# Multi-item interval valued solid transportation problem with safety measure under fuzzy-stochastic environment

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## Abstract

In this paper we introduce “safety factor” in transportation problem. Here we solve Multi Item Interval Valued Solid Transportation Problem (MIIVSTP) with safety factor under Desire Safety Measure (DSM) fuzzy-stochastic and stochastic. When items are transported from origins to destinations through different conveyances, there are some difficulties/risks to transport the items due to bad road, insurgency etc. in some routes specially in developing countries. Due to this reason desired total safety factor is being introduced. Also our goal is to evaluate the solution of MIIVSTP using Global Criteria Method. Here we developed five model with taking DSM as fuzzy-stochastic and stochastic and safety factor as crisp, fuzzy, interval, stochastic, fuzzy-stochastic. Here the transportation costs are intervals, the corresponding multi-objective transportation problem is formulated using “mean and width” technique. Then the problem is converted to a single objective transportation problem taking convex combination of the objectives according to their weights. Finally all the models are solved by Generalized Reduced Gradient (GRG) method using LINGO software. Numerical examples are used to illustrate the model and methodologies.

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## Author information

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Correspondence to U. K. Bera.

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Baidya, A., Bera, U.K. & Maiti, M. Multi-item interval valued solid transportation problem with safety measure under fuzzy-stochastic environment. J Transp Secur 6, 151–174 (2013). https://doi.org/10.1007/s12198-013-0109-z