Sensitivity analysis in convex quadratic optimization: Simultaneous perturbation of the objective and right-hand-side vectors

In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval are generalized to the case of simultaneous perturbation. Criteria for convexity, concavity or linearity of the optimal value function on invariancy intervals are derived. Furthermore, differentiability of the optimal value function is studied, and linear optimization problems are given to calculate the left and right derivatives. An algorithm, that is capable to compute the transition points and optimal partitions on all invariancy intervals, is outlined. We specialize the method to Linear Optimization problems and provide a practical example of simultaneous perturbation parametric quadratic optimization problem from electrical engineering

A General Modeling Framework for the Long-Term Scheduling of Multiproduct Pipelines with Delivery Constraints

Common carrier pipelines are one of the most economic modes for transportation of petroleum refined products over land, especially when huge amounts of these products have to be pumped toward long-distance terminals. This paper introduces a novel Mixed Integer Linear Programming (MILP)-based approach for the long-term scheduling of a real world multiproduct pipeline connecting a unique refinery to several distribution centers. This approach allows consideration of multiple due dates for demands at period ends, flow rate limitation on pipeline segments, and simultaneous deliveries at distribution centers. The proposed model results in substantial reduction in pump operation and maintenance costs in comparison with the available models. Computational results and data are reported

Bi-parametric optimal partition invariancy sensitivity analysis in linear optimization

Linear optimization, Bi-parametric sensitivity analysis, Optimal partition, Invariancy region, Optimal value function,