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

Kent D. Messer, Maik Kecinski, Xing Tang and Robert H. Hirsch IV


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. (JEL D61, Q24)


Most conservation programs are not cost-effective—often, they are far from it. Although numerous studies have pointed to the benefits of cost-effective conservation (Gardner 1977; Polasky, Camm, and Garber-Yonts 2001; Ando et al. 1998; Kline 2006; Kline and Wichelns 1996; Messer 2006; Wu, Zilberman, and Babcock 2001; Duke, Dundas, and Messer 2013; Babcock et al. 1997; Rosenberger 1998; Malcolm, Duke, and Mackenzie 2005; Naidoo and Ricketts 2006), none so far have measured actual increases in conservation benefits achieved using cost-effective parcel selection methods with on-the-ground data. We examine transactions for 118 parcels in Baltimore County, Maryland, over a three-year period (2007–2009) and illustrate how methods that are truly cost-effective can increase conservation benefits and the number of preserved acres.

Acres of farmland in the state of Maryland dropped from 4 million to 2.2 million between 1950 and 2000 due to residential and commercial development (Lynch and Musser 2001). Maryland’s population, on the other hand, is projected to increase by 1.1 million between 2010 and 2040, and the number of households is expected to increase by 25% during the same period (Maryland Department of Planning 2014a, 2014b). Population growth coupled with declining household size and communication technologies that make it easier for people to work in widely dispersed communities will likely increase demand for land for development and drive further losses of farmland. Between 1987 and 2012, Baltimore County lost 24% of its farmland to de-velopment, and as of 2012, there were 640 farms, 15% fewer than in 2007. In 2012, Baltimore County had 70,419 acres of farmland, down from 78,419 in 2007 (Maryland Department of Planning 2014a, 2014b).

In terms of acres of agricultural conservation easements acquired, Baltimore County ranked in the top 12 local programs in the nation in 2003. The county’s is the first program in the United States to adopt cost-effectiveness analysis as its primary selection method.1 However, the results of this study show that there is room for significant improvement. Given the large number of conservation groups2 and government programs currently operating at state and county levels, we seek to address this multifunding situation through the use of a simultaneous binary integer programing (BIP-SIM) model, also referred to as multiple-knapsack optimization, to take advantage of its ability to combine multiple conservation program efforts to maximize total conservation benefits and acres preserved.

Combining funds from different funding sources provides the advantage of making use of potentially large budget remainders that could exist if funds were optimized individually. These budget remainders may be too small to purchase more parcels or would otherwise be used on low-quality parcels. The combination of funds, therefore, reduces the waste from optimizing for each program separately (see Duke, Dundas, and Messer [2013] for additional discussion of the challenges of budget remainders in the context of conservation programs). Moreover, optimizing multiple knapsacks simultaneously can provide the conservation program the opportunity to purchase parcels that provide substantially more acres or more conservation benefits, but would otherwise be too expensive for an individual program to acquire. This may be of particular importance when a parcel’s value depends on contiguity or adjacency to other protected areas.

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).3 The cost-effectiveness of each method is determined by applying it to the Baltimore County dataset and comparing the derived benefits and preserved acres of each method. The method that produces the largest conservation benefit, ceteris paribus, is the most cost-effective. Given the budget constraints faced by conservation programs, the optimal (efficient) outcome may not be fundable. Hence, it is cost-effectiveness rather than efficiency that such programs seek.

This research makes two important contributions. First, it demonstrates how in situations that involve coordinating funding from multiple sources, a simultaneous optimization model (also referred to as multiple-knapsack optimization) yields substantially more land preserved and conservation benefits for the same amount of expenditure. Second, by using program data from Baltimore County, Maryland, this research shows how conservation programs, when using multiple-knap-sack optimization, can preserve more acres and realize more conservation benefits than BT, CEA, and sequential knapsack optimization.

Our analysis suggests that BIP-SIM is the superior selection method, outperforming BT, CEA, and BIP-SEQ. For example, for 2008 and 2009, BIP-SIM would have spent just 43% of what Baltimore County paid using CEA while yielding 71% of the benefit gained by the county in those two years. If Baltimore County had used simultaneous optimization instead of CEA, the same amount of funds could have protected an additional 242 acres of high-quality agricultural land valued at approximately $1.7 million. Although the data analyzed in this study were collected from Baltimore County, the results are widely applicable and serve as a prototype for how BIP-SIM can provide greater cost-effectiveness in land conservation. The results of this study offer government agencies and nonprofit conservation groups a relatable example of a method that can improve their efforts to generate the greatest possible benefit from a limited budget.


Ongoing losses of farmland, forestland, and open space to development and the ever-limited funding available to conservation organizations increase the importance of cost-effective conservation. By strategically targeting the most desirable agricultural conservation easements, programs can achieve a variety of objectives, including protecting the farmland that is most vulnerable to development, adjusting existing development patterns, forming large contiguous areas of protected open space to provide social and ecological benefits, and reinforcing urban growth boundaries. These conservation activities have a positive impact on the rate and probability of farmland being preserved, block development in unsuitable areas, maintaining rural amenities near urban residents, and controlling growth (Lynch and Liu 2007; Stoms et al. 2009).

Budget constraints typically limit how many parcels conservation programs can acquire. To ensure that the limited quantity of funds is spent responsibly, the programs need to find selection processes that deliver the greatest benefit possible given the budget constraint or preserve a particular number of acres of land at minimal cost. Large sums of public and private money are devoted to the task. The 2008–2012 U.S. Farm Bill allocated $13 billion to land retirement programs alone (see Duke, Dundas, and Messer 2013), and a number of studies have identified and measured the benefits of farmland preservation (Gardner 1977; Kline and Wichelns 1996; Rosenberger 1998; Johnston and Duke 2009; Geoghegan, 2002; Hajkowicz, Collins, and Cattaneo 2009). Cost-effective conservation not only maximizes the benefit, but adheres to the bounds of social responsibility. According to Perhans et al. (2008), cost-effective conservation is always preferred to cost-only or benefit-only models, regardless of the conservation goal.

A common form of parcel selection by government agencies and conservation organizations is BT, which selects the parcels that offer the greatest conservation benefits but does not consider the cost of acquiring the benefits in the decision process. BT selects one parcel at a time, starting with the parcel that the conservation program ranks as the one with the highest conservation value. If available funds are insufficient to purchase the top-ranked parcel, BT proceeds on to the next highest ranked parcel that can be purchased given the available funds. In the situation where multiple parcels rank equally, the one with the lowest cost is acquired first. This process continues until all funds have been spent or the remaining funds are too small to purchase another parcel. BT is not cost-effective and leaves considerable room for improvement. For example, a large literature has shown that binary linear programming models (i.e., constraint optimization) yield substantially greater conservation benefits and preserve more acres of land than BT (Duke, Dundas, and Messer 2013). Additionally, BT does not traditionally adjust its rankings to account for potential benefits that can be achieved via agglomeration of protected areas.

Baltimore County started using CEA as a pilot program in 2007 to find the least costly projects by computing the ratio of the value of the estimated nonmonetary benefit to the actual monetary cost. While the CEA method can be suboptimal in some situations (Messer 2006), it does deliver greater aggregate benefits than BT because it accounts for cost. However, CEA cannot ensure truly optimal results because there may be incentives for landowners to bring previously underdeveloped land into agricultural production in response to higher commodity prices brought about by conservation efforts (Wu, Zilberman, and Babcock 2001; Wu 2004). Knapsack optimization models (BIP-SIM), borrowing from operations research and mathematical programming, deliver cost-effective conservation by ensuring that decisions achieve the greatest amount of benefit possible given the budget (Hajkowicz et al. 2007).

During the past two decades, there has been a rapid increase in the development of mathematical programming models, mainly due to advances in heuristic methodologies and computing power (Higgins and Hajkowicz 2007). Mathematical programming has applications in land allocation planning (Mallawaarachchi and Quiggin 2001), watershed protection (Ferraro 2003), connection of fragmented landscapes (Williams and Snyder 2005), and soil conservation (McSweeny and Kramer 1986), among others. Although knapsack models deliver cost-effective conservation for individual conservation programs, there is potential room for improvement when considering conservation efforts by multiple groups simultaneously rather than sequentially. Specifically, sequential parcel selection may not fully take advantage of disparities in appraised parcel values and the thresholds for conservation of various programs. In addition, individual program budgets may be underutilized because of poor coordination between programs.

To address these issues, we introduce a multiple-knapsack problem involving several programs that are coordinating their efforts to establish the most cost-effective plan for purchasing easements. The multiple-knapsack model has been widely applied to various fields, including capital budgeting projects (Koc et al. 2009), municipal construction (Kozanidis, Melachrinoudis, and Solomon 2005), and the shipping industry (Ang, Cao, and Ye 2007). However, to the best of our knowledge, this is the first time it has been applied to land conservation. By adopting a multiple-knap-sack model, we take advantage of remainders of budgets to improve cost-effectiveness and escape the sequential time constraint.

Fooks and Messer (2012) point out that conservation professionals face numerous political and strategic difficulties when adopting cost-effective conservation. Typically, the programs receive funds from multiple sources, both private and public, and are expected to represent those interests accordingly. For example, private funders may expect particular parcels to be preserved, including parcels that might not receive consideration otherwise. Given that these difficulties arise within a single program, we expect that a simultaneous knapsack model that combines funds from multiple groups is likely to also present political and strategic challenges. In addition, coordination problems could arise between programs and potentially increase the cost of transactions.


Benefit Targeting

Consider a set of I parcels where parcel i offers conservation benefit vi and costs ci. Let Ri denote the rank of parcel i among the I parcels with respect to vi. The BT selection algorithm essentially prioritizes parcels for purchase according to their rank, Ri. Parcel i is selected first for purchase when Ri = 1, and parcel −i is selected second when Ri =2. The selection process ends when all allocated funds have been depleted or the funds that remain are insufficient to purchase the next parcel. Parcels with the same rank are selected according to least cost. BT is a popular method used in land conservation because of its simplicity and convenience. And given its simplicity, it is also a relatively transparent process, a characteristic that is important to landowners and conservation professionals (Hajkowicz et al. 2007; Messer et al. 2014). Since BT ignores the cost associated with purchasing each parcel, the process typically selects a few parcels that offer relatively large conservation benefits even if those parcels are relatively expensive per the amount of benefit provided, and thus it is not cost-effective. Since the cost of farmland tends to be heterogeneous, especially when some of it is considered attractive for development, applying BT to land conservation tends to preserve fewer parcels and fewer acres of farmland. Moreover, BT is inconsistent; increases in the budget do not necessarily improve the portfolio of overall achieved conservation benefits. Therefore, with BT, money may be wasted on a few high-ranking parcels that generate smaller total benefits.

Cost-effectiveness Analysis

Programs funded by Baltimore County currently use CEA as their selection method. CEA operates under the same procedure as BT but ranks the parcels by a ratio (Ri) of conservation benefit vi to cost ci, rather than solely targeting benefits. CEA inherits BT’s advantages—convenience, simplicity, and transparency—and outperforms BT in terms of cost-effectiveness, delivering results that approach an optimal outcome. Optimality is not guaranteed, though, since this method, unlike binary integer programming, fails to take all potential alternatives into account when selecting the portfolio. As under BT, an increase in budget does not necessarily improve the outcome under CEA.

Sequential Binary Integer Programming

A BIP-SEQ model is also known as a knapsack model. It is an optimization algorithm that identifies optimal portfolios of conservation sites (Kaiser and Messer 2011). Consider a set of N = {1, . . ., n } items and a set of M = {1,...,m } knapsacks (portfolios of items). Every item, iN, has a weight of wi>0 and a benefit of ui>0. Every knapsack, jM, has a capacity of ej>0. Some items cannot be assigned to some knapsacks; thus, assignment of item i is limited to the set of AiM. The following assumption is imposed: wi < ej. That is, every knapsack has enough capacity for any item i. The objective is to fill the knapsack with a collection of items that will yield the maximal benefit. BIP-SEQ takes one knapsack at a time, fills it with items to obtain the greatest possible benefit, and then moves on to the next knapsack. This mechanism ensures that each knapsack is optimized given the choice of items available for it. The aggregate benefit of all of the knapsacks is calculated as the sum of the optimized benefits from each knapsack.

In the case of land preservation, each con-servation program is a knapsack with a budget limit, Bj, that represents the program’s capac-ity, ej. The selection process aims to fill the conservation programs’ knapsacks with land parcels to achieve the greatest possible con-servation benefit.

Suppose there are I parcels and J conservation programs. The decision variables of the model take the form of xi,j = (0,1) where 0 denotes that parcel i is not recommended for purchase by program j and 1 denotes that parcel i is recommended for purchase by program j. The objective function seeks to maximize the conservation benefit for program j. In the following model specification, the constraint in equation [2] ensures that only one program can purchase an easement but an easement need not be purchased. The constraint in equation [3] ensures that any purchase made is constrained by the program’s budget. Embedded Image [1] such that Embedded Image [2] and Embedded Image [3]

In Baltimore County’s case, the Maryland Agricultural Land Preservation Foundation (MALPF) takes index j = 1, and the county programs take indices j = 2, 3, 4. Thus, if xi,j = 1, xi,j +1. . .,xi,J = 0, and a parcel that has been sold cannot be included in future program selections. In the model, vi denotes the conservation benefit for parcel i, Bj denotes the budget for program j, and ci,j denotes the cost of parcel i in program j. After the selections are made for all programs J, we calculate the aggregate conservation benefit. BIP-SEQ is solved using Risk Solver Platform V9.5 in Microsoft Excel (Frontline Solvers 2015).

Simultaneous Binary Integer Programming

Unlike BIP-SEQ, BIP-SIM seeks to fill all of the knapsacks (programs’ budgets) simultaneously, ensuring that each is optimized for the entire set of items available. Multiple-knapsack optimization has not previously been explored in the land conservation literature, even though it can provide potentially large additional conservation benefits, acres, and parcels compared to the sequential approach. Again, suppose there are I parcels and J conservation programs. The decision variables of the model take the form of xi,j = {0,1}, where 0 denotes that parcel i is not recommended for purchase by program j and 1 denotes that parcel i is recommended for purchase by program j. The objective function seeks to maximize the aggregate conservation value for J programs, subject to the same constraints as under BIP-SEQ. Embedded Image [4] such that Embedded Image [5] and Embedded Image [6]

Again, Microsoft Excel’s Risk Solver Platform V9.5 is used to run the optimization model.

Case Study: Selection of Farmland Preservation in Baltimore County

Historically, the process of acquiring easements in Baltimore County began with a voluntary formal application for participation by owners of parcels that met the entry threshold requirements of the program. Once the applications were submitted, the conservation benefits of the parcels were appraised and ranked quantitatively.

To evaluate the potential conservation benefits of the parcels, Baltimore County staff have relied on Land Evaluation and Site Assessment (LESA) scores. Developed in the 1980s by the U.S. Department of Agriculture Soil Conservation Service, LESA is composed of two parts: land evaluation and site assessment (Zurbrugg and Sokolow 2006). The land evaluation score focuses primarily on the productivity of the soils, where the parcel’s soil quality is assigned a relative value between 0 and 100, with 0 being the worst and 100 the best. The site assessment score evaluates the property on a number of factors such as its location in terms of development pressure, the distance to towns and cities, the quality of roads adjacent to the sites, availability of sewer and water, and agricultural support services. Since a parcels’ LESA score comes from the average of its per-acre scores, problems can arise when using this value for maximization (Messer and Allen 2010). To avoid this problem, in this analysis, the LESA values were scaled by parcel size to determine the parcel’s overall conservation benefits.4

Since the 1990s, Baltimore County has administered two pools of funding related to agricultural lands preservation programs: funds from the state-level MALPF program and funds from a county-level program. Initially these separate pools arose due to state funding cutbacks and a desire by the county to con-tinue preserving agricultural lands. During times when state funding was more abundant, the county program continued to help accelerate the rate of conservation. Over time, the programs have evolved to be different with regard to deadlines, entry requirements, source of funds, pricing policies, and annual budgets. MALPF is funded via cost-sharing between the state of Maryland and Baltimore County. This program uses appraisals to set the willingness to pay for the program and has fewer requirements for entry, and its budgets are set primarily by the state. The Baltimore County program is funded primarily by the county, uses a formula to set its willingness to pay (the maximum amount increases with parcels’ soil quality, size, and the number of development rights conveyed), and has more requirements for entry; its budgets are set exclusively by the county. Additionally, MALPF has an earlier application deadline, so some applicants make the county deadline but are too late for consideration by the MALPF program. Due to these differences, selection of parcels by each program traditionally has been done in a sequential manner with one program selecting parcels at a time, as shown in Figure 1.5


Sequential Selection Method Used by Baltimore County

This study’s dataset consists of information on 118 parcels that were submitted to conservation programs in Baltimore County, Maryland, from 2007 to 2009. Table 1 provides descriptive statistics of the candidate parcels in the dataset, including the program funds available, the cost of acquiring all of the qualified easements, and the percent variance between the budget and the total acquisition cost, which reflects the sufficiency of the budget. MALPF’s appraisal of the value of the candidate parcels in 2007 averaged $399,902 per parcel, 31% greater than the county appraisal of $304,306. In 2008, only 13 parcels satisfied the state program’s threshold. MALPF’s average appraisal value per parcel was $860,635, 15% greater than the county average of $748,782. In 2009, the appraisal value of MALPF’s average parcel was 80% greater than the county’s. Since MALPF consistently assigned higher appraisal values than the county programs, landowners preferred to sell the easements to the state program. Parcels that qualified for the state program, on average, had higher LESA scores and more acres than parcels that qualified only for county programs. Thus, the pool of candidate easements that qualified only for MALPF generated greater benefits under LESA.


Descriptive Statistics of Dataset of Participating Easements

The average cost per acre of easement, $6,715.98, was calculated by averaging the information for the state and county appraisals for all three years: (total cost of all candidate easements/total number of qualifying easements and total acres per easement)/6. The average cost per conservation benefit, $112.76, was calculated by dividing the sum of all of the easement costs by the sum of the easements’ conservation benefits. We use these averages in the results section to calculate any savings that would have resulted from using a different parcel selection method.


The results of applying each method to the 118 parcels in the dataset are presented in Tables 24 and Figures 2 and 3. Table 2 shows the results of comparing BT and CEA. 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.6 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 protects 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) are multiplied by the average cost per acre ($6,715.98). The reported cost-savings values shown in Tables 24 are all calculated as average cost per conservation benefit in dollars and average cost per acre in dollars to monetize the changes. Applying CEA instead of BT allows Baltimore County to improve both the number of acres preserved and the amount of conservation benefit.7


Conservation Benefits Achieved by Each Method for 2007–2009 and Total (BT, Benefit Targeting; CEA, Cost-effectiveness Analysis; BIP-SEQ, Sequential Binary Integer Programming; BIP-SIM, Simultaneous Binary Integer Programing)


Acres Preserved by Each Optimization Method for 2007–2009 and Total (BT, Benefit Targeting; CEA, Costeffectiveness Analysis; BIP-SEQ, Sequential Binary Integer Programming; BIP-SIM, Simultaneous Binary Integer Programing)


Comparison of Results of Benefit Targeting (BT) and Cost-effectiveness Analysis (CEA) Methods

Table 3 reports the comparison of CEA and BIP-SEQ. As previously noted, 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. As shown in Table 3, BIP-SEQ consistently outperforms CEA and BT in terms of acquired conservation benefits. Over the three-year observation period, the conservation benefit generated by BIP-SEQ is 8,115 greater than the benefit achieved by CEA, a 3.2% ($0.9 million) improvement. Since BT slightly outperforms 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.


Comparison of Results of Cost-effectiveness Analysis (CEA) and Sequential Binary Integer Programming (BIP-SEQ) Methods

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 provides relative to CEA. However, the argument is less important when considering a simultaneous knapsack optimization problem because BIP-SIM’s improvements are substantial.

Table 4 presents the comparison of BIP-SEQ to BIP-SIM. BIP-SIM preserves an additional 3 (0.0%) conservation benefits and19 (1.1%) more acres than BIP-SEQ in 2007. In 2008, BIP-SIM yields 9.6% greater conservation benefits and 7.2% more acres than BIP-SEQ. In 2009, it produces 7.3% greater conservation benefits and 4.6% more acres. For 2008 and 2009 combined, BIP-SIM generates 71% of the total benefits obtained with BIP-SEQ, while spending only 43% the amount spent by BIP-SEQ. Over the three-year study period, compared to BIP-SEQ, BIP-SIM pro-tects an additional 181 high-quality acres worth $1.2 million.


Comparison of Sequential Binary Integer Programming (BIP-SEQ) and Simultaneous Binary Integer Programming (BIP-SIM) Models

BIP-SIM also produces better results than CEA, which was used by the county programs during those years. Over the three-year period, BIP-SIM generates 9.1% greater conservation benefits, an improvement valued at $2.6 million. BIP-SIM protects 6.0% more acres of land that are worth $1.6 million.

When we compare BIP-SIM to BT, the cost saving is $5.5 million in terms of conservation benefits and $5.6 million in terms of preserved acreage over three years. Figures 2 and 3 present the results of each conservation method in terms of conservation benefits and acres preserved. For all three years combined, in terms of both conservation benefits and acres, BIP-SIM outperforms the other three methods.

As with BIP-SEQ, a disadvantage of BIP-SIM is the need for software and sophisticated programming. The complexity of a simultaneous analysis increases substantially as the number of candidate parcels rises. Nonetheless, the results confirm the superiority of binary integer programming in securing the best possible portfolios for conservation programs. When we relax the constraint of sequential parcel selection, cost-effectiveness improves and conservation professionals in the various programs can coordinate their selection plans optimally.


Traditionally, both regional and federal conservation programs have used BT to select parcels of land for preservation. That method, though not cost-effective, has the advantage of being simple, convenient, and transparent, making it easy to implement for conservation professionals, who may not set cost-effectiveness as the top priority. However, it can be argued that conservation professionals who work for government agencies have a responsibility to conserve the greatest amount of benefits possible from the public and private funds used for conservation. Economists have proposed multiple techniques for improving the selection process to make it more cost-effective. We chose three methods that are used in land preservation—BT, CEA, and BIP-SEQ—and compared their effectiveness to BIP-SIM. All four methods were applied to data collected from Baltimore County, Maryland. Baltimore County introduced CEA as its primary parcel-selection method in 2007 as a pilot program in an effort to improve cost-effectiveness.

First, the results show that Baltimore County was able to improve the amount of conservation benefits by 11.2% and acres preserved by 17.2% using CEA instead of BT. Second, the results suggest that Baltimore County’s benefits and acres preserved can be further improved using more complex mathematical programming techniques. Specifically, BIP-SEQ can do slightly better than CEA, and BIP-SIM can do substantially better than CEA. Using BIP-SIM instead of BIP-SEQ provides an additional 5.7% in total conservation benefits on top of the 3.2% increase provided by BIP-SEQ. In terms of total acres, BIP-SIM preserves 4.4% more than BIP-SEQ, which preserves 1.5% more than CEA.

Although CEA substantially improves selection of the “best” parcels for a conservation program relative to BT, it cannot guarantee cost-effectiveness, and thus, more complex tools are needed. BIP-SIM’s mathematical complexity and resource consumption (financial and technical) may present significant challenges in introducing its use. However, various programs could jointly invest in the software and training to reduce the impact on individual programs. Losing the simplicity, convenience, and transparency that make BT an attractive method can be addressed through training for conservation staff members and educational seminars for landowners, another cost that could be shared by multiple agencies.

In sum, this study is the first application of multiple-knapsack optimization to land conservation. The presented theoretical model shows how conservation programs can improve the cost-effectiveness of their conservation efforts, and this model has been applied to data from agricultural land preservation programs in Baltimore County, Maryland. Baltimore County’s program is the first case of true cost-effective conservation in the United States. Both the model and its application can serve as an example for other state, regional, and federal conservation programs endeavoring to improve the conservation benefits obtained with their available funds.


We would like to thank Wally Lippincott from Baltimore County for his support. Funding was provided by the U.S. Department of Agriculture Economic Research Service (58-6000-1-0037 and 59-6000-4-0064 (CBEAR)) and the National Science Foundation #EPS-1301765.


  • The authors are, respectively, Unidel Howard Cosgrove Chair for the Environment and professor, Department of Applied Economics and Statistics, University of Delaware, Newark; postdoctoral researcher, Department of Applied Economics and Statistics, University of Delaware, Newark; graduate student, Department of Applied Economics and Statistics, University of Delaware; and Baltimore County natural resource specialist, Baltimore County Department of Environmental Protection and Sustainability, Towson, Maryland.

  • 1 Baltimore County first introduced CEA in 2007. Due to resulting gains in conservation benefits and acres preserved, the county has continued to use CEA with clearly identifiable and measurable success. For example, in 2012, the county was able to preserve an additional 852 acres with a 10% gain in conservation benefits compared to the previously used method, BT (data provided by Baltimore County Department Environmental Protection and Sustainability).

  • 2 According to the 2010 census report by the National Land Trust, there were 1,723 land trust organizations in the United States; 1,699 were state and local groups and 24 were national land trusts, and together the groups had secured 47 million acres by the end of 2010.

  • 3 BT is used in a number of local and state conservation programs throughout the United States, such as the Maryland GreenPrint Program (Messer 2006), Great Outdoors Colorado, Delaware’s Open Space Program (Wiest, Shriver, and Messer 2014), the Florida Forever program, New Jersey’s Green Acres program, and Pennsylvania’s Dirt and Gravel Road program for nonpoint source pollution prevention (Fooks and Messer 2013). Federal programs that use BT include the U.S. Fish and Wildlife Service (Wu 2004), the U.S. Department of Agriculture’s Forest Legacy Program (Fooks and Messer 2012), the U.S. Department of Defense’s Readiness and Environmental Protection Integration program (Messer et al. 2015), and the National Park service’s establishment and funding for national parks (Babcock et al., 1997; Wu, Zilberman, and Babcock 2001). Programs that use elements of CEA include the U.S. Department of Agriculture’s Conservation Reserve Program and Environmental Quality Incentives Program (Wu, Zilberman, and Babcock 2001) and the Wetlands Reserve Program (Hellerstein and Nickerson 2006).

  • 4 Measuring the quality of the environmental benefits can be done in variety of ways. For example, the Conservation Reserve Program uses the Environmental Benefits Index. However, the general findings of this paper should apply to a wide variety of benefit scoring systems.

  • 5 The selection process varied slightly during those three years. In 2008, the parcels had to have a threshold LESA score of 61 to qualify for consideration by MALPF. The threshold was set at roughly the mean of the scores of all of the parcels in the applicant pool and had the effect of removing parcels of below-average quality. The county-level programs required parcels to have development potential or to be located in an agricultural preservation or “rural legacy” area to qualify for the county round. In 2007 and 2009, no such requirements were placed on candidate parcels. These variations did not substantively affect the results of the analysis presented in this paper.

  • 6 Data made available by the Baltimore County Department of Environmental Protection and Sustainability show that the county was able to report an additional conservation benefit of $1.2 million for 2010 through 2014 by using CEA instead of BT.

  • 7 For large budget remainders, CEA may provide lower results compared to BT (Duke, Dundas, and Messer 2013). This is evident in 2008 where BT produced slightly lower conservation benefits. In this particular case the budget remainder is $391,393, which was too low to purchase any of the remaining parcels.