Optimal lot streaming for multiple products in a two-machine flow shop

This paper treats the optimal lot streaming problem for multiple products in a two-machine flow shop with job setup times and sublot transfer times. If production lots are not preempted, an independent transfer lot sizing problem is obtained for each job; this problem is the same for any regular measure of performance. For continuous transfer lot sizes a closed-form optimal solution is obtained, while for integer valued lot sizes a fast polynomial algorithm is developed. The makespan minimization problem with lot streams is reduced to an equivalent two-machine makespan problem without lot streams or setup/transfer times but with modified processing times, and can thus be solved by Johnson's algorithm. The procedures are illustrated in an example.