In this paper, we apply the concept of discrete sliding modes (DSMs) in designing efficient supply policy for a class of perturbed processes with delay - goods flow control in supply chain. In the considered systems, the stock used to satisfy the unknown, time-varying demand placed at a goods distribution center is replenished with delay from a remote supply source. The order quantity is fixed, leaving the time between the consecutive orders as a decision variable, which perfectly suits the switched nature of input signals obtained in DSM control systems. It is shown that under the proposed nonlinear policy the stock level does not exceed the assigned storage space. Moreover, it is also demonstrated that the stock is never entirely depleted, which guarantees full demand satisfaction and maximum service level.