Maximization Of Present Value Research Articles

Optimal design and planning of sustainable chemical supply chains under uncertainty

AbstractThis article addresses the design of sustainable chemical supply chains in the presence of uncertainty in the life cycle inventory associated with the network operation. The design task is mathematically formulated as a bi‐criterion stochastic mixed‐integer nonlinear program (MINLP) that simultaneously accounts for the maximization of the net present value and the minimization of the environmental impact for a given probability level. The environmental performance is measured through the Eco‐indicator 99, which incorporates the recent advances made in Life Cycle Assessment. The stochastic model is converted into its deterministic equivalent by reformulating the probabilistic constraint required to calculate the environmental impact in the space of uncertain parameters. The resulting deterministic bi‐criterion MINLP problem is further reformulated as a parametric MINLP, which is solved by decomposing it into two sub‐problems and iterating between them. The capabilities of the proposed model and solution procedure are illustrated through two case studies for which the set of Pareto optimal, or efficient solutions that trade‐off environmental impact and profit, are calculated. These solutions provide valuable insights into the design problem and are intended to guide the decision maker towards the adoption of more sustainable design alternatives. © 2008 American Institute of Chemical Engineers AIChE J, 2009

Optimum design and operating conditions of multiple effect evaporators: Tomato paste

Agro industry is a very important industrial sector worldwide, especially for countries like New Zealand and Chile. The main objective of this research was to propose a new economic evaluation procedure to optimize the design and operation of multiple effect evaporators and compare it with the traditional chemical engineering approach of total cost minimization. The proposed strategy incorporates a quality factor expressed as a function of lycopene concentration on the final product to find the optimal number of effects and operating conditions through the maximization of the net present value. The mathematical model was implemented using Microsoft Excel and considered mass and energy balances, specific relations for tomato concentration and a first order degradation kinetic for lycopene. The results indicate that when augmenting the capacity of the evaporation system of 5 effects from 50 to 75 Ton/h, the lycopene retention increases from 95.25% to 96.27%. When evaluating the system through the logic of the total cost minimization, an optimum of 4 effects is found, but when evaluating the system using the maximization of the Net Present Value including lycopene as a quality parameter, the optimum is 3 effects. It appears of extreme relevance to consider quality as an intrinsic and integral part of the process design, as it will then be possible to identify several potential improvements in different food processes.

An AHP-based decision-making tool for the solution of multiproduct batch plant design problem under imprecise demand

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessarily involves the way that equipment may be utilized, which means that plant scheduling and production must form an integral part of the design problem. This work relies on a previous study, which proposed an alternative treatment of the imprecision (demands) by introducing fuzzy concepts, embedded in a multi-objective Genetic Algorithm (GA) that takes into account simultaneously maximization of the net present value ( NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The results showed that an additional interpretation step might be necessary to help the managers choosing among the non-dominated solutions provided by the GA. The analytic hierarchy process (AHP) is a strategy commonly used in Operations Research for the solution of this kind of multicriteria decision problems, allowing the apprehension of manager subjective judgments. The major aim of this study is thus to propose a software integrating the AHP theory for the analysis of the GA Pareto-optimal solutions, as an alternative decision-support tool for the batch plant design problem solution.

The discrete time/cost trade-off problem: extensions and heuristic procedures

Time/cost trade-offs in project networks have been the subject of extensive research since the development of the critical path method (CPM) in the late 50s. Time/cost behaviour in a project activity basically describes the trade-off between the duration of the activity and its amount of non-renewable resources (e.g., money) committed to it. In the discrete version of the problem (the discrete time/cost trade-off problem), it is generally accepted that the trade-off follows a discrete non-increasing pattern, i.e., expediting an activity is possible by allocating more resources (i.e., at a larger cost) to it. However, due to its complexity, the problem has been solved for relatively small instances. In this paper we elaborate on three extensions of the well-known discrete time/cost trade-off problem in order to cope with more realistic settings: time/switch constraints, work continuity constraints, and net present value maximization. We give an extensive literature overview of existing procedures for these problem types and discuss a new meta-heuristic approach in order to provide near-optimal heuristic solutions for the different problems. We present computational results for the problems under study by comparing the results for both exact and heuristic procedures. We demonstrate that the heuristic algorithms produce consistently good results for two versions of the discrete time/cost trade-off problem.

A fuzzy multiobjective algorithm for multiproduct batch plant: Application to protein production

This paper addresses the problem of the optimal design of batch plants with imprecise demands and proposes an alternative treatment of the imprecision by using fuzzy concepts. For this purpose, we extended a multiobjective genetic algorithm (MOGA) developed in previous works, taking into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The former is computed by comparing the fuzzy computed production time to a given fuzzy production time horizon and the latter is based on the additional fuzzy demand that the plant is able to produce. The methodology provides a set of scenarios that are helpful to the decision's maker and constitutes a very promising framework for taken imprecision into account in new product development stage.

Selection and evaluation of projects to conserve ecosystem services

Climate and land use changes are reducing ecosystem services. Ecosystem managers can alleviate such adverse impacts by being more efficient in allocating limited budgets to projects designed to conserve ecosystem services, and ensuring that implemented projects are effective in stemming losses in ecosystem services. A conceptual framework is developed that managers can use for this purpose. The framework consists of two elements: (1) an a priori optimization model for selecting projects that minimize present value loss in ecosystem services subject to a budget constraint; and (2) an a posteriori model for determining the extent to which implemented projects have decreased ecosystem losses. An optimization model is formulated for three cases, which assume the ecosystem manager: (1) knows for sure how project expenditures influence losses in ecosystem services (certainty case); (2) does not know for sure how project expenditures influence losses in ecosystem services, but is able to specify the probabilities of service losses for different projects (risk case); and (3) is uncertain how project expenditures influence losses in ecosystem services (uncertainty case). Efficient selection of projects is evaluated for two areas of an ecosystem in mathematical and graphical terms using a continuous negative exponential relationship between present value losses and project expenditures for the certainty case, and for five expenditure classes in the risk and uncertainty cases. Two versions of the certainty case are evaluated, weak sustainability and strong sustainability. Weak sustainability allows gains in one ecosystem service to compensate for losses in another ecosystem service; strong sustainability does not. The risk case requires the manager to specify the conditional probabilities for present value losses given project expenditures, and utilizes expected costs and expected budget amounts in the budget constraint. It is solved by allocating the budget among projects so as to equalize the expected marginal present value losses in ecosystem services across projects. The uncertainty case requires the manager to specify ecosystem sustainability states and the present value losses in ecosystem services for combinations of states and projects. It is solved by selecting projects that minimize the maximum present value loss in ecosystem services subject to the budget constraint. The a posteriori evaluation method uses Bayesian statistical inference to test hypotheses about the extent to which implemented projects reduce losses in ecosystem services. It requires specifying ecosystem states that describe conditions for ecosystem services, and decides which hypothesis is true based on posterior probabilities of ecosystem states.

Forest valuation and the AASB 141 accounting standard

Summary This paper examines issues relating to forest valuation using the Australian Accounting Standards Board accounting standard AASB 141 for large and medium-sized forestry entities. Current practices generally follow AASB 141:25 that states that an independent valuation of land may (emphasis added) be deducted from the present value of the combined asset to yield a value for the living trees (i.e. value of the biological asset), from which gains or losses relative to the previous year may be brought to account in the income statement. Such an approach distorts the income statement by gains and losses that are arbitrarily one-sided because the value of the living trees becomes a residual whose value is influenced by any movements in land value, sometimes masking the inherent productivity and value of the living trees. The paper reviews key terminology and principles of AASB 141 and other standards, including the definitions of biological assets, non-current assets, fair value, active markets, combined assets, and highest and best use. In the absence of an active market for medium and large forestry assets, which is generally the case in Australia and New Zealand, the estimation of fair value using the present value of expected cash flows is central to valuation. Whatever the respective form of ownership, land and living trees constitute a combined asset in which the roles are inseparable biologically. To be consistent with the use of fair value of the combined asset based on the present value of expected cash flows, the planning horizon needs to be extended to a uniform future year for the entire asset. This is to enable the optimum schedule of wood and cash flows and hence the maximum present value to be estimated. We describe an operational method to derive the present value of the living trees (the biological asset value as rigidly defined in AASB 141) by discounting the cash flows relating solely to those living trees, in essence the current crop. Segmenting those cash flows from those used in evaluating the present value of the combined asset can do this. Assuming the going concern is viable, such that forestry is the highest and best use, the remaining issue is how to ensure that the fair value of the combined asset is properly reflected in the balance sheet. This can be done by deducting the present value of the living trees (i.e. the value of the biological asset) from that of the combined asset (after due adjustment for land improvements). The resulting present value of ‘future rotations’ should then be shown as a non-current asset under ‘property, plant and equipment’. Finally, the discount rates used in forest valuations generally allow for taxation (and risk) in using a weighted average of the discount rates for equity and debt. Post-tax evaluation of cash flows is therefore recommended, rather than pre-tax, subject to avoiding double counting of any tax liabilities or debts elsewhere in the accounts.

Discrete–continuous project scheduling with discounted cash flows—A tabu search approach

In this paper discrete–continuous project scheduling problems with discounted cash flows are considered. In discrete–continuous project scheduling activities require for their processing discrete and continuous resources. The processing rate of an activity depends on the amount of the continuous resource allotted to this activity at a time. A positive cash flow is associated with each activity. Two common payment models—lump-sum payment and payments at activities’ completion times—are considered. The objective is the maximization of the net present value of all cash flows of the project. Some properties of optimal schedules are discussed, and the formulation of a mathematical programming problem for an optimal continuous resource allocation is presented. Applications of a local search metaheuristic—tabu search, as well as simple search methods—multi-start iterative improvement and random sampling are described. The algorithms are compared on the basis of a computational experiment, the results are analyzed and discussed. Some conclusions as well as directions for further research are given.

Genetic algorithms for optimization of a mine system under uncertainty

The production planning of a mine system associated with mining, processing and refining stages dictates to determine optimal system parameters such as optimal production rates, location of refining facility and the best reconstruction time of production rates. This paper proposes a combination of the chance constrained programming (CCP) and the genetic algorithms (GA) to find the optimal system parameters simultaneously. In generic form the problem is expressed as the maximization of net present value of future cash flows such that the capacity constraint and predefined specifications are satisfied. The blending requirements expressed in the CCP are transformed into deterministic equivalents. A new form of the problem is solved by the GA. The approach was demonstrated on extraction, processing and refining of four iron ore mines with varying reserves, ore qualities, geological and topographic conditions, four mineral processing units and one refining facility. The results showed that the proposed algorithm could be used to determine optimal production rates, the facility location and the best reconstruction time.

Optimizing Treatment Parameters for Enhanced Hydrocarbon Production by Hydraulic Fracturing

Abstract A novel scheme is presented in this paper for hydraulic fracturing design, which integrates reservoir properties, operational limitations, fracture growth control requirements, reservoir production behaviour, and investment-return cash flow behaviour in deciding on the optimum values of various treatment parameters. The capability and robustness of the optimization scheme is demonstrated by applications to a tight gas reservoir for which various designs are obtained: maximum NPV design, maximum production design, a target production design, and a compromised design. Optimum designs are found to be different for different objective functions. It is demonstrated that maximization of NPV, or production, involves a high treatment cost, which can be minimized further by solving a combined objective function, but at the expense of some NPV or production. By tradeoff analysis between production/NPV and treatment cost, 44% of treatment cost saving is indicated at the expense of only a 12% sacrifice in production/NPV. Various other design issues are investigated by sensitivity analyses. Introduction At the design stage of a hydraulic fracturing job for a particular reservoir, the engineer must decide on a set of values for treatment parameters, such as viscosity of fracturing fluid, injection rate of the fluid, injection time, proppant type, proppant concentration, etc. A systematic and integrated procedure can aid the designer to perform this design task efficiently and to enforce a favourable hydraulic fracture geometry that meets various design objectives. In most hydraulic fracturing design works(1–4), maximization of net present value (NPV) is used as a design objective. The improvement in NPV is attempted by parametric sensitivity analysis systematically varying a number of treatment parameters and fracture length. Such a procedure is tedious and does not guarantee to achieve the "best possible" design because it often fails to explore all potential design scenarios and to address various operational factors (e.g., pump capacity, tubular strength, and pressure rating of surface equipment) and fracture growth control requirements. Furthermore, there may be benefits in considering other design objectives, such as maximizing production/NPV with minimum treatment costs or achieving a specific production target. Yang et al.(5) attempted procedural optimization of hydraulic fracturing considering only the injection rate, injection time, and proppant concentration as the free variables. The work, however, ignored operational factors and fracture growth control requirements. The three variables were optimized within their specified ranges to maximize NPV, systematically varying the fracture length with a fixed height. Thus, the work failed to exploit the full benefit of procedural optimization. Mohaghegh et al.(6) recently reported a hybrid Neuro-genetic approach for hydraulic fracture treatment design optimization based on historical data. Their approach avoids the problem of mathematical formulation and lacks the generality of a physics-based integrated approach. Mahrer(7) recently reviewed research work on hydraulic fracture geometry and treatment practice, and rightly concluded "optimizing treatment procedures based on in situ conditions is an area of technology that requires research and development." The current authors have therefore developed an optimization scheme to integrate the effects of various issues discussed above with the hydraulic fracturing design procedure.

An integrated model for part-operation allocation and investments in CNC technology

This study addresses the issue of investment appraisal of new technology, specifically computer numerical control (CNC) machine tools in conjunction with optimal allocation of parts and operations on CNC machines as the investments take place. Part-operation allocation is the allocation of parts and operations to either the conventional machines or to the new technology as they are acquired. It is shown that part allocation is an important consideration in the assessment of profitability from investments in CNC technology. A mixed integer programming model is presented to (1) determine the optimal allocation of parts and operations to conventional machines and to new CNC machine tools; and (2) determine the optimal investment sequence and timing of investments in CNC machine tools. The optimality criterion is based on a maximization of net present value (NPV) over a specified planning horizon. The application of the model is illustrated using a numerical example, and the implications for industrial practice are also indicated.

The economic value of a forested catchment with timber, water and carbon sequestration benefits

This paper examines the optimal management strategy for a forested catchment that yields timber, water and carbon sequestration benefits. The Faustmann multiple rotation model is extended to allow for the maximisation of the net present value of these timber and non-timber benefits. The model is applied to the Thomson Catchment in Central Gippsland, Victoria. Carbon sequestration benefits are modelled via total stand biomass accumulation. The cost of carbon release back into the atmosphere upon logging is estimated as a function of rotation age using an adjusted pulpwood/sawlog ratio. The allowance for both non-timber benefits is found to lengthen the optimal rotation, in a large range of cases to infinity.

An integrated survey of deterministic project scheduling

There have been many survey papers in the area of project scheduling in recent years. These papers have primarily emphasized modeling and algorithmic contributions for specific classes of project scheduling problems, such as net present value (NPV) maximization and makespan minimization, with and without resource constraints. Paralleling these developments has been the research in the area of project scheduling decision support, with its emphasis on data sets, data generation methods, and so on, that are essential to benchmark, evaluate, and compare the new models, algorithms and heuristic techniques. These investigations have extended the frontiers of research and application in all areas of project scheduling and management. In this paper, we survey the vast literature in this area with a perspective that integrates models, data, and optimal and heuristic algorithms, for the major classes of project scheduling problems. We also include recent surveys that have compared commercial project scheduling systems. Finally, we present an overview of web-based decision support systems and discuss the potential of this technology in enabling and facilitating researchers and practitioners in identifying new areas of inquiry and application.

Timber production possibilities and capital yields from the Norwegian forest area

How intensely should a forest be grown? This is a fundamental question in the process of formulating policy guidelines for the management of a forest area, both at the individual property level as well as at the national level. The question is related to a number of factors; the objective(s) of the forest owner, the productivity of the forestland, the initial growing stock, the accessibility within the forest, assumptions regarding future prices and costs and the required real rate of return. This paper presents an applied analysis with the objective of mapping possible future paths for the growing stock on, and timber harvest from the productive forest area in Norway. The analysis is deterministic. The regeneration strategy is a key factor for the long run development of a forest and is thus given particular attention. The analysis is restricted to deal with timber production only and maximisation of the net present value of the forest area is used as the objective function. The required real rate of return is varied and used as the driving force to find the best (optimal) level of intensity in silvicultural management and thus optimal paths for harvesting and growing stocks.

Four Payment Models for the Multi-Mode Resource Constrained Project Scheduling Problem with Discounted Cash Flows

In this paper, the multi-mode resource constrained project scheduling problem with discounted cash flows is considered. The objective is the maximization of the net present value of all cash flows. Time value of money is taken into consideration, and cash in- and out-flows are associated with activities and/or events. The resources can be of renewable, nonrenewable, and doubly constrained resource types. Four payment models are considered: lump sum payment at the terminal event, payments at prespecified event nodes, payments at prespecified time points and progress payments. For finding solutions to problems proposed, a genetic algorithm (GA) approach is employed, which uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an example problem. Sensitivity analyses are performed over the mark up and the discount rate. A set of 93 problems from literature are solved under the four different payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is compared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it.

A heuristic treatment of tardiness and net present value criteria in resource constrained project scheduling

Considers the resource‐constrained project scheduling problem where cash inflows and outflows are tied to the occurrence of events. The objective is the maximization of the project net present value (NPV) as well as the minimization of project tardiness in the presence of a project due date. Develops hybrid scheduling rules with both NPV and tardiness considerations to enhance both objectives. Experiments extensively with a set of benchmark problems originally designed for the objective of minimizing the project duration. Demonstrates that thje hybrid rules developed here are superior in performance with respect to both objectives when compared with well known rules which are developed for the two objective of minimizing the project duration. Demonstrates that the hybrid rules developed here are superior in performance with respect to both objectives when compared with well‐known rules which are developed for the two objectives taken individually. Furthermore, the iterative algorithm improves the performance of all tested rules significantly.

Is the monopolist the friend of the conservationist? Two remarks on the Hotelling-Solow paradox

In this paper, we consider the efficient use of an exhaustible resource. The well known Hotelling-Solow paradox states that the monopolist is the friend of resource conservationist. We examine it from two different aspects. One is from the aspect of uncertainty, especially the uncertainty of demand fluctuation. The other is from the market competitive effect given by the probability of entry of a competing supplier. We show that such uncertain factors as demand fluctuations are crucial determinants of the extraction policy of the resource owner. There may be a case in which the Hotelling-Solow paradox does not hold. The risk factor might cause the resource owner to discount the existing amount of resource stock. This serves to establish a counterexample to the Hotelling-Solow paradox. Secondly, market competitive power works against resource conservation. The resource owner's optimal pricing policy is developed under the assumption that the entry probability is a non-decreasing function of the resource price and the objective is present value maximization. It is shown that the optimal pre-entry price is set lower than the one in the case without uncertain entry. In this sense, the resource is exhausted more rapidly and there is a possibility for market power working against conservation.

An interactive multiobjective approach to harvest decisions in forest planning

A hierarchical approach to forest planning is formulated, where harvest schedules are first determined, followed by a decision about harvest methods (harvest regime). Choice of harvest methods is particularly important because of concerns about harvest‐related site disturbance. In the decision model developed in this article, determination of a harvest regime is expressed as a multiple‐objective decision incorporating maximization of net present value and minimization of cumulative site disturbance for different site classes, subject to maintaining high levels of production, an even flow of timber, and avoiding adjacency violations. The search for preferred harvest regimes is performed interactively over a set of non‐dominated harvest schedules with alternative aspiration levels identified for the various objectives to reflect values of different stakeholders.

An exact solution of cash flow for an integrated evaluation of investment in inventory and credit

In a recent paper, Kim and Chung suggested a method for jointly evaluating inventory and accounts receivable based on the criteria-net present value (NPV) maximization. They were fairly confident of the concavity of NPV (8) \\[the function of all future cash flows] and proposed a lot of conclusions about the optimal batch sales volumes. This paper refutes the concavity of NPV(8) and conclusions expressed or implied by Kim and Chung. It is proved that NPV(8) is unimodal. Finally, an exact solution of cash flow for an integrated evaluation of investment in inventory and credit is presented. Numerical examples are included.

Non-linear structure of a Metzlerian inventory cycle model

This study considers optimizing behavior of an inventory-holding firm. Its main purpose is to investigate a consistent microeconomic foundation of the non-linear macrodynamic model that generates inventory cycles. It solves present value maximization problems under two different specifications of expectation formations: one is specifying expectation formation independently of the optimizing process of the firm (I call it a myopic perfect formation of expectation); the other is incorporating the expectation formation in the optimizing process (I call it a dynamic perfect formation of expectation). The analysis demonstrates that the firm with the myopic perfect formation can posses sufficient nonlinearity for generation of cyclical macrodynamics, whereas the firm with the dynamic perfect formation cannot. These results suggest that the myopic perfect treatment of expectations of economic agents can be a source of macro fluctuations like inventory cycles.