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This study presents a new risk-averse multi-stage stochastic epidemics-ventilator-logistics compartmental model to address the resource allocation challenges of mitigating COVID-19. This epidemiological logistics model involves the uncertainty of untested asymptomatic infections and incorporates short-term human migration. Disease transmission is also forecasted through a new formulation of transmission rates that evolve over space and time with respect to various non-pharmaceutical interventions, such as wearing masks, social distancing, and lockdown. The proposed multi-stage stochastic model overviews different scenarios on the number of asymptomatic individuals while optimizing the distribution of resources, such as ventilators, to minimize the total expected number of newly infected and deceased people. The Conditional Value at Risk (CVaR) is also incorporated into the multi-stage mean-risk model to allow for a trade-off between the weighted expected loss due to the outbreak and the expected risks associated with experiencing disastrous pandemic scenarios. We apply our multi-stage mean-risk epidemics-ventilator-logistics model to the case of controlling COVID-19 in highly-impacted counties of New York and New Jersey. We calibrate, validate, and test our model using actual infection, population, and migration data. We also define a new region-based sub-problem and bounds on the problem and then show their computational benefits in terms of the optimality and relaxation gaps. The computational results indicate that short-term migration influences the transmission of the disease significantly. The optimal number of ventilators allocated to each region depends on various factors, including the number of initial infections, disease transmission rates, initial ICU capacity, the population of a geographical location, and the availability of ventilator supply. Our data-driven modeling framework can be adapted to study the disease transmission dynamics and logistics of other similar epidemics and pandemics.

We derive a nested risk measure for a maximization problem and implement it in a scenario-based formulation of a multi-stage stochastic mixed-integer programming problem. We apply the risk-averse formulation to the surveillance and control of a non-native forest insect, the emerald ash borer (EAB), a wood-boring beetle native to Asia and recently discovered in North America. Spreading across the eastern United States and Canada, EAB has killed millions of ash trees and cost homeowners and local governments billions of dollars. We present a mean-Conditional Value-at-Risk (CVaR), multi-stage, stochastic mixed-integer programming model to optimize a manager’s decisions about surveillance and control of EAB. The objective is to maximize the benefits of healthy ash trees in forests and urban environments under a fixed budget. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected benefits from ash trees and the expected risks associated with experiencing extremely damaging scenarios. We define scenario dominance cuts (sdc) for the maximization problem and under the decision-dependent uncertainty. We then solve the model using the sdc cutting plane algorithm for varying risk parameters. Computational results demonstrate that scenario dominance cuts significantly improve the solution performance relative to that of CPLEX. Our CVaR risk-averse approach also raises the objective value of the least-benefit scenarios compared to the risk-neutral model. Results show a shift in the optimal strategy from applying less expensive insecticide treatment to more costly tree removal as the manager becomes more risk-averse. We also find that risk-averse managers survey more often to reduce the risk of experiencing adverse outcomes.

This paper presents a new and general approach, named “Stage-t Scenario Dominance,” to solve the risk-averse multi-stage stochastic mixed-integer programs (M-SMIPs). Given a monotonic objective function, our method derives a partial ordering of scenarios by pairwise comparing the realization of uncertain parameters at each time stage under each scenario. Specifically, we derive bounds and implications from the “Stage-t Scenario Dominance” by using the partial ordering of scenarios and solving a subset of individual scenario sub-problems up to stage t. Using these inferences, we generate new cutting planes to tackle the computational difficulty of risk-averse M-SMIPs. We also derive results on the minimum number of scenario-dominance relations generated. We demonstrate the use of this methodology on a stochastic version of the mean-conditional value-at-risk (CVaR) dynamic knapsack problem. Our computational experiments address those instances that have uncertainty, which correspond to the objective, left-hand side, and right-hand side parameters. Computational results show that our “scenario dominance"-based method can reduce the solution time for mean-risk, stochastic, multi-stage, and multi-dimensional knapsack problems with both integer and continuous variables, whose structure is similar to the mean-risk M-SMIPs, with varying risk characteristics by one-to-two orders of magnitude for varying numbers of random variables in each stage. Computational results also demonstrate that strong dominance cuts perform well for those instances with ten random variables in each stage, and ninety random variables in total. The proposed scenario dominance framework is general and can be applied to a wide range of risk-averse and risk-neutral M-SMIP problems.

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

In this paper, we address the controversies of epidemic control planning by developing a novel Simulation-Deep Reinforcement Learning (SiRL) model. COVID-19 reminded constituents over the world that government decision-making could change their lives. During the COVID-19 pandemic, governments were concerned with reducing fatalities as the virus spread but at the same time also maintaining a flowing economy. In this paper, we address epidemic decision-making regarding the interventions necessary given of the epidemic based on the purpose of the decision-maker. Further, we intend to compare different vaccination strategies, such as age-based and random vaccination, to shine a light on who should get priority in the vaccination process. To address these issues, we propose a simulation-deep reinforcement learning (DRL) framework. This framework is composed of an agent-based simulation model and a governor DRL agent that can enforce interventions in the agent-based simulation environment. Computational results show that our DRL agent can learn effective strategies and suggest optimal actions given a specific epidemic situation based on a multi-objective reward structure. We compare our DRL agent's decisions to government interventions at different periods of time during the COVID-19 pandemic. Our results suggest that more could have been done to control the epidemic. In addition, if a random vaccination strategy that allows super-spreaders to get vaccinated early were used, infections would have been reduced by 32% at the expense of 4% more deaths. We also show that a behavioral change of fully quarantining 10% of the risky individuals and using a random vaccination strategy leads to a reduction of the death toll by 14% and 27% compared to the age-based vaccination strategy that was implemented and the New Jersey reported data, respectively. We have also demonstrated the flexibility of our approach to be applied to other locations by validating and applying our model to the COVID-19 case in the state of Kansas.

Breast cancer is the leading cause of cancer deaths among women. The selection of an effective, patient-specific treatment plan for breast cancer has been a challenge for physicians because the decision process involves a vast number of treatment alternatives as well as treatment decision criteria, such as the stage of the cancer (e.g., in situ, invasive, metastasis), tumor characteristics, biomarker-related risks, and patient-related risks. Furthermore, every patient's case is unique, requiring a patient-specific treatment plan, while there is no standard procedure even for a particular stage of the breast cancer. In this paper, we first determine a comprehensive set of criteria for selecting the best breast cancer therapy by interviewing medical oncologists and reviewing the literature. We then present two analytical hierarchy process (AHP) models for quantifying the weights of criteria for breast cancer treatment in two sequential steps: primary and secondary treatment therapy. Using the weights of criteria from the AHP model, we propose a new multi-criteria ranking algorithm (MCRA), which evaluates a large variety of patient scenarios and provides the best patient-tailored breast cancer treatment alternatives based on the input of nine medical oncologists. We then validate the predictions of the multi-criteria ranking algorithm by comparing treatment ranks of the algorithm with ranks of five different oncologists, and show that algorithm rankings match or are statistically significantly correlated with the overall expert ranking in most cases. Our multi-criteria ranking algorithm could be used as an accessible decision-support tool to aid oncologists and educate patients for determining appropriate and effective treatment alternatives for breast cancer. Our approach is also general in the sense that it could be adapted to solve other complex decision-making problems in medicine, healthcare, as well as other service and manufacturing industries.

This study presents a new risk-averse multi-stage stochastic epidemics-ventilator-logistics compartmental model to address the resource allocation challenges of mitigating COVID-19. This epidemiological logistics model involves the uncertainty of untested asymptomatic infections and incorporates short-term human migration. Disease transmission is also forecasted through a new formulation of transmission rates that evolve over space and time with respect to various non-pharmaceutical interventions, such as wearing masks, social distancing, and lockdown. The proposed multi-stage stochastic model overviews different scenarios on the number of asymptomatic individuals while optimizing the distribution of resources, such as ventilators, to minimize the total expected number of newly infected and deceased people. The Conditional Value at Risk (CVaR) is also incorporated into the multi-stage mean-risk model to allow for a trade-off between the weighted expected loss due to the outbreak and the expected risks associated with experiencing disastrous pandemic scenarios. We apply our multi-stage mean-risk epidemics-ventilator-logistics model to the case of controlling the COVID-19 in highly-impacted counties of New York and New Jersey. We calibrate, validate, and test our model using actual infection, population, and migration data. The results indicate that short-term migration influences the transmission of the disease significantly. The optimal number of ventilators allocated to each region depends on various factors, including the number of initial infections, disease transmission rates, initial ICU capacity, the population of a geographical location, and the availability of ventilator supply. Our data-driven modeling framework can be adapted to study the disease transmission dynamics and logistics of other similar epidemics and pandemics., Comment: 35 pages, 6 figures, 10 tables, Under Review for a Journal

Emerald ash borer (EAB), a wood-boring insect native to Asia and invading North America, has killed untold millions of high-value ash trees that shade streets, homes, and parks and caused significant economic damage in cities of the United States. Local actions to reduce damage include surveillance to find EAB and control to slow its spread. We present a multistage stochastic mixed-integer programming (M-SMIP) model for the optimization of surveillance, treatment, and removal of ash trees in cities. Decision-dependent uncertainty is modeled by representing surveillance decisions and the realizations of the uncertain infestation parameter contingent on surveillance as branches in the M-SMIP scenario tree. The objective is to allocate resources to surveillance and control over space and time to maximize public benefits. We develop a new cutting-plane algorithm to strengthen the M-SMIP formulation and facilitate an optimal solution. We calibrate and validate our model of ash dynamics using seven years of observational data and apply the optimization model to a possible infestation in Burnsville, Minnesota. Proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. Our comparative analysis shows that the M-SMIP model outperforms six different heuristic approaches proposed for the management of EAB. Results from optimally solving our M-SMIP model imply that under a belief of infestation, it is critical to apply surveillance immediately to locate EAB and then prioritize treatment of minimally infested trees followed by removal of highly infested trees. Summary of Contributions: Emerald ash borer (EAB) is one of the most damaging invasive species ever to reach the United States, damaging millions of ash trees. Much of the economic impact of EAB occurs in cities, where high-value ash trees grow in abundance along streets and in yards and parks. This paper addresses the joint optimization of surveillance and control of the emerald ash borer invasion, which is a novel application for the INFORMS society because, to our knowledge, this specific problem of EAB management has not been published before in any OR/MS journals. We develop a new multi-stage stochastic mixed-integer programming (MSS-MIP) formulation, and we apply our model to surveillance and control of EAB in cities. Our MSS-MIP model aims to help city managers maximize the net benefits of their healthy ash trees by determining the optimal timing and target population for surveying, treating, and removing infested ash trees while taking into account the spatio-temporal stochastic growth of the EAB infestation. We develop a new cutting plane methodology motivated by our problem, which could also be applied to other stochastic MIPs. Our cutting plane approach provides significant computational benefit in solving the problem. Specifically, proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. We calibrate and validate our model using seven years of ash infestation observations in forests near Toledo, Ohio. We then apply our model to an urban forest in Burnsville, Minnesota, that is threatened by EAB. Our results provide insights into the optimal timing and location of EAB surveillance and control strategies.

Emerald ash borer (EAB), a wood‐boring insect native to Asia, was discovered near Detroit in 2002 and has spread and killed millions of ash trees throughout the eastern United States and Canada. EAB causes severe damage in urban areas where it kills highvalue ash trees that shade streets, homes, and parks and costs homeowners and local governments millions of dollars for treatment, removal, and replacement of infested trees. We present a multistage, stochastic, mixed‐integer programming model to help decision‐makers maximize the public benefits of preserving healthy ash trees in an urban environment. The model allocates resources to surveillance of the ash population and subsequent treatment and removal of infested trees over time. We explore the multistage dynamics of an EAB outbreak with a dispersal mechanism and apply the optimization model to explore surveillance, treatment, and removal options to manage an EAB outbreak in Winnipeg, a city of Manitoba, Canada.

Emerald ash borer (EAB), a wood-boring insect native to Asia and invading North America, has killed untold millions of high-value ash trees that shade streets, homes, and parks, and caused significant economic damage in cities of the United States. Local actions to reduce damage include surveillance to find EAB and control to slow its spread. We present a multi-stage stochastic mixed-integer programming (M-SMIP) model for the optimization of surveillance, treatment, and removal of ash trees in cities. Decision-dependent uncertainty is modeled by representing surveillance decisions and the realizations of the uncertain infestation parameter contingent upon surveillance as branches in the M-SMIP scenario tree. The objective is to allocate resources to surveillance and control over space and time to maximize public benefits. We develop a new cutting plane algorithm to strengthen the M-SMIP formulation and facilitate optimal solution. We calibrate and validate our model of ash dynamics using seven-years of observational data and apply the optimization model to a possible infestation in Burnsville, Minnesota. Proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. Our comparative analysis shows that the M-SMIP model outperforms six different heuristic approaches proposed for the management of EAB. Results from optimally solving our M-SMIP model imply that, under a belief of infestation, it is critical to apply surveillance immediately to locate EAB and then prioritize treatment of minimally infested trees followed by removal of highly infested trees.

Human immunodeficiency virus (HIV) is a key global health concern, with 33 million people living with HIV worldwide and 2.7 million new infections occurring annually. To prevent the spread of this widely prevalent epidemic disease, prevention and treatment intervention strategies urgently need to be implemented. The goal of this study is to propose stochastic dynamic programming (SDP) and approximate dynamic programming (ADP) algorithms that will optimally allocate the limited intervention budget among the HIV disease compartments and determine the best set of interventions that should be applied to each disease compartment, while minimizing the number of HIV-infected and people diagnosed with acquired immune deficiency syndrome (AIDS) as well as related deaths over a multi-year planning horizon. A compartmental model is constructed and formulated as a nonstationary Markov decision process (MDP) in order to capture the progression of the disease among the highest risk group—African American/black men who have sex with men (BMSM). In order to alleviate the computational difficulties arising from the exponentially growing state space in the SDP, we propose ADP algorithms that determine the approximately optimal budget allocation policies over six years. Our results suggest a greater allocation of the limited budget to prevention measures rather than treatment interventions, such as antiretroviral therapy (ART). As opposed to traditional policies that allocate the budget only once at the beginning of the time horizon, the ADP model suggests using a dynamic proportional budget strategy, allocating the budget dynamically over a multi-period planning period as the uncertainty in disease transmission is revealed. Results show that our ADP approach provides significant increases in health benefits and cost savings in HIV prevention and intervention.

In this paper, we study a mixed-integer programming model of the single-level multi-item capacitated lot-sizing problem (MCLSP), which incorporates shared capacity on the production of items for each period throughout a planning horizon. We derive valid bounds on the partial objective function of the MCLSP formulation by solving the first t periods of the problem over a subset of all items, using dynamic programming and integer programming techniques. We also develop algorithms for strengthening these valid inequalities by back-lifting techniques. These inequalities can be utilized within a cutting-plane algorithm, in which we perturb the partial objective function coefficients to identify violated inequalities to the MCLSP polytope. Our computational results show that the envelope inequalities are very effective for the MCLSP instances with different capacity and cost characteristics, when compared to the (l, S) inequalities.

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.

Battery Asset Management problem determines the minimum cost replacement schedules for each individual asset in a group of battery assets that operate in parallel. Battery cycle life varies under different operating conditions including temperature, depth of discharge (DOD), charge rate, etc., and a battery deteriorates due to usage, which cannot be handled by current asset management models. This paper presents a new battery asset management methodology where battery cycle life prognosis is integrated with parallel asset management to reduce lifecycle cost of the Battery Energy Storage Systems (BESS). For the battery failure time prognosis, a nonlinear physics-based battery capacity fade model is developed and incorporated in parallel asset management model to update battery capacity over time. Experiment results have shown that the developed battery asset management methodology can be conveniently used to facilitate BESS asset management decision making thereby decreasing asset lifecycle costs.

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.

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.

We study the multiple style and type parallel asset replacement problem (MST-PRES), which determines an optimal policy for keeping or replacing a group of assets that operate in parallel under a limited budget. Operating assets generally suffer from deterioration, which results in high operation and maintenance (O&M) cost and decreased salvage value, and technological improvements make it possible for new assets to operate more efficiently at a lower cost. In order to address these issues, we formulate a multi-objective mixed-integer programming (MIP) model that minimizes fixed and variable costs of purchasing new assets, O&M cost, inventory cost, and penalty cost for unmet demand minus salvage values, while considering technological advances and deterioration as a gain and loss in capacity, respectively. We apply our model to a case study involving two different styles of assets: a full-body magnetic resonance imaging (MRI) machine and a smaller extremity magnetic resonance imaging (eMRI) machine...

Invasive species cause large economic losses and are difficult to control due to the high cost of locating and treating the continual emergence of new individuals. The national strategy against invasive species encompasses prevention, early detection, and rapid response. In particular, determining an optimal route for search and treatment under limited budget is critical to reducing management costs. In this paper, we present a new integrated simulation-optimization framework to effectively search and treat invasive species under a limited management budget. The simulation mimics invader growth over a landscape and 12 years, while a bio-economic optimization model finds an optimal search and treatment path to minimize its economic damage to agricultural production. Our optimization model is new in the sense that it prescribes the optimal path for searching and treating sites for controlling the invader. This study is also the first in the literature to present and combine simulation and optimization models of the complex bio-economic search-path problem, and to prescribe a pathway for search and treatment that is applicable to the real-world management of invasive species. Our case study data and parameter calibration are based on the large-scale field data on Sericea, an aggressive invasive plant threatening the Great Plains of the U.S., collected over twelve pastures in Kansas during the past two years. Solving simulation and optimization models in a consecutive fashion provides a considerable computational advantage to find an optimal solution to practical size problems in a reasonable time. Our results imply that applying yearly treatment with a slow search-and-treatment speed results in the biggest bang for the buck under most invasion scenarios.

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.

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.

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.

Biofuel production from food crops leads to debates about the increase in food prices and security of the food supply. On the other hand, biofuels derived from cellulosic (energy) crops offer positive environmental impacts. In this study, we develop a multi-objective mixed-integer optimization model to investigate the trade-offs and competition between biofuel and food production using switchgrass and corn. This model maximizes total economic and environmental benefits and provides optimal decisions regarding land allocations to food and energy crops, seeding time, harvesting time and amount, and budget allocations to farm operations. A piecewise linear lower approximation is developed to linearize the nonlinear revenue curve of corn grain sales. Spatio-temporal environmental impacts such as soil erosion prevention, carbon sequestration and emissions, and nitrogen pollution are included in the model. The application of the model in Kansas indicates that switchgrass is more profitable than corn in cropland, while it requires Conservation Research Program (CRP) incentives for production on marginal land unless priority is given to the environment. In order to ensure food security, our study advises managers and policy makers to provide CRP incentives or to adjust the sustainability factor, which restricts cropland availability for biofuel production. Our spatio-temporal optimization model can also be adapted to different regions with alternative energy and food crops under various management scenarios.

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.

Biofuel production from second-generation feedstock has become critical due to environmental concerns and the need for sustainable energy supply. This paper provides a unique optimization approach of quantifying and formulating the economic and environmental benefits of switchgrass production at the farm level. In particular, we propose a multi-objective mixed-integer programming model, which maximizes the revenue from harvested switchgrass biomass and the economic value obtained from the positive environmental impacts of switchgrass yield during a ten-year planning horizon. Environmental impacts include soil erosion prevention, sustainability of bird populations, carbon sequestration, and carbon emissions, while economic impacts are analyzed under various budget, yield, and sustainability scenarios. The proposed model is then applied to a case study in the state of Kansas. Results show that given the current market prices, switchgrass cultivation on grassland and cropland is highly profitable. The model results also suggest that if utilized by the government, conservation reserve program (CRP) incentives could make marginal land more favorable over cropland. We perform sensitivity analysis to address the uncertainty in budget, yield, and utilization of cropland, and present insights into the economic and environmental impacts of switchgrass production. This model can also be extended to biomass production from any other types of energy crops to identify the most efficient production planning strategies under various management scenarios.

The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement schedules for each individual asset in a group of assets that operate in parallel. A fixed cost is incurred in any period in which an asset is purchased. These fixed costs induce economies of scale, making replacement schedules for these assets economically interdependent. We prove that PRES is NP-hard and present integer programming formulations for four variants of the problem in which multiple asset types, or challengers, are available for replacement (MPRES). We then derive valid inequalities for PRES and MPRES, which are similar in structure to flow cover inequalities developed in the context of fixed charge network problems. Experiments illustrate that the inequalities are effective in improving the integrality gap of MPRES instances.

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.

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.

Metabolic pathways show the complex interactions among enzymes that transform chemical compounds. The state of a metabolic pathway can be expressed as a vector, which denotes the yield of the compounds or the flux in that pathway at a given time. The steady state is a state that remains unchanged over time. Altering the state of the metabolism is very important for many applications such as biomedicine, biofuels, food industry, and cosmetics. The goal of the enzymatic target identification problem is to identify the set of enzymes whose knockouts lead the metabolism to a state that is close to a given goal state. Given that the size of the search space is exponential in the number of enzymes, the target identification problem is very computationally intensive. We develop efficient algorithms to solve the enzymatic target identification problem in this paper. Unlike existing algorithms, our method works for a broad set of metabolic network models. We measure the effect of the knockouts of a set of enzymes as a function of the deviation of the steady state of the pathway after their knockouts from the goal state. We develop two algorithms to find the enzyme set with minimal deviation from the goal state. The first one is a traversal approach that explores possible solutions in a systematic way using a branch and bound method. The second one uses genetic algorithms to derive good solutions from a set of alternative solutions iteratively. Unlike the former one, this one can run for very large pathways. Our experiments show that our algorithms' results follow those obtained in vitro in the literature from a number of applications. They also show that the traversal method is a good approximation of the exhaustive search algorithm and it is up to 11 times faster than the exhaustive one. This algorithm runs efficiently for pathways with up to 30 enzymes. For large pathways, our genetic algorithm can find good solutions in less than 10 minutes.

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.

Enzymes play a significant role in metabolism. They catalyze the chemical reactions that transform a set of substrates (i.e., input compounds) into products (i.e., output compounds). Metabolic engineering techniques often aim to manipulate a small set of genes to alter the speed of the targeted enzymatic reactions. Their eventual goal is to reach a desired level of compound concentrations produced or consumed by these reactions. One way to alter the speed of the reactions dramatically is to knockout a set of enzymes. When an enzyme is knocked out, it cannot catalyze a subset of the reactions, resulting in changes to the productions of compounds. When detailed in silicomodels are available, computational methods can be successfully used to determine the enzyme set to knockout. These methods, when applicable, have much lower time and cost requirements as compared to in vitro or in vivo experiments conducted in wet labs. Wet-lab experiments often require substantial effort and time of the domain experts and overall time requirements may be hours to several days. Moreover, the cost of wet-lab experimentation significantly increases when the number of enzymes that needs to be knocked out is more than one. Manipulations that involve four to six enzymes are not uncommon. As a result, biologists often employ computational methods as a preprocessing step to filter out less promising compounds. 17