Time–cost trade-off in a transportation problem with multi-constraint levels

In this paper we consider a problem where transportation from any supply point to any demand point is based on the modern marketing philosophy, which means suppliers must supply the customers with the best service. As such, the trade-off we seek is between the total transportation expense and the total time weighted by the amount transported. The mathematical formulation of MC2 transportation problem is described and the MC2 decision method is presented for identifying all the time–cost trade-off solutions. An algorithm is developed based on some new definitions and theorems. A numerical example is given to demonstrate the applicability of the algorithm in solving such real-world transportation problems.