This paper presents a procedure of numerically solving a Multi-Item Single Machine Lot Size Scheduling Problem by Quasi-Variational Inequality Theory. First, in order to obtain the optimal cost function (u^0(x), …, u^m(x)) characterized as the maximum element of a set of functions defined appropriately, approximated expressions of the optimality condition are derived. Second, we propose an algorithm that enables us to solve u^d(x) numerically as the fixed point of a certain operator. Third, we present an accelerated algorithm which decreases monotonously and converges in a finite number of iterations. Finally, we illustrate computational aspects generating lot size schedules by the QVI approach.