$​ captures how much earlier service begins compared to the soft earliest time $eis$​, provided that the route is active $(xjiv=1)$⁠. This ensures that earliness is only registered when relevant.

Constraint (15) defines the maximum earliness $εimax$​ for customer $i$⁠, by taking the maximum value among all $εjiv$​ associated with that node. This ensures that customer dissatisfaction reflects the most severe earliness experienced.

Constraint (16) calculates the normalized earliness dissatisfaction $δie$​ by dividing $εimax$​ by the range of acceptable early arrival, $(eis−eih)$​. The corresponding value lies between 0 and 1 and is used in the third objective function to quantify the penalty due to early service.

Constraint (17) defines the waiting time $τijv$ before service at node $j$⁠, ensuring vehicles wait $(τijv≥0)$ if they arrive before the allowable service start time (⁠$atijv≤ejh)$⁠.

Constraint (18) ensures compliance with hard time windows $ljh$⁠, by enforcing that the vehicle arrives early enough at customer node $j$ (⁠$atijv≤(ljh−sj))$ to complete service before the end of the customer's hard time window $ljh$⁠.

Constraint (19) ensures proper service start time behavior at customer node $j$ when no vehicles enter. If no incoming arc $(i→j)$ is selected for any vehicle $v$⁠, the sum is zero and the constraint enforces $a‾j≥ejs$​, so any departure from node $j$ must occur after the soft earliest time​. If at least one vehicle enters node $j$⁠, the large constant $M$ relaxes the lower bound, and $a‾j$ is instead determined by other time-sequencing constraints.

Constraint (20) links the service start time $a‾j$​ to the vehicle departure decision. If no vehicle departs from node $j$⁠, then $xjlv$ = 0 for all $l$ and $v$⁠, which makes the right-hand side of the inequality zero and enforces $a‾j≤0$⁠. Since $a‾j$​ is a non-negative variable, this condition fixes $a‾j=0$⁠, ensuring that unvisited customers have no assigned service start time. When a vehicle departs from node $j$⁠, the large constant $M$ relaxes the upper bound, allowing $a‾j$ to take a feasible value determined by other time-sequencing constraints.

Constraint (21) models normalized lateness dissatisfaction $δjl$​ as a piecewise-linear function that increases when service begins after the threshold $(ljs−sj)$⁠. If the service starts on time or earlier $(a‾j≤ljs−sj)$⁠, the dissatisfaction is zero $(δjl=0)$⁠.

Constraints (22)–(28) define the decision variables and impose non-negativity and boundedness conditions.

The proposed model contains several nonlinear elements, including conditional constraints, bilinear terms, and max and piecewise-defined operators. To obtain a solvable MILP formulation, these nonlinearities are linearized. The complete linearization of Constraints (5), (10), (12)–(15), (17), (19), and (21) is presented in Supplementary Material 1.

This section presents a case study to demonstrate the practical application of the proposed model. The case study reflects a typical urban operation, where used or returned products are collected from customers (e.g. households or local stores) and transferred through local consolidation points under dual time window constraints. To replicate realistic operating conditions faced by 3PL providers in dense metropolitan areas managing decentralized return flows, the model is applied to synthetically generated data, the details of which are provided below.

The network consists of 25 customer nodes and a central depot. Each node represents a customer from which used or returned products are collected. Four vehicle types $(V=1,2,3,4)$ are considered, each with distinct size, capacity, fuel consumption, and emission characteristics. The transportation cost for each vehicle type $v$ is determined by distance-based and time-based coefficients $dcv$ and $tcv$⁠, as defined in Section 3. Table 2 summarizes the key specifications of each vehicle type, including transportation cost coefficients $dcv$ and $tcv$⁠, maximum load weight $CvW$⁠, maximum load volume $CvV$⁠, base fuel consumption $ρ0v$​, load-dependent fuel consumption coefficient $αv$⁠, idle CO₂ emission rates $λv$⁠, and emission conversion factors $efv$⁠, and waiting-time bonuses $ξv$​. The cost coefficients capture the combined effects of fuel usage, driver wages, and operational overheads. Larger vehicles incur higher costs per kilometer and per minute due to greater fuel consumption and increased operating complexity. Waiting-time bonuses, reflecting the economic compensation required for vehicle idle periods, are modeled using a uniform distribution: $U(0.50,0.80)$ $€/min$ for smaller vehicles (types 1 and 2) and $U(0.80,1.20)$ $€/min$ for larger vehicles (types 3 and 4). Larger vehicles achieve higher load-adjusted fuel efficiency due to their design.

An unlimited number of vehicles of each type is assumed to be available. This provides operational flexibility, enabling the model to dynamically allocate fleet resources based on demand, vehicle capacity, and routing efficiency.

To illustrate the cost calculation, suppose a Type 3 vehicle travels from node $i$ to node $l$ over a distance of $dil=20$ kilometers in $til3=40$ minutes. Using the coefficients in Table 2, the transportation cost is computed by summing the distance component and the time component. The distance cost is calculated as $dc3×dil=1.0×20=20€$⁠, and the time cost is $tc3×til=0.3×40=12€$⁠. Therefore, the total transportation cost for this route segment is 32 $€$⁠. This example demonstrates how the model integrates distance- and time-related expenses to capture realistic operating costs for each route segment.

The remaining model inputs, which define service times, travel characteristics, customer demands, and time window settings, are presented in Table 3. Each customer node $i$ requires a fixed service duration $si=4$ minutes. Travel times between any two nodes $i$ and $l$ using a vehicle of type $v$ are randomly generated from a uniform distribution $U(10,100)$ minutes as $tilv$⁠, and the corresponding travel distances $dil$ are scaled proportionally to maintain realistic speed assumptions. Customer demand $qi$ is stochastic, following a uniform distribution $U(0,80)$ boxes, where each box weighs $wbox=13.6$ kg and occupies $vbox=1$ m³, directly influencing both vehicle capacity limits and emissions. The maximum permitted delivery duration is set to $dtmax=150$ minutes, and a large constant $M=150$ is introduced in Big-M formulations to linearize constraints involving time, vehicle capacity, and routing logic.

To capture both customer preferences and operational feasibility, the problem assigns dual time windows to each customer. The soft time window $[eis,lis]$ represents the preferred delivery interval, where the lower and upper bounds are generated from uniform distributions $U(10,20)$ and $U(30,50)$ minutes, respectively. The corresponding hard time window $[eih,lih]$ defines the acceptable operational bounds, where $eih=0.7eis$ and $lih=1.3lis$⁠. Service outside the preferred interval is permitted but results in dissatisfaction penalties. Customer dissatisfaction is evaluated asymmetrically, with a weight of $wδil=0.7$ for lateness and $wδie=0.3$ for earliness, reflecting stronger sensitivity to delays. In addition, each customer $i$ is assigned an importance factor $γi$⁠, randomly drawn from a uniform distribution $U(1,3)$⁠, where 1 indicates low importance and 3 represents high importance. This parameter allows the model to adjust dissatisfaction penalties according to customer priority.

Because the proposed model simultaneously minimizes transportation cost and CO₂ emissions while maximizing customer satisfaction, these objectives are inherently conflicting, and no single solution is optimal for all criteria. The analysis therefore focuses on identifying Pareto-optimal solutions, for which no objective can be improved without worsening another. These solutions are generated using the $ε$-constraint method (Haimes, 1971), where one objective is optimized while the others are imposed as constraints. In our case, this is formulated as: Min $Z1$​ subject to $Z2≤ε2$​ and $Z3≥ε3$⁠, where $ε2$ and $ε3$​ are the adjustable bounds for the second and third objectives, respectively. By varying these $ε$-levels, a set of non-dominated solutions is obtained ^[1].

To generate candidate solutions for the ε-constraint method, each objective function is first optimized individually to identify its best achievable value (anchor point) and the corresponding values of the remaining objectives.

Optimizing transportation cost (⁠$Z1$⁠) yields a minimum cost of 531.5, with associated CO₂ emissions of 226.3 and customer satisfaction of 87.1. When CO₂ emissions (⁠$Z2$⁠) are minimized, the optimal emission level is 218.3, with a transportation cost of 573.4 and customer satisfaction of 93.6. Maximizing customer satisfaction (⁠$Z3$⁠) results in a satisfaction level of 100, accompanied by a cost of 1281.2 and emissions of 299.2. These anchor values (531.5, 218.3, and 100) define the feasible ranges of the objectives and are used to select appropriate ε-levels for identifying Pareto-optimal solutions.

Transportation cost $Z1$​ is selected as the primary objective, while the remaining objectives are imposed as $ε$-constraint: $Z2≤ε2$​ and $Z3≥ε3$⁠. Based on the extreme solutions, the feasible range of CO₂ emissions and customer satisfaction are [218.3, 299.2], and [87.1, 100], respectively. To systematically explore trade-offs, three $ε$-levels (minimum, midpoint, and maximum) are considered for each objective. Accordingly, $ε$-levels for CO₂ emissions are set to 218.3, 258.7, and 299.2, while those for customer satisfaction are set to 100, 93.6, and 87.1. The resulting $(ε2,ε3)$ combinations and corresponding solutions are summarized in Table 4.

Solving the model for the nine $(ε2,ε3)$ combinations yields the corresponding objective values. The first combination $(ε2=218.3,ε3=100)$ is infeasible, as no feasible solution satisfies both $Z2≤218.3$ and $Z3≥100$⁠. The remaining eight combinations produce feasible solutions, each associated with an optimal set of values (⁠$Z1*,Z2*,Z3*)$⁠.

As shown in Table 4, all solutions are distinct, but most are dominated. For example, Solution 8 is dominated by Solution 4, which achieves lower cost and emissions while providing higher customer satisfaction. Only Solutions 2 and 4 are therefore identified as non-dominated solutions. Selecting a preferred compromise among these alternatives depends on managerial preferences and strategic priorities. This choice can be supported by multi-criteria decision-making (MCDM) methods such as the weighted sum method (WSM), TOPSIS, or the analytic hierarchy process (AHP), which enable decision-makers to assign relative importance to objectives and rank the solutions accordingly (see, e.g. Tzeng and Huang, 2011).

To compare the non-dominated solutions obtained from the $ε$-constraint procedure, we apply WSM to Solutions 2 and 4. Let $w1$⁠, $w2$⁠, $w3$ denote managerial preference weights for cost (⁠$Z1$​), emissions (⁠$Z2$​), and customer satisfaction (⁠$Z3$⁠), respectively, with $w1+w2+w3=1$⁠. To reflect an emphasis on emission reduction with moderate importance assigned to cost and customer satisfaction, the weights are set to $w1=0.3$⁠, $w2=0.5$⁠, and $w3=0.2$⁠. These weights are used solely for post-solution evaluation. After normalizing the objectives using standard min–max normalization, aggregated scores are computed as $S=w1Z˜1+w2Z˜2+w3Z˜3$ ^[2]. The solution with $Z1=573.4$⁠, $Z2=218.3$⁠, and $Z3=93.6$ yields a lower aggregated weighted score (0.2) than the alternative solution with $Z1=760.1$⁠, $Z2=258.1$⁠, and $Z3=100$ (score 0.8), and is therefore selected as the preferred solution.

The optimal values of the decision variables for the selected solution are presented in Table 5. To illustrate, consider route [22–14–0], which consists of two consecutive arcs: Arc 22 and Arc 14. Arc 22 uses vehicle type 1 (⁠$C1W=25,C1V=1$⁠) to carry 1 box (equal to the demand of node 22) from node 22 to node 14. The vehicle starts service at node 22 at minute 15 from the beginning of the collection process. After spending 4 min at node 22, it departs and travels to node 14, arriving and starting service there at minute 31. Because this is the only incoming arc to node 14, the service start time at node 14 is $a‾15=31$⁠.