Skip to main content
Springer Nature Link
Log in

Solving the petroleum replenishment and routing problem with variable demands and time windows

  • S.I. : BALCOR-2017
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In this paper we develop a methodological framework for designing the daily distribution and replenishment operations of petroleum products over a weekly planning horizon by taking into account the perspectives of both the transporter and its customers. The proposed approach considers the possibility of having late deliveries due to the variability of the customers’ demands and expected time windows. We first develop an inventory model for the customers to identify the optimal order quantities and time windows. Then, we solve a sequence of mixed-integer optimization models for designing distribution routes based on the order quantities and time windows selected by the inventory models. We design the optimization models so that late deliveries are balanced among the customers in order to mitigate the overall customer dissatisfaction. We test the proposed approach by solving a set of instances adapted from the literature. The empirical results show that the proposed approach can be used for designing the distribution plan for delivering petroleum products in conditions where the operational capabilities of the transporter are limited for generating optimal on-time plans.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Al-Khayyal, F., & Hwang, S. J. (2007). Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, part i: Applications and model. European Journal of Operational Research, 176(1), 106–130.

    Google Scholar 

  • Andersson, H., Hoff, A., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Combined inventory management and routing. Computers & Operations Research, 37(9), 1515–1536.

    Google Scholar 

  • Avella, P., Boccia, M., & Sforza, A. (2004). Solving a fuel delivery problem by heuristic and exact approaches. European Journal of Operational Research, 152(1), 170–179.

    Google Scholar 

  • Baldacci, R., Mingozzi, A., & Roberti, R. (2012). Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. European Journal of Operational Research, 218(1), 1–6.

    Google Scholar 

  • Bausch, D. O., Brown, G. G., & Ronen, D. (1995). Consolidating and dispatching truck shipments of mobil heavy petroleum products. Interfaces, 25(2), 1–17.

    Google Scholar 

  • Ben Abdelaziz, F., Roucairol, C., & Bacha, C. (2002). Deliveries of liquid fuels to SNDP gas stations using vehicles with multiple compartments. In 2002 IEEE international conference on systems, man and cybernetics (Vol. 1, pp. 478–483).

  • Bertsimas, D. J. (1992). A vehicle routing problem with stochastic demand. Operations Research, 40(3), 574–585.

    Google Scholar 

  • Bianchi, L., Birattari, M., Chiarandini, M., Manfrin, M., Mastrolilli, M., Paquete, L., et al. (2006). Hybrid metaheuristics for the vehicle routing problem with stochastic demands. Journal of Mathematical Modelling and Algorithms, 5(1), 91–110.

    Google Scholar 

  • Bräysy, O., & Gendreau, M. (2005a). Vehicle routing problem with time windows, part I: Route construction and local search algorithms. Transportation Science, 39(1), 104–118.

    Google Scholar 

  • Bräysy, O., & Gendreau, M. (2005b). Vehicle routing problem with time windows, part II: Metaheuristics. Transportation Science, 39(1), 119–139.

    Google Scholar 

  • Brown, G. G., Ellis, C. J., Graves, G. W., & Ronen, D. (1987). Real-time, wide area dispatch of mobil tank trucks. Interfaces, 17(1), 107–120.

    Google Scholar 

  • Brown, G. G., & Graves, G. W. (1981). Real-time dispatch of petroleum tank trucks. Management Science, 27(1), 19–32.

    Google Scholar 

  • Campbell, A., Clarke, L., Kleywegt, A., & Savelsbergh, M. (1998). The inventory routing problem. In T. G. Crainic & G. Laporte (Eds.), Fleet management and logistics, centre for research on transportation (pp. 95–113). New York: Springer US. chap 4,

    Google Scholar 

  • Campbell, A., & Savelsbergh, M. W. P. (2004). A decomposition approach for the inventory-routing problem. Transportation Science, 38(4), 488–502.

    Google Scholar 

  • Caramia, M., & Guerriero, F. (2009). A milk collection problem with incompatibility constraints. Interfaces, 40(2), 130–143.

    Google Scholar 

  • Chajakis, E. D., & Guignard, M. (2003). Scheduling deliveries in vehicles with multiple compartments. Journal of Global Optimization, 26(1), 43–78.

    Google Scholar 

  • Christiansen, C. H., & Lysgaard, J. (2007). A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Operations Research Letters, 35(6), 773–781.

    Google Scholar 

  • Christiansen, M., Fagerholt, K., Flatberg, T., Haugen, Ø., Kloster, O., & Lund, E. H. (2011). Maritime inventory routing with multiple products: A case study from the cement industry. European Journal of Operational Research, 208(1), 86–94.

    Google Scholar 

  • Coelho, L. C., Cordeau, J. F., & Laporte, G. (2013). Thirty years of inventory routing. Transportation Science, 48(1), 1–19.

    Google Scholar 

  • Cohn, A., Root, S., Wang, A., & Mohr, D. (2007). Integration of the load-matching and routing problem with equipment balancing for small package carriers. Transportation Science, 41(2), 238–252.

    Google Scholar 

  • Committee on America’s Energy Future, National Academy of Sciences. (2009). America’s energy future: Technology and transformation. Washington: National Academies Press.

  • Cordeau, J. F., Laporte, G., Savelsbergh, M. W. P., & Vigo, D. (2007). Vehicle routing. In C. Barnhart & G. Laporte (Eds.), Transportation (Vol. 14, pp. 367–428). Amsterdam: Elsevier.

    Google Scholar 

  • Cornillier, F., Boctor, F. F., Laporte, G., & Renaud, J. (2007). An exact algorithm for the petrol station replenishment problem. Journal of the Operational Research Society, 59(5), 607–615.

    Google Scholar 

  • Cornillier, F., Boctor, F. F., Laporte, G., & Renaud, J. (2008). A heuristic for the multi-period petrol station replenishment problem. European Journal of Operational Research, 191(2), 295–305.

    Google Scholar 

  • Cornillier, F., Boctor, F. F., & Renaud, J. (2012). Heuristics for the multi-depot petrol station replenishment problem with time windows. European Journal of Operational Research, 220(2), 361–369.

    Google Scholar 

  • Cornillier, F., Laporte, G., Boctor, F. F., & Renaud, J. (2009). The petrol station replenishment problem with time windows. Computers & Operations Research, 36(3), 919–935.

    Google Scholar 

  • Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91.

    Google Scholar 

  • Dayarian, I., Crainic, T. G., Gendreau, M., & Rei, W. (2016). An adaptive large-neighborhood search heuristic for a multi-period vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review, 95(Supplement C), 95–123.

    Google Scholar 

  • Derigs, U., Gottlieb, J., Kalkoff, J., Piesche, M., Rothlauf, F., & Vogel, U. (2011). Vehicle routing with compartments: Applications, modelling and heuristics. OR Spectrum, 33(4), 885–914.

    Google Scholar 

  • Eksioglu, B., Vural, A. V., & Reisman, A. (2009). The vehicle routing problem: A taxonomic review. Computers & Industrial Engineering, 57(4), 1472–1483.

    Google Scholar 

  • Fallahi, A. E., Prins, C., & Wolfler Calvo, R. (2008). A memetic algorithm and a tabu search for the multi-compartment vehicle routing problem. Computers & Operations Research, 35(5), 1725–1741.

    Google Scholar 

  • Federal Motor Carrier Safety Administration. (2015). Rules of practice for motor carriers, intermodal equipment provider, broker, freight forwarder, and hazardous materials proceedings. Technical report, U.S. Department of Transportation.

  • Federgruen, A., & Simchi-Levi, D. (1995). Analysis of vehicle routing and inventory-routing problems. In M. O. Ball, T. L. Magnanti, C. Monma, & G. L. Nemhauser (Eds.), Handbooks in operations research and management science (Vol. 8, pp. 297–373). Amsterdam: Elsevier.

    Google Scholar 

  • Feillet, D. (2010). A tutorial on column generation and branch-and-price for vehicle routing problems. 4OR, 8(4), 407–424.

    Google Scholar 

  • Feillet, D., Gendreau, M., Medaglia, A. L., & Walteros, J. L. (2010). A note on branch-and-cut-and-price. Operations Research Letters, 38(5), 346–353.

    Google Scholar 

  • Gendreau, M., & Tarantilis, C. D. (2010). Solving large-scale vehicle routing problems with time windows: The state-of-the-art. Montrea: CIRRELT.

    Google Scholar 

  • Hallenbeck, M., Rice, M., Smith, B., Cornell-Martinez, C., & Wilkinson, J. (1997). Vehicle volume distributions by classification. Technical report.

  • Hemmelmayr, V. C., Doerner, K. F., & Hartl, R. F. (2009). A variable neighborhood search heuristic for periodic routing problems. European Journal of Operational Research, 195(3), 791–802.

    Google Scholar 

  • Henke, T., Speranza, M. G., & Wäscher, G. (2015). The multi-compartment vehicle routing problem with flexible compartment sizes. European Journal of Operational Research, 246(3), 730–743.

    Google Scholar 

  • Jetlund, A. S., & Karimi, I. A. (2004). Improving the logistics of multi-compartment chemical tankers. Computers & Chemical Engineering, 28(8), 1267–1283.

    Google Scholar 

  • Kallehauge, B., Larsen, J., Madsen, O. B. G., & Solomon, M. M. (2005). Vehicle routing problem with time windows. In D. J. Gand Desrosiers & M. M. Solomon (Eds.), Column generation (pp. 67–98). New York: Springer US (book section 3).

  • Kytöjoki, J., Nuortio, T., Bräysy, O., & Gendreau, M. (2007). An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Computers & Operations Research, 34(9), 2743–2757.

    Google Scholar 

  • Lahyani, R., Coelho, L. C., Khemakhem, M., Laporte, G., & Semet, F. (2015). A multi-compartment vehicle routing problem arising in the collection of olive oil in Tunisia. Omega, 51, 1–10.

    Google Scholar 

  • Lozano, L., Duque, D., & Medaglia, A. L. (2016). An exact algorithm for the elementary shortest path problem with resource constraints. Transportation Science, 50(1), 348–357.

    Google Scholar 

  • Mendoza, J. E., Castanier, B., Guéret, C., Medaglia, A. L., & Velasco, N. (2010). A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands. Computers & Operations Research, 37(11), 1886–1898 (metaheuristics for Logistics and Vehicle Routing).

  • Miettinen, K. (1999). Nonlinear multiobjective optimization. Kluwer Academic Publishers.

  • Mladenovic, N., & Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24(11), 1097–1100.

    Google Scholar 

  • Moin, N. H., & Salhi, S. (2006). Inventory routing problems: A logistical overview. Journal of the Operational Research Society, 58(9), 1185–1194.

    Google Scholar 

  • Muyldermans, L., & Pang, G. (2010). On the benefits of co-collection: Experiments with a multi-compartment vehicle routing algorithm. European Journal of Operational Research, 206(1), 93–103.

    Google Scholar 

  • Ng, W. L., Leung, S. C. H., Lam, J. K. P., & Pan, S. W. (2007). Petrol delivery tanker assignment and routing: A case study in hong kong. Journal of the Operational Research Society, 59(9), 1191–1200.

    Google Scholar 

  • Nguyen, L. X., Zhang, J., Zhou, S., Beningo, S., Chambers, M., Ford, C., & Notisand, K. (2015). National transportation statistics. Technical report, U.S. Department of Transportation’s Bureau of Transportation Statistics.

  • Pillac, V., Gendreau, M., Guéret, C., & Medaglia, A. L. (2013). A review of dynamic vehicle routing problems. European Journal of Operational Research, 225(1), 1–11.

    Google Scholar 

  • Prins, C. (2004). A simple and effective evolutionary algorithm for the vehicle routing problem. Computers & Operations Research, 31(12), 1985–2002.

    Google Scholar 

  • Reed, M., Yiannakou, A., & Evering, R. (2014). An ant colony algorithm for the multi-compartment vehicle routing problem. Applied Soft Computing, 15, 169–176.

    Google Scholar 

  • Simchi-Levi, D., Chen, X., & Bramel, J. (2005). The logic of logistics. New York: Springer.

    Google Scholar 

  • Spliet, R., & Desaulniers, G. (2015). The discrete time window assignment vehicle routing problem. European Journal of Operational Research, 244(2), 379–391.

    Google Scholar 

  • Spliet, R., & Gabor, A. F. (2015). The time window assignment vehicle routing problem. Transportation Science, 49(4), 721–731.

    Google Scholar 

  • Strocko, E., Sprung, M., Nguyen, L., Rick, C., & Sedor, J. (2014). Freight facts and figures 2013. Technical report. Federal Highway Administration

  • Sungur, I., Ordoñez, F., & Dessouky, M. (2008). A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty. IIE Transactions, 40(5), 509–523.

    Google Scholar 

  • Toth, P., & Vigo, D. (2014). Vehicle routing: Problems, methods, and applications (2nd ed.). Philadelphia: SIAM.

    Google Scholar 

  • van der Bruggen, L., Gruson, R., & Salomon, M. (1995). Reconsidering the distribution structure of gasoline products for a large oil company. European Journal of Operational Research, 81(3), 460–473.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University at Buffalo, The State University of New York, 342 Bell Hall, Buffalo, NY, 14260, USA

    Yan Cheng Hsu, Jose L. Walteros & Rajan Batta

Authors
  1. Yan Cheng Hsu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jose L. Walteros
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Rajan Batta
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jose L. Walteros.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hsu, Y.C., Walteros, J.L. & Batta, R. Solving the petroleum replenishment and routing problem with variable demands and time windows. Ann Oper Res 294, 9–46 (2020). https://doi.org/10.1007/s10479-018-3042-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-018-3042-5

Keywords