We present a simple model that allows hysteresis loops with exchange bias to be reproduced. The model is a modification of the $T=0$ random-field Ising model driven by an external field and with synchronous local relaxation dynamics. The main novelty of the model is that a certain fraction f of the exchange constants between neighboring spins is enhanced to a very large value ${J}_{E}.$ The model allows the dependence of the exchange bias and other properties of the hysteresis loops to be analyzed as a function of the parameters of the model: the fraction f of enhanced bonds, the amount of the enhancement ${J}_{E},$ and the amount of disorder, which is controlled by the width $\ensuremath{\sigma}$ of the Gaussian distribution of the random fields.