A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second … Read more
Energy efficiency and renewable energy become more attractive in smart grid. In order to efficiently reduce global energy usage in building energy systems and to improve local environmental sustainability, it is essential to optimize the operation and the performance of combined heat and power (CHP) systems. In addition, intermittent renewable energy and imprecisely predicted customer … Read more
We introduce the Stochastic multistage fixed charge transportation problem in which a producer has to ship an uncertain load to a customer within a deadline. At each time period, a fixed transportation price can be paid to buy a transportation capacity. If the transportation capacity is used, the supplier also pays an uncertain unit transportation … Read more
We present a two-stage stochastic linear programming model to manage the inventory of vaccine vials in developing countries. In these countries immunization programs often involve targeted outreach services in remote locations. Organizations managing these programs are in need of tools which identify inventory replenishment and vaccine utilization plans to minimize costs and wastage while achieving … Read more
Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions which depend on a randomization device producing uniformly distributed samples that are independent of all … Read more
In this paper, we first consider the stability analysis of a convex quadratic programming problem and its restricted Wolfe dual in which all parameters in the problem are perturbed. We demonstrate the upper semi-continuity of solution mappings for the primal problem and the restricted Wolfe dual problem and establish the Hadamard directionally differentiability of the … Read more
Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions and the objective function is a dynamic measure of risk. For this reason, we propose a scenario tree decomposition approach, namely group subproblem approach, … Read more
We consider unconstrained minimization of a finite sum of $N$ continuously differentiable, not necessarily convex, cost functions. Several gradient-like (and more generally, line search) methods, where the full gradient (the sum of $N$ component costs’ gradients) at each iteration~$k$ is replaced with an inexpensive approximation based on a sub-sample~$\mathcal N_k$ of the component costs’ gradients, … Read more
In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such ”infinite” problems are practically impossible to solve as they are formulated and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e. finite … Read more
Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ … Read more