Skip to main content

Alternative fuel station location model with demand learning

Abstract

In this paper, we study the optimal location decision for a network of alternative fuel stations (AFS) servicing a new market where the demand rate for the refueling service can be learned over time. In the presence of demand learning, the firm needs to make a decision, whether to actively learn the market through a greater initial investment in the AFS network or defer the commitment since an overly-aggressive investment often results in sub-optimal AFS locations. To illustrate this trade-off, we introduce a two-stage location model, in which the service provider enters the market by deploying a set of stations in the first stage under uncertainty, and has the option to add more stations in the second stage after it learns the demand. The demand learning time (length of the first stage) is endogenously determined by the service provider’s action in the first stage. To solve this problem, we develop an efficient solution method that provides a framework to achieve a desired error rate of accuracy in the optimal solution. Using numerical experiment, we study the trade-off between active learning and deferred commitment in AFS deployment strategy under different market characteristics. Further, we find that the lack of planning foresight typically results in an over-commitment in facility investment while the service provider earns a lower expected profit.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3

References

  1. Ballou, R. H. (1968). Dynamic warehouse location analysis. Journal of Marketing Research, 5(3), 271–276.

    Article  Google Scholar 

  2. Baron, O., Milner, J., & Naseraldin, H. (2010). Facility location: a robust optimization approach. Production and Operations Management, 20(5), 772–785.

    Article  Google Scholar 

  3. Berman, O., & Drezner, Z. (2008). The p-median problem under uncertainty. European Journal of Operational Research, 189(1), 19–30.

    Article  Google Scholar 

  4. Berman, O., & Krass, D. (2002). The generalized maximal covering location problem. Computers & Operations Research, 29(6), 563–581.

    Article  Google Scholar 

  5. Berman, O., Krass, D., & Drezner, Z. (2003). The gradual covering decay location problem on a network. European Journal of Operational Research, 151(3), 474–480.

    Article  Google Scholar 

  6. Campbell, J. (1990). Locating transportation terminals to serve an expanding demand. Transportation Research. Part B: Methodological, 24(3), 173–192.

    Article  Google Scholar 

  7. Census.gov (2010). http://www.census.gov/main/www/cen2000.html.

  8. Church, R., & ReVelle, C. (1974). The maximal covering location problem. Papers in Regional Science, 32(1), 101–118.

    Article  Google Scholar 

  9. Church, R., & Weaver, J. R. (1986). Theoretical links between median and coverage location problems. Annals of Operations Research, 6(1), 1–19.

    Article  Google Scholar 

  10. CNN.com (2013). 9 questions for Tesla’s Elon Musk. http://money.cnn.com/2013/06/12/autos/tesla-elon-musk.fortune.

  11. Current, J., Ratick, S., & ReVelle, C. (1997). Dynamic facility location when the total number of facilities is uncertain: a decision analysis approach. European Journal of Operational Research, 110(3), 597–609.

    Article  Google Scholar 

  12. Daskin, M. S. (1983). A maximum expected covering location model: formulation, properties, and heuristic solution. Transportation Science, 17, 48–70.

    Article  Google Scholar 

  13. Daskin, M. S. (1995). Network and discrete location: models, algorithms, and applications. New York: Wiley.

    Book  Google Scholar 

  14. Daskin, M. S., Hopp, W. J., & Medina, B. (1992). Forecast horizons and dynamic facility location planning. Annals of Operations Research, 40(1), 125–151.

    Article  Google Scholar 

  15. Dixit, A., & Pindyck, R. S. (1994). Investment under uncertainty. Princeton: Princeton University Press.

    Google Scholar 

  16. Drezner, T. (2009). Location of retail facilities under conditions of uncertainty. Annals of Operations Research, 167(1), 107–120.

    Article  Google Scholar 

  17. Drezner, Z., Wesolowsky, G. O., & Drezner, T. (2004). The gradual covering problem. Naval Research Logistics, 51(6), 841–855.

    Article  Google Scholar 

  18. Drezner, T., Drezner, Z., & Goldstein, Z. (2010). A stochastic gradual cover location problem. Naval Research Logistics, 57(4), 367–372.

    Google Scholar 

  19. Farahani, R. Z., Drezner, Z., & Asgari, N. (2009). Single facility location and relocation problem with time dependent weights and discrete planning horizon. Annals of Operations Research, 167(1), 353–368.

    Article  Google Scholar 

  20. Hale, T. S., & Moberg, C. R. (2003). Location science research: a review. Annals of Operations Research, 123(1–4), 21–35.

    Article  Google Scholar 

  21. Hiller, R., & Shapiro, J. (1986). Optimal capacity expansion planning when there are learning effects. Management Science, 32(9), 1153–1163.

    Article  Google Scholar 

  22. Jacobson, S. K. (1990). Multiperiod capacitated location models. In P. B. Mirchandian & R. L. Francis (Eds.), Discrete location theory. New York: Wiley.

    Google Scholar 

  23. Jerusalem Post (2011). Baran to build 51 battery switch stations for electric cars. http://www.jpost.com/Breaking-News/Baran-to-build-51-battery-switch-stations-for-electric-cars.

  24. Ke, T. T., Shen, Z. J. M., & Li, S. (2013). How inventory cost influences introduction timing of product line extensions. Production and Operations Management, 22(5), 1214–1231.

    Google Scholar 

  25. Kuby, M., & Lim, S. (2005). The flow-refueling location problem for alternative-fuel vehicles. Socio-Economic Planning Sciences, 39(2), 125–145.

    Article  Google Scholar 

  26. Kuby, M., & Lim, S. (2007). Location of alternative-fuel stations using the flow-refueling location model and dispersion of candidate sites on arcs. Networks and Spatial Economics, 7(2), 129–152.

    Article  Google Scholar 

  27. Levy, M., & Weitz, B. (2008). Retailing management (7th ed.). New York: McGraw-Hill.

    Google Scholar 

  28. Mahajan, A., & Munson, T. (2010). Exploiting second-order cone structure for global optimization. Argonne National Laboratory. Working paper.

  29. MIT Technology Review (2013). Tesla’s superchargers matter only because it already sells a car people want. http://www.technologyreview.com/view/515596/teslas-superchargers-matter-only-because-it-already-sells-a-car-people-want.

  30. Oral, M., & Kettani, O. (1992). A linearization procedure for quadratic and cubic mixed-integer problems. Operations Research, 40(1), 109–116.

    Article  Google Scholar 

  31. Plastria, F. (2002). Continuous covering location problems. In Z. Drezner & H. W. Hamacher (Eds.), Facility location: applications and theory. Berlin: Springer.

    Google Scholar 

  32. Rob, R. (1991). Learning and capacity expansion under demand uncertainty. Review of Economic Studies, 58(4), 655–675.

    Article  Google Scholar 

  33. Shen, Z. J. M. (2006). A profit-maximizing supply chain network design model with demand choice flexibility. Operations Research Letters, 34, 673–682.

    Article  Google Scholar 

  34. Shu, J. (2010). Integrated location and two-echelon inventory network design under uncertainty. Annals of Operations Research, 181, 233–247.

    Article  Google Scholar 

  35. Snyder, L. (2006). Facility location under uncertainty: a review. IIE Transactions, 38(7), 537–554.

    Article  Google Scholar 

  36. Upchurch, C., Kuby, M., & Lim, S. (2009). A model for location of capacitated alternative-fuel stations. Geographical Analysis, 41(1), 95–106.

    Article  Google Scholar 

  37. Van Roy, T., & Erlenkotter, D. (1982). A dual-based procedure for dynamic facility location. Management Science, 28(10), 1091–1105.

    Article  Google Scholar 

  38. Wang, X., Lim, M. K., & Ouyang, Y. (2013). A continuum approximation approach to the dynamic facility location problem. University of Illinois. Urbana-Champaign. Working paper.

  39. Wesolowsky, G. O. (1973). Dynamic facility location. Management Science, 19(11), 1241–1248.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Michael K. Lim.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bhatti, S.F., Lim, M.K. & Mak, HY. Alternative fuel station location model with demand learning. Ann Oper Res 230, 105–127 (2015). https://doi.org/10.1007/s10479-014-1530-9

Download citation

Keywords

  • Alternative fuel station operations
  • Facility location
  • Maximal covering problem
  • Demand learning