1. Optimizing the Adoption
Process at the
Kentucky Humane Society
STEFANIE O. VILLAJUAN
INDUSTRIAL ENGINEERING
UNIVERSITY OF LOUISVILLE
JULY 12, 2016
2. Optimizing the Adoption Process at the
Kentucky Humane Society
• Introduction
• Problem Description
• KHS Locations
• Current KHS Methodology
• Solutions and Methodology
• Results/Outcomes and Analysis
• Dog Allocation
• Conclusions
• Future Improvements
4. Problem Description
• Biggest problem of KHS: lack of space
• Area for improvement: adoption process
• Answer to problem: allocate animals to specific locations so that the length of
stay is minimized, which will allow for more space for future animal intake
5. KHS Locations
• Clarksville
• Dixie
• East Campus
• Fern Creek
• Hikes Point
• Main Campus
• Pewee Valley
• Preston
• Springhurst
• St. Matthews
6. Current KHS Methodology
• KHS has no current mathematical way of allocating animals to each location
• A small group of employees designate where animals go based on experience
of how likely an animal is to be adopted at a location
• Employees make decisions based on the following:
• Space availability
• Size availability
• Highly adoptable animals at a specific location
• Financial standing of the location
7. Solutions and Methodology
• Create a mathematical model to optimize the allocation
• Organize animals into groups (4 for cats, 10 for dogs)
• Groups organized by size (for dogs) and age
• Create probability table for each location
• Find expected length of stay in a certain location for an animal in a given group
14. Example of Dog Allocation
• 13 in Group 1 (Puppy)
• 7 in Group 2 (Small, Age Group 1)
• 2 in Group 3 (Small, Age Group 2)
• 1 in Group 5 (Medium, Age Group 1)
• 3 in Group 8 (Large/Extra-large, Age Group 1)
16. Conclusion
• Mathematical model provides a way
to allocate animals such that total
length of stay is minimized
• There may be situations in which
the number of animals to be
allocated is greater than the
available cages
17. Future Improvements
• Validate current model with KHS
• Create a five-day allocation model
• Include maximization of revenue
The Kentucky Humane Society, also referred to as KHS is Kentucky’s largest pet adoption agency and largest no-kill animal shelter. KHS is committed to saving every healthy, behaviorally sound animal they take in. Their boldest principle is that they will never euthanize an animal due to lack of space.
Thousands of animals are taken in throughout the year, with the intention to save their lives by returning them to their owners, placement in another rescue, and primarily adoption. KHS’s success is measured in the number of animals saved, which has increased since 2003, as seen in the chart. Additionally, the number of lives lost through euthanasia has decreased. KHS will only euthanize an animal if they are too ill, too dangerous or too behaviorally unsound to be rehabilitated and adopted.
There are a number of reasons as to why progress continues at KHS. Some of these reasons include refusing to euthanize animals due to lack of space, as well as the number of adoptions increasing. Although the organization has continued success, they wish to allocate their space better in order to be able to accept more animals, leading to saving more lives.
One of the biggest areas of improvement that can be made at KHS is with the adoption process. In 2012, KHS transitioned to admissions by appointment to ensure that they have adequate kennel space, eliminating euthanasia due to lack of space. Although this process has allowed for more animals to be saved, the lack of space is still one of the most challenging issues that KHS has been facing. Even though the number of incoming animals has decreased to spay/neuter efforts, there are still thousands of animals that come through on an annual basis. The issue is not due to the number of incoming animals, the problem actually lies with the adoption process and how animals can be better allocated to all ten adoption sites. KHS believes that by improving the rate at which people adopt their current “stock” of animals, they will be freed up to take in all the animals in need of help.
Each location has a set amount of spaces (of fixed sizes) to house the animals, and each location has a certain clientele that it caters to.
East Campus and Main Campus are the biggest adoption locations, as they have more space available. Main Campus is the only campus where animals are processed to be adoption-ready. This is where surgeries like spay and neuter take place, as well as behavioral programs.
The other eight locations are all located within a Feeders Supply.
Since KHS has been operating, they have had no mathematical way to delegate which animals should go to each location. The way animals are currently designated to their location is by a small group of experienced employees looking at a list of animals that are ready to be adopted every morning. From there, the employees determine which animal goes to a specific location. Their decision is based on a few things – space availability, size availability, highly adoptable animals at a specific location, and financial standing of the location.
For example, a large beagle may be available for adoption. From previous knowledge, beagles are known to be highly adoptable at the Fern Creek location. Unfortunately, only a small kennel is available, so it will have to be placed at a different location.
Here are the basic steps that were taken when working through this project. The most challenging part was figuring out how to group the animals in such a way that would provide meaningful information. Thus, size and age determined which group to assign the animal.
Here is the mathematical model that was used.
Equation (1) minimizes the cumulative expected length of stay of total animals allocated to all locations. Equation (2) allocates all animals. Equation (3) is the capacity constraint at each location. The expected value is calculated using a probability table, which will soon be shown. The capacity constraints are provided by KHS.
As previously stated, cats and dogs each have a different number of groups, so each has their own mathematical model. It was important to keep cats and dogs separate as their average length of stay were very different from one another. Across all locations, cats had an average length of stay of 33.1 days, whereas dogs had an average length of stay of 18.2 days.
This is a quick snapshot of the Length of Stay report exported from the KHS database, PetPoint. All adoption records for cats and dogs dated from April 1, 2014 – March 31, 2016 are listed here. Although KHS has been operating for years, the Shelter Operations Director suggested that the data not be considered for more than two years since a lot has changed in such a short amount of time – such as fewer puppy intakes, less variation in dog breeds, and kittens were born at a different time of the year.
Once it was understood what details the report listed, the next step was to re-export the report into a comma-separated values format.
Here is a quick snapshot of the Length of Stay report in a comma-separated values format. Notice there are fewer categories shown. These were the seven main categories used when organizing animals into groups.
Now that the categories, groups and observations are easily identifiable, the next step would be creating the probability tables.
Here is an example of the probability tables created for the Clarksville location. As previously stated, animals are categorized according to their size (for dogs only) and age. Cats did not need to be organized by size as there are no specific sizes for cat condos.
The intervals you see shaded in gray are different length of stay categories. The row above it is the midpoint of each category, which was used when calculating the expected value of each group. From this, the expected value is used in the allocation model previously stated.
Before going further, let’s look at the most adoptable cats and dogs.
Across all ten locations, Beagles, Chihuahua, Short Coat, and Retriever, Labrador make up 31.3% of dogs adopted.
And across all ten locations, Domestic Shorthair, Domestic Medium Hair, and Domestic Longhair make up 93.3% of all cats adopted.
Here are two charts displaying the average length of stay and number of adoptions across all ten locations. As seen on the chart on the left, cats have the highest average length of stay, whereas puppies have the lowest. One can easily make the assumption that this directly correlates with the number of adoptions. However, the chart on the right shows slightly different – cats, as suspected, have the lowest total number of adoptions whereas dogs have the highest number of adoptions.
As a frame of reference, kittens and puppies are considered as 6 months old and younger.
Now let’s look at an example of how to allocate dogs.
When dogs are taken into KHS, they have a processing date of about 5 days until they are ready to go out onto the adoption floor. This number was suggested by the Shelter Operations Director.
As an example, we look at dogs that have an intake date of March 1, 2016. On that day, there were 13 dogs in Group 1, 7 in Group 2, 2 in Group 3, 1 in Group 5, and 3 in Group 8.
Ideally, these animals will be ready to go out for adoption on March 6, 2016. On that day, there are size specific cages available at each location. For the sake of this example, we will assume that all locations have their maximum available capacity.
For this specific input data, it can be seen by the table above that all 26 dogs were allocated to specific locations. This would give an optimal solution of an expected length of stay of 176.013 days. Again, this was making the assumption that all locations had their maximum available capacity on a given day. Of course, this may not happen on a daily basis.
Since the model specifies that the decision variables be integers, the model may not return a feasible solution if the number of available cages were less than the number of animals to be allocated. In this case, KHS would have to use their judgement, with the assistance of the model, to allocate animals appropriately.
In conclusion, using the allocation model to be able to allocate animals to appropriate locations, while minimizing the expected length of stay, will allow for KHS to have more space to intake more animals. It is important to keep in mind that there may be times that the number of animals to be allocated is greater than the number of available cages on a given day. Since one of the constraints in the model is that the decision variables be integers, it is possible for the model to provide an unfeasible solution, such that the decision variables are no longer integers. In this case, the employees will have to make a decision where to allocate the animals, in addition to seeking guidance from the model and the non-integer solutions.
Although this model has offered a way to increase the amount of space at KHS, there are definitely more improvements that can be made.
The most important step in improving the model is to first validate this current model with KHS.
From there, the current model can be improved. As of now, it only allows for a one-day allocation, so in the future, it should be improved to become a five-day allocation. In other words, the model will eventually be able to predict what animals should be expected to be ready for adoption five days ahead of time.
In addition, the future model will need to include revenue, so that KHS can not only minimize the length of stay, but also maximize their revenue. This will help to increase the revenue at all locations that may need a revenue boost on a given month.
