Practical guidelines for solving difficult linear programs

TL;DR: In this paper, the authors present suggestions for appropriate use of state-of-the-art optimizers and guidelines for careful formulation, both of which can vastly improve performance of mixed integer programs.

TL;DR: This tutorial demonstrates methods to expedite solutions for instances of the open-pit production-scheduling problem variant through variable definition, preprocessing, algorithmic choice, and the provision of an initial feasible solution.

TL;DR: A novel scheduling formulation that explicitly considers the uncertainty in elective operation durations and also plans for potential randomly arriving urgent demands is developed, showing that incorporating uncertainty via scenarios increases profit and OT utilization when compared to deterministic scheduling methods.

TL;DR: The art of formulating and solving a class of stochastic resource-constrained scheduling problems for elective surgery scheduling and downstream capacity planning is described and areas of opportunity for developing tractable, implementable, and data-driven approaches that might be applicable within and outside healthcare operations.

TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).

TL;DR: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization as mentioned in this paper, which is a standard of graduate-level courses since 1972.

TL;DR: The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal solution in polynomial-time.