Multiple-warehouse sliding mode control with a predefined demand trajectory profile

The paper discusses the inventory management problem with a single product stored in two warehouses, where each has its unique suppliers with certain lead times. Moreover, one of the warehouses may act as a backup supplier for the other. In other words, product exchange between two different warehouses within one company is allowed. The first warehouse operates under an a priori known time-variant contractual demand and a bounded random one. Its secondary goal is to accumulate emergency stock that can be delivered to the second warehouse within one time period. For this warehouse we use a desired trajectory generator to shape the required stock level and then utilize a trajectory following control law. The demand in the second warehouse is unknown but bounded, and its suppliers have limited delivery capacity. The challenge is to fulfill the customers’ needs, although they might exceed the order limit. Therefore, occasional backup supplies from the first warehouse are necessary. For the control of the second warehouse, a simple sliding mode (SM) scheme is applied. The paper proves that, with appropriate compensation of the emergency deliveries in the first warehouse, our proposed control scheme ensures full demand satisfaction in both warehouses despite the second one’s control limit.