Design and analysis of facility location experiments applied to sanitizer dispensers

AbstractThe number and location of facilities is a fundamental problem in transportation and logistics. While many authors argue that customer demands depend on location choices, efforts to determine the dependencies empirically have been limited. We study the problem of optimal experimentation on facility locations and find that it relates to a novel type of split plot experiment, where the whole plots are the time periods. Our empirical models include so-called “network effects” which derive from the period-specific configurations of facilities. We propose a modified exchange algorithm that accounts for network effects. We use numerical examples to study to identify relatively robust settings to assumptions about uncertainties. Also, we provide a case study involving the placement of two types of Alcohol Based Hand Sanitizer (AHBS) dispensers over four periods. In our study, our model involving the site attributes and period effects achieves approximately 50% R-squared on the log demand. Further, we compare demands in periods with two co-located dispensers compared with the same site having only a single dispenser. A paired t-test reveals statistical significance (p-value < 0.001), indicating a robust difference in average demand. Notably, average demand substantially increases by 2.3 times when facilities are strategically co-located (placing two facilities in the same place).