A Mass-flow based MILP Formulation for the Inventory Routing with Explicit Energy Consumption

Yun He, Cyril Briand, Nicolas Jozefowiez

Abstract

In this paper, we present a new mass-flow based Mixed Integer Linear Programming (MILP) formulation for the Inventory Routing Problem (IRP) with explicit energy consumption. The problem is based on a multi-period single-vehicle IRP with one depot and several customers. Instead of minimizing the distance or inventory cost, the problem takes energy minimization as an objective. In this formulation, flow variables describing the transported mass serve as a link between the inventory control and the energy estimation. Based on physical laws of motion, a new energy estimation model is proposed using parameters like vehicle speed, average acceleration rate and number of stops. The solution process contains two phases with different objectives: one with inventory and transportation cost minimization as in traditional IRP, the other with energy minimization. Using benchmark instances for inventory routing with parameters for energy estimation, experiments have been conducted. Finally, the results of these two solution phases are compared to analyse the influence of energy consumption to the inventory routing systems.

References

  1. Abdelmaguid, T. F., Dessouky, M. M., and nez, F. O. (2009). Heuristic approaches for the inventory-routing problem with backlogging. Computers and Industrial Engineering, 56(4):1519-1534.
  2. Andersson, H., Hoff, A., Christiansen, M., Hasle, G., and Lø kketangen, A. (2010). Industrial aspects and literature survey: Combined inventory management and routing. Computers and Operations Research, 37(9):1515-1536.
  3. André, M., Hassel, D., and Weber, F.-j. (1998). Development of short driving cycles-Short driving cycles for the inspection of in-use cars -Representative European driving cycles for the assessment of the I/M schemes. Technical Report May, INRETS - LEN, Laboratoire Ónergie Nuisances.
  4. Anily, S. and Federgruen, A. (1990). One Warehouse Multiple Retailer Systems with Vehicle Routing Costs. Management Science, 36(1):92-114.
  5. Archetti, C., Bertazzi, L., Laporte, G., and Grazia Speranza, M. (2007). A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem. Transportation Science, 41(3):382-391.
  6. Archetti, C., Bianchessi, N., Irnich, S., and Grazia Speranza, M. (2014). Formulations for an inventory routing problem. International Transactions in Operational Research, 21:353-374.
  7. Bektas¸, T. and Laporte, G. (2011). The pollution-routing problem. 45:1232-1250.
  8. Bell, W. J., Dalberton, L. M., Fisher, M. L., Greenfield, A. J., Jaikumar, R., Kedia, P., Mack, R. G., and Prutzman, P. J. (1983). Improving the Distribution of Industrial Gases with and On-Line Computerized Routing and Scheduling Optimizer. Interfaces, 13(6):4-23.
  9. Burns, L. D., Hall, R. W., Blumenfeld, D. E., and Daganzo, C. F. (1985). Distribution Strategies that Minimize Transportation and Inventory Costs.
  10. Coelho, L. C., Cordeau, J.-F., and Laporte, G. (2013). Thirty Years of Inventory Routing. Transportation Science, 48(1):1-19.
  11. Demir, E., Bektas¸, T., and Laporte, G. (2014). A review of recent research on green road freight transportation. European Journal of Operational Research, 237:775- 793.
  12. Dror, M. and Ball, M. (1987). Inventory/routing: Reduction from an annual to a short-period problem. Naval Research Logistics (NRL), 34:891-905.
  13. EcoTransIT World Initiative (EWI) (2014). Ecological Transport Information Tool for Worldwide Transports Methodology and Data-Update .
  14. Fish, L. A. (2015). Applications of Contemporary Management Approaches in Supply Chains.
  15. Kara, I., Kara, B. Y., and Yetis, M. K. (2007). Energy Minimizing Vehicle Routing Problem. Verlag Berlin Heidelberg, 1:62-71.
  16. Lin, C., Choy, K. L., Ho, G. T. S., Chung, S. H., and Lam, H. Y. (2014). Survey of Green Vehicle Routing Problem: Past and future trends. Expert Systems with Applications, 41:1118-1138.
  17. Sahin, B., Yilmaz, H., Ust, Y., Guneri, A. F., and Gulsun, B. (2009). An approach for analysing transportation costs and a case study. European Journal of Operational Research, 193(1):1-11.
  18. Samaras, Z. and Ntziachristos, L. (1998). Average hot emission factors for passenger cars and light duty trucks. Technical Report LAT report No. 9811, Lab. of Applied Thermodynamics, Aristotle University of Thessaloniki.
  19. Savelsbergh, M. and Song, J. H. (2007). Inventory routing with continuous moves. Computers and Operations Research, 34:1744-1763.
  20. Treitl, S., Nolz, P. C., and Jammernegg, W. (2014). Incorporating environmental aspects in an inventory routing problem. A case study from the petrochemical industry. Flexible Services and Manufacturing Journal, 26:143-169.
  21. Walkowicz, K., Duran, A., and Burton, E. (2014). Fleet dna project data summary report. Technical report, NREL.
  22. Xiao, Y., Zhao, Q., Kaku, I., and Xu, Y. (2012). Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Computers and Operations Research, 39(7):1419-1431.
Download


Paper Citation


in Harvard Style

He Y., Briand C. and Jozefowiez N. (2016). A Mass-flow based MILP Formulation for the Inventory Routing with Explicit Energy Consumption . In Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-171-7, pages 242-251. DOI: 10.5220/0005698802420251


in Bibtex Style

@conference{icores16,
author={Yun He and Cyril Briand and Nicolas Jozefowiez},
title={A Mass-flow based MILP Formulation for the Inventory Routing with Explicit Energy Consumption},
booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2016},
pages={242-251},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005698802420251},
isbn={978-989-758-171-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - A Mass-flow based MILP Formulation for the Inventory Routing with Explicit Energy Consumption
SN - 978-989-758-171-7
AU - He Y.
AU - Briand C.
AU - Jozefowiez N.
PY - 2016
SP - 242
EP - 251
DO - 10.5220/0005698802420251