Decreased minimum total transportation–inventory cost bounds assuming variability in supplies and demands

Assuming variable supplies and demands at sources and destinations respectively within fixed ranges of a homogeneous product, a mathematical model was developed. The minimum total cost bounds of transportation were obtained by LINGO solver. Later this model had been extended by incorporating inventory cost during transportation and retailing. The impact of this incorporation in increasing the minimum total cost bounds was illustrated with the solutions to some example problems. We use this LINGO solver to find the minimum aggregate cost bounds of the latter model for given ranges of supplies and demands. Here first we demonstrate that this incorporation decreases both the lower and the upper minimum total cost bounds reasonably. Considering numerical example problems in certain situations, we highlight significant decreases in the lower minimum total cost bound, with either zero or a negligible decrease in the upper minimum total cost bound. Thus, this study validates that better bounds of the minimum total cost of such an incorporated transportation and inventory could be achieved. This clearly highlights the inefficiencies of the earlier methods in finding such decreased minimum total cost bounds. Finally, we perform sensitivity analyses to see the impact of increase in the transportation time from another supplier to each of the buyers by the same amount. As this time increment increases, the decrease in the lower minimum total cost bound increases significantly, which is a new finding. Conclusion is drawn by discussing the contribution, limitations of this study and indicating its further research scope.