Solution of a transshipment problem with uncertain parameters under impaired and enhanced flow

Apart from the general formulation of a transshipment problem, we have considered the shipments via some intermediate points from sources to sinks, shipments between sources and also between transient points are allowed, in our proposed model. Sometimes, for circumstantial changes or emergencies a decision maker wishes to keep reserve stock at sources and hence the flow/shipment of goods has to be reduced or restricted. While at times, the flow needs to be enhanced due to extra demand. Further, supply and demand may be uncertain depending on various situations. So, we have applied impaired flow and enhanced flow in our proposed model considering the supply as a fuzzy (as supply can be assumed by the decision maker, in general) variable and demand as a random variable (depends on physical phenomenon). Taking into account all the aforementioned different situations, in this paper, our purpose is to propose seven different models of transshipment problem. To make these models deterministic, all the fuzzy constraints are defuzzifed using credibility measure theory while demand constraints are derandomized using the inverse normal distribution. We have also shown how to handle fuzzy and random variables together at the same constraint occurred in one of the models. Further, to solve the models in an easier way, we have used C++ code for the Fourier elimination method where variables are to be eliminated one by one except the objective function. At last, the models are validated by suitable non-trivial numerical examples.