Scheduling pre-emptible tasks with flexible resourcing options and auxiliary resource requirements

Abstract

Scheduling problems are ubiquitous and arise in numerous real-life applications. In this article situations involving resourcing flexibility, auxiliary resource requirements and pre-emption are targeted as they are particularly challenging and complex. Every activity requires an assortment of resources of different types. There are many resourcing options for each activity and exclusive resources must be shared judiciously. Multiple resources must be acquired at the same time and this requires meticulous synchronization to ensure efficiency and performance of the system. To create optimal schedules, a generic mixed integer programming (MIP) model is proposed. Our model can describe any number of additional resource types, resourcing options and permits pre-emptions. We believe this model can easily handle additional restrictions and technical conditions that may arise in practice. To demonstrate this assertion two contemporary maritime applications are considered, and necessary extensions are described. Numerical testing is performed and comments and insights concerning the solvability of instances of varying size and complexity are made. Our numerical testing shows that problems of the size encountered in industry can be solved to optimality when additional restrictions like tidal and departure windows are imposed, and some pre-emption is performed. Permitting too much pre-emption however does not result in large improvements and drastically increases the intractability of the proposed model, thus highlighting the need for advanced meta-heuristics.