Abstract. In this paper, an algorithm is developed to find the paradoxical solution of multi objective transportation problem with linear constraints. It also attempts to obtain its best paradoxical pair and paradoxical range of flow by using the sufficient condition of the existing paradox. Numerical illustration is also provided to check the feasibility.
IntroductionThe term Paradox arises when a transportation problem admits a total cost which is lower than the optimum. This is attainable by shipping larger quantities of goods over the same routes that were previously chosen as optimal which is unusual phenomenon noted by Szwarc (1971). The classical transportation problem is the name of a mathematical model has a special mathematical structure. The mathematical formulation of a large number of problems conforms to this special structure. Hitchcock (1941) originally developed the basic linear transportation problem. Klingman and Russel (1974 and 1975) introduced a specialized method for solving a transportation problem with several additional linear constraints. Hadley (1987) gave the detailed solution procedure for solving linear transportation problem. Till date, several researchers studied comprehensively to solve transportation problem cost minimizing its cost in various ways.In some situations, if we obtain more flow with lesser cost than the flow corresponding to the optimum cost then we say paradox occurs. Charnes and Klingman (1971), Szwarc (1973), Adlakha and Kowalski (1998) and Storoy (2007) considered the paradoxical transportation problem. Gupta et al (1993) considered a paradox in linear fractional transportation problem with mixed constraints. Joshi and Gupta (2010) studied paradox in linear plus fractional transportation problem. Basu, Acharya and Das (2012) developed an algorithm for finding all paradoxical pairs in a linear transportation problem. Acharya, Basu and Das(2015), discussed more-for-less paradox in a transportation problem under fuzzy environment with linear constraints. Sophia Porchelvi and Anna Sheela (2015) developed an algorithm to find linear multi-objective fractional transportation problem and its paradoxical solution.
This paper studies a CETD model for finding the peak age group of people affected by Dengue in Nagapattinam District of Tamil Nadu, India. The data are analyzed by using fuzzy time dependent data matrices and some useful suggestions and concluding remarks are provided.
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