In this paper we propose two algorithms for solving both unweighted and weighted constrained two-dimensional two-staged cutting stock problems. The problem is called two-staged cutting problem because each produced (sub) optimal cutting pattern is realized by using two cut-phases.

IN this paper, we consider a two-level optimization problem (S) (weak Stackelberg problem) in which the constraints of the upper level problem depend on the set of optimal solutions of the lower level problem, supposed not necessarily a singleton. Using penalty methods, we give an approximation...

Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report hereon a deterministic equivalent linear programming model of 1,111,112 constraints and...

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and...

Sequential meta heuristic implementations for the irregular stock-cutting problem have highlighted a number of common problems. The implementation in this paper adopts a hybrid tabu search approach that incorporates two very different optimisation routines which utilise alternative neighborhoods...

The Envelope Theorem is showm to involve comparisons between the performance of the optimal policy and that of alternative policies, which satisfy the constraints of the problem and may also have other features. The theorem is activated whenever parameter values are such that the extreme value...

This paper analyzes the effect of educational debt and loan-forgiveness programs on both law school entry decisions and the subsequent career choices of law school graduates using a dynamic optimization model and data on several cohorts of graduates from the University of Michigan Law School.

In this paper we study the concepts of equilibrium and optimum in static transportation networks with elastic and non-elastic demands. The main mathematical tool of our paper is the theory of variational inequalities. We demonstrate that this theory is useful for proving the existence theorems....

We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant fucntions, but for the main results, we give...

In this paper we develop a new version of the algortihm proposed in [17] for solving exactly some variants of (un)weighted constrained two-dimensional cutting stock problems. We introduce one-dimensional bounded knapsacks in order to obtain an improved initial lower bound for limitating...