An approximate solution approach for a scenario-based capital budgeting model

Costa, Anabela; Paixão, José M. P.

doi:10.1007/s10287-009-0117-4

Cited by 9 publications

(6 citation statements)

References 25 publications

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“…We consider a number of potential projects ranging between 10 and 20. Such numbers of projects are typical for the capital rationing problem, as the project selection is typically preceded by a screening phase in which homogeneous groups of projects are defined and are later on subjected to a joint evaluation [7]. The project outflows ξ i j and project values V j have been randomly generated from a uniform distribution (see [4,31]) defined on [300, 600] and [10,1000], respectively.…”

Section: Proposition 32 For Every Inequality Z Jmentioning

confidence: 99%

“…, r are independent random variables with (d i + 1)decreasing densities for some d i > 0 for large values of p. Considering a Gaussian technology matrix in (3), Van Ackooij et al [33] designed an efficient method to compute the gradients and value of the multivariate Gaussian distribution functions with the code developed by Genz [9]. A possible approach is to approximate a multi-row chance constraint with random technology matrix (3) with individual chance constraints (7). This can be done by using, for example, Boole's inequality and requiring that:…”

Section: Introductionmentioning

confidence: 99%

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Threshold Boolean form for joint probabilistic constraints with random technology matrix

Kogan

Lejeune

2013

Math. Program.

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We develop a new modeling and exact solution method for stochastic programming problems that include a joint probabilistic constraint in which the multi-row random technology matrix is discretely distributed. We binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined Boolean function (pdBf) representing the probabilistic constraint. We then construct a tight threshold Boolean minorant for the pdBf. Any separating structure of the tight threshold Boolean minorant defines sufficient conditions for the satisfaction of the probabilistic constraint and takes the form of a system of linear constraints. We use the separating structure to derive three new deterministic formulations equivalent to the studied stochastic problem. We derive a set of strengthening valid inequalities for the reformulated problems. A crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty. The computational study, based on instances of the stochastic capital rationing problem, shows that the MIP reformulations are much easier and orders of magnitude faster to solve than the MINLP formulation. The method integrating the derived valid inequalities in a branch-and-bound algorithm has the best performance.

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Section: Proposition 32 For Every Inequality Z Jmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Threshold Boolean form for joint probabilistic constraints with random technology matrix

Kogan

Lejeune

2013

Math. Program.

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“…Since the proposal of the Black-Scholes equation to calculate the premium of a European option [23], the method originally conceived for valuing financial options has been widely used for the analysis of different managerial decisions, including corporate valuation [24][25][26], investment projects [27][28][29][30], research and development [31,32], and budgeting [33].…”

Section: Methodsmentioning

confidence: 99%

Managing Reputational Risk through Environmental Management and Reporting: An Options Theory Approach

et al. 2017

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Abstract:Reputation is a complex and multidimensional concept that may be organized in downside and upside reputational risk. In this article, we present a formal modelling for the management capabilities of environmental management and reporting over reputational risk, considering that reputational risk is becoming increasingly important for organizations and it directly depends on the information available about companies' environmental performances. As long as the effectiveness of communication and disclosure plays a key role in the process, the usefulness of environmental management and reporting as a hedging instrument for reputational risk is addressed through different levels of information transparency. When considering a scenario of voluntary reporting, we show that environmentally concerned companies can reduce the cost of environmental management as a reputational risk strategy, as well as reducing the potential loss of reputational value from reputational threats and increasing the potential profit from reputational opportunities. In the context of mandatory reporting, we highlight the role of assurance companies as bearers of the risk of bad reputations for non-concerned companies. As a result, this novel approach applies theoretical oriented research from options theory to reputational risk management literature, so that it benefits from the option's well known theory, robustness, and conclusions.

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“…The size of the instances is in line with the application considered. In effect, the number of projects jointly evaluated is typically limited (see [12]) since a pre-evaluation phase is usually performed with the aim of defining homogeneous groups (for nature, length, correlation and so on).…”

Section: Numerical Resultsmentioning

confidence: 99%

Capital rationing problems under uncertainty and risk

2011

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Capital rationing is a major problem in managerial decision making. The classical mathematical formulation of the problem relies on a multi-dimensional knapsack model with known input parameters. Since capital rationing is carried out in conditions where uncertainty is the rule rather than the exception, the hypothesis of deterministic data limits the applicability of deterministic formulations in real settings. This paper proposes a stochastic version of the capital rationing problem which explicitly accounts for uncertainty. In particular, a mathematical formulation is provided in the framework of stochastic programming with joint probabilistic constraints and a novel solution approach is proposed. The basic model is also extended to include specific risk measures. Preliminary computational results are presented and discussed.

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An approximate solution approach for a scenario-based capital budgeting model

Abstract: Real options, Capital budgeting, Scenario-based optimization, 0-1 Integer programming,

Cited by 9 publications

References 25 publications

Threshold Boolean form for joint probabilistic constraints with random technology matrix

Threshold Boolean form for joint probabilistic constraints with random technology matrix

Managing Reputational Risk through Environmental Management and Reporting: An Options Theory Approach

Capital rationing problems under uncertainty and risk

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