A simple randomised algorithm for convex optimisation: Application to two-stage stochastic programming

We consider maximising a concave function over a convex set by a simple randomised algorithm. The strength of the algorithm is that it requires only approximate function evaluations for the concave function and a weak membership oracle for the convex set. Under smoothness conditions on the function and the feasible set, we show that our algorithm computes a near-optimal point in a number of operations which is bounded by a polynomial function of all relevant input parameters and the reciprocal of the desired precision, with high probability. As an application to which the features of our algorithm are particularly useful we study two-stage stochastic programming problems. These problems have the property that evaluation of the objective function is #P-hard under appropriate assumptions on the models. Therefore, as a tool within our randomised algorithm, we devise a fully polynomial randomised approximation scheme for these function evaluations, under appropriate assumptions on the models. Moreover, we deal with smoothing the feasible set, which in two-stage stochastic programming is a polyhedron

Improving the Decision-making of Reverse Logistics Network Design Part II: An Improved Scenario-based Solution Method and Numerical Experimentation

The study of the network design problems related to reverse supply chain and reverse logistics is of great interest for both academicians and practitioners due to its important role for a sustainable society. However, reverse logistics network design is a complex decision-making problem that involves several interactive factors and faces many uncertainties. Thus, in order to improve the reverse logistics network design, this paper proposes a new optimization model under stochastic environment and an improved solution method for network design of a multi-stage multi-product reveres supply chain. The study is presented in a series of two parts. Part I presents the relevant literature and formulates a stochastic mixed integer linear programming (MILP) for improving the decision-making of the reverse logistics network design. Part II improves the solution methods for the proposed stochastic programming and illustrates the application through a numerical experimentation

The workload balancing problem at air cargo terminals

10.1007/s00291-006-0035-6OR Spectrum284705-72