An optimization of solid transportation problem with stochastic demand by Lagrangian function and KKT conditions

In this paper, a stochastic solid transportation problem (SSTP) is constructed where the demand of item at destinations are randomly distributed. Such SSTP formulated with profit maximization form containing selling revenue, cost and holding/shortage item. The proposed framed as nonlinear which optimized through Karush–Kuhn–Tucker (KKT) conditions Lagrangian function. primary model bifurcated into three different models for continuous discrete patterns. concavity objective functions also presented here very carefully. Finally, numerical example illustrated to stabilize models.