In this paper we consider multiple constrained resource allocation problems, where the constraints can be specified by formulating activity dependency restrictions or by using game-theoretic models. All the problems are focused on generic resources, with a few exceptions which consider financial resources in particular. The problems consider low-risk circumstances and the values of the uncertain variables which are used by the algorithms are the expected values of the variables. For each of the considered problems we propose novel algorithmic solutions for computing optimal resource allocation strategies. The presented solutions are optimal or near-optimal from the perspective of their time complexity. The considered problems have applications in a broad range of domains, like workflow scheduling in industry (e.g. in the mining and metallurgical industry) or the financial sector, motion planning, facility location and data transfer or job scheduling and resource management in Grids, clouds or other distributed systems.