A robust optimization approach for inventory management with limited-time discounts and service-level requirement under demand uncertainty

A multi-period inventory management problem is considered for a retailer offering limited-time discounts and having a joint service-level requirement over the discount periods under demand uncertainty. In each period, the retailer, only knowing a reference value and the bounds of the uncertain demand, has to determine the order quantity of the product before demand realizations to maximize the total profit over the planning horizon while achieving the required service level over the discount periods. A budgeted uncertainty set is adopted to accommodate demand uncertainty and a joint chance constraint is used to formulate the service-level requirement. The retailer problem is formulated as an affinely adjustable robust chance-constrained model and is transformed into a linear program. A double-layer iterative approach is proposed to solve the problem. The outer layer uses a posteriori method to update the budget coefficient. The inner layer solves the affinely adjustable robust chance-constrained model with the updated budget coefficient, and obtains the updated order quantities. A case study based on real data demonstrates that the proposed approach outperforms other approaches by better balancing the average realized profit and the realized service level. Moreover, the results show that the retailer can obtain a larger average realized profit by gradually than abruptly changing the prices.