Wednesday, June 15, 2016

Multiple-Knapsack Optimization in Land Conservation: Results from the First Cost-effective Conservation Program in the United States

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.
Photo of a small road surrounded by trees on the Agricultural Center property. 
by Kent D. Messer, Maik Kecinski, Xing Tang, and Robert H. Hirsch IV
Land Economics
Volume. 92, Number 1; February 1, 2016; pages 117-130

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