Affinely adjustable robust optimization for a multi-period inventory problem with capital constraints and demand uncertainties

This study focuses on a multi‐period inventory problem with capital constraints and demand uncertainties. The multi‐period inventory problem is formulated as an optimization model with a joint chance constraint ( JCC ) requiring the purchase cost for each period not to exceed the available capital with a probability guarantee. To hedge against demand uncertainties, an affinely adjustable robust optimization approach is used to convert the developed model into a robust counterpart. By approximating the JCC under a budgeted uncertainty set to which the demands belong, the robust multi‐period inventory model with the JCC is transformed into a linear programming model, which can be solved efficiently. Numerical studies are reported to illustrate the robustness, practicality, and effectiveness of the proposed model and the solution approach. The numerical results show that the proposed model and solution approach outperform the sample average approximation approach. Numerical studies are used further to analyze the impact of the budget coefficient and the upper bound parameter on the inventory costs and the realized capital constraint satisfaction rate. The proposed model and solution approach are further extended to the multi‐product case.