AN INTEGRATED INTERTEMPORAL LINEAR PROGRAMMING MODEL UNDER RISK FOR SHORT-TERM FINANCIAL PLANNING*

Abstract

LINEAR PROGRAMMING MODELS are frequently used in financial literature as vehicles for determining the firm's theoretical optimal operating plan. Only one integrated linear programming model has been successfully applied to a non-financial business.t Since the value of theory is confirmed through repeated applications, the purpose of this research was to build, test, and evaluate another linear programming model for short-term financial planning. One multi-product firm, a food processor, served as the subject of this study since it complied with inherent assumptions of linear programming models. The objective function of this model was structured to maximize revenue over six monthly time periods. The rates of return for production of real goods were included in the objective function along with external financial rates of return. The integrated intertemporal linear programming model for this firm had 1745 variables and 503 constraints. Before this model was used to calculate an optimal operating plan, however, the model was tested against prior data to verify its duplication of the firm's actual resource consumption and allocation. The model's optimal operating plan had an objective function value which exceeded the firm's actual performance by 33 per cent. The model was structured to have the option of investing funds in operations, repaying debt or purchasing Treasury bills. Consequently, the model's operating plan produced the optimal multi-period schedule for the acquisition and commitment of funds. Dual values, or shadow prices, were analyzed to determine the marginal values of all constrained resources. In particular, the dual value of funds was used as the basis for calculating the marginal revenue product schedule of funds. Shadow prices also were used in conjunction with the range of the objective function to measure the interaction of commodity market returns and financial market returns on the firm. Two methods of quantifying product market price variability, or risk, were incorporated into the model. The first method was to substitute the reciprocal of the coeffi/X cient of variation a for the objective function's revenue coefficients. The second method was to substitute in the revenue coefficients of the model the upper and lower limits of revenue forecasts. Since both methods incorporating risk had a higher objective function value than the firm, if can be concluded that the firm overestimated the effects of risk on the operating plan. This study demonstrated the linear programming models can be used for short-term financial planning, and that the cost of building such models is minimal compared to the direct monetary benefits obtained from using the model. * A dissertation completed at Georgia State University in 1971. t C. W. Young, Linear Programming and Short-Term Financial Planning (Unpublished Ph.D.