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<span lang="EN-US">Generally, in traditional transportation problems, single items are transported from a set of origins to a set of destinations in such a way that the transportation cost is minimized. To face the challenges that arise in modelling transportation problem various parameters are to be considered. In this work to provide an optimal transportation policy to the decision maker, we have studied a fixed-charge bi-objective multi-product <br /> 4-dimensional transportation problem with vehicle speed under budget constraints under uncertain environment. The objective of the proposed model is to have the maximum profit with the minimum time taken of transporting the goods. An equivalent deterministic model of the proposed model is obtained to deal the uncertain variable using expected value-chance constraint properties on uncertainty theory and its compromise solution is obtained by using the goal programming technique. A numerical example is discussed to provide more clarity on the proposed model.</span>

The In this work, multi objectives multi item four dimensional transportation problem with vehicle speed consisting of uncertain variable parameters is studied. Due to bad road conditions, the rate of variation of speed of the vehicle may vary in different routes and the speed of different vehicles are also considered first time in the time minimization transportation model. Equivalent deterministic models for the uncertain programming model are proposed by using chance constrained and expected value method. Finally goal programming technique is applied to derive a suitable compromise solution of the uncertain multi objective multi item four dimensional transportations problems with consideration of vehicle speed. An illustrative real life situation is discussed and optimal results are displayed to demonstrate the proposed methodology..