Novel Optimality Cuts for Two-Stage Stochastic Mixed-Integer Programs The applicability and use of two-stage stochastic mixed-integer programs is well-established, thus calling efficient decomposition algorithms to solve them. Such typically rely on optimality cuts approximate the expected second stage cost function from below. In “A Converging Benders’ Decomposition Algorithm Recourse Models,”...

Abstract—In the restructured electricity markets, the generators and the Independent System Operator (ISO) play important roles in the balance of electricity supply and demand. We consider a mixed integer bi-level model reformulated as a mathematical program with complementary constraints (MPCC) in which a single conceptual leader decides the transmission line expansion plan and generators plan...

We study the problem of integrated staffing and scheduling under demand uncertainty. This problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules. The wait-and-see decision is to adjust these schedules at a time closer to the actual date of demand realization. We show that the mixed-i...

Let Sf be the Schwartz space of all rapidly decreasing functions on R, Sf be the topological dual space of Sf and for each positive integer p,Sfp be the space of all elements of £f' which are continuous in the p-th norm defining the nuclear Frechet topology of Sf. The main purpose of the present paper is to show that if {Xtί t e [0, + oo)} is an ^'-valued Gaussian process and for any fixed φβ^ ...

Abstract This paper presents a parametric study on multi-objective integer quadratic programming problem under uncertainty. The proposed procedure presents a quadratic multi-objective integer programming problem with a stochastic parameters in the right hand sides, and all constraints occurs under certain probability. We consider all random variables are normally distributed. We shall be essent...

Recently, in the paper “Threshold Boolean form for joint probabilistic constraints with random technology matrix” (Math. Program. 147:391–427, 2014), Kogan and Lejeune proposed a set of mixed-integer programming formulations for probabilistically constrained stochastic programs having random constraint matrix and finite support distribution. We show that the proposed formulations do not in gene...

Operating room (OR) scheduling is an important operational problem for most hospitals. In this study, we present a novel two-stage stochastic mixed-integer programming (SMIP) model to minimize total expected operating cost given that scheduling decisions are made before the resolution of uncertainty in surgery durations. By using our model, we quantify the benefit of pooling ORs as a shared res...

In this paper, we deal with multiobjective integer programming problems involving random variable coefficients in objective functions and/or constraints. After reformulation of them on the basis of a probability maximization model for the chance constrained programming, incorporating fuzzy goals of the decision maker for the objective functions, we propose an interactive fuzzy satisficing metho...

In this study we consider a multiobjective integer linear stochastic programming problem with individual chance constraints. We assume that there is randomness in the right-hand sides of the constraints only and that the random variables are normally distributed. Some stability notions for such problem are characterized. An auxiliary problem is discussed and an algorithm as well as an illustrat...

The purpose of this paper is to formally describe new optimization models for distributed telecommunication networks. Modern distributed networks put more focus on the processing of information and less on the actual transportation of data, than we are traditionally used to in telecommunications. This paper introduces new models for decision support at operational, tactical and strategic levels...