Optimal Investment Plan Research Articles

Linear Models for Optimization of Infrastructure for $\hbox{CO}_{2}$ Capture and Storage

This paper presents linear models of the most common components in the value chain for capture and storage. The optimal investment planning of new gas power plants traditionally includes the cost of fuel versus sales of electricity and heat from the plant. If a new power plant also causes additional investments in gas infrastructure, these should be included in the optimization. With the increasing focus on global emissions, yet another aspect is introduced in the form of technology and infrastructure for capture, transport, and storage of . To be able to include all these aspects in the planning of new power plants, linear models for capture and storage are formulated consistent with current models for gas, electricity, and heat infrastructures. This paper presents models for the following infrastructure: source, combined cycle gas turbine producing electricity, heat and exhaust, capture plant, pipeline, liquefaction plant, storage, ship transport, injection pump, and demand/market.

An algorithm for construction of optimal timing solutions in problems with a stochastic payoff function

A dynamic model of optimal timing is applied to the problem of optimization of an innovation process in a competitive market environment. The basic element of the model is a block for optimization of the stopping time of the investment process. The problem of optimal timing is solved in parallel with adjoint problems of assessment of the market potential innovation and optimal control synthesis of the investment process. For construction of the optimal control synthesis the basic elements of models of optimal economic growth are used. In the econometric block, a probabilistic model is applied for design of market trajectories described by distribution functions. These distribution functions determine a market share of commercialized projects and probability of presence of competitors on the market at the current moment of time. Stochastic models for specification of the price formation mechanism are constructed for a series of distribution functions. An algorithm for construction of the optimal commercialization time and optimal investment plan is proposed. The algorithm is based on qualitative analysis of extremal points of the utility function which correspond to intersection points of a market distribution function and marginal costs of the innovation process. The algorithms are realized in the program software for simulation of optimal investment plans.

Operations Risk Management: Overview of Paul Kleindorfer's Contributions

This paper reviews Paul Kleindorfer's contributions to Operations Management (OM), with a special focus on his research on risk management. An annotated bibliography of selected other contributions reviews the breadth of topics that have occupied Kleindorfer's research attention over his now 45 + years of research. These include optimal control theory, scheduling theory, decision sciences, investment planning and peak load pricing, plus a number of important applications in network industries and insurance. In the area of operations risk management, we review recent work that Kleindorfer and his colleagues in the Wharton Risk Center have undertaken on environmental management and operations, focusing on process safety and environmental risks in the chemical industry. This work is directly related to Kleindorfer's work in the broader area of “sustainable operations”, which he, Kal Singhal and Luk Van Wassenhove recently surveyed as part of the new initiative at POMS to encompass sustainable management practices within the POMS community. Continuing in the area of supply chain risks, the paper reviews Kleindorfer's contributions to the development of an integrated framework for contracting and risk hedging for supply management. The emphasis on alignment of pricing, performance and risk management in this framework is presaged in the work undertaken by Kleindorfer and his co‐authors in the 1980s on after‐sales support services for high‐technology products. This work on supply chain risk, and its successors, is reviewed here in light of its growing importance in managing the unbundled and global supply chains characteristic of the new economy.

A novel branch and bound algorithm for optimal development of gas fields under uncertainty in reserves

We consider the problem of optimal investment and operational planning for development of gas fields under uncertainty in gas reserves. Assuming uncertainties in the size and initial deliverabilities of the gas fields, the problem has been formulated as a multistage stochastic program by Goel and Grossmann (2004). In this paper, we present a set of theoretical properties satisfied by any feasible solution of this model. We also present a Lagrangean duality based branch and bound algorithm that is guaranteed to give the optimal solution of this model. It is shown that the properties presented here achieve significant reduction in the size of the model. In addition, the proposed algorithm generates significantly superior solutions than the deterministic approach and the heuristic proposed by Goel and Grossmann (2004). The optimality gaps are also much tighter.

Knowledge Acquisition via Three Learning Processes in Enterprise Information Portals: Learning-by-Investment, Learning-by-Doing, and Learning-from-Others

An enterprise information portal (EIP) is viewed as a knowledge community. Activity theory provides a framework to study such a community: members of an EIP conduct specific tasks that are assigned through a division of labor. Each member of an enterprise information portal can undergo three distinct types of learning processes: learning-by-investment, learning-by-doing, and learning-from-others. Through these three types of learning processes, each member achieves specialized knowledge that is related to his or her own task. Cumulative knowledge resulting from the learning processes is considered in terms of two distinct attributes: depth and breadth of knowledge. This paper formulates a mathematical model and defines the goal of an EIP member as maximizing the net benefits of knowledge resulting from individual investment and effort. Numerical examples are provided to analyze patterns of optimal investment and effort plans as well as the resulting accumulated knowledge. The results provide useful managerial implications. In business conditions characterized by high interest rates or high internal rate of returns, it is preferable for members to delay spending their resources for learning. Intensive investment and efforts to obtain knowledge are preferable when the discount rate of costs is high, when knowledge is durable, when the value of knowledge is high, when the initial level of knowledge is high, when the productivity of the learning process is high, and when sufficient knowledge is transferred from other members. On the other hand, the size of the EIP has a positive or negative effect depending on the attribute of knowledge and the productivity of learning processes. Further properties of the optimal decisions and learning processes are analyzed and discussed.

Optimal Investment Planning for Distributed Generation in a Competitive Electricity Market

This paper proposes a new heuristic approach for distributed generation (DG) capacity investment planning from the perspective of a distribution company (disco). Optimal sizing and siting decisions for DG capacity is obtained through a cost-benefit analysis approach based on a new optimization model. The model aims to minimize the disco's investment and operating costs as well as payment toward loss compensation. Bus-wise cost-benefit analysis is carried out on an hourly basis for different forecasted peak demand and market price scenarios. This approach arrives at the optimal feasible DG capacity investment plan under competitive electricity market auction as well as fixed bilateral contract scenarios. The proposed heuristic method helps alleviate the use of binary variables in the optimization model thus easing the computational burden substantially.

Balance set and Pareto solutions in linear space with application to ongoing optimal resource allocation, investment planning, production, and control problems with multiple objectives

The notion of balance set is extended onto infinite-dimensional linear spaces. For multiobjective problems of ongoing optima, resource allocation, continuing investment planning with risk forecasting, optimal production models with time-varying objectives, the notion of finite causality is introduced leading to separable programs and sequential (not necessarily convergent) balance and Pareto sets. Selector sequences (or functions for continuous models) are proposed to determine particular Pareto solutions obtained from infinite sequences of the balance set equations. The method is extended onto multicriteria, global optimal control problems, and the use of Schauder bases is made for obtaining monotonic approximations to the sets of balance points and Pareto solutions. An algorithm is tien proposed for computing those approximations and illustrated by a practical example of the bicriteria min-time, min-fuel vertical soft landing problem to facilitate software design.

Cubic algorithm for global optimization with box and equality constraints and application to optimal allocation of resources

C++ code of the cubic algorithm [1] is proposed for nonconvex global optimization of continuous functions with box and equality constraints, and for the solution of nonlinear systems of equations, including underdetermined and overdetermined systems. The algorithm is upgraded for application to problems with linear and nonlinear equality constraints usually encountered in optimal resource allocation, investment planning, construction projects, and many engineering applications. It is further extended for visualization analysis of high dimensional sets of global optimizers by means of projections on linear subspaces and on arbitrary planes. C++ windows are presented for input, output, algorithmic control, and special research possibilities including graphics and screen display. The code does not create ill-conditioned situations.

A stochastic programming approach to planning of offshore gas field developments under uncertainty in reserves

In this work we consider the optimal investment and operational planning of gas field developments under uncertainty in gas reserves. The resolution of uncertainty in gas reserves, and hence the shape of the scenario tree associated with the problem depends on the investment decisions. A novel stochastic programming model that incorporates the decision-dependence of the scenario tree is presented. A decomposition based approximation algorithm for the solution of this model is also proposed. We show that the proposed approach yields solutions with significantly higher expected net present value (ENPV) than that of solutions obtained using a deterministic approach. For a small sized example, the proposed approximation algorithm is shown to yield the optimal solution with more than one order of magnitude reduction in solution time, as compared to the full space method. “Good” solutions to larger problems, that require up to 165,000 binary variables in full space, are obtained in a few hours using the proposed approach.

Future Utilization and Optimal Investment Strategy for Inland Waterways: New Model from U.S. Army Corps of Engineers to Assist Policy Makers

For nearly three decades, the U.S. Army Corps of Engineers (the Corps) has been measuring incremental system navigation transportation costs for proposed infrastructure investments in search of the National Economic Development (NED) plan: local optimization in a system-level evaluation. The increasingly complex and sophisticated analysis requires the development of additional modeling modules. The traditional analysis assumed a most-likely traffic forecast and a set investment timing. Cost-benefit analyses on various alternatives were compared to determine the without-project condition and the recommended with-project NED plan. Sensitivity analyses of traffic forecasts and investment timing were done on the with-project plan. The second generation of analysis factored in the impacts of scheduled chamber closure differences between alternatives, and the third generation of analysis factored in the impacts of unscheduled ones. The goal is to be able to optimize investments simultaneously across a system (not just investments at one site) under a series of forecast scenarios while capturing structural reliability differences (scheduled and unscheduled closures). As the demands of the analysis increased, there was a need to consolidate and dynamically link the various models and techniques developed over the years and to develop new techniques to simultaneously manage investment permutations and automatically select optimal investment plans; the desire was to perform system optimization in a system-level evaluation. The innovative analysis techniques and relational database management structure of the new Ohio River Navigation Investment Model are introduced, as is a set of flexible, integrated analysis modules that move the Corps closer to these ideals.

Optimal waste reduction and investment planning under uncertainty

Ever-changing production campaigns complicate the management of recovery and treatment options for unavoidable effluents at pharmaceutical plants. Each campaign produces large amounts of by-products differing in their number, amount as well as composition. Future business strategies designed to address changing market demands add uncertainty to this already challenging design problem. In such a dynamic and uncertain environment, the selection of operating policies as well as decisions to support future business operations by plant investments such as new reactors and separators is a formidable task. This paper will introduce a systematic planning methodology for obtaining long-term waste management strategies for entire batch manufacturing sites. Rigorous modeling of future business and regulatory changes will allow plant managers to assess their long-term monetary, infrastructural and ecological impact. The methodology will be illustrated with the help of quasi industrial case studies.

Investing in Quality Under Autonomous and Induced Learning

The reduction of variability in product performance characteristics is an important focus of quality improvement programs. Learning is intrinsically linked to process improvement and can assume two forms: (i) autonomous learning; and (ii) induced learning. The former is experientially-based, while the latter is a result of deliberate managerial action. Our involvement in quality and capacity planning with several major corporations in different industries suggested that it would be instructive to devise a model that would prescribe an optimal combination of autonomous and induced learning over time to maximize process improvement. We thus propose such a model to investigate the optimal quality improvement path for a company given that quality costs depend on both autonomous and induced types of learning experienced on a number of quality characteristics. Several properties of an optimal investment path are developed for this problem. For example, it is shown that decisions maximizing short-term gains may actually lead to suboptimal resource utilization decisions when total costs associated with a longer planning horizon are taken into account. Numerical examples are used to assess the sensitivity of the optimal investment plan with respect to changes in several model parameters.

Performance Programming: Guiding Resource Allocation to Achieve Policy Objectives

The Montana Department of Transportation’s (MDT) performance programming process (P3) is defined as “a method to develop an optimal investment plan and measure progress in moving toward strategic transportation system goals.” Transportation goals are based on the policy directions defined in the statewide long–range transportation plan. The distribution of funding is established through a series of trade-off analyses based on analyzing how the program can best meet overall performance goals. P3 allows system performance to be tracked over time and for various policy options to be systematically analyzed. In addition, P3 commits projects to the Statewide Transportation Improvement Program, whose contribution to system performance was estimated through an analytical process. A case study of the MDT process is provided. The Montana context that led to the development of P3 and the key steps of P3 are described, and the impact of the process on MDT decision making is explained. A discussion of implementation issues and next steps in MDT’s incremental implementation of this process is provided.

A highway corridor planning model: QROAD

This model calculates an optimal investment plan for a highway corridor or number of corridors, subject to budget constraints. The available options include upgrading the current alignment, constructing a bypass highway over a different alignment, or various combinations. The budget constraints can be specified as a total budget restriction, or as an available budget each period. The highway system is described by K different road links. Each link consists of the current alignment which may be described by any number of sections, and a bypass section over a new alignment. The model finds the construction plan for each link that maximizes discounted benefits, subject to the financial constraints on the maintenance and capital expenditures. The problem is formulated as a large combinatorial optimization problem. A Lagrangian relaxation of the budget constraints is used, and the problem decomposes by link. A dynamic programming (DP) model is used to solve for the optimal expansion path for each link, given the dual variables. The sub-gradient dual optimization problem is a linear programming problem which is solved for the optimal dual variables. An application is presented based on the World Bank's Third National Highway Project in India, which is a US$1.3 billion project for upgrading approximately 2000 km of the Indian National Highway System. The project was approved based on results from this model.

Power generation expansion planning with environmental consideration for Lebanon

This work describes the development and usage of a generation expansion planning (GEP) tool based on dynamic programming, probabilistic production simulation, and environmental assessment. The problem of GEP is solved in stages using tunnel dynamic programming to determine the optimal investment plan of unit additions. The objective function of the planning exercise is to minimize either the cost or the environmental impact or some weighed function of the two. The production costing methodology is based on combining a probabilistic generation model with the load duration curve of the system to deduce a risk model from which the expected energy not supplied and the expected energy produced by each unit are estimated. Estimation of environmental emissions is conducted based on fuel type, heat rate, and energy produced by each unit. The program can model hydroelectric units as well as energy limited units, under economical and environmental load dispatches. The model is illustrated by a planning case study of the Lebanese electric power system to examine the impact of various technical, economic and environmental parameters on the proposed plans.

Optimal investment in derivative securities

We consider the problem of optimal investment in a risky asset, and in derivatives written on the price process of this asset, when the underlying asset price process is a pure jump Levy process. The duality approach of Karatzas and Shreve is used to derive the optimal consumption and investment plans. In our economy, the optimal derivative payoff can be constructed from dynamic trading in the risky asset and in European options of all strikes. Specific closed forms illustrate the optimal derivative contracts when the utility function is in the HARA class and when the statistical and risk-neutral price processes are in the variance gamma (VG) class. In this case, we observe that the optimal derivative contract pays a function of the price relatives continuously through time.

Investment with an arithmetic process and lags

This paper presents an explicit solution of a simple investment problem with entry lags and when the underlying stochastic process is arithmetic. It is shown that, without abandonment, the optimal investment plan is independent of the length of the lag. Copyright © 2000 John Wiley & Sons, Ltd.

Competitive equilibrium and public investment plans

Abstract We examine a one-sector growth model in which public capital is an external input to private production functions. Revenues from taxing capital and labor income are used to fund public investments. The competitive equilibrium can be obtained by solving an artificial planning problem. We prove that there exists a unique competitive equilibrium which can be characterized by Euler equations and a transversality condition. We then establish the existence of an optimal public investment plan.

The role of technology in sustaining agriculture and the environment

Visions of sustainable development often leave unanswered the question: What actions taken by the current generation will ensure that future generations can meet their economic and environmental needs? In this context, we assess the role of technology in steering agriculture along a more sustainable path. From the agricultural sector's perspective, this requires an optimal investment plan for a nation's stock of environmental assets that accounts for an intergenerational fulfillment of sustainability's dual goals: (1) satisfying food and fiber needs at reasonable costs to consumers; and (2) providing environmental service flows. In reviewing agricultural indicators to assess the nation's performance in meeting these goals, we find productivity growth has increased while rates of soil erosion, wetland conversion, and pesticide application have declined. However, individuals continue to demand more environmental services while private markets undersupply environmental services. The capacity of the agricultural sector to meet food and fiber and environmental service demands partially depends on the availability and adoption of new technology. Several market impediments explain the undersupply of sustainable technologies: (1) firms cannot fully appropriate rents from technology development; (2) success may vary with farm structure; (3) the heterogeneity of the resource base influences adoption; and (4) farmers cannot capture the benefits of environmental services. To address these market failures, sustainable agriculture policy should: (1) support research and development in sustainable technologies and provide incentives to encourage adoption; (2) ensure that conservation efforts reflect the efficient and sustainable allocation of environmental assets; and (3) legitimize markets for foods produced under more sustainable practices.

Risk of extreme events via multiobjective decision trees: application to telecommunications

Simultaneous transmission of high-resolution video, digital audio, and data over fiber optic cables is only one of the many new services that the rapidly changing telecommunications industry will soon be providing to users. Currently, federal regulations are restraining telephone companies from entering the video entertainment business, but with the capabilities that technology can provide, their entrance into the market in the long run is inevitable. Telephone companies are facing the decision of whether or not to invest in fiber optic cables in local telephone loops. They also need a way of determining optimal timing for the installation of fiber optic technology in the network. The authors focus on the risks involved in developing an optimal investment plan for expansion of a telecommunications network. This problem is modeled using a multiobjective decision tree where the objective of monetary return from a particular alternative is traded off against the customer satisfaction which that alternative achieves. At each chance node in the decision tree, a continuous probability distribution represents the possible outcomes. To examine the risk of extreme events, the probability distribution is required, rather than only the expected value. To retain all distribution information, a simulation is used to generate a set of Pareto optimal alternatives for various scenarios considered in the model.