Extensions to Competitive Facility Location with Multi-purpose Trips

Abstract

Existing location models considering multi-purpose shopping behavior limit the number of stops a customer makes to two. We introduce the multi-purpose (MP) competitive facility location model with more than two stops. We locate one or more facilities in a competitive environment, assuming a shopper may stop multiple times during one trip to purchase different complementary goods or services. We show that when some or all trips are multi-purpose, our model captures at least as much market share as the MP models with fewer purposes. Our extensive simulation experiments show that the MP models work best when multiple new facilities are added. As the number of facilities increases, however, the returns diminish due to cannibalization. Also, with significant increases in complexity for each additional stop added, expanding the model beyond three purposes may not be practical.

Appendix

Figure 4 shows the best-known locations of the solutions to 1P, 2P and 3P models for different numbers of added facilities ($p=2$, $p=3$, $p=4$ and $p=5$) and different combinations of proportions. The results show clustering of locations similar to that observed by Kalczynski et al. (2024) with only a few outliers. Only those 3P locations were annotated, for which the 3P model yielded the largest increases in market share over 1P and 2P.

Table 5 presents the comparisons of the relative market share improvements for different combinations of proportions and for different numbers of added facilities ($p=2$, $p=3$, $p=4$ and $p=5$). Each is the best result of SNOPT optimization with 100 random starts. They provide strong support for our conclusions.

Table 5 Comparisons for different combinations of proportions and different numbers of added facilities ($p=2$, $p=3$, $p=4$ and $p=5$), $n=100$