Identical parallel machine scheduling with discrete additional resource and an application in audit scheduling

Resource scheduling has been one of the most prominent problems due to its technical challenges and prevalence in real-life. In this paper, we focus on an extension of the parallel machine scheduling problem with additional resources, which can be classified as a static resource-constrained parallel machine scheduling problem with unspecified job-machine assignment. The novelty of the problem we tackle stems from the additional resource that consists of components with discrete levels. The allocation of this resource to machines induces general covering constraints. This distinct characteristic of the additional resource also arises in a real-life audit scheduling problem, in which local branches of a financial firm are to be audited by a set of auditors with different experience levels. The quantification of the auditor experience and the branch experience requirement enable us to model this problem as an extension of the aforementioned scheduling problem with extra constraints related to the auditing process. We propose mathematical models for these problems and two constructive heuristic algorithms. The upper bounds attained by these algorithms are improved by a tabu-search algorithm, and an efficient lower bounding technique is developed for comparative purposes. We conduct extensive computational experiments to assess the performance of the proposed algorithms.