Using simulation and reliability concepts to set starting times in multitask projects with random duration and a common deadline

In production and transportation logistics, it is frequent to have projects in which different tasks must be processed in parallel and completed before a common deadline. Usually, it is not desirable to assign scarce resources to a new project earlier than strictly necessary, since they might be currently occupied in other projects. When these tasks have random completion times, some natural questions arise: (i) how much can we delay the starting time of each task in the new project so that it can be completed by the deadline with a given probability? and (ii) how to compute these ‘optimal’ starting times when not all tasks need to be necessarily finished to consider the project as completed? This paper proposes a hybrid approach, combining reliability concepts with simulation and optimization techniques, to support decision makers in finding the optimal starting times for each task under the described uncertainty scenario.