Minimum-Cost Cattle Feed Under Probabilistic Protein Constraints

Abstract

The optimal composition of cattle feed, which can be formulated as a linear programming problem in the case of certainty, is considered when compositions of inputs vary. In the corresponding linear programming formulation the coefficients of the constraints are not constant but can be considered as stochastic. Reformulating the constraints as chance constraints, a nonlinear programming problem results. For an illustrative example this problem is solved using one of Zoutendijk's methods of feasible directions.

Distribution sensitivity in stochastic programming

“…However, under additional hypotheses discussed in Remark 5.2 conclusions on qualitative stability w.r.t, weak convergence may be drawn. For particular models with one joint chance constraint (a nonlinear model with random right-hand side, a linear model with random technology matrix [42]) we established quantitative stability under verifiable conditions (Corollaries 5.6 and 5.9).…”

Models and algorithms for network design problems

“…Previous results in this direction assume that all random variables are normally distributed. In that case, the probabilistic constraints can be rewritten as quadratic constraints (Kataoka, 1963;Prékopa, 1995;van de Panne and Popp, 1963), convex under some assumption on the condence level (Parikh, 1968). If all variables are binary, the constraints can be further linearized using classical techniques (Hansen and Meyer, 2009).…”

Chance Constrained Programming and Its Applications to Energy Management

“…A classical result by van de Panne & Popp (1963) and by Kataoka (1963) states that if the random matrix A(ξ) reduces to just one line A 1 (ξ),t h e mapping g is the identity (i.e., g(x)=x), ξ has a regular multivariate normal distribution and p ≥ 0.5, then the set (8) is convex. A first difference with the log-concavity properties stated above is that convexity of the feasible set does no longer hold true for arbitrary probability levels but only for sufficiently large ones.…”