Controlling a divergent 2-echelon network with transshipments using the consistent appropriate share rationing policy : working paper

Consider a two-echelon inventory system consisting of a central depot (CD) and a number of retailers. Only the retailers face customer demand. The CD is allowed to hold stock. In all stockpoints, the echelon inventory position is periodically raised to certain order-up-to-levels. At the central depot, incoming stock is allocated by using the consistent appropriate share rationing (CAS) policy. This means that this policy attempts to keep the ratio of the projected net inventory at any retailer over the system projected net inventory constant at any time. The size of this ratio depends on the customer service level every retailer requires, and the behaviour of the demand process. When the orders arrive at the retailers, an instantaneous rebalancing of the total net stock of the retailers takes place, so as to maintain all end stockpoint inventory at a balanced position. This rebalancing is realized by the transshipment of stock, assuming that the time to transship stock from one retailer to another is negligible compared to the replenishment lead time (lead time between CD and a retailer). Object of this analysis is the determination of all the control parameters (integral order-up-to-level, parameters of allocation policy at the CD and of the rebalancing policy at the retailer), so that the desired (different) service levels are attained at the retailers at minimal expected total costs. Exact expressions are developed to determine these parameters. However we will use some heuristics to actually compute these parameters, because of the intractability of the exact expressions. All analytical results are validated by Monte-Carlo simulation. The model developed will be compared with the same model without periodic, instantaneous rebalancing at the retailer. This yields insight into the conditions under which transshipment could be useful.