A multi-objective risk-based approach for airlift task scheduling using stochastic bin packing

An important aspect of airlift problems is to find the smallest fleet of aircraft to move cargo from one or more locations to a destination. In critical airlift operations, such as emergency evacuations, disaster relief and defence operations, a compromise needs to be struck between minimizing the time needed for completing all tasks and minimizing the size of the fleet. Usually, the time to complete a task is stochastic. A deterministic model, therefore, will under-estimate fleet size which results in increased levels of risk to achieve the overall airlift mission. In this paper, we introduce a stochastic version of the two-dimensional bin packing problem. We test a number of objective functions to measure different levels of risk. We then use an evolutionary multi-objective algorithm to solve a number of test problems. Analysis demonstrates that the different risk functions and level of variability/uncertainty in performing each task affect solutions non-linearly. Moreover, the multi-objective approach provides the analyst with an estimate of the range of risk; thus solutions can be selected based on criticality of meeting airlift demands.