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Das, Chandan Bikash
- An Approach to Solve Capacitated Transportation Problem Under N-Vehicle Cost Varying Transportation Problem
Authors
1 Sonakhali Girl's High School, Sonakhali, Daspur, Paschim Midnapore, West Bengal, IN
2 Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, Purba Midnapur, West Bengal, IN
Source
Fuzzy Systems, Vol 5, No 7 (2013), Pagination: 191-204Abstract
In capacitated transportation problem there are some rim conditions or route restrictions. To obey this conditions, the vehicles are chosen such a way that their capacities are not violated the restriction.In urban region unit transportation cost is not fixed but the vehicles are pre-paid system in nature. So unit transportation cost depends on the transport quantities or amount. This type of transportation problems are known as cost varying transportation problem.
In this paper we represent a N-vehicle cost varying transportation model to solve capacitated transportation problem. In this model the transportation cost is vary due to capacity of vehicles as well as amount of transport quantity. At first we propose an algorithm to determine unit transportation cost with initial allocation to the basic cells by North-West corner rule. Then solve it. The unit transportation cost is varied during optimality test when allocations are changed.
Numerical examples are presented to illustrate the N-vehicle cost varying transportation problem (TVCVTP). Finally, comparison is given to show better effective of this model.
Keywords
Capacitated Transportation Problem, Cost Varying Transportation Problem, Basic Cell, Non-Basic Cell, North West Corner Rule.
- Fuzzy Programming Approach to Multi-Objective Capacitated Transportation Problem under 2-Vehicle
Authors
1 Department of Mathematics, Tamralipta, Mahavidyalaya, Tamluk, Purba Midnapur, West Bengal, IN
Source
Fuzzy Systems, Vol 8, No 9 (2016), Pagination: 235-242Abstract
In this paper we represent a two-vehicle multi-objective cost varying transportation model to solve multi-objective capacitated transportation problem. In this multi-objective model the unit transportation cost varies due to capacity of vehicles as well as amount of transport quantities. The rim conditions of the multi-objective capacitated transportation problem redundance by the proper choice of vehicles. This converts to -vehicle multi-objective cost varying transportation model which is a Bi-level Mathematical programming model. To built this model, we propose an algorithm to determine unit transportation costs with initial allocation to the basic cells by North-West corner rule. Then determine unit transportation costs for non-basic cells. Then solve it by fuzzy programming technique. This methodology is illustrated through a numerical example with considering several type of membership functions.