LQ optimal inventory control for multi-supplier periodic-review systems with disparate lead-time delay

The paper addresses the problem of inventory control in production-inventory systems stressing the dynamical aspects of stock replenishment process. In the considered systems, the stock used to satisfy the unknown, time-varying demand can be refilled from multiple supply sources. The orders issued in each review period are realized with delay, which differs among the suppliers and transport alternatives. For the considered discrete-time nth-order system, a new inventory policy is developed using strict control-theoretic methodology. In contrast to the classical, stochastic approaches, the proposed policy is obtained through dynamical optimization with quadratic performance index. The designed policy ensures that the demand is always entirely satisfied from the on-hand stock (yielding zero lost-sales cost) and the warehouse capacity is not exceeded (what eliminates the risk of high-cost emergency storage). The closed-form solution of the linear-quadratic (LQ) optimization problem allows for a straightforward implementation of the developed control strategy in real systems.