In a standard linear programming (LP) problem one solves for an optimal decision vector x, given the set ΞΈ = (A, b, c) of parameters. However in most applied problems the parameters in the set ΞΈ are unknown constants and therefore not given, but sample observations are usually available. Thus, in production problems, input -output data are usually available for a crosssection sample of firms, each producing multiple outputs by using multiple inputs. In such cases we have the problem of estimating the input coefficients which are the unknown parameters. Most frequently, two types of method are applied in such LP problems with unknown but estimatable parameters. One is the approach of stochastic programming with recourse, 1,2 where one computes the first-stage optimal solution vector x on the basis of prior information on ΞΈ, then adjoins to the original objective function of the LP problem suitably defined expected penalty costs to reflect the deviation of the first stage optimal solution from the correct optimal solution. This two-stage sequential solution may, however, be difficult to apply empirically, owing to inadequate knowledge of the prior information and the difficulty of determining the expected penalty costs. A second method, mostly used in applied studies, is to estimate ΞΈ by ΛΞΈ = ( ΛΞΈ | I T ), conditional on all the information available (I T ) up to t = 1,2, β¦, T and then to formulate a suitable programming model (e.g. either linear, quadratic or nonlinear) to compute the optimal solutions ΛΞΈT either sequentially one time point ahead or over a planning horizon. Thus Holt et al. in their production planning model, known as the HMMS model, estimated the parameters ΞΈ of the various cost functions of production, inventories and labour force over the past observed data of a paint factory and then, on the basis of the least squares estimates ΛΞΈ of ΞΈ they minimized a quadratic expected cost function over the future planning horizon to determine the optimal levels of output, inventories and workforce. Note that this production scheduling model which has been frequently applied in recent models of operations research, 6,7 has two flexible features that can be easily applied to LP models with unknown parameters. One feature is that it combines regression and mathematical programming techniques in an explicit form by a