A GENERALIZED TIME-COST TRADE-OFF TRANSPORTATION PROBLEM

In the classical transportation problem if the unit costs and transpor tation durations are considered, the time-cost trade-off solutions can be determined by the well-known threshold approach assuming that all the transportations are permitted to be simultaneous in time. If all t he unit costs are linear functions of time over a specified interval o f time, a parametric technique can be applied for identifying all the time-cost trade-off solutions pertaining to this interval. In this pap er, the unit costs considered are piece-wise linear non-increasing fun ctions of time and transportations are allowed to be simultaneous. It is shown that a parametric method involving a finite sequence of param etric transportation problems reveals all the time-cost trade-off solu tions of this generalized trade-off problem. Computational experience is included. If the transportation problem has considerable degeneracy , the parametric approach may pose some computational difficulty. This difficulty can be reduced by using an alternative method involving th e bicriteria optimization approach of Aneja and Nair. Also, a direct m ethod is outlined for the case where a finite set of discrete alternat ives of unit cost-time pairs is available.