Incorporating robust and quasi-robust optimisation methods to model the relief distribution problem under uncertainty

This paper addresses the problem of modelling uncertainty in supply, demand, and travel time parameters in relief distribution optimisation models. The model aims to minimise the deprivation cost, expressed as a function of deprivation time, and updates the deprivation status of demand nodes at the beginning of each time period in the planning horizon. The uncertainty realisations in travel time are thus discretised and delays are expressed as number of time periods behind the expected delivery time. The first part of the article adapts the reasonable worst case robust optimisation approach to model uncertainties in supply and demand parameters which are assumed to be uniformly distributed. The second part introduces a novel quasi robust optimisation approach to model uncertainty in travel time where delays in each arc are assumed to be proportional to the assigned arc load for more protection against constraints' violation. The model is tested and verified empirically.