The Roman domination problem is considered. An improvement of two existing Integer Linear Programing (ILP) formulations is proposed and a comparison between the old and new ones is given. Correctness proofs show that improved linear programing formulations are equivalent to the existing ones regardless of the variables relaxation and usage of lesser number of constraints.

Concave Mixed-Integer Quadratic Programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work we describe two algorithms that find an -approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithms is polynomial in the size of the problem and in 1/ , provided ...

This manuscript introduces ANTIGONE, Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-p...

This study extends a mathematical model that integrates the location, allocation, inventory replenishment and routing decisions simultaneously. To cope with inherent uncertainty of parameters, we implement a continuous-time Markov process and derive the performance measures of the system. Using the obtained results, the problem is formulated as a mixed integer nonlinear programing model (MINLP)...

We study split cuts and extended formulations for Mixed Integer Conic Quadratic Programming (MICQP) and their relation to Conic Mixed Integer Rounding (CMIR) cuts. We show that CMIR is a linear split cut for the polyhedral portion of an extended formulation of a quadratic set and it can be weaker than the nonlinear split cut of the same quadratic set. However, we also show that families of CMIR...

After occurrence of some disturbances in power system that causes the sever imbalance between generation power and electrical load, the power system frequency begins to decrease. To prevent power system frequency instability and stop the frequency decay below the power system allowable frequency limitation, load shedding schemes should be utilized by applying under frequency load shedding relay...

We focus on a three-stage supply chain problem for fast moving consumer goods including a supplier, a manufacturer and customers. There are different orders over identical cycles, to be processed in production site. The problem is to find a joint cyclic schedule of raw material procurement and job scheduling minimized the total cost comprised of raw material ordering cost and holding cost, prod...

This paper designs a reliability distribution network with limited capacity under partial and complete facility disruptions. To increase the reliability of the distribution network, a new mixed integer linear programing model is developed by considering multiple mitigation strategies including diversification, fortification, and transshipment. The distribution network constitutes of reliable di...