Assigning Watercraft Inspection Stations to …...Problem Formulation Locate a fixed number of...
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Assigning Watercraft Inspection Stations to Minnesota Lakes An Operations Research Approach Robert G Haight USDA Forest Service Northern Research Station Nicholas Phelps Minnesota Aquatic Invasive Species Research Center University of Minnesota PHOTO BY BRAD HENLEY PHOTO BY MN DNR
Assigning Watercraft Inspection Stations to …...Problem Formulation Locate a fixed number of watercraft inspection stations to maximize the number of inspected watercraft that enter
Assigning Watercraft Inspection Stations to Minnesota LakesAn Operations Research Approach
Robert G HaightUSDA Forest ServiceNorthern Research Station
Nicholas PhelpsMinnesota Aquatic Invasive Species Research CenterUniversity of Minnesota
PHOTO BY BRAD HENLEY
PHOTO BY MN DNR
Presenter
Presentation Notes
I am an economist with the USDA Forest Service, stationed in Minnesota since 1991. For the last several years, I’ve been working on surveillance and control programs for forest insects and diseases, including emerald ash borer in MN. A couple of years ago I met Nick Phelps, who told me about the problem of preventing or slowing the movement of aquatic invaders among MN lakes, using boat inspection and decontamination. I noted that programs to slow the spread of aquatic invaders have similarities to slowing the spread of forest pests: there are vectors of movement (like watercraft or firewood), inspection and decontamination protocols to detect and eradicate pests, and limited budgets so that locations where inspection and eradication take place need to be selected cost-effectively. Operations research methods used by economists are valuable tools to address these types of surveillance and control problems, and the story I want to tell is the application OR methods to watercraft inspection programs. MN created a Watercraft Inspection Program in 1992, in response to legislation proposed by the DNR, Minnesota Lakes Associations, and angling groups The program’s goal is to prevent the spread of AIS within Minnesota through boater education, watercraft inspections, and watercraft decontaminations at public water accesses In 2011, legislation was passed to strengthen the program, allowing inspectors to visually and tactilely inspect and decontaminate watercraft prohibiting the launching or operation of watercraft that owners refuse to have inspected. The inspection program has two parts: DNR hires inspectors (around 100 in 2017) who are trained and assigned to lakes throughout the state DNR allocates funds to counties for them to undertake watercraft inspection. Here I will be talking about county-level inspection programs, where a county receives funds from the state and other sources and needs to hire inspectors and assign them to lakes within the county.
Watercraft Inspection Location Problem
• Where do we put inspection stations within a county?
• Objective: minimize the risk of zebra mussel moving into un-infested lakes GLEN STUBBE • Star Tribune State DNR inspectors checked every boat being launched or pulled from Lake
Minnetonka in Spring Park recently.
Presenter
Presentation Notes
Our problem is to locate a fixed number of watercraft inspection stations at lakes within a county to minimize the risk of AIS moving into and establishing in uninfested lakes. I will present three examples inspection location to slow the spread of zebra mussel within Ramsey, Washington, and Crow Wing counties
Data for Zebra Mussel• Location of infested and uninfested lakes within
counties
• Number of watercraft moving from infested lakes to uninfested lakes
• Within the county
• Within the county to outside
• Outside the county to within the county
• Observations aggregated over inspection period 2014-2017 and adjusted for non-uniform sample size
• Risk of establishment of AIS in un-infested lakes
For zebra mussel, we have the following information for each MN county: Location of infested and uninfested lakes within counties Number of watercraft moving from infested lakes to uninfested lakes Within the county Within the county to outside Outside the county to within the county Observations aggregated over inspection period 2014-2017 and adjusted for non-uniform sample size; Hopefully you went to Nick’s presentation earlier to get the details of how this information was collected and analyzed. Great credit goes to his team of students who put it together. Risk of establishment of AIS in un-infested lakes
Given this data on watercraft movement between infested and uninfested lakes, we formulate the problem as follows: Locate a fixed number of inspection stations at county lakes to maximize the number of inspected watercraft that move from infested to un-infested lakes. We allow inspection stations to be placed at either infested or un-infested lakes within the county Our only constraint is an upper bound on the number of inspection stations, which represents a budget limitation. There may be other worthy objectives; perhaps the audience can articulate them for us and then we can re-formulate the problem.
Here’s a warm-up problem we can work out together. Four lakes, two infested and two uninfested, with watercraft movement as indicated. If you have one inspection station, which lake would you choose to maximize number of inspected boats entering uninfested lakes?
If you add up the watercraft, there are 40 leaving each infested lake, and 50 and 30 entering the two infested lakes. If you picked lake three, you’re right because there you would maximize the number of inspected boats that move from infested to un-infested lakes.
𝑥𝑥𝑖𝑖 = 0-1 variable for whether station is located at lake i
𝑦𝑦𝑗𝑗 = 0-1 variable for whether station is located at lake j
𝑎𝑎𝑖𝑖𝑗𝑗 = 0-1 variable for whether boats moving between lakes i and j are inspected as the leave lake i
𝑏𝑏𝑖𝑖𝑗𝑗 = 0-1 variable for whether boats moving between lakes i and j are inspected as the enter lake j
Presenter
Presentation Notes
The problem becomes more difficult to solve as the number of lakes and vectors between lakes increases. We can write a mathematical program to represent this problem
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Ramsey County Washington County
Incoming boats from infested lakes (zebra mussel)
• 31 uninfested lakes• 1 infested lake (Pleasant)• 0 boats from infested lake
in county to uninfected lakes in county
• 2,616 boats from infested lake in county to uninfected lakes outside county
• 3,216 boats from infested lakes outside county to uninfected lakes in county
Presenter
Presentation Notes
Now we are going to look at Ramsey and Washington Counties. We have boat movement data for 32 lakes in Ramsey County and 37 lakes in Washington County. The circle represent the numbers of incoming boats from zebra-mussel infested lakes inside or outside the county. We applied our inspection station location problem to each county separately. And then we applied the model to the two counties together.
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Ramsey County Washington County
Incoming boats from infested lakes (zebra mussel)
• 31 uninfested lakes• 1 infested lake (Pleasant)• 0 boats from infested lake
in county to uninfected lakes in county
• 2,616 boats from infested lake in county to uninfected lakes outside county
• 3,216 boats from infested lakes outside county to uninfected lakes in county
Presenter
Presentation Notes
For Ramsey County, we have 31 uninfested lakes and 1 infested lake
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Ramsey County Washington County
Incoming boats from infested lakes (zebra mussel)
• 31 uninfested lakes• 1 infested lake (Pleasant)• 0 boats from infested lake
in county to uninfested lakes in county
• 2,616 boats from infested lake in county to uninfested lakes outside county
• 3,216 boats from infested lakes outside county to uninfested lakes in county
Presenter
Presentation Notes
0 boats from infested lake in county to uninfested lakes in county 2,616 boats from infested lake in county to uninfested lakes outside county 3,216 boats from infested lakes outside county to uninfested lakes in county
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Ramsey County
Incoming boats from infested lakes (zebra mussel)
Best solution with upper bound of 4 stations:
• 1 infested lake (Pleasant)
• 3 uninfested lakes (Turtle, Bald Eagle, Phalen)
Presenter
Presentation Notes
With an upper bound of four stations, best solution is to locate one station at pleasant lake, because over 2000 boats exit Pleasant lake and move out-of-county and locate three inspection stations at un-infested lakes that receive the most boats from out-of-county infested lakes: Turtle, Bald Eagle, and Phalen.
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Ramsey County
Incoming boats from infested lakes (zebra mussel)
Best solution for a maximum of 4 stations:
• 1 infested lake (Pleasant)
• 3 uninfested lakes (Turtle, Bald Eagle, Phalen)
00.10.20.30.40.50.60.70.80.9
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0 2 4 6 8 10Prop
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Number of stations
Presenter
Presentation Notes
We can re-run the optimization model for increasing upper bounds on numbers of inspection stations and observe the maximum number of boats inspected. In this figure, we plot the percent of the boats inspected for increasing number of inspection stations and we see the diminishing returns. Also note that four inspection stations cover about 90% of the watercraft moving from infested to uninfested lakes. This is valuable for evaluating the gains from increasing capacity.
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Washington County
Incoming boats from infested lakes (zebra mussel)
• 31 uninfested lakes• 1 infested lake (Pleasant)• 0 boats from infested lake
in county to uninfested lakes in county
• 2,616 boats from infested lake in county to uninfested lakes outside county
• 3,216 boats from infested lakes outside county to uninfested lakes in county
• 35 uninfested lakes• 2 infested lakes (Forest,
White Bear)• 634 boats from infested
lake in county to uninfected lakes in county
• 3,233 boats from infested lake in county to uninfected lakes outside county (693 to Ramsey County)
• 2,787 boats from infested lakes outside county to uninfected lakes in county
Presenter
Presentation Notes
In Washington County, we have 35 uninfested lakes and two infested lakes: Forest and White Bear.
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Washington County
Incoming boats from infested lakes (zebra mussel)
• 31 uninfested lakes• 1 infested lake (Pleasant)• 0 boats from infested lake
in county to uninfested lakes in county
• 2,616 boats from infested lake in county to uninfested lakes outside county
• 3,216 boats from infested lakes outside county to uninfested lakes in county
• 35 uninfested lakes• 2 infested lakes (Forest,
White Bear)• 634 boats from infested
lake in county to uninfested lakes in county
• 3,233 boats from infested lake in county to uninfested lakes outside county (693 to Ramsey County)
• 2,787 boats from infested lakes outside county to uninfested lakes in county
Presenter
Presentation Notes
634 boats from the two infested lakes to uninfested lakes in county 3,233 boats from the two infested lakes in county to uninfested lakes outside county (693 to Ramsey County) 2,787 boats from infested lakes outside county to uninfested lakes in county
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Washington County
Incoming boats from infested lakes (zebra mussel)
Best solution for upper bound of 4 stations:
• 2 infested lakes (Forest, White Bear)
• 2 uninfested lakes (Goose, Big Marine)
Presenter
Presentation Notes
With an upper bound of four stations, the best solution is to locate stations at the two infested lakes because they export many boats out of county and locate the other two stations at Goose lake and Big Marine lake, which have the highest numbers of incoming boats from infested lakes (inside and outside the county).
0 - 25
26 - 70
71 - 277
278 - 880
881 - 2,596
Washington County
Incoming boats from infested lakes (zebra mussel)
Best solution for a maximum of 4 stations:
• 2 infested lakes (Forest, White Bear)
• 2 uninfested lakes (Goose, Big Marine)
00.10.20.30.40.50.60.70.80.9
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0 1 2 3 4 5 6 7 8 9 10
Prop
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Number of stations
Presenter
Presentation Notes
In this figure, we plot the percent of the boats inspected for increasing number of inspection stations and we see the diminishing returns. Also note that four inspection stations cover about 75% of the watercraft moving from infested to uninfested lakes.
We wanted to know the gains if Ramsey and Washington Counties combined resources and selected lakes for inspection stations jointly. We combine the data for both counties and include boat movement between infested and uninfested lakes between the two counties and well as within counties. For example boats from White Bear and Forest Lakes, which are infested, travel to several infested lakes in Ramsey county as well as Washington County. When we locate eight stations to both counties simultaneously, the solution is different than what we would do separately: five lakes in Washington County and three in Ramsey. The difference is that the station at Lake Phalen in Ramsey is moved to Demontreville Lake in Washington County.
Stations at these eight lakes cover 84% of the boats moving from infested to uninfested lakes (9889 boats out of 11767 boats) For comparison, when stations are located at the best four lakes in each county determined independently, the stations cover 81% of the boats moving from infested to uninfested lakes (9579 out of 11767 boats), two percentage points less then the optimal solution.
Crow Wing County• 23 infested lakes
• 134 uninfested lakes
Z
Presenter
Presentation Notes
Our last example is Crow Wing County, which has we infested lakes and 134 uninfested lakes, ash shown in pink and blue on the attached DNR map
• 8,491 boats from infested lakes in county to uninfested lakes outside county
• 5,978 boats from infested lakes outside county to uninfested lakes in county
Z
Presenter
Presentation Notes
5,272 boats from infested lakes in county to uninfested lakes in county 8,491 boats from infested lakes in county to uninfested lakes outside county 5,978 boats from infested lakes outside county to uninfested lakes in county
Crow Wing CountyBest solution for upper bound of 10 stations:
• 7 infested lakes Edward, Pelican, Whitefish, North Long, Round, Little Rabbit
• 3 uninfested lakes Bay, Horseshoe, Emily
Presenter
Presentation Notes
With an upper bound of ten stations, the best solution is to locate stations at seven of the 23 infested lakes and 3 of the 134 uninfested lakes. These are the infested lakes that export the most boats to uninfested lakes inside and outside the county, and the uninfested lakes that receive the most boats from infested lakes outside the county.
Crow Wing CountyBest solution for a maximum of 10 stations:
• 7 infested lakes Edward, Pelican, Whitefish, North Long, Round, Little Rabbit
• 3 uninfested lakes Bay, Horseshoe, Emily
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Number of stations
Presenter
Presentation Notes
With stations, we can cover about 60% of the boats moving from infested to uninfested lakes. Doubling the number of inspections stations (20) would increase the coverage beyond 80% of the boats.
Conclusions
• Knowing boat movement among lakes, we can set up quantitative measures for evaluating inspection strategies
• This is a work in progress• Inspection costs, potential losses (property value, recreation value)
• Determine inspection locations to maximize expected net benefits (avoided loss minus cost of inspection)
Presenter
Presentation Notes
Work in progress Knowing boat movement among lakes, we can set up quantitative measures for evaluating inspection strategies For example, for counties with few infested lakes, like Ramsey and Washington, and with an objective of maximizing the number of inspected boats moving between infested and uninfested lakes, best solution is put inspections stations at the infested lakes and at uninfested lakes with the most incoming traffic from out-of-county lakes. For counties with a lot of infested lakes, like Crow Wing, it is best to prioritize infested lakes with a lot of boat traffic and uninfested lakes with a lot of incoming traffic from out-of-county.
