Goal programming model applied to waste paper logistics processes
Introduction
Considering the increasing consumption of resources as a consequence of the increased world population, the generation of solid waste has taken on large proportions. Thus, there is a vast body of literature on processes concerning solid waste management, such as planning and recycling [1], [2], [3], [4]. In particular, sustainable development issues have drawn increasing attention, focusing on optimization processes. As a result, many studies address quantitative modeling and sustainability problems [5], [6], [7].
According to information obtained from the literature, formulations may vary depending on the company, the region, the city, or country studied, and developing countries may have differences in the structure of the logistics network [8], [9], [10], [11]. Despite having government policies to encourage the development of formal waste collection organizations, in Brazil, for example, most of the materials collected for recycling are from informal collections [12], [13]. Therefore, the importance of intermediate centers for organizing and selling collected material for recycling, such as waste paper recycling, can be observed.
Intermediate centers are facilities that play an intermediate role in the logistics process of waste paper recycling. In these centers, material, collected or delivered by customers, is checked and follows classification, segregation, baling and storage steps to be sold later [14].
In some studies found in waste paper recycling systems, multi-objective formulations were identified, including economic and environmental objectives, as in [15], [16], [17], [18], [19] and also social, as in [20]. In [15], the objective was to develop a network for planning and evaluating logistics networks balancing economic and environmental problems. Tseng et al. [19] presents a model of Mixed Integer Linear Programming considering ”full truckloads”.
A current literature review on quantitative methods applied to reverse logistics of paper recycling can be found in [11] and a short review on Goal Programming Model applied to management problems will be presented in the next Section.
In this context, the objective proposed for this study is to develop a multi-objective optimization model for the waste paper recycling system comprising sustainable factors. The research questions that guided the development of this work are the following: how is it possible to optimize the waste paper recycling system by building a model whose objectives integrate the pillars of sustainability? Which solution approaches should be used?
This work focuses on optimizing the logistic steps of a waste paper recycling system, considering the processes experienced by intermediate centers. The problem boils down to defining how much to collect in each period in order to maximize the amount collected of material relevant to recycling, maximize production and meet demand and minimize costs. The studied problem considers the material and demand variations occurring due to the seasonal availability of waste. Moreover, it is a conflicting-objective problem related to sustainability, once the increase in the collected amount of material maximizes the production and the meeting demand, which is directly related to the increase in the recycling rates, but also to the increase in costs.
For the resolution of the model, the Weighted Goal Programming technique (WGP) [21], [22], [23] was used to deal with multiple objectives and the Revised Multi-Choice Goal Programming technique [24] was used to incorporate the occurrence of uncertainty in the available quantity for collection, a parameter used as a goal at soft constraints and as limiting in hard constraints.
Thus, an important contribution of this work is to propose a new mathematical formulation using methods and techniques to optimize the logistical echelons of waste paper recycling, considering uncertainty in the quantity of available waste collection, to assist the decision-making process of managers for more efficient management of the network.
This work is organized as follows: Section 2 presents a literature review on Goal Programming models. Section 3 presents the problem definition and Mathematical Modeling. Section 4 details the computational experiments, and Section 5 presents the conclusions.
Section snippets
Literature review on Goal Programming
Taken from studies in the literature and observations made during technical visits to an intermediate center, we identified the participation of managers in the decision-making process of all logistical processes due to the wide range of parameters in the periods. Therefore, Goal Programming was chosen to be an approach that allows decision makers to participate directly in the process of modeling and solving multi-objective problems, such as the choice of aims and, when necessary, the
Problem definition and mathematical modeling
To identify the research problem, the objectives and parameters were identified taking examples from the literature, and making observations and conducting interviews with managers carried out during technical visits to companies in the industry.
Some parameters and objectives related to minimization of cost and waste paper collection, in addition to the Goal Programming technique, were inspired by [16]. The approaches for vehicle routing and the sub-route elimination constraints were based
Computational experiments
Table 2 presents the data used in test R1. Other tests were performed with variations of the parameters of this instance, as described in Table 3. The scenarios were generated not only to represent an intermediate center, but variations that happen in different intermediate centers. That is, the scenarios illustrate the possibilities of the model to represent processes of different intermediate centers. The distances between the collection points ([km]) were estimated using the software
Constraints with uncertainty - Revised Multi-Choice Weighted Goal Programming
In the studied problem, daily variations in the quantity of material available for collection occurred due to variations in the availability of waste. Thus, an adaptation of the Revised Multi-Choice Goal Programming model proposed by [24] was performed to incorporate uncertainty in the parameter regarding the quantity of material available for collection, which is part of both soft constraints, as a goal, and hard constraints, as limiting. Based on the formulation proposed in [42], for
Discussion on management applications and sustainability issues
The objective of this paper was to develop a multi-objective optimization model for the waste paper recycling system, including factors associated with the pillars of sustainability.
This study contributes to the literature, especially when presenting a new Weighted Goal Programming model for the waste paper recycling logistic system that optimizes the processes of an intermediate center and considers: the stage of vehicle routing with vehicles of different capacities; the possibility of not
Conclusions
The objective of this work was to develop a multi-objective optimization model for the waste paper recycling system, including sustainable factors and uncertainty.The Weighted Goal Programming was used as an approach for the model with many objectives and the Revised Multi-Choice Goal Programming approach was considered to deal with the variability of the parameters.
The results showed that, as expected, the tests that allow the storage of material at the collection points presented lower stock
Acknowledgments
This study was financed in part by the National Council for Scientific and Technological Development (CNPq - 302730/2018-4; CNPq - 303350/2018-0), the So Paulo State Research Foundation (FAPESP - 2018/06858-0; FAPESP- 2018/14433-0) and the Coordination for the Improvement of Higher Education Personnel - Brazil (CAPES) - Finance Code 001.
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