Capital Budgeting Under Capital Rationing: An Analytical Overview of Optimization Models for Government

Khan, Aman

doi:10.1080/01900690701411016

Cited by 3 publications

(2 citation statements)

References 37 publications

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“…A survey considering Fortune 500 firms indicates that more than 60% of them place a limit on the internal capital available for investment plans [21]. We refer to [16] for a review of the mathematical programming approaches used for capital rationing purposes. The problem of rationing capital under uncertainty was first studied by Lorie and Savage [20] who describe the challenges of capital rationing problems involving multi-period projects that generate inflows and outflows dispersed across their lifetimes.…”

Section: Strengthened Mixed-integer Linear Programming Formulationmentioning

confidence: 99%

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: Strengthened Mixed-integer Linear Programming Formulationmentioning

confidence: 99%

Threshold Boolean form for joint probabilistic constraints with random technology matrix

Kogan

Lejeune

2013

Math. Program.

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“…The general problem of resource allocation under budget constraint is not new and there is an abundant literature on the subject. Khan (2008) achieved a short but very complete review, showing that linear programming, which dates back at least to Lorie and Savage (1955), has been widely used. But strangely enough, none of those papers addresses the characteristics of transport investments, which are: the set of projects is a list of discrete ones; the year of implementation of each project is not yet decided but is a variable to decide on; their NPVs and, in the case of private funding, the revenues they yield depend on this year of implementation.…”

confidence: 99%

Cost–Benefit Indicators and Transport Programming*

Quinet¹

2011

Fiscal Studies

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The methodology of investment appraisal through cost–benefit analysis has received a lot of attention in the economics literature. However, the major part of the work has focused on the evaluation of yearly benefits and their components. Most guidelines list some indicators, such as the internal rate of return, the net present value per euro spent or the first‐year benefit–cost ratio, but with no clear indication of how and in which cases they should be used. Building on the transport case, this paper aims to fill this gap. It recalls the teachings of economic analysis for project prioritisation, based on the principle of maximising the net present value. Through simulations, it examines how the various indicators perform, considering two situations, with and without budget constraints. It turns out that the various indicators perform roughly the same as long as the projects under comparison have similar benefit patterns over time, and using them does not induce losses that are too large, though the order of implementation is rather different from the optimal one. However, the indicators lead to huge under‐optimisations when the projects have different patterns. The conclusion is that rigorous programme optimisation should be preferred to the use of indicators, and would encourage a wider use of cost–benefit analysis, which is presently too often limited to checking projects one by one.

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Introduction

Kalyebara¹,

Islam²

2013

Contributions to Management Science

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Capital Budgeting Under Capital Rationing: An Analytical Overview of Optimization Models for Government

Cited by 3 publications

References 37 publications

Threshold Boolean form for joint probabilistic constraints with random technology matrix

Threshold Boolean form for joint probabilistic constraints with random technology matrix

Cost–Benefit Indicators and Transport Programming*

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