In this paper we consider a transportation problem under uncertainty related to gypsum replenishment for a cement producer. The problem is to determine the number of vehicles to book at the beginning of each week to replenish gypsum at all the cement factories of the producer in order to minimize the total cost, given by … Read more
Dual-sourcing inventory systems, in which one supplier is faster (i.e. express) and more costly, while the other is slower (i.e. regular) and cheaper, arise naturally in many real-world supply chains. These systems are notoriously difficult to optimize due to the complex structure of the optimal solution and the curse of dimensionality, having resisted solution for … Read more
We discuss the incorporation of risk measures into multistage stochastic programs. While much attention has been recently devoted in the literature to this type of model, it appears that there is no consensus on the best way to accomplish that goal. In this paper, we discuss pros and cons of some of the existing approaches. … Read more
Multistage stochastic programs bring computational complexity which may increase exponentially in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal solution are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value … Read more
In this paper, we propose two block coordinate gradient (BCG) methods for the online convex programming: the BCG method with the cyclic rule and the BCG method with the random rule. The proposed methods solve a low dimensional problem at each iteration, and hence they are efficient for large scale problems. For the proposed methods, … Read more
Reward-risk ratio optimization is an important mathematical approach in finance. In this paper, we revisit the model by considering a situation where an investor does not have complete information on the distribution of the underlying uncertainty and consequently a robust action is taken against the risk arising from ambiguity of the true distribution. We propose … Read more
The intermittent nature of wind energy generation has introduced a new degree of uncertainty to the tactical planning of energy systems. Short-term energy balancing decisions are no longer (fully) known, and it is this lack of knowledge that causes the need for strategic thinking. But despite this observation, strategic models are rarely set in an … Read more
This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, … Read more
In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution of uncertain model parameters, and the outer risk measure quantifies the risk that occurs when estimating … Read more
We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using … Read more