Open source solution approaches to a class of stochastic supply chain problems

This research proposes a variety of solution approaches to a class of stochastic supply chain problems, with normally distributed demand in a certain period of time in the future. These problems aim to provide the decisions regarding the production levels; supplier selection for raw materials; and optimal order quantity. The typical problem could be formulated as a mixed integer nonlinear program model, and the objective function for maximizing the expected profit is expressed in an integral format. In order to solve the problem, an open source solution package BONMIN is first employed to get the exact optimum result for small scale instances; then according to the specific feature of the problem a tailored nonlinear branch and bound framework is developed for larger scale problems through the introduction of triangular approximation approach and an iterative algorithm. Both open source solvers and commercial solvers are employed to solve the inner problem, and the results to larger scale problems demonstrate the competency of introduced approaches. In addition, two small heuristics are also introduced and the selected results are reported

Overview on mixed integer nonlinear programming problems

Many optimization problems involve integer and continuous variables that can be modeled as mixed integer nonlinear programming (MINLP) problems. This has led to a wide range of applications, in particular in some engineering areas. Here, we provide a brief overview on MINLP, and present a simple idea for a future nonconvex MINLP solution technique.Fundação para a Ciência e a Tecnologia (FCT

Numerical experiments with nonconvex MINLP problems

We present a methodology to solve nonconvex Mixed-Integer Nonlinear Programming problems, that combines the Branch-and-Bound and simulated annealing type methods, which was implemented in MATLAB. A set of benchmark functions with simple bounds and different dimensions was used to analyze its practical behaviour. We exhibit computational results showing the good performance of the method.Fundação para a Ciência e a Tecnologia (FCT

Hybrid evolutionary techniques for constrained optimisation design

This thesis a research program in which novel and generic optimisation methods were developed so that can be applied to a multitude of mathematically modelled business problems which the standard optimisation techniques often fail to deal with. The continuous and mixed discrete optimisation methods have been investigated by designing new approaches that allow users to more effectively tackle difficult optimisation problems with a mix of integer and real valued variables. The focus of this thesis presents practical suggestions towards the implementation of hybrid evolutionary approaches for solving optimisation problems with highly structured constraints. This work also introduces a derivation of the different optimisation methods that have been reported in the literature. Major theoretical properties of the new methods have been presented and implemented. Here we present detailed description of the most essential steps of the implementation. The performance of the developed methods is evaluated against real-world benchmark problems, and the numerical results of the test problems are found to be competitive compared to existing methods