A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

In this paper, a multi-objective solid transportation problem (MOSTP) for damageable item is formulated and solved. First, we minimised the total cost of transportation and transportation time and maximise the reliability of transportation system. Here, transportation costs, resources, demands and capacities of conveyances are random fuzzy in natures. The transported item is likely to be damaged during transportation and damageability are different for different conveyances along different roots. The solid transportation problem (STP) is formulated as a decision making model optimising possibilistic value at risk (pVaR) by incorporating the concept of value at risk (VaR) into possibility and necessity measure theory. The reduced deterministic constrained problem is solved using generalised reduced gradient (GRG) method (LINGO-14.0). Some particular models has been presented. The model is illustrated with numerical examples and some sensitivity analysis is made on damageability.