We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … Read more
Freight consolidation is a logistics practice that improves the cost-effectiveness and efficiency of transportation operations, and also reduces energy consumption and carbon footprint. A “fair” shipping cost sharing scheme is indispensable to help establish and sustain the cooperation of a group of suppliers in freight consolidation. In this paper, we design a truthful acyclic mechanism … Read more
We present a new exact method for bi-objective pure integer linear programming, the so-called Multi-Stage Exact Algorithm (MSEA). The method combines several existing exact and approximate algorithms in the literature to compute the entire nondominated frontier of any bi-objective pure integer linear program. Each algorithm available in MSEA has multiple versions in the literature. Hence, … Read more
We consider a system with an evolving state that can be stopped at any time by a decision maker (DM), yielding a state-dependent reward. The DM does not observe the state except for a limited number of monitoring times, which he must choose, in conjunction with a suitable stopping policy, to maximize his reward. Dealing … Read more
We revisit the correspondence of competitive partial equilibrium with a social optimum in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources which can be stored. The agents can also trade risk using Arrow-Debreu securities. In this … Read more
The Stochastic Dual Dynamic Programming (SDDP) algorithm has become one of the main tools to address convex multistage stochastic optimal control problem. Recently a large amount of work has been devoted to improve the convergence speed of the algorithm through cut-selection and regularization, or to extend the field of applications to non-linear, integer or risk-averse … Read more
We consider a general class of infinite horizon dynamic programmes where state and control sets are convex and compact subsets of Euclidean spaces and (convex) costs are discounted geometrically. The aim of this work is to provide a convergence result for these problems under as few restrictions as possible. Under certain assumptions on the cost … Read more
For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty barrier for the feasible set and a sequence of nonnegative penalty parameters. Differently from the single-valued procedure, MBM is implemented by means of an auxiliary … Read more
As an alternative to traditional integer programming (IP), decision diagrams (DDs) provide a new solution technology for discrete problems based on their combinatorial structure and dynamic programming representation. While the literature mainly focuses on the competitive aspects of DDs as a stand-alone solver, we investigate their complementary role by studying IP techniques that can be … Read more
This paper studies risk in a stochastic auction which facilitates the integration of renewable generation in electricity markets. We model market participants who are risk averse and reflect their risk aversion through coherent risk measures. We uncover a closed-form characterization of a risk-averse generator’s optimal pre-commitment behaviour for a given real-time policy, both with and … Read more