Optimization and Allocation in Some Decision Problems with Several Agents or with Stochastic Elements

Abstract

This dissertation addresses sorne decision problems that arise in project management, cooperative game theory and vehicle route optimization. We start with the problem of allocating the delay costs of a project. In a stochastic context in which we assume that activity durations are random variables, we propose and study an allocation rule based on the Shapley value. In addition, we present an R package that allows a comprehensive control of the project, including the new rule. We propose and characterize new egalitarian solutions in the context of cooperative games with a coalitional structure. Also, using a necessary player property we introduce a new value for cooperative games, which we later extend and characterize within the framework of cooperative games with a coalitional structure. Finally, we present a two-step algorithm for solving multi-compartment vehicle route problems with stochastic demands. This algorithm obtains an initial solution through a constructive heuristic and then uses a tabu search to improve the solution. Using real data, we evaluate the performance of the algorithm.