Abstract Scalarization is a frequently used approach for finding efficient solutions that satisfy the preferences of the Decision Maker (DM) in multicriteria optimization. The applicability of a scalarization problem to solve integer multicriteria problems depends on the possibilities it provides for the decrease of the computing complexity in finding optimal solutions of this class of problems. This paper presents a reference-neighbourhood scalarizing problem, possessing properties that make it particularly suitable for solving integer problems. One of the aims set in this development has also been the faster obtaining of desired criteria values, defined by the DM, requiring no additional information by him/her. An illustrative example demonstrates the features of this scalarizing problem.