In this paper we will describe a Multi-Agent System which is capable of finding a feasible solution of a specially structured linear programming problem. Emphasis is given to correctness issues and termination detection.

In this paper we generalize the so-called first-in-last-out pivot rule and the most-often-selected-variable pivot rule for the simplex method, as proposed in Zhang \cite{Z91}, to the criss-cross pivot setting where neither the primal nor the dual feasibility is preserved. The finiteness of the...

We propose a polynomial time primal-dual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rank-one updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the...

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach...

In this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face is...

In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a right--hand side...

We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a min-sum or min-max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results...

Airline seat inventory control is a very profitable tool in the airline industry. Mathematical programming models provide booking limits or bid-prices for all itineraries and fare classes based on demand forecasts. But the actual revenue generated in the booking process fails to meet...

This paper studies decision rules for accepting reservations for stays in a hotel based on deterministic and stochastic mathematical programming techniques. Booking control strategies are constructed that include ideas for nesting, booking limits and bid prices. We allow for multiple day stays....