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Optimal policies for stock redistribution in a retail network: Mathematical modeling and algorithmic solution

Julio González-Díaz, Ángel M. González-Rueda, Irene Llana-García, Jorge Rodríguez-Veiga

Abstract

We study the problem of stock replenishment and transshipment in the retail industry. We develop a model that can accommodate different policies, including centralized redistribution (replenishment) and decentralized redistribution (lateral transshipments), allowing for direct comparisons between them. We present a numeric analysis in which the benchmark instances stem from the collaboration with a high-end clothing retail company. The underlying model, as usually in the field, is a large-scale mixed-integer linear programming problem. We develop a specific algorithmic procedure to solve this MILP problem and compare its performance with the direct solution via state-of-the-art solvers.

Optimal policies for stock redistribution in a retail network: Mathematical modeling and algorithmic solution

Abstract

We study the problem of stock replenishment and transshipment in the retail industry. We develop a model that can accommodate different policies, including centralized redistribution (replenishment) and decentralized redistribution (lateral transshipments), allowing for direct comparisons between them. We present a numeric analysis in which the benchmark instances stem from the collaboration with a high-end clothing retail company. The underlying model, as usually in the field, is a large-scale mixed-integer linear programming problem. We develop a specific algorithmic procedure to solve this MILP problem and compare its performance with the direct solution via state-of-the-art solvers.

Paper Structure

This paper contains 23 sections, 5 equations, 9 figures, 3 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Contribution to Existing Literature
  3. Model Discussion and Mathematical Formulation
  4. Main model: Transferring problem
  5. Model features: Discussion
  6. Enhancing the final solution: Packing problem
  7. Comparison of Redistribution Policies
  8. Redistribution policies
  9. Numeric comparison
  10. T-P: The Direct Solution Procedure
  11. RT-R-P: An Algorithm for Large-Scale Problems
  12. RT-R-P. Phase 1: Relaxed transferring
  13. RT-R-P. Phase 2: Rounding
  14. Objective function in problem r$^\text{\sc{p}}$
  15. Minimum cost flow formulation
  16. ...and 8 more sections

Figures (9)

  • Figure 1: Different redistribution policies captured by the model developed in Section \ref{['sec:model']}.
  • Figure 2: Scheme for Zara's periodic redistribution process as reported in Caro2010a and Caro2010b.
  • Figure 3: Illustrating the role of constraints \ref{['cons:T_dsiyn']}.
  • Figure 4: Average worsening with respect to best redistribution policy as a function of the scaling factor for the shipping cost of packages involving warehouses.
  • Figure 5: Rounding scheme as a minimum cost flow problem.
  • ...and 4 more figures