Abstract
Conservation groups often piece together their parcel selections by combining funds from multiple sources. When applying multiple-knapsack optimization, substantial increases in conservation benefits, acreage, and number of parcels preserved can be achieved. Specifically, we show that multiple-knapsack optimization substantially outperforms benefit targeting, cost-effectiveness analysis, and sequential binary integer programming. This study uses data from the first known cost-effective land conservation program in the United States—in Baltimore County, Maryland—and shows that multiple-knapsack optimization can deliver additional benefits.
http://www.baltimorecountymd.gov/Agencies/recreation/countyparks/mostpopular/agcenter.html
Conservation groups often piece together their parcel selections by combining funds from multiple sources. When applying multiple-knapsack optimization, substantial increases in conservation benefits, acreage, and number of parcels preserved can be achieved. Specifically, we show that multiple-knapsack optimization substantially outperforms benefit targeting, cost-effectiveness analysis, and sequential binary integer programming. This study uses data from the first known cost-effective land conservation program in the United States—in Baltimore County, Maryland—and shows that multiple-knapsack optimization can deliver additional benefits.
...
In addition to analyzing data using multiple-knapsack optimization, this study
compares the performance of three popular methods used by conservation professionals:
(1) benefit-targeting (BT), (2) cost-effectiveness analysis (CEA), and (3) sequential binary
integer programming (BIP-SEQ).
Overall, CEA achieves greater conservation benefits, and acquires both more acres and
more parcels than BT. During the study period, the conservation benefits generated by CEA
are 11.2% ($2.8 million) greater than those generated by BT. To convert the additional
benefits achieved through CEA into a dollar value, we multiply the additional benefit
achieved (25,521) by the average cost per conservation benefit ($112.76). When
considering total acres preserved, CEA protected an additional 596.3 acres valued at $4
million, a 17.2% improvement over BT. To compute the monetary value for the additional acres preserved, the additional acres (596.3) were multiplied by the average cost per acre
($6,715.98).... Applying CEA instead of BT allowed Baltimore County to improve
both the number of acres preserved and the amount of conservation benefit....
CEA does
not consistently provide and cannot guarantee cost-effective outcomes because it cannot
consider the entire range of options. Binary programming, on the other hand, can. BIP-SEQ consistently outperforms CEA and BT in terms of acquired
conservation benefits. Over the three-year observation period, the conservation benefits
generated by BIP-SEQ was 8,115 greater than the benefit achieved by CEA, a 3.2% ($0.9
million) improvement. Since BT slightly outperformed CEA in 2008 in terms of
conservation benefits, we compare BT to BIP-SEQ. Not surprisingly, BIP-SEQ outperforms
BT by increasing the conservation benefits by 5,033 ($567,521). In terms of acres
preserved, BIP-SEQ selects fewer acres in 2007 and 2009 because parcel size is not the
target of the maximization problem. Moreover, parcel size and conservation benefits are
not always perfectly associated; smaller parcels may score higher in terms of conservation
benefits if they provide benefits related to biodiversity or have other especially beneficial
properties. Nonetheless, over the three-year period, BIP-SEQ acquires 61 more acres
(valued at $0.4 million) than CEA.
Although BIP-SEQ is superior to CEA in terms of conservation benefits, the
suitability of applying mathematical programming to all conservation programs is debatable. BIP-SEQ’s increase in conservation benefits (3.2%) and acres (1.5%) over CEA is
not as substantial as CEA’s improvements over BT (11.2% and 17.2%, respectively). Also,
BIP-SEQ normally requires investments in software and training that may reduce the
budget available for conservation. Binary programming is less convenient, less transparent,
and more difficult for conservation professionals to use and for landowners to understand.
This argument against binary programming is important when considering the rather small
addition in overall benefit it provided relative to CEA. However, the argument is
significantly less important when considering a simultaneous knapsack optimization
problem because BIP-SIM’s improvements are substantial.
... 
by Kent D. Messer, Maik Kecinski, Xing Tang, and Robert H. Hirsch IV
http://le.uwpress.org/content/92/1/117.abstract
http://le.uwpress.org/content/92/1/117.abstract
Land Economics http://le.uwpress.org
Volume. 92, Number 1; February 1, 2016; pages 117-130
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