In a previous work, we have introduced an algorithm, called RaBVItG, used for computing Feedback Nash equilibria of deterministic multiplayers Differential Games. This algorithm is based on a sequence of Game Iterations (i.e., a numerical method to simulate an equilibrium of a Differential Game), combined with Value Iterations (i.e, a numerical method to solve a … Read more
We study new generalizations of the classical capacitated lot-sizing problem with concave production (or transportation), holding, and subcontracting cost functions in which the total production (or transportation) capacity in each time period is the summation of capacities of a subset of n available modules (machines or vehicles) of different capacities. We refer to this problem … Read more
We consider a distributionally robust Partially Observable Markov Decision Process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint … Read more
We study a variant of the multi-period vehicle routing problem, in which a service provider offers a discount to customer in exchange for delivery flexibility. We establish theoretical properties and empirical insights regarding the intricate and complex relation between the benefit from additional delivery flexibility, the discounts offered to customers to gain additional delivery flexibility, … Read more
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost to go functions. An example of such a class of cuts are those derived using … Read more
The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. … Read more
This paper develops an exact solution algorithm for the Multiple Sequence Alignment (MSA) problem. In the first step, we design a dynamic programming model and use it to construct a novel Multi-valued Decision Diagrams (MDD) representation of all pairwise sequence alignments (PSA). PSA MDDs are then synchronized using side constraints to model the MSA problem … Read more
Planning under uncertainty is a frequently encountered problem. Noisy observation is a typical situation that introduces uncertainty. Such a problem can be formulated as a Partially Observable Markov Decision Process (POMDP). However, solving a POMDP is nontrivial and can be computationally expensive in continuous state, action, observation and latent state space. Through this work, we … Read more
Mathematical programming formulation to identify the optimal value function of a negative Markov decision process (MDP) is non-convex, non-smooth, and computationally intractable. Also note that other well-known solution methods of MDP do not work properly for a negative MDP. More specifically, the policy iteration diverges, and the value iteration converges but does not provide an … Read more
The minimum color-degree perfect b-matching roblem (Col-BM) is a new extension of the perfect b-matching problem to edge-colored graphs. The objective of Col-BM is to minimize the maximum number of differently colored edges in a perfect b-matching that are incident to the same node. We show that Col-BM is NP-hard on bipartite graphs by a … Read more