Multi stage Multi-objective Transportation Problem under Uncertainty Environment
Manoranjan Mishra1, Debdulal Panda2

1Manoranjan Mishra, Department of Mathematics, Gandhi Institute For Technology, Bhubaneswar, Odisha, India.
2Debdulal Panda, School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar, Odisha, India.

Manuscript received on 11 August 2019. | Revised Manuscript received on 14 August 2019. | Manuscript published on 30 September 2019. | PP: 4056-4060 | Volume-8 Issue-3 September 2019 | Retrieval Number: C5370098319/2019©BEIESP | DOI: 10.35940/ijrte.C5370.098319
Open Access | Ethics and Policies | Cite | Mendeley | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (

Abstract: In present scenario due to high competition in market, there are lots of pressures on organizations involbs with transportation industry, to provide the service in a better and effective manner. The distribution of products among the customers in systematic manner is not an easy task. Transportation models provide an effective framework to meet these challenges. If the parameters involved with multi-objective transportation model are expressed in terms of fixed parameter then it is not easy to address them in an uncertainty environment, rather it is easy to handle them when they are represented in terms of linguistic variables. It is noticed that, all the objectives of a transportation model are affected by different criteria like route of transportation, weather condition, vehicles used for transportation etc. In the present study a multi-stage transportation model with multiple numbers of objectives is developed with fuzzy relations. Minimization of both transportation cost and transportation time are considered as two different objectives of first stage which are associated with a number of different criteria like deterioration time, fixed charge and mode of transportation. In second stage, another objective i.e quantity of transported amount is considered on the performance basis of objectives of first stage. All these factors considered for this model are fuzzy parameters and are expressed in terms of linguistic variables. The fuzzy rule based transportation model is developed and the solution is obtained by Genetic Algorithm for multi-objective problems (MOGA). The model is presented with a numerical problem and optimum result is discussed.
Key words: Multi Stage Multi-Objective Transportation Problem, Genetic Algorithm

Scope of the Article:
Transportation Engineering