The impacts of mergers, capacity expansion and adoptions on animal shelter performance: A queuing analysis

According to the American Society for the Prevention of Cruelty to Animals (ASPCA), approximately 23% of the animals that enter shelters each year are euthanized. Many animal shelters strive to reduce euthanization and the stray animal population through capacity expansion, adoption increasing programs, and mergers. In this paper, we define, compare and perform sensitivity analysis of performance metrics for animal shelter involving loss queues. We ultimately provide recommendations for animal shelters on the most efficient investments, and analyze the effects of mergers and capacity expansion on various performance metrics. We represent animal shelters by utilizing loss queues with and without reneging and perform sensitivity analysis by calculating the asymptotic expansion of the performance metrics for various cases. We find that the euthanization in traditional shelters is not monotonically decreasing with increases in the demand for animals. A counterintuitive result shows that increasing the capacity in a traditional shelter (or merging two traditional shelters together) does not necessarily decrease the number of animals euthanized. Our results related to the performance metrics Erlang loss queues can be utilized for any type of queuing system with involuntary departures.