I. Esra Büyüktahtakın

A stochastic multi-criteria decision analysis for sustainable biomass crop selection

We propose a stochastic analytical hierarchy process (SAHP) method.Sustainable biomass crop selection has economic, environmental, and social dimensions.Switchgrass is found to be the most sustainable crop type for biofuel production.Wheat and corn get high scores if economic factor is emphasized in decision making.The proposed SAHP model can utilize imprecise expert opinions in decision making. Selecting the most sustainable biomass crop type for biofuel production is a multi-criteria decision-making (MCDM) problem involving various conflicting criteria. In this paper, we propose a unique stochastic analytical hierarchy process (AHP) that can handle uncertain information and identify weights of criteria in the MCDM problem. By utilizing the beta distribution and approximating its median, we convert various types of expert evaluations including imprecise values into crisp values. We ensure consistency in each evaluation matrix before aggregating expert judgments. We then demonstrate use of the model by applying it to sustainable biomass crop selection. In order to define a comprehensive list of the selection criteria, we utilize the existing literature and opinions of experts including farmers, government specialists from the U.S. Department of Agriculture (USDA), and faculty members in the areas of biomass and bioenergy. The evaluation model includes three main sustainability criteria defined as economic, environmental, and social aspects associated with a total of 16 sub-criteria. We apply the proposed model to biomass alternatives including switchgrass, Miscanthus, sugarcane, corn, and wheat in Kansas. Results show the weights of economic, environmental, and social aspects to be 0.59, 0.26, and 0.15, respectively. The sensitivity analysis indicates that the score of switchgrass increases if environmental criteria are emphasized. On the other hand, wheat and corn become more favorable than other alternatives if priority is given to economic factors. The most sustainable biomass sources in different regions can be determined by applying the presented selection hierarchy. The proposed stochastic AHP methodology can also be utilized for other complex multi-criteria decision-making problems with uncertain information and multiple stakeholders.

A dynamic model of controlling invasive species

A dynamic model of controlling invasive weeds is first developed which is a large scale, nonlinear 0-1 integer programming problem. This model is then applied for the case of control of the invasive grass, Pennisetum ciliare (buffelgrass), in the Arizona desert. The large size of the problem makes the application of direct optimization methods impossible, instead the most frequently suggested strategies were analyzed and their consequences compared. The model is more advanced and complex than those examined in earlier studies.

Dynamic-programming-based inequalities for the capacitated lot-sizing problem

Iterative solutions of forward dynamic programming formulations for the capacitated lot sizing problem are used to generate inequalities for an equivalent integer programming formulation. The inequalities capture convex and concave envelopes of intermediate-stage value functions and can be lifted by examining potential state information at future stages. Several possible implementations that employ these inequalities are tested and it is demonstrated that the proposed approach is more efficient than alternative integer programming–based algorithms. For certain datasets, the proposed algorithm also outperforms a pure dynamic programming algorithm for the problem.

Invasive species control optimization as a dynamic spatial process: an application to buffelgrass (Pennisetum ciliare) in Arizona.

Abstract Buffelgrass (Pennisetum ciliare) is a fire-prone, African bunchgrass spreading rapidly across the southern Arizona desert. This article introduces a model that simulates buffelgrass spread over a gridded landscape over time to evaluate strategies to control this invasive species. Weed-carrying capacity, treatment costs, and damages vary across grid cells. Damage from buffelgrass depends on its density and proximity to valued resources. Damages include negative effects on native species (through spatial competition) and increased fire risk to land and buildings. We evaluate recommended “rule of thumb” control strategies in terms of their ability to prevent weed establishment in newly infested areas and to reduce damage indices over time. Two such strategies—potential damage weighting and consecutive year treatment—used in combination, provided significant improvements in long-term control over no control and over a strategy of minimizing current damages in each year. Results suggest specific recommendations for deploying rapid-response teams to prevent establishment in new areas. The long-run population size and spatial distribution of buffelgrass is sensitive to the priority given to protecting different resources. Land managers with different priorities may pursue quite different control strategies, posing a challenge for coordinating control across jurisdictions. Nomenclature: Buffelgrass, Pennisetum ciliare (L.) Link. Management Implications: A key challenge facing land managers is how best to allocate limited resources to control invasive plant species across space and time. Optimization models are useful tools for exploring alternative strategies to optimally allocate scarce resources, such as treatment control teams and budgets, and to protect valued resources from invasion of nonnative species. In this article, we developed a mathematical model to provide guidance to land managers for addressing the following concerns: (1) the optimal size of treatment teams; (2) where, when, and what size of infestation those teams should target; and (3) the number of years for which follow-up treatments should continue. Because of the many variables interrelated across both space and time, solving such a completely forward-looking (i.e., takes full account of how all current decisions affect all future options and decisions) problem may prove intractable. Instead, we compare three “rules-of-thumb” strategies: (1) minimize current invasive species damage; (2) minimize current damage, given that any areas treated are treated in at least 3 consecutive yr; and (3) prioritize treatment based not only on current damages but also on the potential future damages of leaving an infested area untreated. The second and third strategies are also considered in combination. We evaluate those rules of thumb for their ability to prevent weed establishment in newly infested areas and to reduce damage indices over time. The rules have the advantage of telling land managers to “treat these lands now.” Another advantage of this approach is its applicability because Microsoft Excel spreadsheets—used broadly by land and resource managers in the area—are customized to (1) manage data layers, (2) use cell formulae to maintain relationships across space and time, and (3) use the chart function to produce maps of costs, damages, weed population, and treatment recommendations. The ILOG CPLEX software package (IBM), a powerful tool for solving linear integer (binary) programs, interfaces with Excel programs so that model solutions can be readily converted to treatment priority (and other) maps. We found that the long-run population size and spatial distribution of buffelgrass are sensitive to priority weights for protecting resources. Results also indicate that resources must be increased because they are currently insufficient to control the spread of buffelgrass.

A multi-objective optimization approach for invasive species control

In this paper, we formulate and analyse a long-term multi-objective dynamic model for controlling invasive species. This optimization framework is then applied to the case of buffelgrass control in the Arizona desert. The proposed model simultaneously optimizes three objectives corresponding to three different valued and threatened resources including saguaros (a native cactus species), buildings and vegetation. The model is used to decide the optimal allocation of labour to these resources to control the population of the species in a multi-period planning horizon. The computational method to solve this problem is based on multi-objective integer programming.

Optimizing invasive species management: A mixed-integer linear programming approach

Controlling invasive species is a highly complex problem. The intricacy of the problem stems from the nonlinearity that is inherent in biological systems, consequently impeding researchers to obtain timely and cost-efficient treatment strategies over a planning horizon. To cope with the complexity of the invasive species problem, we develop a mixed-integer programming (MIP) model that handles the problem as a full dynamic optimization model and solves it to optimality for the first time. We demonstrate the applicability of the model on a case study of sericea (Lespedeza cuneata) infestation by optimizing a spatially explicit model on a heterogeneous 10-by-10 grid landscape for a seven-year time period. We evaluate the solution quality of five different linearization methods that are used to obtain the MIP model. We also compare the model with its mixed-integer nonlinear programming (MINLP) equivalent and nonlinear programming (NLP) relaxation in terms of solution quality. The computational superiority and realism of the proposed MIP model demonstrate that our model has the potential to constitute the basis for future decision-support tools in invasive species management.

A review of operations research models in invasive species management: state of the art, challenges, and future directions

Invasive species are a major threat to the economy, the environment, health, and thus human well-being. The international community, including the United Nations’ Global Invasive Species Program (GISP), National Invasive Species Council (NISC), and Center for Invasive Species Management (CISM), has called for a rapid control of invaders in order to minimize their adverse impacts. The effective management of invasive species is a highly complex problem requiring the development of decision tools that help managers prioritize actions most efficiently by considering corresponding bio-economic costs, impacts on ecosystems, and benefits of control. Operations research methods, such as mathematical programming models, are powerful tools for evaluating different management strategies and providing optimal decisions for allocating limited resources to control invaders. In this paper, we summarize the mathematical models applied to optimize invasive species prevention, surveillance, and control. We first define key concepts in invasive species management (ISM) in a framework that characterizes biological invasions, associated economic and environmental costs, and their management. We then present a spatio-temporal optimization model that illustrates various biological and economic aspects of an ISM problem. Next, we classify the relevant literature with respect to modeling methods: optimal control, stochastic dynamic programming, linear programming, mixed-integer programming, simulation models, and others. We further classify the ISM models with respect to the solution method used, their focus and objectives, and the specific application considered. We discuss limitations of the existing research and provide several directions for further research in optimizing ISM planning. Our review highlights the fact that operations research could play a key role in ISM and environmental decision-making, in particular closing the gap between the decision-support needs of managers and the decision-making tools currently available to management.

A new epidemics–logistics model: Insights into controlling the Ebola virus disease in West Africa

Compartmental models have been a phenomenon of studying epidemics. However, existing compartmental models do not explicitly consider the spatial spread of an epidemic and logistics issues simultaneously. In this study, we address this limitation by introducing a new epidemics–logistics mixed-integer programming (MIP) model that determines the optimal amount, timing and location of resources that are allocated for controlling an infectious disease outbreak while accounting for its spatial spread dynamics. The objective of this proposed model is to minimize the total number of infections and fatalities under a limited budget over a multi-period planning horizon. The present study is the first spatially explicit optimization approach that considers geographically varying rates for disease transmission, migration of infected individuals over different regions, and varying treatment rates due to the limited capacity of treatment centers. We illustrate the performance of the MIP model using the case of the 2014–2015 Ebola outbreak in Guinea, Liberia, and Sierra Leone. Our results provide explicit information on intervention timing and intensity for each specific region of these most affected countries. Our model predictions closely fit the real outbreak data and suggest that large upfront investments in treatment and isolation result in the most efficient use of resources to minimize infections. The proposed modeling framework can be adopted to study other infectious diseases and provide tangible policy recommendations for controlling an infectious disease outbreak over large spatial and temporal scales.

Dynamic programming approximation algorithms for the capacitated lot-sizing problem

This paper provides a new idea for approximating the inventory cost function to be used in a truncated dynamic program for solving the capacitated lot-sizing problem. The proposed method combines dynamic programming with regression, data fitting, and approximation techniques to estimate the inventory cost function at each stage of the dynamic program. The effectiveness of the proposed method is analyzed on various types of the capacitated lot-sizing problem instances with different cost and capacity characteristics. Computational results show that approximation approaches could significantly decrease the computational time required by the dynamic program and the integer program for solving different types of the capacitated lot-sizing problem instances. Furthermore, in most cases, the proposed approximate dynamic programming approaches can accurately capture the optimal solution of the problem with consistent computational performance over different instances.

A mixed-integer programming approach to the parallel replacement problem under technological change

The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement policies for each asset in a group of assets that operate in parallel and are subject to fixed and variable purchase costs. We study the mixed-integer programming formulation of PRES under technological change by incorporating capacity gains into the model such that newer, technologically advanced assets have higher capacity than assets purchased earlier. We provide optimal solution characteristics and insights about the economics of the problem and derive associated cutting planes for optimising the problem. Computational experiments illustrate that the inequalities are quite effective in solving PRES under technological change instances.