An assembly production system with n facilities has a constant external demand occurring at the end facility. Production rates at each facility are finite and nonincreasing along any path in the assembly network. Associated with each facility are a setup cost and positive echelon holding cost rate. The formulation of the lot sizing problem is developed in terms of inter-ratio lot size policies. This formulation provides a unification of the integer-split policies formulation of L.B. Schwarz and L. Schrage and the integer-multiple policies formulation of J.P. Moily, allowing either assumption to be operative at any point in the system. A relaxed solution to this unified formulation provides a lower bound to the cost of any feasible policy. The derivation of this Lower Bound Theorem is novel and relies on the notion of path holding costs, which is a generalization of echelon holding costs. An optimal power-of-two lot size policy is found by an O(n5) algorithm and its cost is within 2% of the optimum in the worst case.
