New model for addressing supply chain and transport safety for disaster relief operations

The supply chain and logistical operations uncertainty are the most significant part for both businesses and economic activities. This paper investigates multi-item multi-stage solid transportation problem with fuzzy-stochastic environment to maximize the total route safety under safety constraint, in which the unit transportation costs, availabilities, demands, conveyance capacities, safety factors and desire total safety measure are supposed to be fuzzy-stochastic in nature. The multi-stage solid transportation model is developed in such a way that the cargoes are transported from sources to destinations via intermediate destination centers (DCs), where the DCs for stage-1 is reduced to the supply points for stage-2 and DCs for stage-2 is reduced to the supply points for stage-3 and similarly the DCs for the stage-$$(\hbox {n}-1)$$(n-1) is converted to the supply points for stage-n. The smooth transportation in the developing countries or rural areas or disaster affected areas is difficult due to hilly region, bad road, insurgency activities, landslides, etc. and for this reason, the safety objective function is considered to maximize under additional safety constraints. Two reduction procedures are used to get the equivalent deterministic form of the fuzzy-stochastic model. In the first procedure, the mean expectation is calculated considering lower $$\alpha $$α-cut, upper $$\alpha $$α-cut and signed distance of fuzzy numbers. However, for the second procedure, credibility measure, mean chances and expectation are taken into account to find the deterministic equivalent of the fuzzy-stochastic events. The modified GRG technique (LINGO.13.0 optimization solver) is used to solve the reduced deterministic model. Finally, a numerical example is provided to illustrate the model and methodology.