Coordinated timing of replenishments within supply systems can provide high system effectiveness when compared to non-coordinated supply systems. In this work coordination of supply chain inventory replenishments will be based on integer-ratio policies. In integerratio policy the ratio of warehouse inventory replenishment interval to retailer inventory replenishment interval is an integer or an integer reciprocal for all retailers. The best known integer-ratio policy is power-of-two policy in which all integer-ratios are powers of two. In integer-partitioned power-of-U policies all warehouse replenishment interval to retailer replenishment interval ratios will be among 1, 2, 3,...,U-1, U, 2U, 3U,...,(U-1)U, UU, 2UU, 3UU...,UUU,... or among the reciprocals of such integers. Two integer-partitioned power-of-U policy variants are developed. In the first variant the aggregate inventory related total cost for all retailers with non-unity integer-ratios is assumed to be higher than the respective cost for the warehouse and all retailers with unity integer-ratios. In the second variant the aggregate inventory related total cost for all retailers with non-unity integer-ratios is assumed to be lower than the respective cost for the warehouse and all retailers with unity integer-ratios. With integer-partitioned power-of-U policies it is possible to construct integer-ratio lotsizing solutions with higher lower bound of maximum effectiveness than in power-of-two policy. Effectiveness results for integer-partitioned power-of-U policies for distribution systems have been developed.

Both inventory replenishment cost and inventory holding cost can be based on or approximated by affine or power cost functions. Holding cost reallocation is shown to apply in the case of affine cost functions so optimal integer-ratio policies can be developed. Power cost functions can be transformed into respective affine cost functions so holding cost reallocation is possible for power cost functions, too. Effectiveness results for power-of-two policy have been developed for four cost function type combinations. Methods for finding optimal or at least near-optimal power-of-two lot-sizing solutions are presented. Effectiveness results for integer-partitioned power-of-U policies for distribution systems have also been developed. In many-to-one assembly systems are several upstream facilities supplying one downstream facility facing the market demand. It will be shown that the prerequisites for the use of different integer-partitioned power-of-U policies described above are met so it is possible to use these policies on many-to-one supply systems, too.