Joint price and quantity optimization in multi-retailer and multi-period systems

For firms with geographically dispersed retailers facing price-dependent demand, effectively managing initial non-replenishable inventories by dynamically adjusting pricing and allocating to the retailers is crucial in optimizing their profits. In this thesis, joint pricing and inventory decisions within a one warehouse and multi-retailer setting are considered. For the single product case, structural properties of the optimal solution are derived and a mixed-integer quadratically constrained programming model is introduced to efficiently obtain the global optimal solution. Furthermore, it is proven that when the initial inventory at the warehouse is sufficiently large, it is possible to solve the problem optimally in polynomial time. Additionally, two heuristic methods are proposed by decomposing the exact model with respect to the pricing and allocation decisions. Then, the latter problem is extended to a multi-product setting accounting for the cross elasticity of demand effects. To maximize the total profit, a mixed-integer linear programming model is presented, incorporating sets of discrete permissible prices and general demand functions that capture the cross elasticity of demand. Given the combinatorial nature of the problem, a matheuristic based on an iterative fix-and-optimize approach is devised to efficiently obtain high-quality solutions. Additionally, an optimal decision tree-based demand forecasting model is proposed for substitute products. For learning, a mixed-integer quadratic programming model along with a CART-based approach for obtaining a starting solution is developed. Under the assumption that substitutes exhibit similar demand characteristics, the proposed model features high interpretability but also accounts for the cross elasticity of demand. In the computational study carried out using randomly generated instances, the effectiveness of the developed approaches is shown, and several managerial insights are presented.