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In today’s highly competitive market the organization have a challenge to find better ways to create and deliver products to the customers. When and how much of products is to be sent to the customers in a cost-effective manner is even more challenging. Transportation model is a powerful frame work to overcome this situation. The physical distribution of products from supply to demand points, minimization of the cost and time, requirement of goods at each demand point, variety of roots and manners, are the basic point of a transportation problem (TP). The basic transportation model was originated by Hitchcock (1941) and discussed in details by Koopmans (1949).
TP is considered as a special type of multiobjective programming problems (MOPPs) which arises in many practical applications. Multiobjective transportation problem (MOTP) is a special class of multiobjective linear programming problem with non-commensurable and conflicting objectives as well as constraints with special structure. Most of the researchers have given serious attention on solving MOTPs in recent times. In conventional TPs, it is assumed that decision makers (DMs) are sure about the precise value of transportation costs, availability and demand of the products. But, in real world applications all these parameters are not known precisely due to some uncontrollable factors. The probability theory and fuzzy set theory are the avenues to analyze these uncertain situations.
To deal with the parameters involving random variables associated with the system constraints Charnes and Cooper (1959) introduced chance constrained programming (CCP) technique for solving probabilistic linear programming problems. Generalizing the concept of CCP methodology Dantzig (1963) formulated stochastic programming. The method is further studied by Vajda (1972), Sengupta (1972), Luhandjula (1983). Considering the random variables associated with supply and demand Ringuest and Rinks (1987) proposed an interactive algorithm for multiobjective stochastic TP. Azadi & Saen, (2013) developed a chance constrained programming model for selecting third party reverse logistics providers.
It is to be noted here that in a TP, the cost of transporting unit products or time required for transporting unit product may not be defined precisely due to different uncontrollable factors. Realizing the above fact Oheigeartaigh (1982) proposed an algorithm for solving TPs where the capacities and requirement are fuzzy sets (Zadeh, 1965) with linear or triangular membership functions. Chanas et al. (1984) presented fuzzy linear programming model (Zimmermann, 1978) for solving TP with crisp cost coefficients and fuzzy supply and demand values. The TP with fuzzy cost coefficients expressed as fuzzy numbers was studied by Chanas and Kuchta (1996). Liu & Kao (2004) described a method for solving fuzzy TP based on extension principle. A two-stage cost minimizing fuzzy TP with supply and demand as trapezoidal fuzzy numbers presented by Gani and Razak (2006). Li et al. (2008) proposed a new method based on goal programming for solving fuzzy TP with fuzzy costs. Lin (2009) applied genetic algorithm for solving TP with fuzzy coefficients. Ghatee, Hashemi, Zarepisheh and Khorram (2009) introduced a method for solving fuzzy minimal cost flow problem with fuzzy costs. A technique for solving fully fuzzy transportation problem was presented by Kumar and Kaur (2011). Roy and Mahapatra (2014) presented a methodology for solving solid transportation problem with stochastic supply and demands. Radhakrishnan and Anukokila (2014) presented a methodology for fractional solid TP with interval cost using fractional goal programming approach. Erol and Yilmaz (2016) presented a literature survey for hazardous materials transportation.