A new mixed-integer modeling approach for capacity-constrained continuous-time scheduling problems

Nowadays, scheduling and resource management are increasingly important issues for organizations. Indeed, they do not only constitute an underlying necessity to make things work properly within the companies, but are and will always be more critical means to reduce costs and get competitive advantage in the market. Different approaches have been typically employed for these problems during the years. Among the others, linear programming techniques represent a valid tool that, despite applicable only to instances of limited dimension, offers an extremely flexible modeling opportunity, able to produce either optimal or approximate solutions of certified quality. In this spirit, the definition of suitable indicator variables and the use of particular constraints are proposed in the present work, with the aim of providing a useful basis for different mathematical models, taking into account scarce resources and other potential limitations. More in detail, a very well-known problem from the literature, the Resource Constrained Project Scheduling Problem, is investigated, and a new mixed-integer linear formulation is introduced, which treats time as a continuous variable. The considered model presents several advantages from the computational point of view, that are deeply studied and compared with those of one of the best methods recently developed in the same field. Extensive experiments reveal the good performances achieved by the proposed formulation over all the KPIs included in the analysis, thus motivating further applications to derived problems, such as the workforce planning and scheduling framework presented at the end of this dissertation.