How to challenge the suppliers’ cost breakdowns :- machine cost, labour cost, material cost, overheads and margin ?

Apart from machine, labour, material, overheads & margin costs we can try to minimise Freight, Insurance and logistics costs 

A very useful way to challenge is by analysing the previous costing trend i.e. benchmarks, it will provide an insight and shall also alarm / indicate where a major shift is

Normally, the RM/PM/FOH cost have a ration of70:25:5 every industry has its cost norms, the way to challenge cost sheet of supplier is through 

Raw material cost trending, 

general labour rates per hour is standardized by the govt,so , it can be reversed calculated by production capacity (noted at the time of initial Supplier evaluation)

Visit supplier premises observing the production process whether it is labor intensive or mechanical or totally automated. this can give you a fair idea of production cost 

Margins are also derived through challenging  RM/PM and Factory costs.

by checking if his feedback is reasonable or not

and by depending on  metrics and having standards for prodcutivity , salary , consumption , waste etc.