High-resolution Fuzzy Component Scheme for Second-order Differential Equation Appearing in Single Commodity Stochastic Production Planning

The article deals with the second-order nonlinear differential equation that models stochastic production planning. We describe a fuzzy transform technique for obtaining the approximate analytic solution to a single commodity stochastic production-inventory model. In general, the classical solution is not known; thus, numerical treatment helps to analyze optimal inventory levels. The present description implements a fuzzy transform that approximates solutions at the interior of the domain with high-order accuracy. The approximate fuzzy components implementing a sinusoidal basic function are arranged with a three-point solution value. A non-singular matrix system relates the solution values and approximate fuzzy components, thus optimizing accuracy to fuzzy components affects the solution exactness. If the exact solution is known, the estimates of error are monitored by integrated absolute error for approximate analytical solutions. If the exact analytic solution is unknown, the approximate analytic closed-form solution by using spline interpolation is an additional reward to the scheme.