In this paper we describe a two-stage optimization model for determining robust rolling stock circulations for passenger trains. Here robustness means that the rolling stock circulations can better deal with large disruptions of the railway system. The two-stage optimization model is formulated as a large Mixed-Integer Linear Programming model. We first use Benders decomposition to determine op...

In this paper, we propose new mathematical programming approaches for computing time-dependent bid prices in network revenue management problems. In contrast with previous models, ours can accommodate more than one customer request between two successive bid price updates, as frequently occurs in practice. As a first approach, we introduce a simplified version of our time-dependent bid price mo...

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint ove...

The problem of scheduling under uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to Mixed-Integer Linear Programming (MILP) problems produces “robust” solutions that are, in a sense, immune against uncertainty. The robust optimization approach is applied to the scheduling under uncertainty problem. Based on a novel and effective continuous-time sh...

Introduction: A chance constrained optimization problem involves constraints with stochastic data that are required to be satisfied with a pre-specified probability. When the underlying distribution of the stochastic data is not known precisely, an often used model is to require the chance constraints to hold for all distributions in a given family. Such a problem is known as a distributionally...

This paper presents a new nonlinear mathematical model to solve a cell formation problem which assumes that processing time and inter-arrival time of parts are random variables. In this research, cells are defined as a queue system which will be optimized via queuing theory. In this queue system, each machine is assumed as a server and each part as a customer. The grouping of machines and parts...

This paper presents the simultaneous solution of the optimal sequencing and optimal dynamic transitions of two multigrade polymerization CSTRs. The simultaneous formulation results in a Mixed-Integer Dynamic Optimization (MIDO) problem. The profiles of the state variables during dynamic transitions are discretized using orthogonal collocation on finite elements, transforming the MIDO problem in...

In this paper methods of mixing decision rules are investigated and applied to the so-called multiple job type assignment problem with specialized servers which is modeled as continuous time Markov decision process. Performance optimization is difficult for this assignment problem, but optimization over the class of static policies is tractable. By applying the described mixing methods a suitab...

Duality theory is important in finding solutions to optimization problems. For example, linear programming problems, the primal and dual problem pairs are closely related, i.e., if optimal solution of one known, then for other can be obtained easily. In order an solved through dual, first step formulate its analyze characteristics. this paper, we construct model uncertain multi-objective as wel...