Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels (original) (raw)

We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand processes. In case of a stock-out at a local warehouse, a demand can be fulfilled via a lateral transshipment (LT). Each warehouse is assigned a predetermined sequence of other warehouses where it will request for an LT. However, a warehouse can hold its last part(s) back from such a request. This is called a hold back pooling policy, where each warehouse has hold back levels determining whether a request for and LT by another warehouse is satisfied. We are interested in the fractions of the demand satisfied from stock (fill rate), satisfied via a lateral transshipment, and via an emergency shipment from an external source. From this the average costs of a policy can be determined. We present two approximation algorithms for the evaluation of a given policy, approximating the above mentioned fractions. The first one, the Poisson overflow algorithm, is an extension of algorithms known in the literature. The second one, the On/Off overflow algorithm is new and more sophisticated. Instead of approximating the stream of LTrequests from a warehouse as a Poisson process, we use an interrupted Poisson process. This is a process that is turned alternatingly On and Off for exponentially distributed durations. In a numerical study we show that both algorithms perform very well. The On/Off algorithm is significantly more accurate than the Poisson algorithm, but requires longer computation times.