Solution of the maximal covering tour problem for locating recycling drop-off stations

Abstract

Tactical decisions on the location of recycling drop-off stations and the associated collection system are essential in order to increase recycling amounts while keeping operational costs at a minimum. The conflicting nature of the objectives of the problem can be modelled as a bi-objective location-routing problem. In this paper, we address the location-routing problem of recycling drop-off stations by solving the Maximal Covering Tour Problem. To this aim, we propose a heuristic inspired by a variable neighbourhood search. The heuristic is tested on a set of benchmark instances from the TSPLIB and applied to a set of real-life instances from both urban and rural areas in Denmark. Based on the results of the real-life cases, we provide insights on the trade-off between recycling rates and transportation costs.

Waste bins location problem: A review of recent advances in the storage stage of the Municipal Solid Waste reverse logistic chain

“…Aka and Akyüz ( 2018) Antalya (TR) Compromise solutions (recyclable material collected and collection routing distance) Bennekrouf et al (2020) Boudjlida (DZ) Design of a recyclable material collection network of bins considering QoS and investment cost Chang and Wei (1999) Kaohsiung (TW) Set of compromising solutions between QoS, routing cost, and population served by the system for recyclable material Chang and Wei (2000) Kaohsiung (TW) Set of compromising solutions between QoS, routing cost, and population served by the system for recyclable material Cubillos and Wøhlk (2020) Five Danish cities Set of compromising solutions between the population served and the routing costs for recyclable material Flahaut et al (2002) La Buyère (BE) Compromising solution regarding QoS and environmental costs Gautam and Kumar (2005) No real case solved Methodology to find solutions to maximize the QoS González and Adenso (2002) Asturias (ES) Increment of the amount of recyclable material collected Hemmelmayr et al (2017) Not specified region Reduction of total costs when flexible location of vehicle depots or visit schedules for collection points are considered Kao et al (2010Kao et al ( , 2013 Hsinchu (TW) Solutions with high QoS for collecting recyclable material Lin et al (2011) Taichung (TW) Methodology for designing a two-shift bins collection network for recyclable waste López et al (2008) Madrid (ES) Improved efficiency of the collection system by designing a separated collection system for paper/cardboard of small businesses López et al ( 2009 Set of compromise solutions between population served, QoS, and installment costs outperformed current situation in terms of QoS. Ugwuishiwu et al (2020) Enugu (NG) Improved distribution of bins avoiding busy/inconvenient places Vijay et al (2005) No real case study solved Methodology for estimating waste generation and allocating users to bins imporving the QoS provided to the users Vijay et al (2008) No real case study solved Methodology for estimating waste generation and allocating users to bins imporving the QoS provided to the users Vu et al (2018) Hai Phong (TW) Solutions for different QoS and total number of bins to be located Yaakoubi et al (2018) No real case study solved Methodology to solve sequentially the problems of locating bins and scheduling collection routes Zahan and Hasan (2020) Dhaka (BD) Multi-attribute methodology to choose locations for bins considering QoS and environmental issues…”

“…Three articles considered case studies from more than one city: Rossit et al (2020) and Toutouh et al (2020) solved case studies from Bahía Blanca, Argentina and Montevideo, Uruguay, whereas Cubillos and Wøhlk (2020) solved case studies from five different Danish cities.…”

“…Finally, some researches have considered user accessibility under the assumption that each bin serves a certain nearby area. Optimization criteria included maximizing the geographic area (Nithya et al, 2012;Paul et al, 2017;Vu et al, 2018) or the number of users Wei, 1999, 2000;Erfani et al, 2018;Kao et al, 2010;Cubillos and Wøhlk, 2020;Letelier et al, 2021;Vidović et al, 2016). Erfani et al (2018) and Vidović et al (2016) presented an interesting approach for estimating the population served by a bin.…”

“…Thus, these works usually included some metric of the routing efficiency. For example, minimizing the idle time of vehicles (i.e., time for performing collection and travel time between waste bins) (Vidović et al, 2016), travel costs (per distance unit) Wei, 1999, 2000;Hemmelmayr et al, 2013Hemmelmayr et al, , 2017Jammeli et al, 2019;Kim and Lee, 2015b;Sheriff et al, 2017;Vidović et al, 2016;Yaakoubi et al, 2018) or travel distance of the vehicles (Aka and Akyüz, 2018;Cubillos and Wøhlk, 2020), or fixed costs of the fleet of vehicles (Hemmelmayr et al, 2017;Kim and Lee, 2015b). These integrated approaches provide a valuable holistic view of the problem, thus they are further described in Section 8.…”

“…More than a half used single-objective models. Other articles applied multi-objective models to combine different criteria, e.g., a weighting sum approach (Cubillos and Wøhlk, 2020;Herrera et al, 2018;Nevrlỳ et al, 2019Nevrlỳ et al, , 2021Rossit et al, 2018Rossit et al, , 2019Rossit et al, , 2020Tralhão et al, 2010), -constraint (Coutinho et al, 2012;Nevrlỳ et al, 2021;Rossit et al, 2017Rossit et al, , 2020, lexicographic optimization (González and Adenso, 2002;Rossit et al, 2020) or goal programming (Aka and Akyüz, 2018;Tralhão et al, 2010). In several works, MILP exact models were used for solving small instances to validate heuristic approaches, later used to address larger scenarios (Cubillos and Wøhlk, 2020;Ghiani et al, 2012Ghiani et al, , 2014bHemmelmayr et al, 2013Hemmelmayr et al, , 2017Kim and Lee, 2013;Vidović et al, 2016).…”