Multi-stage multi-objective solid transportation problem for disaster response operation with type-2 triangular fuzzy variables

Year 2016, Volume: 45 Issue: 5, 1485 - 1518, 01.10.2016

Abhijit Baidya Uttam Kumar Bera Manoranjan Maiti

Abstract

In this paper, for the first time we formulate and solve multi-stage solid transportation problem (MSSTP) to minimize the total cost and time with type-2 fuzzy transportation parameters. During transportation period, loading, unloading cost and time, volume and weight for each item, limitation of volume and weight for each vehicle are normally imprecise and taken into account to formulate the models. To remove the uncertainty of the type-2 fuzzy transportation parameters from objective functions and constraints, we apply CV-Based reduction methods and generalized credibility measure. Disasters are unexpected situations that require significant logistical deployment to transport equipment and humanitarian goods in order to help and provide relief to victims and sometime this transportation is not possible directly from supply point to destination. Again, the availabilities at supply points and requirements at destinations are not known precisely due to disaster. For this reason, we formulate the multi-stage solid transportation problems under uncertainty (type-2 fuzzy). The models are illustrated with a numerical example. Finally, generalized reduced gradient technique (LINGO.13.0 software) is used to solve the models.

Keywords

Multi-stage solid transportation problem, type-2 fuzzy variable, CVbased reduction methods, generalized credibility, goal programming approach

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