(r, Q) stock replenishment in multi-mode distribution systems with uncertain delivery channels and adaptive channel allocation

Abstract

To mitigate the impact of uncertainty in goods distribution systems, multiple channels and transportation modes may be used. In this paper, a discrete-time model of supplier-depot interaction involving multiple channels of goods relocation is constructed using the concepts of dynamic systems theory. The considered class of systems faces two types of uncertainty: a priori unknown variations of market demand and unpredictable changes of lead-time delay, different for each channel. The variation pattern is arbitrary. As a control mechanism, the nonlinear (r, Q) replenishment policy (provide Q units of goods when the stock falls below r) is considered. As opposed to the previous studies, the policy is demonstrated robust to both sources of uncertainty acting simultaneously using a formal mathematical argument. Moreover, it is shown how to select the policy parameters to obtain full demand realization, thus eliminating backorders, irrespective of the pattern of delay and demand fluctuations. It is also discussed how to assign the depot capacity so that emergency storage will not be required even though deliveries from a few periods arrive concurrently, or out of order. In addition, a new channel allocation strategy, dynamically adapting itself to the channel temporal characteristics, is developed. As evidenced in the tests, the proposed adaptive strategy, by reducing the waiting time for the lot reassembly at the depot, allows for holding cost reduction by several percent with respect to a static strategy.