Modeling and solving an integrated periodic vehicle routing and capacitated facility location problem in the context of solid waste collection

TL;DR

This work tackles an integrated Municipal Solid Waste (MSW) management problem that jointly designs bin capacities at collection points and periodic vehicle routing. It proposes two exact formulations ($MIQP$ and $MILP$) and a mixed GA with a mixed binary-permutation encoding to solve a $PCVRP$-based model that couples bin-installation costs with routing costs through $TT_{vt}$. Using Bahía Blanca data, the authors show the GA matches small-instance exacts and yields feasible, high-quality solutions for large instances within practical times, while the exact solvers excel at bin-cost optimization. The contributions fill a gap in the literature by delivering a scalable, decision-support framework for urban waste collection with real-world applicability, validated on real data and large-scale instances.

Abstract

Few activities are as crucial in urban environments as waste management. Mismanagement of waste can cause significant economic, social, and environmental damage. However, waste management is often a complex system to manage and therefore where computational decision-support tools can play a pivotal role in assisting managers to make faster and better decisions. In this sense, this article proposes, on the one hand, a unified optimization model to address two common waste management system optimization problem: the determination of the capacity of waste bins in the collection network and the design and scheduling of collection routes. The integration of these two problems is not usual in the literature since each of them separately is already a major computational challenge. On the other hand, two improved exact formulations based on mathematical programming and a genetic algorithm (GA) are provided to solve this proposed unified optimization model. It should be noted that the GA considers a mixed chromosome representation of the solutions combining binary and integer alleles, in order to solve realistic instances of this complex problem. Also, different genetic operators have been tested to study which combination of them obtained better results in execution times on the order of that of the exact solvers. The obtained results show that the proposed GA is able to match the results of exact solvers on small instances and, in addition, can obtain feasible solutions on large instances, where exact formulations are not applicable, in reasonable computation times.

Figures (5)

• Figure 1: Collection points (in red) of instance $i.163.1$ (Bahía Blanca, Argentina). The blue triangle marks the location of the depot.
• Figure 2: Main effects when the response variable is the overall cost (US$).
• Figure 3: Main effects when the response variable is the mixed GA runtime (seconds).
• Figure 4: Waste collection routes associated with the solution shown in Table \ref{['tab:tableA1']}. The time taken to complete them (in minutes) is also shown.
• Figure 5: Routes performed by the collection truck each day of the time horizon.