Multi-objective stochastic programming for a multi-commodity multi-modal network flow model for flood disaster relief operations

Abstract

Abstract The increasing and alarming occurrence of disaster caused by flooding in Nigeria has necessitated this research work. There abound publications just describing the problem and calling for urgent help to reduce the effects on the citizenry but there appear no scientific/mathematical solutions offered to tackle the rescue operations. We therefore proposed a Mathematical Programming Model for disaster rescue operations. Our work is a Multi-Objective Stochastic Programming problem that seeks to minimize: (i) proportion of unmet demand satisfaction, (ii) total cost, and (iii) total shipping time. The study has root in practical problems facing the community. An empirical illustration of 2012 flood disaster was used as a case study. We considered four type of supply depots: National centre depot (NCD), Three Local Distribution Centres (LDC) and six points of Distribution (POD). The model comprised of vehicle types (a) air – helicopters and (b) land – trucks. Three basic types of emergency supply (item (l)): food, water and medical facilities were considered as relief materials. In the process, three basic scenarios: mild, medium, and severe situations were considered with associated probabilities: 0.25, 0.5 and 0.25 respectively. The work provided an adequate and efficient, mathematical model for quick response under emergency. This model proved effective and efficient in meeting the urgent needs of the devastated citizens who were involved in the disaster. It was efficient as there was a thin line between demand and demand met. The study equally proved that a minimized cost of about $1,016,673.37 could be used to carryout rescue operations. This figure becomes very necessary for the government, research agencies and other developmental agencies for the purpose of planning. The model by using the air and road transport modes and allowing direct and indirect transporting to the PODs saved time, resulting to many lives being saved.