In the previous lecture, we introduced linear programming using slack form, and we showed how to solve an LP assuming that we have a black box for solving an LP starting from a feasible solution (SimplexInner). In this lecture, we would present SimplexInner. Slack form-a tuple (N, B, A, b, c, v) is an LP. The feasible solution is generated by assigning all the Nonbasic variables the value zero....

Bus schedules cannot be easily maintained on busy lines with short headways: Experience shows that buses offering this type of service usually arrive irregularly at their stops, often in bunches. Although transit agencies build slack into their schedules to alleviate this problem, their attempts often fail because practical amounts of slack cannot prevent large localized disruptions from spread...

Data Envelopment Analysis (DEA) is a mathematical programming-based approach for evaluates the relative efficiency of a set of DMUs (Decision Making Units). The relative efficiency of a DMU is the result of comparing the inputs and outputs of the DMU and those of other DMUs in the PPS (Production Possibility Set). Also, in Data Envelopment Analysis various models have been developed in order to...

This study applies the dynamic slack-based measure (DSBM) model to evaluate the performance of 34 Chinese life insurance companies for the period 2006–2010. This study also examines the relationship between intellectual capital and performance using the truncated regression approach. Our findings indicate that over the period of the study, the mean efficiency scores of life insurers are relativ...

Recent research into the problem of jointly scheduling tasks with both hard and soft time constraints has focused on the development of optimal slack stealing algorithms. Theoretically, these optimal algorithms offer significant performance improvements over previous bandwidth preserving algorithms such as the Sporadic Server or Extended Priority Exchange algorithm. However, there are problems ...

In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave well under polarity and have efficien...

The Slack and Slick genes encode potassium channels that are very widely expressed in the central nervous system. These channels are activated by elevations in intracellular sodium, such as those that occur during trains of one or more action potentials, or following activation of non-selective cationic neurotransmitter receptors such as AMPA receptors. This review covers the cellular and molec...