40th International Conference on Production Engineering of Serbia
ICPES 2025
Nis, Serbia, 18-19th september 2025
APPLICATION OF THE MATHEMATICAL CONVOLUTION OPERATOR IN THE OPTIMIZATION OF RESOURCE PLANNING AND SCHEDULING
Aleksandar Stankovic, Milica Milunovic, Goran Petrovic
DOI: 10.46793/ICPES25.221S
This paper explores the application of the mathematical operator convolution in the context of resource planning and scheduling problems in industrial processes. Convolution is used as a tool for modelling the interactions between different operations and resources, while taking into account time dependencies and system capacities. It is applied in the context of resource planning and scheduling problems in industrial processes to model the combined probability distributions of the durations of individual operations. Mathematically, convolution enables the calculation of the overall impact of available resources on task execution over time, through the integration or summation of corresponding functions that describe operations and resource capacities. The advantage of applying the convolution operator in the context of summing operation execution times lies in its ability to accurately model the combined probability distribution of total process durations, taking into account the variability and uncertainty of individual operation times. This approach shows that applying convolution in resource planning and scheduling leads to more efficient schedules, with significant improvements in overall productivity and reductions in operational costs compared to traditional methods. The results confirm the potential of convolution as a mathematical tool for solving complex optimization problems in industrial and manufacturing systems
Planning and scheduling of resources, convolution, optimization
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