Total cost measures with probabilistic cost function under varying supply and demand in transportation problem

In the present competitive world, it is often said that "Time is Money" in almost every aspect of life. Time is a factor which affects the various real-life problems directly or indirectly. So, in order to incorporate the "time" as a factor in transportation problems (TPs), we have considered the probabilistic cost/profit function termed as "survival cost/profit" which is again a time-dependent function. In this study, we have assumed that the supply and demand quantities are varying between some specified intervals. Due to the variation in the supply and demand quantities, the value of the objective function is also obtained between interval which is bounded by lower and upper values. Based on the above-stated assumptions, we have developed a couple of mathematical optimization models for the TPs. The solution procedure has also been discussed to solve the proposed mathematical models. At last, a numerical illustration has been presented to show the validity of the model and solution procedure which is helpful in the decision-making process.