Multi-objective capacitated transportation: a problem of parameters estimation, goodness of fit and optimization

This paper discusses a solution procedure of a multi-objective capacitated transportation problem (MOCTP) in an uncertain environment. In MOCTP, the primary objective is to find the optimum quantity of the shipment subject to some capacitated restriction on each route. Due to uncertainty in MOCTP, the formulated problem cannot be solved directly for the optimum allocation. The uncertainty in MOCTP has been presented by the multi-choices and probabilistic distributions, respectively. The multi-choice and probabilistic distributions have been transformed into an equivalent deterministic form using the binary variable and stochastic programming approach, respectively. It has been assumed that the demand and supply parameter of the formulated problem follows different kinds of probabilistic distributions, namely, Pareto, Weibull, Normal, Extreme value, Cauchy and Logistic distribution, respectively. The maximum likelihood estimation approach has been used to estimate the unknown parameters of the probabilistic distributions with specified probability level. Finally, Akaike’s information criterion and Bayesian information criterion have been used to identify the goodness-of-fit of probability distributions for the given scenarios. The fuzzy goal-programming technique has been used to obtain the best optimum compromise solution for an equivalent crisp MOCTP model. A case study has been given to illustrate the computational procedure.