Most of the recent work on 2–stage stochastic combinatorial optimization problems have focused on the minimization of the expected cost or the worst–case cost of the solution. Those two objectives can be viewed as two extreme ways of handling risk. In this paper we propose to use an one–parameter family of functionals to interpolate between them. Although such a family has been used in the math...

We study an unrelated parallel machines scheduling problem with sequence and machine dependent setup times. A logicbased Benders decomposition approach is proposed to minimize the makespan. This approach is a hybrid model that makes use of a mixed integer programming master problem and a specialized solver for travelling salesman subproblems. The master problem is used to assign jobs to machine...

This paper presents scaled quadratic cuts based on scaling the second-order Taylor expansion terms for the decomposition methods Outer Approximation (OA) and Partial Surrogate Cuts (PSC) used for solving convex Mixed Integer Nonlinear Programing (MINLP). The scaled quadratic cut is proved to be a stricter and tighter underestimation for the convex nonlinear functions than the classical supporti...

In this paper, a Stochastic Dynamic Facility Location Problem (SDFLP) is formulated. In the first part, an exact solution method based on stochastic dynamic programming is given. It is only usable for small instances. In the second part a Monte Carlo based method for solving larger instances is applied, which is derived from the Sample Average Approximation (SAA) method.

This paper considers the problem of capacity planning and operation of energy grids where the power demands are served from renewable energy sources, such as wind farms, and the transmission network is represented by the High-Voltage Direct Current (HVDC) lines. The principal question considered in this work is whether a risk-averse design of the grid, including the selection of wind farm locat...

In this paper, a two-stage robust optimisation is presented for an uncapacitated hub location problem in which demand uncertain and the level of conservatism controlled by uncertainty budget. first stage, locations establishing facilities were determined, allocation decisions made second stage. An accelerated Benders decomposition algorithm was used to solve problem. Computational experiments s...

We present an algorithmic approach for solving two-stage stochastic mixed 0-1 problems. The first stage constraints of the Deterministic Equivalent Model have 0–1 variables and continuous variables. The approach uses the Twin Node Family (TNF) concept within the algorithmic framework so-called Branch-and-Fix Coordination for satisfying the nonanticipativity constraints, jointly with a Benders D...

The stochastic linear programming problem with recourse has a dual block angular structure. It can thus be handled by Benders decomposition or by Kelley's method of cutting planes; equivalently the dual problem has a primal block angular structure and can be handled by Dantzig-Wolfe decomposition| the two approaches are in fact identical by duality. Here we shall investigate the use of the meth...