Stock prepositioning is one of the most important issues in preparedness stage of emergency logistics response. In a previous research, a stock prepositioning model to support an emergency disaster relief response in the event of earthquake has been proposed. Since the results contained zero proportion of some type of item, which is not allowed in a real system, an improvement of the model is needed. Hence, in this paper we focus on how to prevent the result of zero proportion of a single item type stored in distribution centers, which is the proportion of relief demand satisfied of disaster areas. We propose a new model by adding new variable of proportion of unsatisfied relief demand. Thus, we apply this model to a real case with 33 disaster areas and 16 distribution centers in Indonesia. Finally, the sensitivity analysis is performed to show the effect of different upper bound of the proportion of unsatisfied relief demand.