Adjustable robust optimisation approach to optimise discounts for multi-period supply chain coordination under demand uncertainty

In this research, a problem of supply chain coordination with discounts under demand uncertainty is studied. To solve the problem, an Affinely Adjustable Robust Optimisation model is developed. At the time when decisions about order periods, ordering quantities and discounts to offer are made, only a forecasted value of demand is available to a decision-maker. The proposed model produces a discount schedule, which is robust against the demand uncertainty. The model is also able to utilise the information about the realised demand from the previous periods in order to make decisions for future stages in an adjustable way. We consider both box and budget uncertainty sets. Computational results show the necessity of accounting for uncertainty, as the total costs of the nominal solution increase significantly even when only a small percentage of uncertainty is in place. It is testified that the affinely adjustable model produces solutions, which perform significantly better than the nominal solutions, not only on average, but also in the worst case. The trade-off between reduction of the conservatism of the model and the uncertainty protection is investigated as well.