Resource loading: Applications and complexity analysis

This paper studies the resource loading problem, which consists of a set of jobs that must be scheduled within a given time horizon that is organized into consecutive time periods, where each period is associated with a fixed number of available workers. The objective is to find a feasible schedule that minimizes the number of additional workers needed to execute all the jobs. We describe how this problem arises in industry, and we study six special cases. We present polynomial algorithms for the easy cases and pseudo-polynomial algorithms for weakly NP-hard cases, and we study the approximation of the strongly NP-hard subproblems.