Marginal Risk Constraint Linear Program for Activity Analysis

Abstract

A dichotomous Marginal Risk Constraint (MRC) criterion is proposed to take explicit account of activity income covariance relationships and to restrict the choice of activities within the range of rational combinations. A parametric LP solution procedure is also presented. The E,V boundary approximated is satisfactorily close to that generated from QP.A LTH OU GH the Mean-Variability (E,V) criterion, and thus quadratic programming (QP), is theoretically appealing, it is more difficult to handle computationally than is deterministic linear programming (LP). At the present stage in the art of computation, the computer code for QP models is also much more restrictive in size than are codes available for LP models. These facts place a premium on developing alternative linear models to approximate efficient E, V farm plans. Efficiency of the alternative model can be measured by departure of the approximate E, V boundary from the boundary generated by QP.Hazell has proposed a model which minimizes total absolute deviations and which, he claims, retains the good properties of QP models while allowing use of the LP code [2, 6, 11]. Thomas et al. have used separable programming to approximate the nonlinear total variance constraint when the mean return is maximized [4,10].In this article a Marginal Risk Constraint (MRC) criterion is proposed. This criterion can be fitted into a linear model with dichotomous marginal risk constraints, along with the usual resource restrictions. A multi-stage LP algorithm is proposed to approximate the E,V boundary. The Marginal Risk Constraint Criterion AssumptionsThe return from a set of farm enterprise combinations is assumed to be randomly distributed

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“…1971). marginal risk constrained linear programming (Chen and Baker, 1974) or separable linear programming (Thomas et aL, 1972). In general, these models aid the identification of riskeffcient farm plans from a range of alternatives with specific resource constraints.…”

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Assisting decision‐making in Queensland barley production through chance constrained programming

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