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This paper presents a new continuous-time mathematical formulation for short-term scheduling using an explicit representation of the unit-specific time grid, which is constructed using the time point of the event as a reference. Therefore, unlike the traditional models in which it is necessary to analyze the time variables of the activated tasks, it is not necessary to explore the solution to solve the time grid. Initially two scheduling models are proposed specifically for batch processes and continuous processes. The models are applied in the solution of reference problems presented by Shaik et al. (2006) and Shaik and Floudas (2007), considering unit sharing and finite intermediate storage (FIS) and unlimited (UIS), resulting in 8 case studies solved in GAMS software version 24.4.6 by the Branch and Cut method. The optimal solution was reached for all cases and taking in account the number of events, constraints and variables and computational processing time, the proposed models presented good performance. Thus, a new model for batch and continuous processes was developed and applied in the production schedule of a generic plant of phosphate fertilizers considering a time horizon of 30 days of production. In this case, despite not obtaining the ideal solution of the problem, all constraints imposed by the model were attended and the storage capacity of the plant was not exceeded.

Nova abordagem para problemas de programação da produção de curto prazo com representação contínua do tempo