Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multi-product maximal covering second-level facility location problem

Marta Baldomero-Naranjo, Luisa I. Martínez-Merino, Antonio M. Rodríguez-Chía

Abstract

This paper introduces a new hierarchical facility location model with three levels: first-level facilities which manufacture different products, second-level facilities which act as warehouses and a third-level consisting of the clients who demand the products that have been manufactured in the first level and stored in the second level. In this model, called multi-product maximal covering second-level facility location problem (SL-MCFLP), the aim is to decide the location of the second-level facilities and the products to be stored in each of them maximizing the overall clients' satisfaction with respect their coverage. To deal with this model, we introduce a Mixed Integer Linear Program (MILP) which is reinforced by some families of valid inequalities. Since some of these families have an exponential number of constraints, separation algorithms are proposed. In addition, three variants of a matheuristic procedure are developed. Computational studies are included, showing the potentials and limits of the formulation and the effectiveness of the heuristic.

Multi-product maximal covering second-level facility location problem

Abstract

This paper introduces a new hierarchical facility location model with three levels: first-level facilities which manufacture different products, second-level facilities which act as warehouses and a third-level consisting of the clients who demand the products that have been manufactured in the first level and stored in the second level. In this model, called multi-product maximal covering second-level facility location problem (SL-MCFLP), the aim is to decide the location of the second-level facilities and the products to be stored in each of them maximizing the overall clients' satisfaction with respect their coverage. To deal with this model, we introduce a Mixed Integer Linear Program (MILP) which is reinforced by some families of valid inequalities. Since some of these families have an exponential number of constraints, separation algorithms are proposed. In addition, three variants of a matheuristic procedure are developed. Computational studies are included, showing the potentials and limits of the formulation and the effectiveness of the heuristic.
Paper Structure (21 sections, 31 equations, 5 figures, 6 tables, 3 algorithms)

This paper contains 21 sections, 31 equations, 5 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Model
  3. Valid inequalities
  4. Valid inequalities linking $x$- and $y$-variables
  5. Covering valid inequalities
  6. Separation procedures of covering valid inequalities
  7. Separation procedure of family (\ref{['con:coro']})
  8. Separation procedure of family (\ref{['con:DDVVBRef']})
  9. First phase
  10. Second phase
  11. Third phase
  12. Matheuristic procedure for the SL-MCFLP: Kernel Search
  13. First phase
  14. Second phase
  15. Computational experience
  16. ...and 6 more sections

Figures (5)

  • Figure 1: Graphical representation of the problem.
  • Figure 2: Flowchart of the Adaptive Kernel Search for SL-MCFLP.
  • Figure 3: Performance profile graph of #solved instances using SL-MCFLP and the proposed valid inequalities
  • Figure 4: Raincloud plot of the GAP $\text{G}_{BS}$ of the different variants of the heuristic Algorithm.
  • Figure 5: Raincloud plot of the time (s) of the different variants of the heuristic Algorithm.