(703a) A New Multitasking Continuous Time Formulation for Short-Term Scheduling of Operations in Multipurpose Plants
The problem of short-term scheduling for multipurpose plants has been the subject of significant research over the past two decades. Discrete and continuous formulations that take the form of a mixed-integer linear programming problem (MILP) have been proposed to address this emerging problem in the industry. Despite the burgeoning of continuous time formulations in the past decade, the existing approaches in the literature have not considered the case of machines capable of performing multiple tasks at the same time in multipurpose plants (i.e., multitasking). Plants in sectors such as semiconductor manufacturing and analytical services sectors consider machines capable of performing different tasks simultaneously; hence, the need to develop formulations that enable optimal scheduling of their operations. This paper aims at presenting a novel continuous time formulation for scheduling operations at multipurpose facilities with machines capable of multitasking. The proposed formulation uses the idea of Global event-based formulation to represent time as a continuous variable. Apart from accounting for operational constraints present at multipurpose facilities, e.g. sequential constraints, flow conservation constraint and capacity constraints, the formulation is capable of adopting different operational objective functions such as maximizing throughput or minimizing the turn-around time of the facility. These features make the formulation readily applicable to those multipurpose facilities that have machines with the multitasking feature. To assess the impact of incorporating the multitasking feature of the machines, the performance of the proposed formulation is compared against a continuous time formulation that is not capable of incorporating this feature (essentially, a single tasking formulation). The results, conducted through the solution of multiple instances, ranging from small to relatively large instances, shows that the quality of the solution obtained through the multitasking formulation is considerably better than its single-tasking counterpart. Furthermore, the CPU time obtained for both formulations is very similar for the instances considered in the comparative study. Thus, the proposed multitasking formulation is capable of generating considerably better quality solutions compared to its single-tasking counterpart while requiring similar solution times.