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Comparison of Continuous and Discrete Time Formulations for Load Tracking Scheduling Problems


K. Nolde

vol. AUT08-06

In this paper we presents two load tracking scheduling problem. The first problem deals with the scheduling of employees so that the employee presence tracks a pre-specified demand curve. Requirements such as minimum employee presence or constraints on the shift length have to be respected. The second problem is concerned with the energy-cost optimal scheduling of a steel plant. In the steel plant the total electrical load generated by all machines must track a pre-specified energy curve as close as possible, while respecting constraints that arise from production. For both problems a comparison of discrete-time and continuous-time models of the scheduling problems is made. The results show that in the workforce planning a solution is computed faster for the discrete-time model. In the steel plant scheduling the continuous-time model is superior. It is argued that discrete-time models are superior for problems where only few possible switching time points exist, i. e. time points when tasks can start or end. Continuous-time formulations do not seem restricted by the number of possible time points, but their limitation appears to be in the number of possible arrangements of the tasks that are to be scheduled. Furthermore, we show an example for the continuous-time problem where small parameter changes lead to large changes in the computation time.


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(04)Technical Report

M. Morari

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% Autogenerated BibTeX entry
@TechReport { Xxx:2008:IFA_3097,
    author={K. Nolde},
    title={{Comparison of Continuous and Discrete Time Formulations for
	  Load Tracking Scheduling Problems}},
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