Bi-objective inventory routing problem with uncertain demand: a data-driven robust optimisation approach

This study addresses the single-period inventory routing problem (SIRP) with uncertain demands. We employ the support vector clustering technique to construct a data-driven uncertainty set to characterise demands uncertainty rather than imposing stochastic or fuzzy distribution. We propose a comprehensive expression to granularly calculate the inventory cost of products. Besides minimising the total cost from economics, we also consider the objective of minimising the total deviation level of delivery quantities to match supplies and uncertain demands and further to enhance service quality. We develop a data-driven robust bi-objective SIRP (RBSIRP) model that seeks a trade-off between these two perspectives. We apply the dual theory to obtain equivalent tractable forms of robust counterparts and employ the augmented <i>ε</i>-constraint approach to handle the developed objectives. The experimental results show the practical implications of our model and method. The RBSIRP model based on the constructed data-driven uncertainty set can reduce the conservatism of the delivery solution compared with the classical Budgeted and Box+Ball uncertainty sets while ensuring robustness. The trade-off delivery solution provided by the RBSIRP model is better than the one generated by the model minimising only the total cost.