In this paper we consider an approximation-interpolation approach based on the combination of interpolation method and approximation method. An approximation method for single-machine scheduling theory problem with an unknown objective function that depends on the completion times of jobs is studied. The idea of approximating an unknown function by a linear function with some weight coefficients is considered. An approximation-interpolation algorithm has been developed, which allows to determine the values of weight coefficients of the objective function of single-machine problem of the scheduling theory. In this algorithm the minimization of the total weighted completion times according to the given set of values of the problem parameters and the corresponding known optimal schedules was carried out. Experiments with Lagrange polynomials interpolation and cubic splines have been conducted. The hypothesis of the necessity to take into account long-range bounds when calculating weighting coefficients has been confirmed.