Reducing system nervousness in multi-product inventory systems

In many practical multi-product systems a joint setup cost is incurred when at least one product is ordered and an individual setup cost for each product is ordered. In those cases joint replenishment policies will lead to lower cost compared to independent replenishment of each product. The paper considers periodic review multi-product systems with independent stochastic demand. The object is to find a replenishment policy which minimizes the long-run average setup and holding cost per unit time subject to a service level constraint. The paper examines the behaviour of the system under a rolling-horizon approach. Solving a deterministic problem gives a replenishment schedule for next N periods. The decision for the first period in the deterministic problem is implemented in the stochastic system. Due to the stochastic demand the actual sizes and timing will be different, referred to as system nervousness. The paper proposes a procedure to adjust this decision in order to reduce the system nervousness. Simulation experiments show cost reductions between 2% and 8% and cost performance comparable with can-order strategies.