Several times people on the earth are afflicted by the strike of unpredictable phenomena like a disaster. Although some non-governmental organization (NGO) involving in disaster relief operation, prepositioned some resources in disaster-prone areas, but it is not sufficient for all times. Sometimes, due to the high intensive devastation, help for providing relief is requested to the other national or international aid. This research has introduced a mathematical model for humanitarian logistic considering two optimization criteria minimize the total cost and total time of the relief logistic operation with a collaboration of resource collection by the NGOs. But impreciseness arises due to the chaos of the disastrous environment and therefore some parameters of the model is considered as a triangular neutrosophic number in order to deal the uncertainty. In the manuscript, a new method for defuzzification is proposed for the neutrosophic triangular number. An empirical study to show the efficiency of the model with a numerical example is performed through this study. The multi-objective model is optimized using neutrosophic compromise approach, global criteria method and weighted sum method with the help of LINGO optimization solver for relevant soft computing. Furthermore, a comparative study is analyzed among these three techniques. © 2019 Elsevier Ltd