State space investigation of bullwhip with arbitrary demand processes

Abstract Using state space techniques we study a “myopic” order-up-to policy. The policy is myopic because is it is optimal at minimising local inventory holding and shortage costs. In particular we study the bullwhip effect produced by the replenishment policy reacting arbitrary stochastic demand processes. We reveal that bullwhip is fundamentally caused by the co-variance between the inventory level and the demand forecast. We go on to highlight the impact of a simple control engineering inspired bullwhip reduction technique, a proportional controller in the inventory feedback loop. Although it can be shown this approach is always able to remove bullwhip, we expose that is not possible to arbitrary “tune” the proportional controller, without knowing in advance the likely structure of the demand process.