Transportation-Mission-Based Optimization of Heterogeneous Heavy-Vehicle Fleet Including Electrified Propulsion

Commercial-vehicle manufacturers design vehicles to operate over a wide range of transportation tasks and driving cycles. However, certain possibilities of reducing emissions, manufacturing and operational costs from end vehicles are neglected if the target range of transportation tasks is narrow and known in advance, especially in case of electrified propulsion. Apart from real-time energy optimization, vehicle hardware can be meticulously tailored to best fit a known transportation task. As proposed in this study, a heterogeneous fleet of heavy-vehicles can be designed in a more costand energy-efficient manner, if the coupling between vehicle hardware, transportation mission, and infrastructure is considered during initial conceptual-design stages. To this end, a rather large optimization problem was defined and solved to minimize the total cost of fleet ownership in an integrated manner for a real-world case study. In the said case-study, design variables of optimization problem included mission, recharging infrastructure, loading–unloading scheme, number of vehicles of each type, number of trips, vehicle-loading capacity, selection between conventional, fully electric, and hybrid powertrains, size of internal-combustion engines and electric motors, number of axles being powered, and type and size of battery packs. This study demonstrated that by means of integrated fleet customization, battery-electric heavy-vehicles could strongly compete against their conventional combustion-powered counterparts. The primary focus has been put on optimizing vehicle propulsion, transport mission, infrastructure and fleet size rather than routing.


Introduction
Commercial vehicles are, traditionally, designed to perform a wide range of transportation tasks. However, vehicle optimality is often compromised depending on how the vehicle is desired to be used. Although consumers partly recognize what vehicle type they need to purchase, corresponding operational costs cannot be easily foreseen, and the selected vehicle, therefore, might not be best-suited to perform the assigned task. A major challenge faced by commercial-vehicle manufacturers concerns prediction of transportation needs and corresponding delivery of optimized vehicles.
Normally, a transportation company selects a set of vehicles and plans routes to meet present transportation demands. As [1] argues, a single transportation-related problem formulation cannot reflect all real-life applications, and that it does not make sense to include detailed vehicle and routing aspects in strategic fleet-management decisions owing to the inherent high level of uncertainty. However, if a detailed description of repetitive transportation assignments and operational environment can be obtained via communication with future customers, detailed design of vehicle and transportation aspects could be undertaken in an integrated manner by vehicle manufacturers. a concern. The weight and volume of goods, operating range, payload, utilization level, purchase cost, charging infrastructure, battery life, energy consumption, available routes, average speed, and logistics are among the factors that affect the profitability of battery electric heavy vehicles, according to [2,3,5,11,20,23,[26][27][28][29][30][31][32]. TCO provides a good means of estimating profitability and is used for comparative analysis of the competitive technologies [3,5,20,23,[26][27][28][29][33][34][35][36][37][38][39]. Literature suggests that vehicle customization based on the use case helps profitability of the battery electric heavy vehicles. However, the influence of such a customization on TCO is not studied in the literature. Moreover, the driver cost is neglected in TCO calculation of the electric freight vehicles in the literature, and thus additional cost related to the waiting time for charging during operation is omitted. Similarly, the trade-offs between the driver cost and charging time, charging power and cost, battery degradation, and loading-unloading time and cost are neglected in TCO calculations of freight vehicles. In addition, TCO analysis of battery electric trucks in the literature is limited to trucks weighing less than 12 tons.
This study tried to fill the above gaps and is the extension of the work done by [11] to include a transportation network rather than a single mission comprising two nodes. The vehicle-infrastructure optimization was studied in [11], where it was shown that such an optimization helps competitiveness of battery electric heavy vehicles against conventional counterparts, while transportation task included only one vehicle type and two pickup and delivery nodes. TCO comparison of different battery electric vehicles by itself does not reflect the profitability, due to the performance constraint imposed by the range and power of batteries. Therefore, this problem can be overcome by optimizing vehicle-infrastructure, e.g., by sizing the batteries for a given transportation scenario. The problem of vehicle-infrastructure design of a vehicle fleet, including route selection coupled with powertrain-component tailoring was first defined in [40]. In such an optimization problem, numbers of each designed-vehicle type on each route were selected as design variables. That study showed that the design of electrified propulsion was influenced by the fleet composition.

Methodology
Among different formulations of a route set in HVRP [15], the route set defined using the set partitioning method, as reported in [41][42][43], best suited the objectives of the proposed study, since cyclic routes defined using the set partitioning formulation demonstrate great relevance to mission definitions or driving cycles used in the tailoring of vehicle powertrain components.
Another class of problems are fleet-size and mix-vehicle routing problem (FSMVRP), extensively studied in the literature. A heterogeneous or mixed fleet refers to vehicles with different payload capacities [15,44]. Moreover, there exists rich literature [1,15] concerning HVRP solutions obtained through use of heuristic and exact methods. An exact method for solving HVRPs of different classes, based on set partitioning formulation, is presented in [43].
In this study, vehicles are different in the powertrain design in addition to the vehicle capacity. Depending on vehicle-design parameters and their corresponding range, i.e., continuous or discrete, the total number of different vehicle types might amount to billions or be infinite. The resulting FSMVRP can, therefore, be very large. Furthermore, addition of every single decision variable (for example, charging-station location, loading-unloading scheme at each node and number of trips) to the routing problem adds a layer of complexity making the structure of the problem different from FSMVRP. Therefore, the applicability of the above methods on very large or infinite number of vehicle types and many layers of complexity needs further investigation. However, for the presented case study comprising a small transportation network, the proposed method in this study yields sufficiently a good solution within the objectives of this study.
To our knowledge, there is no similar work in the literature where many aspects of vehicle design and transportation network, including charging-station-location problem and loading-unloading schemes, were optimized simultaneously. However, the literature reports an extensive work in vehicle routing problems where the vehicle type search space is small and the route search space is very large, in contrast to the problem presented in this paper, where vehicle type search space is very large and the route search space is small. For example, for a small number of vehicle types, in [45], the Benders decomposition approach was employed for solving the charging-station-location problem. Benders decomposition, introduced by [46], has also been demonstrated to be useful in solving heterogeneous vehicle routing problems, wherein relatively a large set of vehicle types are allowed in the fleet [47], the idea being to initialize the optimization problem with a small set of added decision variables whilst fixing all others. Subsequently, the set of fixed decision variables is iteratively improved along with major routing decision variables by solving each optimization subproblem. In case of a rather large set of vehicle types, ref. [47] suggest restricting the number of vehicle types allowed in a given fleet. Benders decomposition subproblems could then be formulated using a small set of vehicles solved iteratively based on column generation. During each iteration, the best-found routes are projected onto the next subproblem iteration, and the set of used vehicles is updated. It was observed that solving subproblems containing vehicles with identical loading capacities, at times, yielded the same routes. The approach was tested on a set of 200 different vehicles types. However, different solutions were obtained for load-dependent costs. In this study, many vehicle types, e.g., about 83,000 in the case study, are considered with a nonlinear cost function together with a small transportation network including charging-station-location problem and loading-unloading; thus, the method described above is not applicable.

Problem Definition
Fleet TCO is the objective of the optimization problem that needs to be minimized. TCO includes operational and depreciation of purchase cost and its detailed definition comes later in this section. The decision (design) variables that influence the TCO comprise the missions, routes within missions, types and numbers of vehicles utilized in each mission, number of trips performed by each vehicle in each mission, charging power of each vehicle at each node, loading-unloading scheme of each vehicle at each node. Finally, the constraints of the optimization problem include vehicle dynamic model constraints, performance constraints and transportation task constraints, described later in this section. Table 1 describes the general vehicle-transportation optimization problem. Table 1. General vehicle-transportation optimization problem, which includes both transportation-and vehicle-design variables.

Decision (Design) Variables Objective Function Constraints
Missions, routes within missions, types and numbers of vehicles utilized in each mission, number of trips performed by each vehicle in each mission, charging power of each vehicle at each node, loading-unloading scheme of each vehicle at each node Fleet total cost of ownership Vehicle dynamic model, performance constraints, transportation task Furthermore, the following terms clarify the definition of the optimization problem.
• "Node" is a place where pickup or delivery of goods together with the maintenance or recharging of the batteries are performed. During a mission, a vehicle must pass through all the specified nodes of the mission. See Figure 1 for example of nodes. • "Transportation network" is defined as an overall requirements on freight delivery and pick-up that must be met by the fleet. It is defined by a set of all nodes with respective known daily requests for the freight pick-up and delivery together with the available routes between them. See Figure 1 for an example of transportation network. • "Fleet" is a group of vehicle-combinations working together to meet requirements of a transportation network. Vehicles in a fleet are heterogeneous, i.e., their types might differ from each other. A type of a vehicle is characterized in terms of its loading capacity and powertrain design. There can be several vehicles with the same type in the fleet. See Figure 1. • "Mission" is a part of a transportation network in which nodes belong to a subset of all nodes that are defined in the transportation network. For example, the freight flow between two nodes could be seen as a mission. The number of nodes in a mission must be more than one. It is required that a vehicle visits all the nodes of a mission. Routes of a mission are defined either by a single cyclic route, or by multiple cyclic routes corresponding to multiple-trips or by a district with several possible cyclic routes. These routes and nodes together with demands on pick-up and delivery form a mission. A vehicle works in a single mission during its service life on a repetitive basis. • "Trip" is an act of driving and visiting all the nodes of a cyclic route, by a vehicle, to meet the entire or a part of requests for pick-up and delivery. A trip is finished when the vehicle is returned to the starting node.
All design variables presented in Table 1 are selected from corresponding given ranges. It must be noted that the range of the missions, i.e., the set of all possible missions, works as an input to the problem, that includes all possible sequences of meeting the nodes of the transportation network, starting/ending from/to the depot. The resulting optimization problem presented in Table 1 is very large, regardless of the size of the transportation network; especially, because there exists many different types of the vehicles. Let us define X V as a set of vehicles containing different vehicle types, and n v as the total number of vehicle types. An example of X V is depicted in Figure 2. The set of vehicle types X V can be constructed using vehicle design space S V . A "design space" is a set containing all design sets of the problem (Figure 3). A "design set" is a set containing all possible choices of a design parameter. A "search space" is a space of optimization design variables. Design space turns to a search space if design sets are treated as ranges of the design variables within an optimization problem.
The vehicle design space, S V can be generalized to a greater extent, thereby covering more aspects of transportation planning and design by not letting design sets S V,k , k = 1 . . . n s be limited to vehicle-design; but, letting S V to include sets concerning transportation tasks, such as the loading-unloading scheme and recharging infrastructure at each network node, as depicted in Figure 3. Therefore, X V can be defined as an n s -fold Cartesian product, without order, of design sets S V,k , k = 1 . . . n s belonging to the vehicle design space S V . Hereinafter, a bold symbol denotes either a set or a matrix.
where, j = 1, . . . , n v . A design set (e.g., S V,k ) denotes a set comprising all possible choices of a k . The total number n v of all possible vehicle types can be calculated as follows. In the above equation, n S V,k denotes the total number of elements in the design set S V,k . As can be realized, by increasing n s and n S V,k , the number of vehicle types increases quadratically. Moreover, if any of S Vk s has a continuous range there would exist infinite number of vehicle types, e.g., if the battery size can be selected from a continuous range. The next section presents a method to solve such a problem by redefining and splitting the general optimization problem shown in Table 1 into several optimization subproblems that help determining a close-to-optimum fleet even for large values of n v .
, , , , Figure 2. Example of X V -set of n v vehicle types. X V denotes the set of vehicle types and X V,i denotes ith vehicle type. The annual fleet TCO is the sum of the annual TCO of each vehicle of the fleet. The annual TCO of each vehicle, denoted as C, can be expressed as where c dep indicates the depreciation or yearly cost of investment defined based on the annuity formula (Equation (5)); and c opr denotes the yearly operational cost given by where variables c elec , c fuel , c driver , c maint , c tax , and c insu , denote annual costs of electricity; fuel; driver labor; vehicle maintenance, including tire, taxes, and insurance, respectively. The annuity formula for calculating depreciation could be defined as where r denotes the interest or discount rate; n y denotes the economic life span or planning horizon in years; R denotes the rest value, i.e., the price of a product after completion of its stipulated service life; and p denotes the price of products, such as vehicle hardware or loading, unloading, and recharging infrastructure, when being used for the first time. The price of products can be calculated using the following equation.
where, p chass denotes price of the vehicle chassis, such as that of a truck, dolly, or semitrailer, without the associated powertrain and propulsion systems; p em , p trans , p batt , p ice , p lu , and p rech denote the cost of electric motors, transmission systems, battery packs, internal combustion engine, loading-unloading components, and recharging infrastructure, respectively; and n rep denotes the number of battery replacements performed during the service life of a vehicle (Equation (A44)), which in this case, has been considered as an investment cost. The battery's operational life is separated from other vehicle's component life and it was calculated using vehicle models described in Appendix E according to [48].
It must be noted that p lu and p rech are non-linear functions of the number of vehicles since components of the loading-unloading and recharging infrastructure could be shared among many vehicles. Consequently, in Equation (3), C is not a linear function of number of vehicles. For example, a straddle carrier can be shared between many vehicles; whilst an "on-board lift" cannot, refer Figures 4 and 5, according to [11]. Thus, design of the loading-unloading scheme depends on the number of vehicles in the fleet and vice versa. Furthermore, the cost of setting up a charging station is high for a single vehicle; however, when many vehicles use the same station, the per-vehicle cost of charging gets reduced. Thus, infrastructure design is affected by the number of vehicles and vice versa.  The said relations have been observed to affect optimum vehicle design as well. Suppose for a single vehicle, by solving the optimization problem shown in Table 1, it is observed that installation of a large battery pack results in lower cost compared to installing a fast-charging power source. However, sharing of the recharging infrastructure between multiple vehicles makes installation of the fast-charging alternative more feasible compared to installation of the larger battery on each vehicle. This dependence can be eliminated if the infrastructure belongs to a third-party company with a fixed cost of electricity usage. Such a case, however, is not considered in this study.
Constraints of the optimization problem shown in Table 1 are categorized into several groups, each representing a different aspect of the problem. Vehicle dynamic model constraints pertaining to the dynamic, recharging, and powertrain models, inclusive of all equations and inequalities, are described in in Appendix E and inspired by [11,40,[49][50][51][52][53][54].
Performance constraints refer to performance-based standards (PBS) that guarantee proper functionality of the vehicles along with on-road safety [55][56][57][58]. In this paper, performance-based standards related exclusively to the longitudinal motion of the vehicle have been considered in terms of gradeability, startability, acceleration, and down-grade holding capability. Gradeability refers to the maximum grade on which a loaded vehicle can maintain forward motion at a certain speed (e.g., 80 km/h). Startability refers to the maximum grade on which a loaded vehicle can start forward motion and travel 10 m in less than 10 s. Acceleration capability denotes time taken by a loaded vehicle to start motion form rest and travel 100 m on a road with zero grade. Finally, down-grade holding capability is defined as the maximum downhill grade on which a loaded vehicle can maintain constant forward speed using auxiliary brakes, such as the engine and/or electric motors. It must be noted that performance-based standards are only affected by vehicle hardware parameters.
Another type of constraints is the one related to transportation tasks and ensures adequate performance of all missions. These constraints, for example, relate to vehicleloading capacity, pick-up, and delivery during a single trip, the working time, recharging infrastructure powers, and rules prescribed for loading-unloading operations.
Loading-unloading of goods can be performed in four different ways: using an on-board lift (OBL), a straddle carrier (SC) for lifting 20-foot and 40-foot containers, an additional semitrailer (AST) at a node for vehicles with at least one semitrailer, and onboard vehicle waiting (OBW) at a node while all pallets of goods are loaded or unloaded, according to [11].
The selection of a feasible loading-unloading scheme does not include tactical decision variables. Therefore, some rules or constraints need to be set to be able to ensure loading-unloading accessibility and evaluate the corresponding cost. A list of concerned rules is explained in Appendix C and ensures accessibility and feasibility of the loadingunloading scheme.
It should be noted that design of a loading-unloading scheme is coupled with the vehicle-design problem. Having an on-board lift on the vehicle adds to the overall vehicle weight, and thus, energy consumption. Additional semitrailers with propelled axles result in an increase in TCO. Furthermore, the loading-unloading duration time can have an influence on vehicle design to compensate for delays. Loading-unloading schemes could be distinguished in terms of the time required for loading-unloading along with the corresponding investment cost.

Method
In this study, it is proposed to split the rather large optimization problem into smaller subproblems or stages. In stage A, a look-up space (i.e., a memory block) of possible best vehicle-infrastructure designs is built by minimizing the unit transportation cost for a given vehicle capacity, mission, and number of vehicles. Here, the vehicle refers to vehicle propulsion hardware, and infrastructure refers to loading-unloading and charging stations positions and powers. In stage B, the look-up space is used in an allocation optimization problem to minimize the fleet TCO, which yields an optimum fleet. The above-defined two stages can be visualized in Figure 6.
The proposed approach for integrated optimization of vehicle-transportation can be used as a solution method for real-world transportation problems involving fleet vehicles powertrain design based on the transportation assignments.  The optimization problem described in Table 1 is rather general, wherein the goal is to determine a group of vehicles with different designs and numbers, the best routes on which they are employed, and corresponding infrastructure. Such a definition helps understanding the complexity of the problem. However, solving such a problem directly might be considered impossible owing to the large number of parameters being sought. The following intuitively obvious postulate was used to split the general optimization problem to several subproblems.
Postulate: for a given mission, loading capacity, and number of vehicles, there exists only one optimum vehicle type with a corresponding mission infrastructure (i.e., loading-unloading and charging stations) that yields lowest unit transportation cost. It seldom occurs that for a fixed loading capacity, several vehicles with different powertrain designs are found optimum to perform similar tasks. If it happens then any of powertrain designs is equally good and can be selected as an optimum solution.
Using above postulate, the large optimization problem presented in Table 1 can be converted into much smaller n m × n lc × N v optimization subproblems, wherein n m denotes number of missions in set X m , which contains all missions, and n lc denotes number of available loading capacities. The number of vehicles used in the fleet is unknown; moreover, optimum vehicle hardware and infrastructure depend on the number of vehicles employed in a mission; there, therefore, exists a third dimension for number of vehicles N v . To bound values of N v , another set of n m × n lc optimizations must be solved for that is explained in Appendix A. The suggested solution procedure is as follows.

•
Stage A: given a set of missions within the transportation network, a look-up space must be built by determining the best vehicle-infrastructure design for each choice of vehicle capacity, mission, and number of vehicles with that capacity within the mission. The objective function, in this case, includes the unit transportation cost while design variables are inclusive of vehicle hardware, recharging power, and the loading-unloading scheme at each mission node. • Stage B: the look-up space must be used during allocation optimization, wherein design variables include the number of vehicles and required round-trips to form the optimized fleet, which accomplishes the overall transportation task whilst incurring minimum cost of ownership. Not all vehicles and missions in the look-up space need to be used in the fleet (refer Section 4.2). The objective function, in this case, is fleet TCO.
These above two stages are illustrated in Figure 6, and a detailed explanation is provided in following sections.
A multigraph was used as representative of a transportation network, wherein there may exist several arcs connecting two nodes [59]. Multiple arcs existing between two nodes tend to better reflect real-world transportation scenarios, wherein there may exist several paths between two nodes. Alternatively, additional nodes could be added to the network, where no pickup and delivery could take place. In that case, special care must be spent on excluding these additional nodes from loading-unloading and installation of charging stations decision variables. Using multigraph has been suggested to avoid these extra work. The directed multigraph can be denoted by G(V, A), wherein V = {0, 1, . . . , n} represents the set of nodes while A denotes the arc set. Node 0 denotes the depot while V c = V \ {0} denotes n customers. Between each pair of nodes (q, p), q, p ∈ V, there exist n hqp arcs a qpl , a qpl ∈ h(q, p), l = 1, . . . , n hqp . Thus, each arc in A, from node q to node p, can be defined as (q, p, l qp ). Finally, a feasible cyclic route connecting nodes (0, q 1 , q 2 , . . . , q k , 0) can be represented by means of a sequence of arcs given by r = ((0, q 1 , l 0q 1 ), (q 1 , q 2 , l q 1 q 2 ), . . . , (q k , 0, l q k 0 )). The index set of all feasible routes can be denoted by X r ; i.e., for all q ∈ X r , r q is feasible. A feasible route is any cyclic route starting and ending at the depot, passing at least one node. The cyclic route is called a district if the depot is visited several times.

Stage A: Optimized Vehicle-Infrastructure Design Candidates
The present stage focuses on determining the best vehicle-infrastructure design for each choice of loading capacity and number of vehicles for a given mission, motivated by the postulate above.
After excluding loading capacity from the search space S V or fixing loading capacities to a single value, the optimization problem of stage A, for a given mission i, loading capacity c j , and number of vehicles N i v,j , can be expressed as where, c t , denotes the annual cost of transporting one unit of freight, which is a nonlinear function of c j and N i v,j ; c j and N i v,j denote given inputs representing the loading capacity j and number of vehicles corresponding to that loading capacity in the mission i; X i r denotes a subset of X r , which contains all possible cyclic routes and districts of mission i. It must be noted that, in the optimization problem (7), the design space, depicted in Figure 3, is treated as a search space with fixed vehicle capacity. A new search space S i RV is defined including S V as well as X i r marking the range of a design variable-route. and The optimization problem (7) can, therefore, be expressed as subject to all constraints; or reformulated as follows using design variables a k .
subject to all constraints.
The optimization problem of the form described in (11), where a k serve as optimization design variables in the n s + 1 dimensional space S i RV , of the range specified by S i RV,k , could be solved using a stochastic optimization technique, such as particle swarm optimization (PSO) [60,61], and according to the algorithm described in [62]. PSO demonstrates good performance when dealing with non-smooth and non-convex problems. However, it is not very efficient at handling design variables exceeding 30 in number. Ref. [61] provided a comprehensive comparison of different methods. Moreover, the optimization problem must be solved for a number of times to reduce the probability of obtaining a solution far from the global optimum. In the presented case-study, many runs resulted in a similar solution referred as an local optimum solution where, considering the fact that each run was initialized with different initial points (i.e., population), there is a high probability that the obtained solution is a global optimum.
Owing to the inherent nonlinearity and coupling between the number of vehicles, with different payload capacities on a mission, and their corresponding hardware setup, the optimization problem (11) must be solved for all possible numbers of vehicles, i.e., for N i v,j = 1, . . . , N i vmax,j . N i vmax,j , in this case, denotes the maximum number of vehicles, of the same capacity c j , which must be used in a given mission i.
To determine the lower bound for N i vmax,j , a corresponding optimization problem must be solved to also determine optimum values of masses m i L,j and m i U,j of the loaded and unloaded freight, respectively, by means of a vehicle performing identical trips within a mission. By having a single vehicle performing n t identical trips or employing n t identical vehicles, each performing a single trip, the total transportation demand of the mission can be satisfied. It should be noted that each vehicle of the same type performs identical trip(s) within a mission. The optimization problem used for finding N i vmax,j , m i L,j and m i U,j is described in Appendix A. After solving optimization problem described in (11) for all missions i = 1, . . . , n m , loading capacities j = 1, . . . , n lc , and quantity of vehicles N i v,j = 1, . . . , N i vmax,j , corresponding solutions obtained must be stored and used as the look-up space S b in stage B. An example of such a space is depicted in Figure 7. The stored information in the look-up space corresponds to a * = (a * 0 , . . . a * n s ), c t , and t tr , i.e., optimized design, the unit transportation cost, and trip duration time, respectively; that is

Unit Yearly Transportation Cost
The total annual cost of a heavy combination vehicle per unit freight transported, denoted as c t , for a given mission can be expressed as c t (a 0 , . . . , a n s , c, N v ) = C(a 0 , . . . , a n s , c, N v ) f tr (13) where, c denotes the loading capacity, f tr indicates the number of freight units transported in a year from/to a depot, and C represents TCO given by Equation (3). Following Equations (3) and (4), operational costs could be calculated as follows.
where p f , p el , n d , and p d denote prices of diesel fuel, electricity, number of working days per year, and driver salary, respectively. F c denotes fuel consumed during a trip (Equation (A23)), E el denotes electricity consumed during a trip (Equation (A32)), c m is a constant, which provides a rough estimate of maintenance costs as a fraction of the energy cost; t tr denotes trip time, which can be calculated using the vehicle dynamic model (Equation (A42)). N tf denotes the maximum number of trips a fully operational vehicle performs per day, and can be expressed as (15) where, w tmax denotes the maximum allowable working time per day. The operator a provides the closet integer equal to or less than a.
Description of a vehicle dynamic model along with the procedure for calculating values of F c , E el , and t tr is given in Appendix E according to [48], and all parameters and prices are included in the Appendix F.
Moreover, the cost of loading-unloading equipments p lu and charging infrastructure p rech for each vehicle in mission i are given by where I i n is a set containing node indices of the ith mission, p LU,k and p CH,k denotes the cost of shared loading-unloading equipments and charging infrastructure at node k, respectively.
Performance constraints, i.e., gradeability G r , startability S r , acceleration capability A c , and down-grade holding capability D g could be summarized in the mathematical form as follows.
G r (a 1 , . . . , a n s ) ≥ G r,min S r (a 1 , . . . , a n s ) ≥ S r,min A c (a 1 , . . . , a n s ) ≤ A c,max D g (a 1 , . . . , a n s ) ≥ D g,min It must be noted that the performance constraints are only affected by vehicle hardware design parameters. Refer Appendix F for selected values of the performance constraints.
Part of transportation constraints must be covered under the optimization problem in stage B (refer Section 4.2). Other constraints that must be considered in the optimization problem (11) relate to vehicle-loading capacity, pick-up, and delivery during a single trip, as described in Appendix A by Equations (A2)-(A8), as well as the working time, given by Equation (A42). Another set of transportation-task constraints pertaining to rules prescribed for loading-unloading operations are explained in Appendix C. No mathematical description about loading-unloading operations is provided in this paper to avoid notational complexity.

Stage B: The Optimized Fleet
By solving the optimization problem (11) for all available mission choices, loading capacities, and number of vehicles, a set or a space S b containing optimum design candidates is obtained. Candidate designs belonging to this space must be optimally allocated by deciding which designs must work together to satisfy the required pick-up and delivery demands of the transportation network. Fleet composition and sizing is finalized in this stage; moreover, the total number of trips to be performed by each vehicle type is also finalized. Minimum value of the total cost of fleet ownership can be realized by solving the following optimization problem.
where N v is a matrix containing the number of vehicles with different loading capacities employed in different missions; N t refers to a matrix containing the total number of round trips per day that N v vehicles perform together; N i t,j corresponds to the total number of identical trips that must be performed by all vehicles with loading capacity c j in the ith mission; N i v,j corresponds to the total number of vehicles with loading capacity c j in the ith mission; n m denotes the total number of missions constituting the set X m ; n lc corresponds to the total number of loading-capacity choices. The objective function C corresponds to the total cost of fleet ownership per year represented as [e/year]. Subscripts f and p translate to fully operational and partially operational, respectively; and n d is the number of working days per year. Fully-operational vehicles perform the maximum number of trips N i tf,j per day before maximum limit of daily working hours w i tmax is violated. Having a flexible maximum limit daily working hours is shortly discussed later in discussion section. A vehicle performing any number of trips less than N i tf,j is referred to as being partially operational. Constraints (19)- (22) yield the number of fully and partially operated vehicles-N i vf,j and N i vp,j along with the maximum number of trips per day N i tf,j as well as number of trips N i tp,j less than maximum. While building the look-up space S b by solving the optimization problem (11), it was assumed that all vehicles are fully operational, i.e., all vehicles perform maximum number of trips per day, by evaluating Equation (13) using Equation (15). We made this assumption to avoid complication of adding a fourth dimension to the look-up space, since most of the fleet vehicles perform the maximum number of trips. If, for some reason, a fully operational vehicle is not required, it must be redesigned for the given required number of trips per day. Any redesigning of vehicles is not considered in this paper, and partially operational vehicles are considered to have a design similar to that of fully operational. For such vehicles, however, the annual ownership cost per unit freight, as described in Equation (13), must be re-evaluated for the assigned number of trips the vehicle performs per day. This implies replacing N i tf,j by N i tp,j in Equation (14). This constraint is expressed by Equation (23), wherein a i jl represents the vehicle-infrastructure design; values of a i jl , c i t,jl , and t i tr,jl are adopted from the look-up space expressed by the constraint (24). The reason why N v is considered as an optimization variable is that it cannot directly be calculated from N t , since vehicle-infrastructure design and correspondingly, the maximum number of trips per day or trip duration time remains unknown if one does not know which block to choose corresponding to the number of vehicles in the look-up space.
The constraint described in (25) ensures that the daily working time is not violated as well as that the selected total number of trips are performed by the selected number of vehicles. Constraints described in (26) and (27) guarantee that the daily demands concerning pick-up and delivery of all nodes of the transportation network are met. In this case, V denotes the set of all nodes in the transportation network and m L and m U denote masses of the loaded and unloaded freight during a trip, respectively, obtained by solving the optimization problem described by (A1)-(A8) in Appendix A, Q p,k denotes individual units (for example mass) of the total daily demand of freight pick-up from node k and Q d,k represents units of the total freight that needs to be delivered to node k.
Vehicle missions within transportation networks may overlap. Constraints above ensure that the entire transportation task of the network is performed via all or some missions within the specified daily working time window. The optimization problem (18)- (27) can also be solved using the PSO method.
The search space within the optimization problem (18)-(27) comprises two 3D spaces, as depicted in Figure 8. The range of design variables is described by the third dimension of space-the number of vehicles and total number of round trips. Both these ranges have the same size starting from zero to a maximum number given by Equations (A1)-(A8).

Case Study: Auto-Freight Project
The case-study problem considered in this study relates to a project called Highly Automated Freight Transports funded by Vinnova (Ref number 2016-05413 and 2016-05415) in Sweden. This project was initiated to design and manage transportation of goods in containers between Gothenburg seaport and city Borås. Here, we investigate a scenario considering a dry port, close to Borås, where goods must be loaded/unloaded onto/from transport vehicles and subsequently transported to local companies.
A dry port is an inland terminal, where goods can be picked-up from or delivered to in a manner similar to a seaport [63,64]. Benefits offered by a dry port include the possibility of switching over to more efficient especially developed transportation solutions and logistic convenience. Road connections for such a transportation network are depicted in Figure 9, wherein r kl represents different road sections and C i denotes the ith customer. The routes within the mission are described in Appendix D. To evaluate the fuel consumption, each cyclic route is described by an operating cycle according to Appendix E.
Requests for pick-up and delivery of goods at each node are listed in Table 2. Goods could be delivered or picked-up in sets of 500-kg pallets, 20-foot, or 40-foot containers. Duration of the normal working time per day was set as 600 min, including minimum 90 min of waiting time at the seaport during each visit. Longer working times were allowed up to 960 min, with extra penalty, however, on operational costs. There were 220 working days per year within an 8-year service life of a vehicle. Total distance covered in a round trip measured approximately 140 km, the exact value varying depending on the route selection. Other mission data related to economics and transportation design could be found in Appendix F. The optimization problem shown in Table 1 was solved for the above case study. The range of the mission design variable included three missions shown in Figure 9. The range of vehicle sizes are depicted in Figure 10. The charging power at each node ranged between 0 and 180 kW. Zero-charging power means that there is no charging station at the node, therefore, the solution of the optimization problem also defined the location of the charging stations. Furthermore, the range of loading-unloading design variable, at each of the nodes and for each of the semitrailers of the vehicles, included four loadingunloading schemes (i.e., OBL, SC, AST, and OBW) together with no-loading-unloading (NLU), meaning that no action should be done at the node regarding loading-unloading for the corresponding container. Vehicle types were defined using the design space given by Equation (A9), that together with possibility of having on-board lift resulted in about 83,000 different vehicle types, despite the small size of the vehicle design sets. Please refer to Appendix B for the description about the ranges of the vehicle design sets.

Presenting the Solution
For the case study problem presented above, stages A and B were solved and the solutions were compared among 20 and 100 runs, respectively, where about 60% of solutions were found to be similar.
The solution yields the optimum vehicle fleet given the set of routes/missions shown in Figure 9. Figure 11 depicts the optimization result for the case-study problem presented above with a maximum daily working time of 10 h and daily demand flow of 226 cubic meters. The optimum fleet includes one vehicle combination comprising one tractor, one dolly, and two semitrailers with a total loading capacity of 132 m 3 and performing two trips per day on the second mission; one vehicle combination comprising one tractor and one semitrailer with a loading capacity of 66 m 3 and making four trips per day on the third mission whilst also comprising three straddle carriers, an additional semitrailer, and two charging stations. Specifications pertaining to vehicle and recharging power are provided in Table 3. All containers measured 33 m 3 volume.    Figure 12, might result in a different optimum-fleet configuration.
Dry port    Designs of vehicle hardware, loading-unloading schemes, and recharging power for the three optimized vehicles selected for the three missions are listed in Table 3 while the number of vehicles is assumed to be one on a mission. Figures 13 and 14 compare annual costs incurred per unit freight transported by optimum conventional, fully electric, and plug-in hybrid vehicles with a loading capacity of 132 m 3 during the first mission. Data depicted in Figures 13 and 14 were obtained by solving optimization problem shown in Table 1 with the powertrain fixed as being either of the conventional, fully electric, or hybrid type. It can be observed that use of the fully-electric vehicle demonstrated a lower TCO per year compared to using conventional and hybrid vehicles. Moreover, the operational cost of the conventional vehicle is seen to be high due to fuel consumption. On the other hand, the investment cost of the batteryelectric and hybrid vehicles is high due to the high battery cost. However, hybrid vehicles offer benefits of good energy-management strategy, which in turn, reduces operational costs. The control strategy here for optimizing the powertrain is ruled-based, which is similar to the instantaneous optimization reported by [49]. Through the use of an optimum energy-management strategy, overall energy costs could be reduced by up to 4% when moving in traffic with a smooth variation in speed on the roads considered in this study.  To investigate the sensitivity of annual costs incurred per unit freight with regards to variation in design parameters, an electric vehicle on the first mission was selected with a fixed design; subsequently, the value of only one parameter was changed within the admissible range. The corresponding result is depicted in Figures 15 and 16. It must be noted that most of the observations and conclusions drawn here about design and performance of electric heavy-vehicles are general and not limited to the case study.
The dependence of mission costs on road conditions can be rather high, if the concerned vehicle fails to complete the trip on time or vehicle hardware is not feasible to operate on the given road. However, the vehicle selected for sensitivity analysis was both feasible and could make the trip on time under all road conditions. Thus, the only sources of incurring extra costs on different roads were the driver and energy costs, in view of the increased trip duration and distance, as depicted on the top-left of Figure 15.  Figure 15, a jump in total cost is observed when 11 electric motors are used in a vehicle. The reason behind this jump is the observed increase in loading-unloading costs, because the 11th electric motor must be placed on the last semitrailer. The total loading-unloading cost, therefore, increases if additional semitrailers with propelled axles are assigned to the mission.
The TCO per ton of freight demonstrated a linear trend with respect to the recharging power as long as no battery replacement was required. Battery degradation increases with large recharging power and small battery size; thus, batteries of a given size and capacity tend to exhaust earlier, if the recharging power is increased. Figure 17 illustrates this behavior. Trade-offs between fast and slow charging have already been discussed by [30] among others in the literature. As can be observed, the TCO is greatly influenced by battery size and charging power, thereby producing several local minima. Battery size influences the total operational time in terms of the optimum recharging time, as well as power needed to fully charge the batteries, thereby facilitating fully electric vehicles to reach the next charging station. Additionally, vehicle speed can also be affected by the maximum available battery power. Moreover, batteries of different sizes possess different lifetimes. Together, all these factors cause a large variation in TCO with respect to battery size, as depicted in Figures 15 and 17. The reason behind having a large drop in most of cost indicators for battery sizes larger than a threshold is that the vehicle could perform one more trip within the given daily time window as the result of higher power availability, thereby increasing the freight transported per day and consequently reducing the annual unit transportation cost. A drop in cost is, therefore, observed corresponding to all cost indicators in the middle-right of Figure 15, except for the driver cost, the reason being that driving time increases accordingly (within the time window) and also there is an increase in waiting time at a charging station in order to charge the batteries sufficiently so that the final trip could be performed. Furthermore, in the same figure, each drop in battery cost with increase in battery size implies that one less battery replacement is needed during the service life of a vehicle.
Further, the optimum battery size as well as recharging power can be affected by the number of vehicles employed during a mission. As previously discussed, investment cost per vehicle reduces via sharing of charging stations; it is, therefore, favorable to have a large recharging power compared to large battery size. Table 4 lists hardware setups and recharging powers for two optimum fully electric vehicles assigned to mission X 1 r . The type depicted in the first row was optimized considering only one vehicle in the mission, whereas the type in the second row was optimized considering two vehicles. The route as well as loading-unloading scheme were maintained fixed in both cases. It can be seen that optimum battery size and charging power are different for different numbers of vehicles. Figure 16 depicts sensitivity of the TCO per ton of freight with regard to different loading-unloading schemes during the first mission for different nodes. The cost of SC and AST are very close to each other, thereby implying that they can be swapped with each other-for example, in cases wherein optimization of missions X 2 r and X 3 r yields different loading-unloading schemes at the shared node (e.g., the dry port in the case study).
Finally, Figure 18 compares annual costs of transportation per ton of freight amongst optimally designed vehicles of different sizes. The largest vehicle demonstrated an average 53% reduction in costs compared to the smallest vehicle. Large vehicles were observed to perform even better during the second mission compared to the first, since they tend to spend less time in loading-unloading during the second mission, thereby resulting in higher vehicle utilization. Moreover, considering the impact of driver and depreciation costs, it is usually the case that trucks with higher capacity are more attractive as long as they are not idle (low temporal utilization) or traveling partially full (low capacity utilization).

Competitiveness Amongst Conventional, Fully Electric, and Plug-in Hybrid Heavy-Vehicle Combinations
Gross combination mass (GCM) is the maximum mass of a vehicle allowed on a road. As regards the case-study problem considered in this study, loading capacities are mostly constrained by volume while the mass constraint remains inactive; thus, GCM is not realized, and the weight of battery packs does not reduce the loading capacity or capacity utilization of fully electric and hybrid vehicles compared to that of conventional vehicles. Moreover, the unit of mass [ton] is considered as a unit of transported freight while calculating the annual TCO per unit freight, thereby implying that a larger transported mass contributes to lower unit-transportation cost.
Another scenario could be considered in the form of transportation of high-density freight, so that the mass constraint becomes active. In such a case, heavy hardware reduces the overall loading capacity, thereby resulting in higher transportation cost. Besides the limited range of electric vehicles and expensive batteries, reduction in loading capacity through use of heavy hardware in both electric and hybrid vehicles makes them infeasible for use in some applications [2] although a value of total vehicle mass exceeding GCM by a small amount is allowed for electric and hybrid heavy-vehicles, in accordance with the directive (EU) 2015/719. Figure 19 depicts how the type of transported freight (lowor high-density), battery cost, and number of vehicles involved in a mission influence optimum vehicle hardware when performing different missions. As a measure of the battery cost, the number of charge-discharge cycles (NOC) performed prior to the end of battery life (EOL) was used. This measure corresponds to battery quality in that a high NOC implies lesser battery replacements needed during the service life of a vehicle (refer batterydegradation model in Appendix E). Figure 19 depicts roughly under what conditions electric and hybrid vehicles become economically more feasible compared to conventional ones. Vehicle combinations employed during missions 1, 2, and 3 demonstrated GCM values of 80, 80, and 35 tons, respectively. The loading-unloading scheme was fixed as described in Table 3. The hardware and recharging power were separately optimized for the given number of vehicles, freight type, and NOC during different missions as well as conventional, electric, and hybrid vehicle types. Likewise, costs of optimum vehicles of the conventional, hybrid, and fully electric type have been separately indicated for different missions and for two cases-volume constraint active considering low-density freight; and mass constraint active considering high-density freight. Plots on the left correspond to the case when only the volume constraint is active, similar to the case-study problem described above. Correspondingly, plots on the right depict the case with active mass constraint. Following conclusions could be drawn from the figure.
Electric and hybrid heavy-vehicle combinations equipped with a medium-quality battery result in lower costs compared to conventional vehicles for the case wherein only the volume constraint is active corresponding to low-density transported freight, such that GCM is not realized even when large batteries are employed. Conventional heavy-vehicle combinations result in lower costs being incurred in cases wherein the mass constraint is active, i.e., no more freight can be loaded because the GCM limit is reached. In such a case, use of heavy batteries reduces the maximum freight that can be loaded. To meet large demands of freight flow during a given mission, more than one vehicle may be required. Thus, the cost of recharging infrastructure can be shared, and the optimum battery size changes accordingly (refer Table 4). In such cases, fully electric and hybrid heavy-vehicle combinations come across as being cheaper, albeit equipped with a medium-quality battery while the mass constraint remains active. Electric vehicles benefit more compared to hybrid vehicles from enhancement in battery quality. The cost per ton of freight decreases when using better batteries, more number of vehicles, and more loaded freight per vehicle. For short missions involving many stops, i.e., mission three, use of conventional vehicles results in lower unit transportation costs compared to hybrid and electric vehicles for transportation of high-density freight. This is because for transportation of heavy freight, a stronger powertrain is needed, and for a mission with multiple stops, the vehicle spends less time on the road, thereby resulting low vehicle temporal utilization. Thus, the depreciation cost of expensive hybrid and electric powertrains, or purchase cost, is higher compared to that of conventional powertrains, as also reported by [20]. As a result of simultaneous optimization, a fleet of fully electric heavy-vehicle combinations can be designed with approximately 5-10% reduction in TCO compared to a fleet of conventional vehicles.
It must also be noted that the unit transportation cost of electric and hybrid vehicles increases if the working time per day is short owing to the high depreciation cost of hardware and low vehicle temporal utilization. In such a case, the vehicle is not used enough to return the cost of investment. Furthermore, tax incentives, future reduction in battery price, increase in diesel price, and extension of vehicle service life or planning horizon all contribute to even cheaper and more competitive electric heavy-vehicle combinations being made available in the near future. Moreover, fuel efficiency and cost are among reasons of coupling between transportation and vehicle design as well as dependence of optimum vehicle hardware to specific use-case (depending on the cost of fuel in region being studied) [5,29].
NOC before EOL of the battery

Discussion and Remarks
The following remarks are relevant to the limitations and clarifications of the suggested methodology. The optimizer might increase the size of batteries more than the needed traveling range and power to minimize the number of battery replacements required during the service life of a vehicle. -Recharging-power design is only performed for daily operation of a vehicle. The charging power and number of charging plugs required while, for example, all vehicles are not in operation (i.e., during night), are not considered. However, battery degradation owing to overnight charging has been considered in this study. -When employing hybrid vehicles, operational costs could be reduced by implementing an optimum energy-management strategy (OEMS), which whilst considering upcoming driving horizon, optimally splits requested power between electric motors and ICE. However, for vehicle configurations identified for operation in smooth traffic, OEMS gain was observed to be less than 4% in terms of reduction in energy and battery-degradation costs [49]. More specifically, for the first mission, the gain is close to zero owing to the large battery size; during the second mission, an approximately 3% gain is observed; lastly, during the third mission, the observed gain again nearly equals zero owing mainly to availability of a near-flat road. In this study, the coupling between OEMS and vehicle-infrastructure design has not been considered. Considering OEMS and an optimum-speed profile together with vehicle-infrastructure design, the optimization exercise might result in the design of hybrid vehicles equipped with smaller batteries as a feasible solution. -A driver can rest during the loading-unloading process. In the case study, the waiting time at seaport is 90 min, which the driver utilizes for resting. -It has been observed that TCO increased up to 30% if an optimum fully-electric vehicle designed to operate in the first mission is used, instead, in the third mission, while the optimum loading capacity is kept similar to the one in the third mission, for both cases.
It should be noted that the best vehicle-infrastructure candidates identified during each mission are exclusively applicable for that mission irrespective of all other missions. This leads to a problem when two different designs are finalized for the loadingunloading scheme at a node shared between two missions. Furthermore, optimum vehicleinfrastructure candidates of a given size are determined exclusively for that size irrespective of other vehicles with different sizes employed in the same mission. The ownership cost of a mission is a nonlinear function of the total number of vehicles employed with different loading capacities. Moreover, charging infrastructure and semitrailers or straddle carriers could be shared among all vehicles involved in a mission, not only among vehicles with the same loading capacity, as was earlier assumed while building the look-up space. The latter problem, however, is not very significant, since there always exists one vehicle size that is dominant in a given mission. If multiple vehicles are needed, they would all be of the same size whilst only one or two vehicles with sizes different compared to dominant one would be employed to fulfill an uneven total demand of freight flow.
The first problem could be overcome by redesigning missions comprising shared nodes with different loading-unloading and/or charging infrastructure designs. The highest redesign priority is assigned to the mission with lower infrastructure cost whilst using information already available from other designed missions.
Another alternative of problem definition is employing a flexible working time constraint, wherein working is allowed more than the maximum daily working time, however, with a penalty on operational costs. Consequently, a parabolic-like cost curve as a function of number of trips per day was observed. If there exists no penalty cost for violating the flexible time window, there would be a steady decrease in cost whit respect to number of trips. In the latter case, annual TCO per unit of freight [ton] can be minimized to find the optimized fleet. However, in the former case, there should be another optimization process which distributes the total number of trips among vehicles, assigning the optimum number of trips to as many vehicles as possible. Figure 20 shows the dependence of the annual cost per freight unit to the number of vehicles and number of trips each vehicle performs, for two cases. First case introduces no-penalty costs; while in the second case, a 50% penalty on operational cost for working time more than eight hours has been introduced.
For an excising carrier fleet, with already known vehicle hardware, to apply the framework described in this study, the range of vehicle powertrain decision variables need to be fixed and the rest of the optimization framework can be applied with no change.
Despite the small size of the transportation network in the case-study, the problem cannot be solved by enumeration. There are approximately 83,000 vehicle types, whereas the number of vehicles and number of trips are unknowns. Assuming maximum 10 vehicles of each type and 10 trips of each vehicle on a route yields (10 × 10) 83,000 different possibilities for a single route. In addition, the case study included at least four missions, on average two routes per mission, six nodes each with an unknown charging power from a set of 18 choices (6 × 18 different possibilities) and unknown loading-unloading (four different possibilities). Therefore, the total number of possibilities is approximately (4 × 2 × 6 × 18 × 6 × 4) × (10 × 10) 83,000 ≈ 10 166,000 . Clearly, such a problem cannot be solved by enumeration because of many different possibilities.
Finally, it must be noted that the presented values are only valid for the missions defined, input data provided, and vehicle models used. However, the methodology of determining the optimum fleet is generally applicable for repetitive transportation assignments and may be modified to include more vehicle-and transportation-design variables; for instance, type of gearbox, location of articulation point(s), inclusion of dynamic charging [65], more options of loading-unloading and charging strategy.

Limitations
In this study, the driving cycle of all trips is considered to be fully deterministic and no variation in traffic due to nondeterministic events has been considered. In case of a high probability of deviation from a given driving cycle (owing to heavy traffic, for example), higher constraints on vehicle performance must be applied.
The solution method described in this paper is based on a given set of missions X m as an input. In case of dealing with a transportation network of low number of route connectivity, the number of possible missions included in X m is low, thereby making the method presented in this paper computationally applicable. However, the method can still be useful for large transportation networks if the number of possible missions or the number of cyclic routes can be reduced by means of a bounding procedure, which allows only potential "good" routes in the X r set. The potential "good" routes could be determined by decoupling the two problems of routing and vehicle-infrastructure design in a large transportation network. Such a decoupling has been motivated by the results reported in [40] stating that, in presence of performance constraints, routing problem is not strongly interconnected with vehicle design. Traditional approaches for solving VRPs could then be employed on a small set of representative vehicle types. For example, a homogeneous VRP reported by [66] can be solved separately for each available loading capacity using a representative vehicle hardware setup. A combination of all separate solutions along with corresponding solutions for heterogeneous VRPs on the same representative set of vehicles yields a reduced set of routes/missions.
In addition, potential "good" missions can be determined by solving network optimization problems or districting [67]. As such, output districts-a group of nodes that could be visited by a single vehicle-serve as inputs to the set of missions, wherein a mission is either defined by a single or multiple cyclic routes corresponding to multiple trips or by a district with several possible cyclic routes.
In the proposed study, the authors have tried to include most aspects important to transportation systems; however, not all aspects could be considered-speed optimization, for example. As reported by [68], allowing a heterogeneous fleet is more important than speed optimization on each arc, and using a fixed speed results in slightly higher energy-consumption compared to moving at an optimized speed. This claim is true for combustion-powered vehicles with fixed hardware running on flat roads. For a vehicle moving on a road with variable grade, having the speed as an optimization variable is useful, as reported by [69,70]. However, speed optimization is not considered in this study owing to increased complexity and computational cost. The effect of average speed on vehicle-infrastructure design is studied in ref. [11].
The approach presented in this study yields an efficient and low-cost vehicletransportation if the vehicle use-case is known during the entire or dominant part of its lifetime. If transportation characteristics, i.e., consumers, routes, the characteristics of the roads, amounts and types of goods transported etc would change considerably over the lifetime of a vehicle, optimizing towards a very specific operation would lead to inefficiency and even in-feasibility in other transport operations. Therefore, to keep the vehicles to operate near their best performance, the deviation from the assignments that they are designed for has to be small.

Conclusions
The proposed study demonstrates that vehicle hardware design can be treated as an integrated optimization problem comprising transportation-mission, logistics, infrastructure, and fleet-size optimization. A case-study problem has been solved according to the proposed methodology. It has been demonstrated that freight-vehicle designs are influenced by the route, transportation mission, fleet-size and recharging power, as well as transportation boundaries, such as loading-unloading schemes, especially in case of battery-electric heavy-vehicle. Moreover, use of an integrated optimization process could lead to increased profitability of battery-electric heavy-vehicle combinations in highway and urban freight transport by about 30%, and up to 10% reduction in TCO compared to a fleet of conventional vehicles. In addition, it has been shown that long heavy-vehicle combinations in a heterogeneous fleet result in an approximate 53% reduction in TCO compared to a homogeneous fleet comprising rigid trucks. The final outcome of the optimization process is a vehicle fleet with minimum TCO and zero emissions provided that electric energy comes from renewable sources and ignoring emissions from vehicle and particularly battery manufacturing. Through use of the proposed integrated fleet design, this study demonstrates that battery-electric heavy-vehicle combinations can compete against their conventional combustion-powered counterparts, and discusses contributing factors such as vehicle utilization level, payload, battery quality, number of vehicles, battery size and charging power. This would create a true incentive for transportation companies to consider switching to electrification.
The resulting optimization problem is very large; thus, a methodology has been proposed to reduce its size by defining and solving several much smaller optimization subproblems. The first stage includes finding the best vehicle-infrastructure candidates, and in the second stage, the final fleet is found among those candidates and corresponding missions and number of trips are assigned. The proposed methodology is limited to the availability of a clear description of a relatively small transportation network and repetitive assignments, that must be obtained through clear communication between stakeholders, already in conceptual design stages of the vehicles.  Acknowledgments: Authors would like to thank Robert Ljunggren, transportation consultant, city Borås for providing the consumer's demands data.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Abbreviations
The following abbreviations are used in this manuscript: The corresponding optimization problem can be defined as follows.
where I i n denotes a set containing node indices of the ith mission ordered in accordance with the order of visit; Q p,k represents individual units (for example mass) of the total daily demand of freight pick-up from node k whilst Q d,k represents units of the total freight that needs to be delivered to node k; c m j represents the maximum vehicle loading mass; c v j denotes maximum loading volume of the vehicle; and ρ L,k and ρ U,k denote densities of the loaded and unloaded freight at node k, respectively. Thus, N i vmax,j = n t , thereby determining the third dimension of the look-up space. Constraints (A2)-(A4) ensure that vehicles are not loaded beyond their corresponding loading capacity in terms of mass and volume at the depot, whereas constraints (A5) and (A6) ensure that the payload is not exceeded in terms of mass and volume at each node. Constraints (A7) and (A8) ensure all demands are satisfied within n t identical trips performed either by a single vehicle or n t identical vehicles. The condition of minimum n t implies loading the vehicles as much as possible loads with a feasible loading-unloading amounts of freight given by m i L,j and m i U,j . It should be noted that if a mission is defined to be of the multi-trip type, i.e., it includes non-identical trips, n t must be determined separately for each trip. Furthermore, correspondingly, the value of N i vmax,j would equal the maximum of all n t values determined. The optimization problem (A1)-(A8) is solved using a stochastic optimization method, such as PSO.

Appendix B. Vehicle-Infrastructure Optimization Design Sets
As regards to optimization problem (11), the design space (or search space) S i RV is an n s + 1 dimensional space, wherein each dimension relates to one optimization design variable. As an example, for the case study problem, the range of a dimension was defined by a set of discrete parameters, such as sets of available routes, vehicle-design sets, loadingunloading design sets, and recharging infrastructure design sets. Thus, where S i RV denotes a design space or search space and S RV,j , j = 0, . . . , n s denotes design sets or dimensions of that space; X i r is a set of available routes for mission i; CEH is a design set that allows selection between conventional, fully electric, and plug-in hybrid propulsion systems; type em is a design set containing different types of electric motors. Corresponding specifications can be found in Appendix F. The parameter N em refers to the number of electric motors used for propulsion. All electric motors installed in a vehicle were of the same type and specified by type em . An assumption made herein was that all propelled axles employed close-wheel transmission, and thus, utilized electric motors. Thus, N em also provides a measure of the number of propelled axles. The maximum number of electric motors equaled (2 N axles ), where N axles denotes the total number of axles in a vehicle. The parameter type pack specifies a design set comprising different types of battery packs, specifications of which are provided in in Table A5. Parameter N pack denotes the number of battery packs specified by type pack . The maximum number of battery packs was constrained by N packmax to bound the range of this design variable. Parameter type ice contained all possible choices of ICE, which mainly differed in size, and thus, maximum output power; LU 1stTr,k and LU 2ndTr,k represent all possible loading-unloading schemes of the first and second trailers at the kth node, respectively; and finally, RC k specifies the recharging power at the kth node. Zero charging power at a node implies that there exists no charging station at that node. It should be noted that type em , N em , type pack , and N pack have no significant effect on vehicle dynamic model and cost evaluation if the selected propulsion system is of the "conventional" or combustion-powered type.
In general, the loading-unloading scheme and recharging power must be decided for each node comprising a mission. However, based on problem requirements and available information, these can be known in advance at some nodes, and can thus, be excluded from the set of design variables. Moreover, loading-unloading schemes must be determined separately for each trailer. If a vehicle does not have a second trailer, the value of LU 2ndTr,k is neglected, and the cost associated to it equals zero.
Selection of one amongst different vehicle combinations or loading capacities is not included in (A9) because the optimization problem (11) must first be solved based on a given and fixed loading capacity.
The design space described in (A9) is defined for the case study problem described in Section 5. Generally, it can include any sought parameter of the vehicle or transportation task provided that there exists a proper model relating the parameter being sought to the objective function, vehicle design, or transportation task. Optimization design variables a k and their corresponding range S RV,k , related to stage A, are depicted in Figure A1, for a mission comprising only two nodes.

Appendix C. Rules of Loading-Unloading
Rules prescribed for loading-unloading operations are as follows. Mathematical formulations are not provided to avoid rotational complexity.
No-loading-unloading of a container corresponds to no action and no costs. However, at least one trailer or container must be loaded or unloaded at a node. The scheme "on-board waiting" corresponds to no investment cost, while waiting time leads to operational cost. If, at a node, an on-board lift is installed on a vehicle unit, investment cost of the on-board lift is calculated only once for that unit at all other nodes. If a straddle carrier is already selected as a loading-unloading scheme for a trailer it may be employed for the other trailer with no extra investment cost. The cost of off-line container loading-unloading has been assumed to be the same for all schemes, thereby it has not been included in the cost function of the optimization problem. It has been assumed that a vehicle operation can be scheduled in a manner that does not block operation of other vehicles. It has been assumed that up to 12 vehicles may share an additional semitrailer or a charging station. In (A9), one of the design variables is the number of electric motors used for propulsion on driven axles. Each driven axle has two electric motors, for hybrid and fully electric vehicles. In the case study problem, the location of the driven axles, as well as the location of battery packs, are not among the design variables, thus a rule needs to be set for their positioning in different units. Otherwise, in case of having additional semitrailers in a fleet it would be unclear if an additional semitrailer has a propelled axle, or if it should carry battery packs. The set rule is as follows. The rear axle group of the first unit (i.e., truck) has the highest priority of being propelled; then, axles of dolly or the front axle of the truck; next, axles of the first (i.e., front semitrailer); and finally, the second semitrailer. The same ordering of units holds for positioning of the battery packs. Here, the maximum number of semitrailers are two, as depicted in Figure 10. If several customers load on a same trailer then employing an additional semitrailer is only possible for the first visited customer during a trip. Likewise, if several customers unload a same trailer then employing an additional semitrailer is only possible for the last visited customer. The first customer that uses an additional semitrailer switches it with the last semitrailer of the vehicle combination. This requirement is needed to minimize the cost, if the first semitrailer of the vehicle combination has a propulsion hardware. At most, two customers can use a same semitrailer for loading-unloading employing an on-board lift or a straddle carrier. This requirement is needed since the smallest allowed container has 33 m 3 capacity, while a semitrailer may carry 66 m 3 . where m(s) is mass of the loaded vehicle,v(s) is the acceleration, and F wh (s) is the sum of propulsion and brake-actuated longitudinal forces of all wheels acting on wheels contact patch with the road at distance traveled s. The resistant force F r (s) is defined by where φ is road grade angle, positive downhill, and g, f r , ρ a , A f , c d and v denote gravitational acceleration, rolling resistance coefficient, air density, front area of the vehicle, aerodynamic drag coefficient and velocity (0 < v), respectively. Rolling resistances are, physically, torques acting on the wheels but, for energy consumption evaluation, they can be represented as forces acting on the vehicle body. The independent variable is distance traveled s rather than time t, because the driving cycle, i.e., road slope, speed limits and consumer location are functions of distance traveled. The time derivative in space domain is described bẏ The gross combination mass, i.e., the mass of the loaded vehicle, can be described as follows.
where m v is the vehicle curb mass excluding drivelines, powertrain, engines, and battery packs, and N em , m ElDrive , N pack , m pack , m ice , m L (s), m U (s) and m obl are number of electric motors, mass of an electric motor and its transmission, number of battery packs, mass of a battery pack, mass of ICE and its associated transmission, mass of loaded freight, mass of unloaded freight and mass of the on-board lift (if any), respectively. Equation (A12) is a differential equation which needs to be integrated; however, F wh (s) andv(s) are unknowns. Therefore, a speed reference signal v ref (s) needs to be used, e.g., a representative or the road legal speed limit. The vehicle tries to keep the reference speed within the constraints of the vehicle powertrain and power sources. Given the reference speed v ref (s), the achieved acceleration can be calculated as follows.
where, F whmax (s) and F whmin (s) are the limits of the longitudinal force delivered by propulsion and braking actuation given by where T and P are the torque and power of the electric motors or ICE, acting on wheels, respectively, Ratio max is the transmission total final ratio, R is the wheel radius, and F fri is the force generated by friction brake.
Furthermore, F ice and F em are defined as propulsion forces actuated by ICE and electric drivelines, respectively, on the contact patch of the wheels as follows.
where n em is the number of electric motors. It should be noted that the road-wheel grip limit and tire slip models are not considered, assuming smooth driving on normal road friction.
After calculating the actual speed v(s), using Equation (A16), the travel time t tor spent on road during a mission can be calculated according to where s f is the length of the mission.

Appendix E.2. Conventional Vehicle and Internal Combustion Engine Model
In this study, the data of highest efficiency versus the normalized power were used for describing different diesel internal combustion engines. It was assumed that a vehicle is equipped with a tightly stepped gearbox with fast changes, or with a continuous variable transmission, and the control system selected the transmission ratio to keep the ICE operation on the highest efficiency for each requested power. The maximum efficiency versus normalized power P ice P icemax is given in Table A1, where a proper interpolation needs to be performed for continuous approximation of the efficiency. The ICE power P ice is can be calculated as follows.
where η ctr is the continuous variable transmission efficiency.For the positive propulsion the ICE power cannot drop below the minimum value given in Table A1. Therefore, the torque and power limits at the wheels level needed for Equations (A17) and (A18) can be calculated as follows, assuming no engine brake is employed.
By change of variable s = v t, the fuel consumption of one trip F c is where η ice is the maximum efficiency of ICE, E pgf is energy per mass of diesel fuel, D f is the fuel density, and t tor is the travel time on road given by Equation (A20). The value of parameters can be found in Appendix F. Total power P em (s) of an electric motor is given by where η tr is the efficiency of the electric driveline. The charge/discharge power of the battery packs can be calculated as follows, provided that the state of charge (SOC) of the battery packs is within the limits, i.e., SOC min ≤ SOC(s) ≤ SOC max .
P b (s) = n em P em (s) + P emloss (s) + n pack P packloss (s) (A25) where P b (s) = n pack P pack (s) is the total power provided by n pack battery packs that are connected in parallel, P pack is the power of a single battery pack, P emloss (s) and P packloss (s) are energy losses in the electric motor and a battery pack (always positive). Therefore, the limits of power and torque acting on the wheels of a fully-electric vehicle can be calculated as follows.

. Battery Pack Energy Loss
The energy loss in battery packs, with a known resistance R bp is calculated as follows.
where the current I pack is given by I pack (s) = n em (P em (s) + P emloss (s)) n pack V pack (s) where V pack = 600 V is the voltage of the battery packs. Battery pack voltage and resistance generally functions of state of charge; however, in this paper, they are assumed to be constants. Moreover, it is assumed that the voltage drop as the result of the battery resistance is considerably smaller than V pack . Refer Table A5.

Appendix E.3.2. Electric Motor Energy Loss
For calculating P emloss , in this paper, it is assumed that the electric motor efficiency is a convex and quadratic function of the electric motor input torque T(s) and speed ω(s) in the form P emloss (s) = k ω ω(s) 2 + k T T(s) 2 (A29) Furthermore, it is assumed that electric motor torque and speed can be selected such that highest efficiency is achieved for a linear relation T(s) = b ω(s) [40]. Therefore, the lowest power loss of electric motors can be calculated as follows.
P emloss (s) = 2 k ω ω(s) 2 (A30) where ω is given by where k ω and b = k ω k T are constants related to the loss map of the electric motor. Refer Table A4.
Finally, the consumed electric energy E el can be calculated as follows.
Appendix E.4. State of Charge and Trip Time SOC needs to be calculated in order to estimate the feasibility of the selected hardware as well as the charging time spent in a charging station. The SOC between charging stations can be calculated as follows.
where s i is the distance of node i from the starting position, I n denotes the index set of all loading-unloading nodes in the mission, and SOC(s i ) is the SOC of the battery packs immediately after leaving node i, given by where SOC(s − i ) is SOC at arrival to node i, P ch,i is the recharging power from the charging station at node i, t ch,i is the charging time, and E bmax denotes the maximum energy capacity of the battery packs. A constant charging power and a linear charging time with respect to SOC are assumed [50]; therefore, For a plug-in hybrid vehicle, the recharging time t ch,i can be assumed the same as the loading-unloading time calculated as t ch,i = min max(t lu,i , t s,i ), where t lu and t s are the loading-unloading time and a fixed minimum service time, respectively. In Equation (A36), it is assumed that the charging time ends if SOC max is reached.
For an electric vehicle, however, the recharging time might be longer than the loadingunloading and service times at a node because it must be ensured that the vehicle can reach the next charging station. Let ∆SOC(s − i+1 ) = SOC(s − i+1 ) − SOC(s i ) be the charge required to reach node (i + 1) from node i. This value can be calculated in advance by simulating the vehicle motion on the road, without considering a minimum limit on SOC.
To reach node (i + 1), ∀i ∈ I n , the following condition must hold: therefore, and Finally, the total trip time t tr can be calculated as t tr = t tor + ∑ i∈I n max(t lu,i , t s,i , t ch,i ). (A42)

Appendix E.5. Battery State of Health
Battery degradation and battery replacement during the vehicle service life are inputs for TCO calculations of BEHVs and hybrid vehicles. In this study, the battery is replaced with a new one when the battery capacity reaches 80% of the initial capacity and evaluation of the state of health of lithium-iron-phosphate batteries S h was inspired by [51][52][53] according to where N cycle is the number of charge-discharge cycles before the end of life of the battery. In general, N cycle is a function of various parameters. In this study, however, it was assumed to be constant for a given battery type. If t denotes the vehicle lifetime, the number of battery replacement n rep can be calculated as where gives closest lower integer.
Appendix E.6. Plug-In Hybrid Vehicles In plug-in hybrid vehicles the total power must be split between electric motors and ICE according to an energy management strategy [69]. A computational-efficient rule-based energy management strategy has been implemented in this paper, which was validated compared to a predictive energy management strategy in [49].
Rule-based controller can be explained as follows. The priority of providing the requested power for propulsion and braking first goes to electric driveline. Any additional positive or negative requested power that passes the limits of the electric driveline must be provided by ICE or friction brakes in parallel. ICE must not work in a power less than a threshold. The threshold corresponds to the power where ICE efficiency drops to less than 0.2. If the requested positive power is less than the threshold, the additional ICE power can be used for charging the batteries.

Appendix E.7. Operating Cycle
Operating cycle refers to all information about surrounding environment and road influencing driving situation [54]. In this study, the operating cycle has been static and deterministic, i.e., the input data about a mission and its driving cycle do not evolve in time and known in advance.
Operating cycle is characterized by the reference speed and topographic data, i.e., elevation, curvature and length of the road. The reference speed is limited by the road legal speed limit and varies in different sections of the road; for example, on rural areas, highway, red light and alongside a curvature, depending on the daily average speed of the respective section. The daily average speed is overridden, while negotiating a curvature, so that the vehicle lateral acceleration remains below 1.5 m/s 2 . The influence of real-time varying traffic was not included.

Appendix F. Parameters
The prices and values of parameters are obtained from Volvo group trucks technology. The data presented in Tables A2-A8 are used for cost evaluation, and in the vehicle dynamic model presented in Appendix E.