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.
Similar content being viewed by others
Abbreviations
- T :
-
Set of tasks
- S :
-
Set of resources
- P i ∈ T :
-
Trip i to be performed
- t s(P i ):
-
Starting time of trip i
- l s(P i ):
-
Starting location of trip i
- t e(P i ):
-
Ending time of trip i
- l e(P i ):
-
Ending location of trip i
- d :
-
Distance for each pair of locations
- R k ∈ S :
-
Vehicle k
- l a(R k ):
-
Actual location of the vehicle k
- c t(R k ):
-
The cost of vehicle k
- e t(R k ):
-
The CO2 emission of vehicle k
- v max(R k ):
-
The maximum speed of vehicle k
- A(P i ):
-
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
- m j :
-
entity j
- o i = (α i , β i ):
-
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
- u i :
-
Upper bound for the volume of activity o i
- l i :
-
Lower bound for the volume of activity o i
- cm j :
-
Price for each resource on target
- cp i :
-
Proportional constant of activity i
- cf i :
-
Fixed charge of activity i
- a ji :
-
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
References
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 12:255–263
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
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 27:1249–1269
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
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 12:177–189
Desaulniers G, Lavigne J, Soumis F (1998) Multi-depot vehicle scheduling problems with time windows and waiting costs. Eur J Oper Res 111:479–494
Friedler F, Tarjan K, Huang YW, Fan LT (1992) Combinatorial algorithms for process synthesis. Comput Chem Eng 16:S313–S320
Friedler F, Tarjan K, Huang YW, Fan LT (1993) Graph-theoretic approach to process synthesis: polynomial algorithm for maximal structure generation. Comput Chem Eng 17:929–942
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 246–250
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 609–626
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 12:291–299
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 York
Lam HL, Varbanov P, Klemes J (2010) Optimisation of regional energy supply chains utilising renewables: P-graph approach. Comput Chem Eng 34:782–792
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 12:709–714
P-graph.com (2010) PNS studio. http://www.p-graph.com. Accessed 14 Nov 2010
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
US EPA (2009) Transportations and climate. U.S. Environmental Protection Agency, Washington. http://www.epa.gov/otaq/climate. Accessed 14 Sept 2010
Varbanov P, Friedler F (2008) P-graph methodology for cost-effective reduction of carbon emissions involving fuel cell combined cycles. Appl Therm Eng 28:2020–2029
Acknowledgments
Authors acknowledge the support of the Hungarian Research Fund under project OTKA 81493K.
Author information
Authors and Affiliations
Corresponding author
Additional information
The variables used in this article include T, S, A, t s, t e, l s, l e, d, l a, c t, e t, v max—vehicle assignment problem; P, R, O, a, c, U c , L p ,U p, l, u—process-network synthesis (PNS) problem; m*, o*, x*, z*—optimal solution of PNS problem.
Rights and permissions
About this article
Cite this article
Barany, M., Bertok, B., Kovacs, Z. et al. Solving vehicle assignment problems by process-network synthesis to minimize cost and environmental impact of transportation. Clean Techn Environ Policy 13, 637–642 (2011). https://doi.org/10.1007/s10098-011-0348-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10098-011-0348-2