Multiple Criteria Optimization of the Joint Vehicle and Transportation Jobs Selection and Vehicle Routing Problems for a Small Road Freight Transportation Fleet

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Transportation Research Procedia 30 (2018) 178–187 www.elsevier.com/locate/procedia

EURO Mini Conference on "Advances in Freight Transportation and Logistics" (emc-ftl-2018) (emc EURO Mini Conference on "Advances in Freight Transportation andVehicle Logistics" (emc-ftl-2018) (emc and Multiple Criteria Optimization of the Joint

Transportation Jobs Selection and of Vehicle Routing Problems the Joint Vehicle and Multiple Criteria Optimization for a Small Freight Fleet Transportation JobsRoad Selection andTransportation Vehicle Routing Problems b for a Small Roada*,Freight Maciej Hojda Jacek akTransportation , Grzegorz Filceka Fleet b University of Science and aTechnology, Faculty of Computer Science anda Management, Wrocław Technology Wybrzeee Wyspiaskiego Wyspia 27, 50-370 Wrocław, Poland b a Poznan University of Technology, Poznan 60 60-965, Faculty of Computer Science and Management, Wrocław University ofPoland Science and Technology, Technology Wybrzeee Wyspiaskiego Wyspia 27, 50-370 Wrocław, Poland b Poland Poznan University of Technology, Poznan 60-965, 60 a

Maciej Hojda *, Jacek ak , Grzegorz Filcek

Abstract Abstract We consider a joint problem of selecting transportation jobs and designing transportation routes for small freight transportation transporta fleet owners. The problem is formulated as a multiple criteria optimization problem with several stakeholders: the driver, the fleet owner and thea clients. The problem formulation includesjobs driving work time regulationroutes constraints, takes into account driv driver We consider joint problem of selecting transportation and and designing transportation for small freight transporta transportation comfort and The safety, as well as the lateness of the criteria job execution and the time constraints the pickupthe anddriver, the delivery. fleet owners. problem is formulated as a multiple optimization problem with severalon stakeholders: the fleet owner and thethe clients. The of problem formulation includes driving and work time regulation takes into account driv Furthermore, selection the vehicle is included as a part of the decision making process.constraints, The problem is heavily constrdriver constrained and cannot solved lvedasexactly in the reasonable Wejob propose an iterative algorithm on which evaluate series of comfort andbesafety, well as latenesstime. of the execution and thesolution time constraints the we pickup and in thea delivery. computational experiments performed on isa subset of as theatransportation network of Poland. Furthermore, the selection of the vehicle included part of the decision making process. The problem is heavily constrained constr and cannot be solved lved exactly in reasonable time. We propose an iterative solution algorithm which we evaluate in a series of ©2018 The Authors. Published by Elsevier Ltd. of the transportation network of Poland. computational experiments performed on a subset This is an open access article under the CC BY-NC NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/ nd/4.0/) Copyright © 2018 Elsevier Ltd. All rights reserved. ©2018 The Authors. Published by Elsevier Ltd. Selection and peer-review review under responsibility of the scientific committee of the EURO M Mini ini Conference on "AdvancesininFreight Selection and peer-review under responsibility of the scientific committee of the EURO Mini Conference on “Advances Freight Transportation and Logistics" ftl2018). This is an openand access article under the(emc-ftl2018) CC BY-NC NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/ nd/4.0/) Transportation Logistics” (emc-ftl2018). Selection and peer-review review under responsibility of the scientific committee of the EURO Mini Mini Conference on "Advances in Keywords: Freight Transportation; Vehicle(emc-ftl2018) Routing; Multiple Criteria Optimization Freight Transportation and Logistics" ftl2018). Keywords: Freight Transportation; Vehicle Routing; Multiple Criteria Optimization

* Corresponding author. Tel.: +48-71-320-41-12; 12; fax: +48-71-321-10-18; +48 E-mail address:[email protected] * Corresponding author. Tel.: +48-71-320-41-12; 12; fax: +48-71-321-10-18; +48 2352-1465© 2018The Authors. Published by Elsevier Ltd. E-mail © address:[email protected] This is an open access article under the CC BY-NC-ND ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)Selection ( Selection and peer-review peer under responsibility of Authors. the scientific committee of the EURO Logis (emc2352-1465© © 2018The Published by Elsevier Ltd. Mini Conference on "Advances in Freight Transportation and Logistics" ftl2018). This is an open access article under the CC BY-NC-ND ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)Selection ( Selection and peer-review peer under responsibility of the scientific committee of the EURO Mini Conference on "Advances in Freight Transportation and Logistics" Logis (emcftl2018). 2352-1465 Copyright  2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the EURO Mini Conference on “Advances in Freight Transportation and Logistics" (emc-ftl2018). 10.1016/j.trpro.2018.09.020

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1. Introduction Surface transportation, including road transportation, is a dominant transportation mode for moving goods/freight world-wide. According to Alam et al (2015) up to 60% of all transportation is done on the surface. Freight road movements play a critical role (next to warehousing) in various logistic networks. Many recent research projects have been carried out and many reports have been published in the area of road freight transportation (see Goel and Gruhn (2006), Goel and Kok (2010), Kok et al (2010), Paquette et al (2012), Prescott-Gagnon et al (2010), Rancourt et al (2010), Rancourt and Paquette (2012), Demir et al (2014), L'och and Dolinayova (2015), Alam et al (2015), Jabir et al (2015), ak et al (2011) or Baran and ak (2013)). Traditional models of freight transportation optimization are single-objective formulations, focused on cost minimization (Crainic (2001), Forkenbrock (2001)). Recently, different authors have proposed more realistic and comprehensive approaches for handling freight transportation problems, including multiple criteria formulations which try to optimize the working conditions of the drivers, increase the driving safety, reduce the emission of harmful substances or reduce the turnover rate. Goel and Kok (2010) and Rancourt et al (2010) emphasize that increased driver fatigue is a direct reason behind a large number of crashes while according to Rancourt and Paquette (2012), poor working conditions are speculated to be the biggest reason for turnover rate in long-haul transportation. Although the idea of management that aims to improve the working conditions in transportation systems is not novel (Bander et al (1998)), currently there is a growing number of papers that indicate the need to incorporate the preferences of the drivers into the decision making processes (Bozkurt et al (2012), Sun et al (2007), Cherry and Adelakun (2012)). Bozkurt et al (2012) consider a multiple criteria routing problem that mixes driver preferences with travel time and travel safety as the main criteria, while Sun et al (2007) model the driver’s behavior using Analytic Hierarchy Process (AHP). Finally, Cherry and Adelakun (2012) consider driver preferences regarding the usage of paid managed lanes. Realistic instances of road freight transportation problems are expected to consider multiple criteria. Work of Dib et al (2016) contains a formulation and a solution procedure for a multiple criteria, multimodal transportation problem focused on efficient changes of transportation modes. L'och and Dolinayova (2015) formulate a multiple criteria ranking problem to evaluate freight transportation quality and use the AHP to rank alternative criteria. Several papers (Demir et al (2014), Sawik et al (2017a), Sawik et al (2017b), Jabir et al (2015)) refer to green freight road transportation and demonstrate multiple criteria formulations for handling transportation processes. One of the examples is paper of Sawik et al (2017b) where the authors consider several quality coefficients (including the environmental-oriented ones), such as: cost, noise, pollution and fuel consumption while solving a vehicle routing problem. They propose a solution procedure that features the balancing and trade-off analysis of the abovementioned criteria, and they conclude that the application of multicriteria optimization methods makes it possible to slightly control and limit the carbon emissions. This is a follow-up of an earlier paper of Sawik et al (2017a) where a green version of the combined traveling salesman and transportation problems was considered. Finally, Demir et al (2014) review recent papers which give priority to such formulations where the optimization focuses on limiting emissions of harmful substances, such as CO2 into the atmosphere. It is crucial to take into account specifics of the road freight transportation such as drivers’ working hours regulations. Goel and Gruhn (2006) and Kok et al (2010) solve a driver routing problem with EU working hours regulations. In the paper of Goel and Kok (2010), a scheduling problem with time windows is considered with USspecific regulations in mind. Paquette et al (2012) solve a multiple criteria dial-a-ride problem with a double objective of transportation cost and quality of service. In paper of Prescott-Gagnon et al (2010) we observe how a vehicle routing problem with time windows and driver regulations (EU) is solved with the use of a very large neighborhood search method. Rancourt et al (2010) solve a long-haul truck driving problem with NA regulations which they formulate as a vehicle routing problem with multiple time windows and a heterogeneous fleet. Finally, Rancourt and Paquette (2012) tackle a multicriteria optimization problem for long-haul freight road transportation. The problem is formulated as a vehicle routing and truck driver scheduling problem and authors seek to improve drivers’ working conditions. This paper further extends the area of multiple criteria oriented road freight transportation research and presents the formulation and a solution procedure for a transportation job selection problem joint with multiple criteria problem of vehicle routing for small fleet owners. The paper focuses on a less-than-truckload routing problem where

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multiple commodities can be transported at the same time – drivers execute multiple transportation jobs in parallel. The approach focuses on obtaining a set of transportation jobs for private truck fleet owners (or a driver, in case of single-driver companies) based on their preferences, the preferences of the driver and the preferences of the clients. To solve the stated problem it is necessary to solve a multiple criteria extension of the vehicle routing problem. However, to solve the vehicle routing problem, a selection of transportation jobs is required. This leads to a complex and interconnected optimization problem that is difficult to solve. The problem is further described in the following section. 2. Problem description We formulate a decision making problem consisting of two main interconnected partial problems. Given a driver and a set of transportation jobs, the fundamental goal considered in the paper is the selection of jobs to be assigned to the driver. Jobs are ranked according to drivers’ preferences and job properties. Secondary goal is to design a route that ensures the execution of all the delivery tasks. To that purpose, a suitable vehicle has to be chosen and break times have to be arranged. We consider a network which is composed of points of interest (further called nodes) such as delivery points, pickup points, parking lots and major crossroads which are, in turn, connected by road segments. Road segments (further called arcs) have properties such as distance from one node to another, travel time, relative comfort and relative safety of travel. The quality measures come from different stakeholders in this decision making process. The driver is interested in safety, comfort, profit and duration of the work time. The business owner is interested in financial gain (or loss) and fitness which is the chance to actually get the contracts under consideration. Clients are interested in timeliness of the delivery. Those criteria are evaluated based on one of many of the four decisions: route, job assignment, vehicle selection and break duration and are also based on the properties of nodes, arcs, jobs and vehicles. The solution, which is the set of jobs and corresponding routes, is subject to various constraints which limit the feasible set. Constraints are divided up into three groups: regarding routes, regarding driver preferences and regarding driver aptitude. First type of the constraints is always present. We permit a situation in which some of the two latter constraint types are inactive, i.e. the driver or the job provider has no preference. Route constraints ensure that the route is made up of correctly interconnected stages, that it starts in one of the given starting points and that it ends in one of the given ending points. They also ensure that pickup takes place before delivery and that all pickups and deliveries are on the route. Preference constraints ensure that minimal safety and comfort constraints are met, that maximal dwelling times are not exceeded and that the profit to cost difference is within acceptable bounds. Furthermore, the constraints guarantee that every job is acceptable from the driver's viewpoint. Aptitude constraints ensure that the driver can perform every job. That includes that the volume of the package is within acceptable bounds and that the truck is equipped with all the necessary appliances, such as a freezer which is typically needed for food transportation. The model permits situations in which the driver is already in the middle of driving (some of the jobs are assigned and partially executed). In this case, it is necessary to evaluate new jobs according to how well they merge with the jobs already assigned. The addition of a new job changes the parameters of the route. New route is computed and evaluated according to a complex quality measure. This is more accurately presented in the following section. 3. Problem formulation We formulate the problem for the following data sets: N = {0, 1, 2, ..., N } – a set of nodes, A ⊂ N 2 – a set of arcs, J = {1, 2, ..., J } – a set of transportation jobs, and I = {1, 2, ..., I } – a set of vehicles. The nodes represent all the intersections of roads and are the place where pickup and delivery takes place and where parking lots are located (or not). Node 0 is artificial and does not represent a real point on the transportation map. It is however a node where the route begins and ends. We assume, that for each node, the following data is given: a set of parking intervals with different fees, availability of parking space, parking intervals starting time, parking interval fees.

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The arcs represent all the roads on which movement can take place. For each arc the following data is given: a node in which it begins, a node in which it ends, travel distance, average safety per kilometer of travel, average comfort per kilometer of travel, road fees, road conditions (parameters used for calculation for a specific vehicle travel times and cost of transportation on this arc). The set of transportation jobs consists of jobs available on the market. Each job is characterized by the given data: pickup node, delivery node, loading and unloading times, safety of the job (for the driver), comfort of the job (for the driver), fixed revenue for the business owner (estimated payment for transport between pickup and delivery points with the use of best-suited for the job vehicle), a set of time windows for pickup and delivery with start and end times, object width, length, and weight, estimated demand for this job. The vehicles which represent the means of transportation (trucks, vans and others) have the following parameters given: safety of the vehicle (for the driver), comfort of the vehicle (for the driver), vehicle width, length, height, and maximum carrying capacity, description of the vehicle (description includes vehicle fuel consumption, number of axis, category, type of body, millage, year of production and is helpful to calculate vehicles’ travel time and cost of transportation on arcs of the road network, as well as value of predisposition of the vehicle for serving the transportation job). For the driver, there are also available data about his/her working hours status. The working hours status includes hours spent on driving and last resting times. Finally, historical data concerning jobs already served by business owner is provided. This data will be used to estimate the chance of contracting the job by the business owner. Based on the given data describing road, jobs and vehicles, the following variables are calculated and provided as input: a set of starting and a set of ending nodes of the journey, information concerning movement of vehicles on arcs given as travel times and costs of transportation, the predisposition of the vehicle for serving the job (calculated based on data provided in job and vehicles descriptions). We do not provide information about the way of calculating the above data, but assume that it is given. Additionally, data concerning preferences of the stakeholders is provided. The preferences refer to the evaluation criteria of the decisions to be made by definition of its’ feasible bounds and their importance. The preferences also concern decision that have been already made, and must be taken into account during decision making (e.g. some transportation job has been already contracted). The decision making consist of the following four tasks: selection of transportation jobs to be undertaken, selection of a vehicle used to perform transportation jobs resulting from undertaken jobs, obtaining route that the selected vehicle should take to do all the selected transportation jobs and assignment of the length of resting times to nodes constituting the route of the vehicle to satisfy the constraints resulting from driver’s working hours regulations. The selection of jobs is done by determining y = [ y j ] j∈J where y j = 1 if job is undertaken (0 if otherwise). The selection of vehicle is done by determining z = [ z i ] i∈I where z i = 1 if the vehicle is selected (0 if otherwise). The route is obtained by determining x = [ x n , m ] n , m∈N where x n , m = 1 if there is movement from node n to node m (0 if otherwise). Arcs, for which x n , m = 1 constitute the route. Finally, the assignment of the length of resting times to nodes is done by determining u = [u n ] n∈N , where u n ∈ [0, T ] . T is the decision making horizon. The decision to be feasible, must satisfy the following sets of constraints: 1. The route must be a proper path which starts and finishes in node 0 (it cannot have sub-cycles, and the graph representing it must be connected). 2. All selected jobs must be properly served on the route. (The route must include all pickup and delivery nodes of the selected jobs and delivery nodes must follow pickup nodes for the same job. The pickup and delivery nodes must be visited in the time windows defined by the appropriate job). 3. Resting can be performed only in the nodes with parking places available for the vehicle serving the jobs, and satisfy driver’s working hours regulation. 4. The first and last real node visited on the route, must be the ones permitted in the input data. 5. The decision variables must be consistent with partially made decisions (e.g. some jobs must be served, or route fragment taken). Those constraints could be used when some previous plan is in the execution phase

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6.

5

(driver is on his way), and because of some change in the data, it is necessary to change a part of the previously made decisions to sustain optimality or even feasibility of the solution. The values of the defined evaluation criteria do not exceed their defined bounds.

The decisions are evaluated based on the following main criteria: safety (S), comfort (C), profit (P), duration (D), gain (G), fitness (F) and lateness (L). Safety consists of the safety of route, total safety of jobs to be served and safety of vehicle. Comfort consists, similarly to safety, of comfort of the route, serving jobs, and vehicle. Profit is what the driver earns. Duration is the time between moments of starting the route and finishing it. Gain is the profit of the business owner calculated based on the difference between revenue from serving transportation jobs and cost of using vehicle and driver for serving the jobs on the given route. Fitness consists of value of predisposition of vehicle for serving the transportation jobs, and a chance of the business owner to sign the contract for serving the job. The chance to sign the contract is calculated based on the estimated demand for the job and history of the jobs served by the business owner (jobs served for a customer, whose jobs were served in the past are more likely to be contracted). Lateness expresses the total lateness of the pickup and delivery calculated as the absolute difference between first delivery start time window for each job and its actual delivery time. As an example, we provide a formula for the safety criterion: S=a



1   xn, m rn.m qn, m + b  xn, m rn, m n∈ N m∈ N

n∈ N m ∈ N

1  y j s j + c  z i pi ,  y j j∈J i∈ I j∈J

where a ∈ [0,1] is the relative importance of the safety regarding routes, b ∈ [0,1] is the relative importance of safety regarding jobs, c ∈ [0,1] is the relative importance of safety regarding vehicles, q n,m ∈ [0,1] is on-arc safety, rn,m ≥ 0 is the arc distance, s j ∈ [0,1] is the safety of the job and p j ∈ [0,1] is the safety of the vehicle. The objective is to find feasible decisions that maximize safety, comfort, profit, gain and fitness, while minimizing duration, and lateness. Under such objectives, the multi-criteria decision making problem is as follows Given: Sets N , A , J , I , values of their elements’ attributes, and preferences of the stakeholders concerning criteria and decision variables. max [ S , C , P,− D, G, F ,− L] , Find: y , x, z ,u

where:

y, x, z, u are selected under the set of constraints (1-6).

The problem is solved with the use of an iterative solution procedure, the outline of which is presented in the following section.

4. Solution algorithm We start solving the problem by aggregating (by the means of a weighted sum) the multiple criteria S , C , P,− D, G, F ,− L into a single criterion which is further called the utility. Then we optimize the criterion in a greedy manner as follows. The greedy solution algorithm is composed of an iterative main loop where jobs are assigned to the driver starting from the best one. The overall idea is presented as follows. 1. Let F, T be the sets of permitted arrival and destination points. Let A = ∅ , B = J , r = (0) 2. For every j ∈ B do 3. Let C = A ∪ { j} 4. Let d j , a j be departure and arrival nodes for the jth job respectively. 5. For possible selection of f ∈ F , t ∈ T

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6. Insert f , t into r , i.e. r = (0, f , t ) . 7. For every possible insertion of d j , a j into the permutation r of nodes do 8. For every i ∈ I do 9. Let y = 0, x = 0, z = 0, u = 0 10. Let y j = 1 ⇔ j ∈ A , zi = 1 11. Determine the shortest route x and rests u (in terms of utility) while visiting nodes in order r . ~ 12. Save the solution y, x, z, u (and j = j , ~ r = r ) if it is better than the currently saved one. ~ ~ 13. If a feasible solution y, x, z, u was saved, let A = A ∪ { j } , B = B \ { j } , r = ~ r . Go to 2. 14. End the algorithm returning the last saved feasible solution. The determination of routes is done with the use of the Dijkstra algorithm with distances defined by the utility. Of all feasible break times, selected are values that minimize the total travel time.

5. Empirical evaluation We evaluate our solution algorithm on a transportation network of 87 nodes comprised of most populated cities of Poland. Evaluated are the execution time of the whole algorithm, the quality of the solution, the partial qualities (both normalized and prior to normalization). The evaluations are performed for nominal data: car capacity 12 tons, number of jobs: 30, less-than-truckload job weight: 4 tons, pickup/delivery time windows: 8h-16h every day, number of days: 1. Since some of the parameters (such as safety and comfort of jobs, their starting and ending points) are randomized, we perform the experiment 50 times for every set of fixed parameters. Results presented here are the average values. We have evaluated the algorithm in a series of 9 experiments. Tested were the following parameters: - number of jobs (10, 30, 50, 70, 90 jobs with randomized parameters), - number of nodes (map was reduced a smaller area with 10, 30, 50, 70 nodes), - number of cars (1, 3, 5, 7, 9 cars were generated with a randomized capacity of 6-18 tons), - capacity of cars (fixed capacity of 6, 12, 18, 24 and 30 tons), - ratio of less-than-truckload jobs to full-load jobs (1:0, 2:1, 1:1, 1:2, 0:1), - time horizon (number of 1, 2, 3, 4, 5, 6, 7 days), - driver versus client preferences (weights with ratio of 0.2, 0.5, 1, 2, 5), - profit versus fitness preferences (weights with ratio of 0.2, 0.5, 1, 2, 5), - safety versus profit preferences (weights with ratio of 0.2, 0.5, 1, 2, 5). Evaluated criteria were: the time of execution, the utility, partial utilities of individual criteria, values of the criteria prior to normalization.

45

time [centiseconds] utility [%]

40 35 30 25 20 15 10 5 0 10

30

50

70

Fig 1. Influence of number of nodes on computation time and utility

50 45 40 35 30 25 20 15 10 5 0

time [centiseconds] utility [%] 10

30

50

70

90

Fig 2. Influence of number of jobs on computation time and utility

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90

50 45 40 35 30 25 20 15 10 5 0

time [centiseconds] utility [%]

80 70 60 50 40 30 20 10 0 1

3

5

7

9

time [seconds] utility [%]

1

Fig 3. Influence of number of cars on computation time and utility

2

3

4

5

6

7

Fig 4. Influence of number of days on computation time and utility

95

60 time [centiseconds] utility [%]

50

90 85

40

80

30

75

20

70

10

65

0

60 0,2

0,5

1

2

5

safety [percent] profit [Basis Point (BPS)] 0,2

Fig 5. Influence of ratio of weight of safety to weight of profit on computation time and utility

0,5

1

2

5

Fig 6. Influence of ratio of weight of safety to weight of profit on safety and profit

Table 1. Influence of number of nodes on computation time and utility 10

30

50

70

time [centiseconds]

33.3

17.0

13.8

13.4

utility [%]

38.3

30.2

28.6

28.7

nodes

Table 2. Influence of number of jobs on computation time and utility jobs time [centiseconds] utility [%]

10

30

50

70

90

2.560

10.771

20.037

38.388

44.799

27.416

27.905

27.846

29.188

28.152

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Table 3. Influence of number of cars on computation time and utility 1

3

5

7

9

time [centiseconds]

11.781

33.398

49.223

67.086

80.637

utility [%]

28.231

29.546

29.660

30.682

30.058

cars

Table 4. Influence of number of days on computation time and utility days

1

time [seconds] utility [%]

2

3

4

5

6

7

0.095

0.596

1.228

2.694

4.251

8.991

8.718

27.003

38.093

42.938

44.433

45.827

46.892

43.772

Table 5. Influence of ratio of weight of safety to weight of profit on computation time and utility 0.2

0.5

1

2

time [centiseconds]

12.521

10.617

11.025

10.421

7.660

utility [%]

13.660

20.384

27.161

35.723

48.901

weight

5

Table 6. Influence of ratio of weight of safety to weight of profit on safety and profit 0.2

0.5

1

2

5

profit [Basis Point (BPS)]

92.436

83.985

83.817

81.347

75.211

safety [percent]

68.833

72.291

72.877

77.184

78.929

weight

As presented in figure 1 and table 1 the increasing number of nodes N in the analyzed network (from 10 to 70) substantially decreases both the computational time T and the overall utility U of the generated solutions. Both functions T ( N ) and U (N) have a non-linear character of a similar shape. The computational time, corresponding to the overall speed of the algorithm, decreases from 0.34 sec. to 0.14 sec. (by 60%) when the number of nodes is 7times increased. It is worth mentioning that the initial dramatic/significant drop of the computational time by roughly 50% (from 0.34 sec. to 0.17 sec.) is achieved through the triple increase of the number of nodes (from 10 to 30). Further increase of the number of nodes in the network improves the computational time but at a much lower rate. This means that one of the conditions of the speed of the algorithm is the density of the considered network (sufficient number of considered nodes). It is not positive that the utility function also decreases with the increased number of considered nodes (by roughly 24%). The relationship between the computational time T and the number of considered jobs J has a linear character. It increases proportionally to the increase of the number of jobs (see figure 2 and table 2). This relationship has an expected shape. The increased complexity of the transportation operations corresponds to computational complexity of the decision problem and results in the increased computational time T . Also the shape of the utility function U (J ) is quite rational. The overall utility of the generated solutions increases with the increased number of the considered transportation jobs until a certain threshold which reveals a saturation of the vehicles capacity and a lack of sufficient resources to carry out additional jobs. Another chart (figure 3) shows that computational time is linearly correlated with the number of considered vehicles I . Similarly to the previous figure 2 it proves that the increased complexity of the transportation operations corresponds to computational complexity of the decision problem and results in the increased computational time T . The increased number of available vehicles results in the increased number of possible transportation job assignments (matches between jobs and vehicles) resulting in substantially longer T . At the same time I does not affect the overall utility of the generated solutions. The U (I ) function is fixed. An interesting phenomenon is associated with the duration of the planning horizon. As presented in figure 4 when we extend the planning interval from 1 to 6 days the computational time increases drastically from 0.1 sec. to 9 sec. This increase has a non-linear character. Further extension of the planning horizon to 7 days does not affect computational time any more. This feature requires further tests but it is expected that it results from the fact that in the seventh day the driver’s weekly labor loads has been exhausted and little transportation jobs can be further assigned. Thus, the computational time does not increase in the seventh day. At the same time the utility function

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has a curved shaped in the 7-day planning horizon. It increases by 50-60% when the planning horizon changes from 1-3 days and then its value remains relatively stable for the planning horizon equal to 4-6 days. In the seven-day planning horizon the utility function deteriorates. Based on both these observation it may be suggested that the planning horizon should be reduced to 5-6 days. As previously stated both human and fixed resources may be already exhausted in the seventh day of the planning horizon and thus the efficiency of the computation may be then reduced. Figure 5 and 6 are an example of the analysis showing the influence of the DM’s preferences on the generated results. The chart presents the impact of the changing values of weights of two criteria: safety - σ and profit π on the computational time T and overall utility U of solutions as well as the values of the considered criteria S and P . It is interesting to point out that the increasing values of weight for safety – S and the corresponding increasing weight values for profit – P result in the increased values of S and relatively stable values of P (figure 5 and 6). At the same time the increased weight of safety and the decreased weight of profit substantially increase the overall utility of solutions. This follows from the fact that safety has overall larger values than profit for all tested cases.

6. Conclusions and further work This paper presents the original approach to solving a multiple criteria optimization problem consisting in selecting vehicles and transportation jobs combined with the design of the vehicle routes. The analysis is carried out for a small size transportation company operating a fleet of 1-9 vehicles. The output of this research is an original multiple criteria mathematical model of the considered decision situation and a heuristic algorithm capable to solve a complex joint problem of vehicle/transportation jobs selection and vehicle routing. The problem formulation includes the interests of different stakeholders, such as: company’s manager/ shareholder (fleet owner), customer and driver (company’s employee). These interests translate into the following criteria proposed in the model: safety (S), comfort (C), profit (P), duration (D), gain (G), fitness (F) and lateness (L). The solution procedure has a heuristic character and it is based on the classic shortest path algorithm proposed by Dijkstra and further extended and modified by the inclusion of time windows and work-time constraints. It has been shown that the proposed solution algorithm performs reasonably well for country-scale transportation networks and can be used as a basis for a real-time system coordinating transportation job division in an environment consisting of multiple competing drivers. From a methodological point of view the presented research generates the following advantages: it allows to include contradictory interests in the problem formulation and balance them to find a compromise solution; it performs the criteria aggregation into a utility function, which is optimized; it generates reasonable solutions in real time (computational time from fractions of seconds to several seconds). From a practical point of view the algorithm was proven to successfully manage foci on preferences of different stakeholders. Furthermore we conclude, that the problem is methodologically similar to the problem of carpooling optimization under multiple criteria (Filcek, Hojda, ak 2017). Further research may include the extension and modification of the decision model and enhancement of the solution algorithms. In the authors’ opinion the problem formulation should include balanced number of criteria representing the interests of different, above mentioned, stakeholders. Thus, the following additional characteristics may be added: a local search procedure to further refine the routes, a method of derivation of multiple rest-time (breaks) scenarios still feasible with time-work constraints in mind and an extension of the algorithm to include multi-week planning cases.

References Alam, A., Besselink, B., Turri, V., Martensson, J., Johansson, K. H., 2015. "Heavy-Duty Vehicle Platooning for Sustainable Freight Transportation: A Cooperative Method to Enhance Safety and Efficiency," in IEEE Control Systems, vol. 35, no. 6, 34-56. Bander, J., Nagarajan, A., 1998. White C, Strategic management of intelligent transportation systems: the case of freight mobility systems in the trucking industry, IEEE Int. Conf. on Systems, Man, and Cybernetics. Baran, J., ak, J., 2013. Multiple Criteria Evaluation of transportation performance for selected agribusiness companies, Procedia - Social and Behavioral Sciences 111, 320-329.

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Bozkurt, A., Yazici, A., Keskin, K., 2012. A Multicriteria Route Planning Approach Considering Driver Preferences, 2012 IEEE Int. Conf. on Vehicular Electronics and Safety, 324-328. Cherry, C., Adelakun, A., 2012. Truck driver perceptions and preferences: Congestion and conflict, managed lanes and tolls, Transport Policy 24, 1-9. Crainic, T., 2000. Service network design in freight transportation, European Journal of Operational Research, 122(2), 272–288. Demir, E., Bektas, T., Laporte, G., 2014. A review of recent research on green road freight transportation, European Journal of Operational Research 237, 775-793. Dib, O., Manier, M., Moalic, L., 2016. Advance Modeling Approach for Computing Multicriteria Shortest Paths in Multimodal Transportation Networks, 2016 IEEE Int. Conf. on Intelligent Transportation Engineering, 40-44. Filcek G., Hojda M., ak J., 2017. A heuristic algorithm for solving a Multiple Criteria Carpooling Optimization (MCCO) problem, Transportation Research Procedia 27, 656-663. Forkenbrock, D., 2001. Comparison of external costs of rail and truck freight transportation. Transportation Research Part A: Policy and Practice, 35(4), 321–337. Goel, A., Gruhn, V., 2006. Drivers' working hours in vehicle routing and scheduling. Transportation Science, 43, 1280-1285. Goel, A., Kok, A., 2010. Truck Driver Scheduling in the United States, Transportation Science, 46. Jabir, E., Panicker, V., 2015. Sridharan R, Multi-objective optimization model for a green vehicle routing problem. Procedia – Social and Behavioral Sciences 189, 33-39. Kok, A., Hans, E., Schutten, M., Zijm, W.H.M., 2011. A dynamic programming heuristic for vehicle routing with time-dependent travel times and required breaks. Flexible Services and Manufacturing Journal. 22, 83-108. L'och, M., Dolinayova, A., 2015. Evaluation Quality the freight Transport through Application of Methods multi-criteria Decision. Procedia Economics and Finance 32, 210-216. Paquette, J., Cordeau, J-F., Laporte, G., M.B., Pascoal, M., 2013. Combining multicriteria analysis and tabu search for dial-a-ride problems. Transportation Research Part B Methodological, 52, 1-16. Prescott-Gagnon, E., Desaulniers, G., Drexl, M., Rousseau, L-M., 2010. European Driver Rules in Vehicle Routing with Time Windows, Transportation Science, 44, 455-473. Rancourt, M-È., Cordeau, J-F., Laporte, G., 2013. Long-Haul Vehicle Routing and Scheduling with Working Hour Rules. Transportation Science, 47, 81-107. Rancourt, M-È., Paquette, J., 2014. Multicriteria Optimization of A Long-Haul Routing and Scheduling Problem. Journal of Multi-Criteria Decision Analysis, 21. Sawik, B., Faulin, J., Pérez-Bernabeu, E., 2017a. Multi-Objective Traveling Salesman and Transportation Problems with Environmental Aspects, Applications of Management Science 18 (eds. Lawrence K., Kleinman G.), Bingley UK: Emerald Group Publishing Limited, 21-55. Sawik, B., Faulin, J., Perez-Bernebeu, E., 2017b. A Multicriteria Analysis for the Green VRP: A Case Discussion for the Distribution Problem of a Spanish Retailer, Transportation Research Procedia 22, 305-313. Sun, Y., Wu, Y., Sun, Z., 2007. Optimal route selection method based on grey incidence analysis, IEEE Int. Conf. on Automation and Logistics, 1-6, 2495-2499. ak, J., Redmer, A., Sawicki, P., 2011. Multiple objective optimization of the fleet sizing problem for road freight transportation, Journal of Advanced Transportation 42, 379-427.