This section presents the literature analysis focusing on two concepts very much related to solid waste collection and management: solid waste management and reverse logistics.
2.1. Reverse Logistics
Reverse logistics is a recent concept that refers to the most effective and economic upstream material flow and merchandise return to the supply chain and to the retrieval of products that were already used for their main purpose [13
]. This concept emerged at the end of the 20th century in developed countries by doing recycling processes [14
] as a key activity for waste management. In countries with a higher income, one-third of the waste could be retrieved, whereas those with a lower income only retrieved 4% [15
]. In most cases, it is expected to generate income or to manage waste.
Such is the case of Uriarte-Miranda et al. [16
], where strategies for waste tire management become important due to its economic, social, and environmental impacts. This article shows a reverse logistics model for the waste tire management systems in México and Russia (two specific processes: remanufacturing and diversification) so that it is affordable and sustainable. Hage et al. [17
] presented a study about waste recycling (plastic, glass, paper, and metal) that demonstrates that, if a container is located adequately, the probability for recycling increases by 28%. Something similar is proposed by Castillo et al. [18
] and applied in Spain.
In the cases of Chang and Wei [19
], Gautam and Kumar [20
], and Alonso [21
], they use optimization models focused on waste or container retrieval for their later recycling.
As could be observed in reverse logistics, it is a sustainable process, as it considers the triple helix: society, economy, and environment. In the presented application as the contribution of this work, whilst it does not consider an economical remuneration as such, it takes it into account due to the cost reduction that it implies, as well as the social impact, as it is a service that improves the quality of life for citizens and the environmental impact related to the solid waste management in green spaces.
Below, we present the works of which the main focus is on urban logistics, that is, those where the main application is on social good.
2.2. Municipal Solid Waste (MSW Collection)
Generally the macro-routing problem is solved by design territories, whilst micro-routing employs mathematical models like Vehicle Routing Problem
(VRP) and Travel Salesman Problem
] or uses computational tools and Geographic Information Systems (GIS) [25
] to minimize the route collection time.
Design territories is a mixed-integer linear programming that consists of grouping small geographical areas, called areas, in larger geographic groupings, called territories, so that the latter are acceptable according to certain criteria. There is a classification according to the context of the problem proposed by Moreno [27
]; these criteria may have economic reasons related to the average potential sales [28
], areas of use of services and equipment located in a fixed location [30
], zones for the provision of services at home [31
], energy resource receiving areas [32
], and political-electoral districts [33
Territorial partitioning in different regions or zones is a problem that is presented in various disciplines related to earth and space sciences and has been treated under various denominations such as partitioning, regionalization, zoning, delineation of zones and/or districts, allocation of spatial units, etc. [36
While most applications are related to the design of territories, there are other applications like the literature review presented by Phuntsho et al. [37
] to determine the solid waste collection plan and schedule in the Bhutan municipality or the work presented by Jayakody et al. [38
] that presents the findings of a municipal solid waste characterization study with a sample size of 2850 persons, estimating that the average for daily waste-generation rate for a household was
kg/cap/day. Also, this paper distinguishes that waste composition and waste management systems play a key role in establishing an integrated sustainable solid waste management system in countries like Sri Lanka. In addition to this, Kaosol [39
] presented a study of the composition of waste collected in Thailand (86%), which is mostly organic waste (paper, plastic, glass, and metal). The integrated MSW system has the potential to maximize the useable waste materials as well as to produce energy as a by-product. While we can observe a qualitative approach in these articles, there are others with a quantitative approach such as ours.
For example, Ayantoyinbo and Adepoju [40
] analyzed the relationship between waste management logistics and metrics for waste management performance. In this case, transport demand system analysis must come in the form of predictive and prescriptive models, while deterministic models make accurate predictions about a system of interest and probabilistic models entail some elements of uncertainty. Dotoli and Epicoco [7
] presented a routing and scheduling vehicle model (i) to determine the optimal routes for HWC (Hazardous Waste Collection), which seeks to find the best trade-off between reduction of traveled distances, maximization of amount of collected waste, and maximization of commercial value of withdrawals and their transportation to the disposal site and (ii) to assign the obtained routes to the available fleet. Similar to this work, Buhrkal et al. [8
] studied the Waste Collection Vehicle Routing Problem with Time Windows (WCVRPTW), where the problem consists of routing vehicles to collect customers waste within a given time window while minimizing travel costs. Laureri et al. [41
] presented a mathematical model based on a Genoa Municipality case study and contemplates various kind of objectives and constraints, making the collection a complex task involving many actors (citizens, politicians, and technical personnel), technological expertise, and investments since it uses WSM concerning the protection of the environment and conservation of natural resources.
Finally, the case study of Son and Louati [42
] developed an effective vehicle routing model that optimizes the total traveling distance of vehicles for MSW collection in Danang City (Vietnam) considering the environmental emissions; the investment cost; and the available node structures, vehicles, and parameters in a generalized context. Moreover, in Das and Bhattacharyya [43
], MSW management systems suffer by the high collection and transportation cost, where typically, collection cost represents 80–90% and 50–80% of municipal solid waste management budget in low income and middle-income countries. Proposed heuristic solutions reduce more than 30% of the total waste collection path length (100 source points, 65 waste collection centers, and 50 transfer stations).
Considering the literature review and the lack of a defined algorithm or model for the design of macro-routing for cleaning and solid waste collection in municipal areas, the problem consists of the optimal grouping of green spaces in the Monterrey Metropolitan Area, so that territories are balanced regarding the workload of each provider and the coverage of the collection service. These two fundamental aspects are not currently in the planning service.
As a consequence of this fact, our proposal consists of improving the territorial design planning of the current collection service through the adaptation of a mathematical model of territory design for cleaning and solid waste collection in the municipal areas and considers the criteria of spatial integrity, homogeneity, contiguity, and compactness.
It is important to mention that the objects to be grouped are parks of the municipality of San Nicolas de los Garza, but due to a large number of parks, a first grouping has been done to reduce the scale of the problem and to simplify the solution. Thus, we then applied model 1 where we group the districts established by the municipality and model 2 to group the parks; both models are similar, and each one is described below.