Integrating packing and distribution problems and optimization through mathematical programming

Article history: Received June 25, 2015 Received in revised format: October 12, 2015 Accepted October 22, 2015 Available online October 24 2015 This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP) problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), which is a variant of the Travelling Salesman Problem (again a NP-Hard problem) with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here. Growing Science Ltd. All rights reserved. 6 © 201

[1]  Mei Chen,et al.  Solving the CVRP Problem Using a Hybrid PSO Approach , 2013 .

[2]  Olli Bräysy,et al.  A Reactive Variable Neighborhood Search for the Vehicle-Routing Problem with Time Windows , 2003, INFORMS J. Comput..

[3]  Daniele Vigo,et al.  An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints , 2007, Transp. Sci..

[4]  Deshi Ye,et al.  A note on a selfish bin packing problem , 2013, J. Glob. Optim..

[5]  Daniele Vigo,et al.  Recent advances on two-dimensional bin packing problems , 2002, Discret. Appl. Math..

[6]  Brian Kallehauge,et al.  Lagrangian duality applied to the vehicle routing problem with time windows , 2006, Comput. Oper. Res..

[7]  Arne Løkketangen,et al.  GRASP-ASP: An algorithm for the CVRP with route balancing , 2014, J. Heuristics.

[8]  Birger Raa,et al.  Using a TSP heuristic for routing order pickers in warehouses , 2010, Eur. J. Oper. Res..

[9]  Josefa Mula,et al.  Mathematical programming models for supply chain production and transport planning , 2010, Eur. J. Oper. Res..

[10]  Herbert Kopfer,et al.  A Dynamic Programming Heuristic for the Vehicle Routing Problem with Time Windows and European Community Social Legislation , 2010, Transp. Sci..

[11]  C. Potts,et al.  A genetic algorithm for two-dimensional bin packing with due dates , 2013 .

[12]  Pawel Sitek,et al.  A Hybrid Approach to the Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) , 2014, Recent Advances in Automation, Robotics and Measuring Techniques.

[13]  Mariano Frutos,et al.  A New Approach to the Optimization of the CVRP through Genetic Algorithms , 2012 .

[14]  Christian Blum,et al.  Solving the Two-Dimensional Bin Packing Problem with a Probabilistic Multi-start Heuristic , 2011, LION.

[15]  Paolo Toth,et al.  A hybrid Granular Tabu Search algorithm for the Multi-Depot Vehicle Routing Problem , 2014, J. Heuristics.

[16]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .