A Continuous-Time Mixed-Binary Linear Programming Formulation for the Multi-Site Resource-Constrained Project Scheduling Problem

The execution of a project is nowadays often distributed among multiple sites. While some resource units are available at a certain site only, other resource units can be moved across the sites. The problem considered here consists of scheduling a single projects' activities which are interrelated by given precedence relationships of the completion-start type, require various renewable resource types during execution, and can be executed at the different sites of the project, such that the project makespan is minimized; transportation times must be taken into account if a resource unit is moved between two sites, or if two activities interrelated by a precedence relationship are executed at different sites. We present a continuous-time formulation of this problem as a mixed-binary linear program. In an experiment based on a set of 480 instances, we compared the performance of this novel formulation with a discrete-time formulation, which is the only formulation known from the literature; it turned out that when using the novel continuous-time formulation, considerably more instances can be solved to feasibility and to optimality, respectively.