The two products-one machine problem is usually solved under the condition that the production of both products takes place in repetitive cycles. Therefore, the resulting production schedule is not always feasible and it is sometimes possible to determine a better (i.e. cheaper) feasible production schedule. We relax this condition and formulate a dynamic programming model which takes into account the present inventory of both products when it schedules one of the products for production. Furthermore, we indicate how an optimal feasible production schedule can be determined by applying Howard's policy-iteration procedure. Finally, we solve three cases by applying this procedure and we compare the results with production schedules which are obtained by applying three other methods.