Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment (original) (raw)
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Journal of Statistics and Management Systems, 2018
In this paper, we study a special class of transportation problem with capacitated restrictions. The formulated multi-objective capacitated transportation problem (MOCTP) has some of the objective functions are linear and fractional; these objectives are conflicting in nature. This problem defined in an uncertain environment where the uncertainty in input information presented by the multi-choices and trapezoidal fuzzy numbers. The multichoice in input information dealt with the binary numbers and transformed it into the equivalent deterministic form by the suitable method. While the other pattern of uncertainty in input information defined by the trapezoidal fuzzy numbers and handled by ranking function approach to get the crisp value. Due to the presence of the uncertainties, and the conflicting objective functions, we cannot directly solve the formulated multi-choice MOCTP. So, therefore, we solve the formulated MOCTP in two phases. In the first stage, we transform the uncertain MOCTP into the deterministic form by using the suitable solution procedure of multi-choice and fuzzy numbers respectively. In the second stage, we have suggested a goal programming solution procedure to linearise the fractional objective function and then solve the resultant MOCTP for the compromise solution. A case study has also done to illustrate the stepwise solution procedure.
Granular computing, 2018
In this paper, we have formulated a new model of multi-objective capacitated transportation problem (MOCTP) with mixed constraints. In this model, some objective functions are linear and some are fractional and are of conflicting in nature with each other. The main objective of this paper is to decide the optimum order of the product quantity which is to be shipped from source to the destination subject to the capacitated restriction on each route. Here the two situations have been discussed for the MOCTP model. In the first situation, we have considered that all the input information of the MOCTP model is exactly known and therefore a fuzzy goal programming approach have been directly used for obtaining the optimum order quantity of the product. While in the second situation the input information of the MOCTP model are uncertain in nature and this uncertainty have been studied and handled by the suitable approaches like trapezoidal fuzzy numbers, multi-choices, and probabilistic random variables respectively. Due to the presence of all these uncertainties and conflicting natures of objectives functions, we cannot solve this MOCTP directly. Therefore firstly we converted all these uncertainties into deterministic forms by using the appropriate transformation techniques. For this, the vagueness in MOCTP defined by trapezoidal fuzzy numbers has been converted into its crisp form by using the ranking function approach. Multichoices in input information parameters have been converted into its exact form by the binary variable transformation technique. Randomness in input information is & Irfan Ali
International Journal of …, 2012
This paper presents chance constrained multi-objective capacitated transportation problem based on fuzzy goal programming problem. Generally, in transportation problem the capacity of each origin and the demand of each destination are random in nature. The inequality constraints representing supplies and demands are probabilistically described. In many real situations, there are capacity restrictions on units of commodities which are shipped from different sources to different destinations. In the model formulation, supply and demand constraints are converted into equivalent deterministic forms. Then, we define the fuzzy goal levels of the objective functions. The fuzzy objective goals are then characterized by the associated membership functions. In the solution process, two fuzzy goal programming models are considered by minimizing negative deviational variables to obtain compromise solution. Distance function is used in order to obtain the most compromise optimal solution. In order to demonstrate the effectiveness of the proposed approach, an illustrative example of chance constrained multiobjective capacitated transportation problem is solved.
Fuzzy Multi-Objective Capacitated Transportation Problem with Mixed Constraints
Journal of Statistics Applications & Probability, 2014
In this article a capacitated transportation problem is considered which is formulated as a multi objective capacitated transportation problem with mixed constraints. To determine the optimum compromise solution of multi objective capacitated transportation problem (MOCTP) with mixed constraints a Fuzzy multi objective programming approach has been applied in which we use three different forms of membership functions viz. linear, exponential and hyperbolic. A numerical illustration has been provided to illustrate the solution procedure.
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This paper focusses on the development of a Multi-choice Multi-objective Transportation Problem (MCMOTP) in the uncertain environment. The parameters associated with the objective functions in MCMOTP are regarded as uncertain variables and the other parameters associated with supply capacity and demand requirements are considered under the multi-choice environment. In this paper, two ranking criteria have been utilized to convert the uncertain objectives into their crisp form. Using these two ranking criteria for the uncertain MCMOTP model, two deterministic models have been developed namely, Expected Value Model (EV Model) and Optimistic Value Model (OV Model). The multi-choice parameters in the constraints are converted to a single choice parameters with the help of binary variable approach. The EV and OV models are solved directly in the LINGO 18.0 software using minimizing distance method and fuzzy programming technique. At last, a numerical illustration is provided to demonstra...