Clean Technologies and Environmental Policy

, Volume 13, Issue 4, pp 637–642 | Cite as

Solving vehicle assignment problems by process-network synthesis to minimize cost and environmental impact of transportation

  • Mate Barany
  • Botond Bertok
  • Zoltan Kovacs
  • Ferenc Friedler
  • L. T. Fan
Original Paper


A method and software are proposed for optimal assignment of vehicles to transportation tasks in terms of total cost and emission. The assignment problem is transformed into a process-network synthesis problem that can be algorithmically handled by the P-graph framework. In the proposed method, each task is given by a set of attributes to be taken account in the assignment; this is also the case for each vehicle. The overall mileage is calculated as the sum of the lengths of all the routes to be travelled during, before, after, and between the tasks (Desaulniers et al. 1998; Baita et al. 2000). Cost and emission are assigned to the mileages of each vehicle type. In addition to the globally optimal solution of the assignment problem, the P-graph framework provides the n-best suboptimal solutions that can be ranked according to multiple criteria. The viability of the proposed method is illustrated by an example.


P-graph Combinatorial optimization Vehicle assignment Transportation 

List of Symbols


Set of tasks


Set of resources

Pi ∈ T

Trip i to be performed


Starting time of trip i


Starting location of trip i


Ending time of trip i


Ending location of trip i


Distance for each pair of locations

Rk ∈ S

Vehicle k


Actual location of the vehicle k


The cost of vehicle k


The CO2 emission of vehicle k


The maximum speed of vehicle k


The set of resources potentially capable of performing task P i


The set of the final targets to be achieved


The set of the initially available resources


The set of entities


entity j

oi = (αi, βi)

Activity i with α i set of preconditions and β i set of targets


The set of candidate activities

\( L_{{p_{j} }} \)

Lower bound on the gross result

\( U_{{p_{j} }} \)

Upper bound on the gross result

\( U_{{c_{j} }} \)

Upper bound on gross utilization


Upper bound for the volume of activity o i


Lower bound for the volume of activity o i


Price for each resource on target


Proportional constant of activity i


Fixed charge of activity i


The difference between the production and consumption rate of entity m j by activity o i


Set of entities in the optimal structure


Set of activities in the optimal structure


The vector of the optimal volumes of activities


Objective value of the optimal solution



Authors acknowledge the support of the Hungarian Research Fund under project OTKA 81493K.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Mate Barany
    • 1
  • Botond Bertok
    • 1
  • Zoltan Kovacs
    • 1
  • Ferenc Friedler
    • 1
  • L. T. Fan
    • 2
  1. 1.Department of Computer Science and Systems TechnologyUniversity of PannoniaVeszprémHungary
  2. 2.Department of Chemical EngineeringKansas State UniversityManhattanUSA

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