A new heuristic for the multi-mode resource investment problem

This paper considers the problem of minimizing resource investment required to execute the tasks in a project network by a given project due date. A project consists of non-pre-emptive tasks executed in a known and required precedence order. Each task is completed in one of its feasible modes, which may differ not only in task duration but also in consumption of renewable resources. A priority rule heuristic with polynomial computational complexity is presented for this computationally intractable problem. This heuristic simultaneously considers due date constraints and resource usage to select and schedule tasks with one decision rule. This differs from prior multi-mode priority rule scheduling heuristics that apply two consecutive decision rules to schedule tasks. Extensive computational testing indicates promising results.