The objective of this project is to minimize total transportation cost plusrnpenalty cost for shortage of supply.rnThe work focused on formulating transportation problem under shortage ofrnsupply and penalty for unmet demand mathematically and converting thernproblem in to minimum cost rnow network .rnThe network simplex method is used to solve the problem.rnThe extended transportation problem which is the transshipment problemrnalso considered in the work. The problem is supported by numerical illustra-rntion and Matlab implementation.