LQ optimal sliding-mode supply policy for periodic-review perishable inventory systems

In this paper we consider the problem of designing an efficient supply strategy for logistic systems with perishable goods. In the analyzed systems, the stock at a distribution center is used to fulfill an unknown, time-varying market demand. The stock deteriorates exponentially, and is replenished with delay from a remote supply source. The objective is to specify a supply strategy such that high level of demand satisfaction is obtained despite unknown pattern of demand variations. As opposed to the previous approaches based mainly on heuristics and static optimization, we apply formal design methodology of sliding-mode control and discrete-time dynamical optimization. We show that the designed controller ensures full demand satisfaction irrespective of the value of delay and the demand uncertainty. Moreover, with the application of appropriate reaching law, the controller is demonstrated to conform to the supplier capacity limitations, and it outperforms the classical order-up-to policy in terms of higher service level, smaller holding costs, and smaller order-to-demand variance ratio.