Model predictive control of cash balance in a cash concentration and disbursements system

This paper presents a Model Predictive Control (MPC) for a revenue account belonging to a cash concentration and disbursements system, based on the application of inventory policies to the cash balance. Dynamic Programming (DP) is used for the prediction model by including a standard forecasting model for uncertainty. Moreover, a band for the uncertainty is established to narrow the input of the DP model, together with a stabilizing regulator in cascade fashion using a linear feedback gain. This combination allows determining a range for the system stability regardless of the size of the prediction horizon. The reference signal used is a sawtooth function, which conveniently adapts to the inventory policy (s,S). Theoretically, and through simulation, it is shown that the proposed controller meets the control objective. Furthermore, the results achieved are equivalent to those obtained by using a traditional inventory control model by directly applying the (s,S) strategy with periodic review, which supports the conclusions in Lee and Wong [44], Wong and Lee [71] and Lee [42] regarding the limited effectiveness when ADP is applied together with MPC. However, the method leaves open the possibility of obtaining promising results if some complexity elements (e.g. delay) are added to model.