Determining the optimal constrained multi-item (Q, r) inventory policy by maximising risk-adjusted profit

The predominant approach to determining replenishment batch sizes for capital constrained multi-item inventories is to assume that at some point in time the replenishment of all items will coincide, and that batch sizes are small enough that the constraint is not violated when this event occurs. However, when an inventory consists of a large number of independently replenished components, the probability that all replenishments coincide is very small. The standard approach thus results in unnecessarily conservative batch sizes that under-utilise the available resource, resulting in lower profit than would be the case if a small risk of violating the constraint was tolerated. In this paper, a new approach to determining constrained batch sizes is presented where, for a certain average investment, the probability of exceeding a binding, or fixed, constraint on capital is determined. This probability is used to define an adjustment factor to be applied to expressions for company profit so that an optimal trade-off between maximising profit and reducing risk of failure is obtained simply by optimising this adjusted profit. By optimising profit adjusted for the risk of exceeding the constraint, the new model yields batch sizes that are larger, and result in greater profitability than those recommended under traditional models.