Online Inventory Problems: Beyond the i.i.d. Setting with Online Convex Optimization
This addresses inventory management challenges for managers by moving beyond unrealistic i.i.d. assumptions, though it is incremental in extending online convex optimization to this domain.
The paper tackles the problem of multi-product inventory control with non-i.i.d. demands and stateful dynamics, proposing the MaxCOSD algorithm that provides provable guarantees for minimizing cumulative losses.
We study multi-product inventory control problems where a manager makes sequential replenishment decisions based on partial historical information in order to minimize its cumulative losses. Our motivation is to consider general demands, losses and dynamics to go beyond standard models which usually rely on newsvendor-type losses, fixed dynamics, and unrealistic i.i.d. demand assumptions. We propose MaxCOSD, an online algorithm that has provable guarantees even for problems with non-i.i.d. demands and stateful dynamics, including for instance perishability. We consider what we call non-degeneracy assumptions on the demand process, and argue that they are necessary to allow learning.