Optimal route planning for multi-level multi-choice transportation problem with uncertain parameters using Lagrange’s interpolating polynomial

his study introduces a multi-level multi-choice multi-objective linear transportation problem (ML-MCMOLTP) that involves uncertain variables. Multi-level programming addresses scenarios in which multiple decision makers are involved in modeling decentralized planning problems inside a hierarchical system. In the model described in this paper, the objective is to maximize profit by selecting the most suitable choice from a set of options for the cost coefficients of the objective function. This is achieved by introducing Lagrange’s interpolating polynomial. It is important to note that all parameters involved, such as supply and demand, are treated as uncertain variables. Additionally, I will provide a numerical illustration of a three-level uncertain linear transit problem.