In this thesis, a number of lot streaming problems in flow, open and job shops are investigated. Lot streaming is the process of splitting a job to allow for overlapping of its operations on various machines resulting in shorter completion times. When there is a single job, the problem is to find the size of the transfer batches (“sublots”) which minimizes a given performance measure (e.g., makespan, mean flow time). Multi-job problems are harder, since sequencing and sizing decisions must be made simultaneously. Most of the current research in lot streaming is concerned with minimum makespan problems in flow shops. In this study, other performance measures and shop structures are also analyzed. Optimal sublot sizes are derived for the single job two machine flow shop mean flow time problem. Solution methods are proposed for the minimum makespan problem in open shops both for multiple job and single job cases.