Disaster planning and management has always been challenging for the relief agencies of the underdeveloped counties, since they usually do not have the well organized and well-funded system in place, like the developed counties. The models developed in the previous literatures either did not address all the relevant logistics issues or are often too complicated to be utilized by the underdeveloped countries. To mitigate the casualties caused by disastrous events, post disaster planning is very important. This research has developed a simple but inclusive multi-objective post disaster logistics planning model to addresses issues like distribution of relief commodity and medical supplies, staffing of medical facilities, evacuation of wounded people to the medical facilities, vehicular and transportation management, unsatisfied demands at affected locations etc., while maintaining service equity. The applicability of the proposed model has been tested via a real-world case study based on the recurrent flash flood problem in the Sylhet district of Bangladesh. A Branch-and-Cut algorithm has been used via CPLEX platform to solve the developed linear integer programming model. Results have been demonstrated both numerically and graphically to aid the decision maker to properly visualize the solutions, which has offered several important managerial implications and insights on the post disaster management. This way the proposed research is expected to help the decision makers to plan an efficient and effective post disaster logistics network to minimize human suffering, wastage of relief goods, and associated operational costs.