This report extensively treats a problem formulation of and a solution method to the radiative transfer problem, including some adaptations to the area of light scattering in paper and print. The resulting model is referred to as DORT2002, and has been implemented in MATLAB using a discrete ordinate model geometry. The main steps to get a numerically stable solution procedure include the continuous formulation with expansion in Legendre functions and Fourier cosine series, the evaluation of normalized associated Legendre functions, the choice of numerical quadrature, the matrix formulation of the discretization, the reduction of the eigenvalue problem, the preconditioning of the system of equations for the boundary conditions, and the avoidance of over- and underflow in the solution and interpolation formulas. Important are also the recognition of potential divide-by-zero situations, and reformulation of those. Comments are given on possible applications in the paper and printing industries. It is suggested that the Kubelka-Munk model should be replaced with DORT2002 in most applications.