Stochastic supply chain, transportation models: implementations and benefits

To transport the commodities in minimum time with maximum safety, the difficulties arise due to mutiny, territory slide, bad road and crashed communication systems, etc. and to overcome these kind of problems, the stochastic solid transportation models with safety and time objective functions under essential constraints are formulated. Taking expected value criterion, Chance-constrained programming technique, uniform distribution $$ {\mathfrak{U}}\left( {a,b} \right) $$ U a , b , exponential distribution $$ {\mathcal{E}\mathcal{X}\mathcal{P}}\left( \beta \right) $$ E X P β and normal distribution $$ {\mathcal{N}}\left( {\mu ,\sigma^{2} } \right) $$ N μ , σ 2 , four new de-randomization processes are proposed to handle the stochastic programming problem. Finally, the deterministic form of the model is solved using generalized reduced gradient techniques (LINGO.13.0 optimization software). Finally, an enlarge comparison of the proposed concept with the earlier concept are presented and the nature of the solutions is discussed.