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Solving the Integrated Bin Allocation and Collection Routing Problem for Municipal Solid Waste: a Benders Decomposition Approach

Arthur Mahéo, Diego Rossit, Philip Kilby

Abstract

The municipal solid waste system is a complex reverse logistic chain which comprises several optimisation problems. Although these problems are interdependent, i.e., the solution to one of the problems restricts the solution to the other, they are usually solved sequentially in the related literature because each is usually a computationally complex problem. We address two of the tactical planning problems in this chain by means of a Benders decomposition approach: determining the location and/or capacity of garbage accumulation points, and the design and schedule of collection routes for vehicles. Our approach manages to solve medium-sized real-world instances in the city of Bahía Blanca, Argentina, showing smaller computing times than solving a full MIP model.

Solving the Integrated Bin Allocation and Collection Routing Problem for Municipal Solid Waste: a Benders Decomposition Approach

Abstract

The municipal solid waste system is a complex reverse logistic chain which comprises several optimisation problems. Although these problems are interdependent, i.e., the solution to one of the problems restricts the solution to the other, they are usually solved sequentially in the related literature because each is usually a computationally complex problem. We address two of the tactical planning problems in this chain by means of a Benders decomposition approach: determining the location and/or capacity of garbage accumulation points, and the design and schedule of collection routes for vehicles. Our approach manages to solve medium-sized real-world instances in the city of Bahía Blanca, Argentina, showing smaller computing times than solving a full MIP model.
Paper Structure (29 sections, 13 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 29 sections, 13 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review
  3. Integrated approaches to collect unsorted waste
  4. Integrated approaches to collect recyclable material
  5. Benders' decomposition in other stages of the MSW reverse logistic chain
  6. Summary and contribution of this work
  7. A mathematical model of MSW
  8. Bin combinations preprocessing
  9. Model formulation
  10. Valid inequalities
  11. Empty start
  12. Vehicle ordering
  13. Furthest visit
  14. A resolution approach based on Benders decomposition
  15. Creating the subproblem
  16. ...and 14 more sections

Figures (4)

  • Figure 2: Visualisation of the two instance sets: University (in blue) and Downtown (in red). The triangle is the depot. The dot size represent the (scaled) daily demand in m^3 per day.
  • Figure 3: Results of using different methods, with or without VIs, to solve a set of reduced instances.
  • Figure 4: Comparison of our Benders approach with and without L-shaped cuts, we report the total solving time in seconds (log scale).
  • Figure 5: Number of instances solved with a MIP or our Benders approach. The black numbers are the total number of instances.