A sensitivity analysis is a study of how the variation in input parameters affects the optimal solution. With this analysis we can checked  that how the developed model is sensitive by variation in the input parameter of the model. In the supply network design the transportation cost, holding cost and other cost are input parameters.

So you have to check your model with the variation of the plus minus % of the particular cost while keeping the other cost as it is.

We always need to perform a sensitive analysis on all the parameters that were estimated in the supply chain network design.

when we have a input  parameter with variety options ,do we need to check its affect?,also sometimes I have seen some researchers check the relation between some other parameters in sensitive analysis.

That may be one part of it -- but I think probably more important is making sure all the parameters are consistent with one another and consistent for the entire product location database. This is generally not discussed. See a full explanation at http://www.scmfocus.com/3s/

generally, the demand information at the retailer end is the one you have to worry about. The change in the demand pattern, how it affects the other nodes of the SC network. all the above mentioned parameters will be constant for a planning horizon. Again, lot of studies discusses the effect of information sharing among the parties involved. The bull whip effect, fill rate, total supply chain cost, inventory etc.. are some of the areas of interest... 

Whereas sensitivity analysis is a process to survey the effects of input parameters including costs, number of members and etc. So usually the impacts of more influence parameters are considered which is depended on the author's intention. It means that the purpose of investigation determine direct of sensitivity analysis.