AbstractConsideration of bounds, discontinuities and the integrality of decision variables is often helpful for responding to many practical requirements. Using the case of quantity discounting as an example, it is shown why the above considerations add realism to a model, and how they may be incorporated in the solution procedure. The bounds on the order quantity are fulfilled by establishing suitable stopping rules, while gaps in order quantities are resolved by modifying the input data. As for integrality, a result is established which shows that the feasible points for the integer optimum can be obtained by suitably rounding those for the continuous optimum. A comprehensive algorithm containing these features is proposed, and analytical proofs of the results are included.