Time-dependent green Weber problem
Section snippets
Introduction and literature review
A single–facility location problem (SFLP) is the problem of finding the location of a single facility which will serve a set of customers so as to minimize an objective function, usually a function of the distances between the facility and the customers. The (discrete) 1-center problem (Agarwal et al., 1998), a discrete facility location problem, and the Weber problem, (Drezner, 1992, Drezner, Hamacher, 2002), a continuous facility location problem, are among the most famous SFLPs.
The Weber
The green Weber problem (GWP)
We assume that the amount of CO2 emitted by a vehicle is proportional to its fuel consumption which is aligned with the related literature, see e.g., Demir et al. (2011). As the fuel consumption model, we use the comprehensive modal emission model (CMEM), suggested in Barth et al. (2005), for heavy-good vehicles. For a review and comparison of different vehicle emission models, the reader is referred to Demir et al. (2011). According to the CMEM, the amount of fuel consumed in liter, f, by a
Illustrative example
In this section, an illustrative example is presented. The solutions of the Weber problem (WP) and the GWP, and the solutions of the GWP and the TD-GWP are compared.
Consider an instance of the Weber problem with four customers in the plane, namely customer 1,2,3, and 4. The coordinates of the customers are (0, 0), (1000, 0), (0, 1000), and (1000, 1000) in kilometers as seen in Fig. 2. We assume identical unit weights for all customers, i.e., . The optimal location of the facility
Computational experiments
In this section, our aim is to compare the total fuel-emission cost in large scale randomly generated distribution systems with and without traffic congestion. We generate two sets of instances. In the first set, there are 500 customers in the distribution system and in the second one 1000 customers.
For the first set of instances, we consider a square with side length of 234 km. Customers with identical unit weights are distributed in this square in 4 groups. Each group consists of 125
Conclusion
Extensions of the classical Weber problem are introduced in this study. In the first problem considered, namely the GWP, the location of the single facility in the plane and the speeds of the vehicles serving the customers are to be determined that result in the minimum total fuel-emission cost in the distribution system. The customers are assumed to have hard one-sided time windows (time limits) and the vehicles serving the customers should finish their service on or before the time limits.
References (22)
- et al.
The pollution-routing problem
Transp. Res. Part B
(2011) - et al.
A comparative analysis of several vehicle emission models for road freight transportation
Transp. Res. Part D
(2011) - et al.
An adaptive large neighborhood search heuristic for the pollution-routing problem
Eur. J. Oper. Res.
(2012) - et al.
The bi-objective pollution-routing problem
Eur. J. Oper. Res.
(2014) - et al.
A review of recent research on green road freight transportation
Eur. J. Oper. Res.
(2014) The impacts of congestion on time-definitive urban freight distribution networks CO2 emission levels: results from a case study in Portland, Oregon
Transp. Res. Part C
(2011)- et al.
A matheuristic approach for the pollution-routing problem
Eur. J. Oper. Res.
(2015) - et al.
Applications of second-order cone programming
Linear Algebra Appl.
(1998) - et al.
The discrete 2-center problem
Discrete Comput. Geom.
(1998) - et al.
Second-order cone programming
Math. Program.
(2003)
Development of a Heavy-Duty Diesel Modal Emissions and Fuel Consumption Model
Technical Report
Cited by (11)
The p-hub centre routing problem with emissions budget: Formulation and solution procedure
2023, Computers and Operations ResearchFacility location decisions for drone delivery: A literature review
2023, European Journal of Operational ResearchA green multi-facilities open location-routing problem with planar facility locations and uncertain customer
2021, Journal of Cleaner ProductionMunicipal solid waste management with cost minimization and emission control objectives: A case study of Ankara
2020, Sustainable Cities and SocietyMulti-facility green Weber problem
2020, Computers and Operations ResearchCitation Excerpt :In Section 2, the notation and the CMEM which is used in CO2 calculations are introduced. In Section 3, the SOCP formulation proposed by Atashi Khoei et al. (2017) for the single facility version of the MF-GWP is reviewed for completeness. In Section 4, an MISOCP formulation of the MF-GWP is given and the proposed heuristic solution methods are explained.
Green hub location problem
2019, Transportation Research Part E: Logistics and Transportation ReviewCitation Excerpt :Environmental impacts of transportation activities are first discussed in relation to vehicle routing problems (Kara et al., 2007; Bektaş and Laporte, 2011). Later, they have also recognized in location problems (Khoei et al., 2017) and location-routing problems (Govindan et al., 2014; Koç et al., 2016; Tricoire and Parragh, 2017) which optimize facility location and vehicle routing decisions simultaneously. For a comprehensive survey on green network design problems, we refer the reader to Dukkanci et al. (2019).