We introduce a new model for robust combinatorial optimization where the uncertain parameters belong to the image of multifunctions of the problem variables. In particular, we study the variable budgeted uncertainty, an extension of the budgeted uncertainty introduced by Bertsimas and Sim. Variable budgeted uncertainty can provide the same probabilistic guarantee as the budgeted uncertainty … Read more
We present a risk-averse multi-dimensional newsvendor model for a class of products whose demands are strongly correlated and subject to fashion trends that are not fully understood at the time when orders are placed. The demand distribution is known to be multimodal in the sense that there are spatially separated clusters of probability mass but … Read more
This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a … Read more
We compare different approaches of optimization under uncertainty in the context of pricing strategies for conspicuous consumption products in recession periods of uncertain duration and strength. We consider robust worst-case ideas and how the concepts of Value at Risk (VaR) and Conditional Value at Risk (CVaR) can be incorporated efficiently. The approaches are generic in … Read more
This article explains, again, why radius of stability models, such as info-gap’s robustness model, are models of local robustness and why they are therefore unsuitable for the treatment of severe uncertainty. CitationWorking Paper SM-12-2, Department of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria, Australia.ArticleDownload View PDF
This paper formalizes and adapts the well known concept of Pareto efficiency in the context of the popular robust optimization (RO) methodology. We argue that the classical RO paradigm need not produce solutions that possess the associated property of Pareto optimality, and illustrate via examples how this could lead to inefficiencies and sub-optimal performance in … Read more
In this paper we introduce a new numerical optimization technique, a Probabilistic-Driven Search Algorithm. This algorithm has the following characteristics: 1) In each iteration of loop, the algorithm just changes the value of k variables to find a new solution better than the current one; 2) In each variable of the solution of the problem, … Read more
This paper is mainly devoted to the study of the so-called full Lipschitzian stability of local solutions to finite-dimensional parameterized problems of constrained optimization, which has been well recognized as a very important property from both viewpoints of optimization theory and its applications. Based on second- order generalized differential tools of variational analysis, we obtain … Read more
This paper provides an overview of developments in robust optimization and robustness published in the academic literature over the past five years. CitationTechnical report, LAMSADE, Universite Paris-Dauphine, Paris, France. (2012)ArticleDownload View PDF
This paper describes a multi-range robust optimization approach applied to the problem of capacity investment under uncertainty. In multi-range robust optimization, an uncertain parameter is allowed to take values from more than one uncertainty range. We consider a number of possible projects with anticipated costs and cash flows, and an investment decision to be made … Read more