Abstract: This paper studies a single machine problem related to the just-In-Time (JIT) production objective in which the goal is to minimize the sum of weighted mean squared deviation of the completion times with respect to a common due date. In order to solve the problem, several structural and dominance properties of the optimal solution are investigated. These properties are then integrated within a branch and-cut approach to solve a time-indexed formulation of the problem. The results of a computational experiment with the proposed algorithm show that the method is able to optimally solve instances with up to 300 jobs within reduced running times, improving other integer programming approaches. (C) 2017 Elsevier B.V. All rights reserved.