A statistical comparison of two safety stock replenishment mechanisms in a cyclic stochastic IRP

Preventing stock-out in a replenishment system, in which customer demand rates are stochastic with constant averages, can be accomplished via safety stocks hold at each customer. These safety stocks should be replenished back to their initial levels each time they are used. However, sometimes it occurs that a truck does not have enough capacity to carry the amount of the product the visited customers need to restore their stocks and safety stocks to their required levels. Therefore, the carried extra amount of the product, intended to replenish safety stocks, should be divided amongst the customers in some optimal or fair manner. To achieve this fair allocation, we propose and analyze two policies, the first called Fair-share and the second Ratio methods. Details on how these two methods are implemented, to achieve the level of service expected at each customer, are discussed and illustrated. In addition a simulation model is developed and used to compare the performance of each policy in the long run