Mathematical programming models for scheduling in a CPU/FPGA architecture with heterogeneous communication delays

This paper deals with the mathematical modelling of a scheduling problem in a heterogeneous CPU/FPGA architecture with heterogeneous communication delays in order to minimize the makespan, Cmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{max}$$\end{document}. This study was motivated by the quality of the available solvers for Mixed Integer Program. The proposed model includes the communication delay constraints in a heterogeneous case, depending on both tasks and computing units. These constraints are linearized without adding any extra variables and the obtained linear model is reduced to speed-up the solving with CPLEX up to 60 times. Computational results show that the proposed model is promising. For an average sized problem of up to 50 tasks and five computing units the solving time under CPLEX is a few seconds.