The balanced lot size for a single-machine multi-product lot scheduling problem

The basic nature of feasible schedules and their lot sizes are investigated for a single-machine multi-product problem, under the assumptions of deterministic demand on infinite time horizon and cyclic production sequence. Feasible schedule is obtained under the balanced lot size which is in proportion to the demand rate of each product and independent of production sequence. It is determined uniquely if the production rate is higher than the sum of demand rate, while there are infinitely many feasible schedules if the production rate is just balanced to the sum of demand rate. The quantitative relation between such related factors as demand rate, production rate, machine idle time, production lot size, can be a practical guide for designing a small lot size production system, as well as determining a feasible schedule on long-term finite planning period.