This paper examines the joint lot sizing problem for minimizing inventory costs for several products of constant demand made on one machine with zero cost setups but with setup times. If total demand requirements do not exceed available capacity then there is always a feasible schedule for any cycle sequence using different lot sizes. The paper describes a four-stage solution procedure, which builds upon the concept of not having any idle time or carryover inventory. The paper demonstrates that, quite often, unequal lot sizes can reduce inventory costs over equal lot sizes in the zero inventory case. Key Words: Lot-Sizing, Scheduling, Setup Time.