An advanced dual algorithm with constraint relaxation for all-integer programming

In this article we present an all-integer cutting plane algorithm called the Reduced Advanced Start Algorithm (RASA). The technique incorporates an infeasible advanced start based on the optimal solution to the LP relaxation, and initially discards nonbinding constraints in this solution. We discuss the results of computational testing on a set of standard problems and illustrate the operation of the algorithm with three small examples.     

An efficient primal approach to bottleneck transportation problems

This article addresses bottleneck linear programming problems and in particular capacitated and constrained bottleneck transportation problems. A pseudopricing procedure based on the poly-ω procedure is used to facilitate the primal simplex procedure. This process allows the recent computational developments such as the Extended Threaded Index Method to be applied to bottleneck transportation problems. The impact on problem solution times is illustrated by computational testing and comparison with other current methods.     

A primal-dual cutting-plane algorithm for all-integer programming

The integer programming literature contains many algorithms for solving all-integer programming problems but, in general, existing algorithms are less than satisfactory even in solving problems of modest size. In this paper we present a new technique for solving the all-integer, integer programming problem. This algorithm is a hybrid (i.e., primal-dual) cutting-plane method which alternates between a primal-feasible stage related to Young's simplified primal algorithm, and a dual-infeasible stage related to Gomory's dual all-integer algorithm. We present the results of computational testing.