Transportation policies for single and multi‐objective transportation problem using fuzzy logic

In this paper, single and multi‐objective transportation models are formulated with fuzzy relations under the fuzzy logic. In the single‐objective model, objective is to minimize the transportation cost. In this case, the amount of quantities transported from an origin to a destination depends on the corresponding transportation cost and this relation is verbally expressed in an imprecise sense i.e., by the words ‘low’, ‘medium’, ‘high’. For the multi‐objective model, objectives are minimization of (i) total transportation cost and (ii) total time for transportation required for the system. Here, also the transported quantity from a source to a destination is determined on the basis of minimum total transportation cost as well as minimum transportation time. These relations are imprecise and stated by verbal words such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Both single objective and multi‐objective problems using Real coded Genetic Algorithms (GA and MOGA) are developed and used to solve the single level and bi‐level logical relations respectively. The models are illustrated with numerical data and optimum results are presented.