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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

Abstract

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.

Keywords

P-graph Combinatorial optimization Vehicle assignment Transportation 

List of Symbols

T

Set of tasks

S

Set of resources

Pi ∈ T

Trip i to be performed

ts(Pi)

Starting time of trip i

ls(Pi)

Starting location of trip i

te(Pi)

Ending time of trip i

le(Pi)

Ending location of trip i

d

Distance for each pair of locations

Rk ∈ S

Vehicle k

la(Rk)

Actual location of the vehicle k

ct(Rk)

The cost of vehicle k

et(Rk)

The CO2 emission of vehicle k

vmax(Rk)

The maximum speed of vehicle k

A(Pi)

The set of resources potentially capable of performing task P i

P

The set of the final targets to be achieved

R

The set of the initially available resources

M

The set of entities

mj

entity j

oi = (αi, βi)

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

O

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

ui

Upper bound for the volume of activity o i

li

Lower bound for the volume of activity o i

cmj

Price for each resource on target

cpi

Proportional constant of activity i

cfi

Fixed charge of activity i

aji

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

m*

Set of entities in the optimal structure

o*

Set of activities in the optimal structure

x*

The vector of the optimal volumes of activities

z*

Objective value of the optimal solution

Notes

Acknowledgments

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

References

  1. Aizura AB, Mahlia TMI, Masjuki HH (2010) Potential fuel savings and emissions reduction from fuel economy standards implementation for motor-vehicles. Clean Technol Env Policy 12:255–263CrossRefGoogle Scholar
  2. Atkins M, Walmsley M, Morrison A, Kamp P (2009) Carbon emissions pinch analysis (cepa) for emissions reduction in the New Zealand electricity sector. Chemical Engineering Transactions 18:261–266. doi: 10.3303/CET0918041 Google Scholar
  3. Baita F, Presenti R, Ukovich W, Favaretto D (2000) A comparison of different solution approaches to the vehicle scheduling problem in a practical case. Comput Oper Res 27:1249–1269CrossRefGoogle Scholar
  4. Barany M, Bertok B, Kovacs Z, Friedler F, Fan LT (2010) Optimization software for solving vehicle assignment problems to minimize costs and environmental impacts of transportation. Chem Eng Trans 21:499–504. doi: 10.3303/CET1021084 Google Scholar
  5. Crilly D, Zhelev T (2010) Further emissions and energy targeting: an application of CO2 emissions pinch analysis to the Irish electricity generation sector. Clean Technol Env Policy 12:177–189CrossRefGoogle Scholar
  6. Desaulniers G, Lavigne J, Soumis F (1998) Multi-depot vehicle scheduling problems with time windows and waiting costs. Eur J Oper Res 111:479–494CrossRefGoogle Scholar
  7. Friedler F, Tarjan K, Huang YW, Fan LT (1992) Combinatorial algorithms for process synthesis. Comput Chem Eng 16:S313–S320CrossRefGoogle Scholar
  8. Friedler F, Tarjan K, Huang YW, Fan LT (1993) Graph-theoretic approach to process synthesis: polynomial algorithm for maximal structure generation. Comput Chem Eng 17:929–942CrossRefGoogle Scholar
  9. Friedler F, Varga JB, Fan LT (1995) Decision-mapping for design and synthesis of chemical processes: application to reactor-network synthesis. In: Biegler LT, Doherty MF (eds) AIChE symposium series, vol 91, pp 246–250Google Scholar
  10. Friedler F, Varga JB, Feher E, Fan LT (1996) Combinatorially accelerated branch-and bound method for solving the MIP model of process network synthesis. In: Floudas CA, Pardalos PM (eds) Nonconvex optimization and its applications state of the art in global optimization computational methods and applications. Kluwer Academic Publishers, Dordrecht, pp 609–626Google Scholar
  11. Ilyas SZ, Khattak AI, Nasir SM, Quarashi T, Durrani R (2010) Air pollution assessment in urban areas and its impact on human health in the city of Quetta, Pakistan. Clean Technol 12:291–299CrossRefGoogle Scholar
  12. Klemes J, Friedler F, Bulatov I, Varbanov P (2010) Sustainibility in the process industry: integration and optimization (Green Manufacturing & Systems Engineering). McGraw-Hill Professional, New YorkGoogle Scholar
  13. Lam HL, Varbanov P, Klemes J (2010) Optimisation of regional energy supply chains utilising renewables: P-graph approach. Comput Chem Eng 34:782–792CrossRefGoogle Scholar
  14. Perry S, Bulatov I, Klemes J (2007) The potential of the EMINENT tool in the screening and evaluation of emerging technologies for CO2 reduction related to bulindings. Chem Eng Trans 12:709–714Google Scholar
  15. P-graph.com (2010) PNS studio. http://www.p-graph.com. Accessed 14 Nov 2010
  16. Tan RR, Foo DC (2009) Recent trends in pinch analysis for carbon emissions and energy footprint problems. Chem Eng Trans 18:249–254. doi: 10.3303/CET0918039 Google Scholar
  17. US EPA (2009) Transportations and climate. U.S. Environmental Protection Agency, Washington. http://www.epa.gov/otaq/climate. Accessed 14 Sept 2010
  18. Varbanov P, Friedler F (2008) P-graph methodology for cost-effective reduction of carbon emissions involving fuel cell combined cycles. Appl Therm Eng 28:2020–2029CrossRefGoogle Scholar

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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