Lot streaming is the process of splitting a production lot into sublots, and scheduling these sublots in overlapping fashion, in order to accelerate the progress of an order in production (Baker, 1993). It is an integration of lot-sizing and scheduling problems. Although lot-sizing and scheduling decisions are strongly interrelated and lot streaming appears to be widely practiced, there is relatively little research work reported on the modeling and solution methods. This research models and solves the lot streaming problems in two stage hybrid flow shops, that is, to decide the optimal number of sublots for each order, the optimal size of each sublot and the optimal sequence of processing sublots so that the production lead time is minimized....[ Read more ]

Lot streaming is the process of splitting a production lot into sublots, and scheduling these sublots in overlapping fashion, in order to accelerate the progress of an order in production (Baker, 1993). It is an integration of lot-sizing and scheduling problems. Although lot-sizing and scheduling decisions are strongly interrelated and lot streaming appears to be widely practiced, there is relatively little research work reported on the modeling and solution methods. This research models and solves the lot streaming problems in two stage hybrid flow shops, that is, to decide the optimal number of sublots for each order, the optimal size of each sublot and the optimal sequence of processing sublots so that the production lead time is minimized.

The study begins with single job lot streaming in two-stage hybrid flow shop with one of the stages having only one machine and another having m identical machines. We show that the single job lot streaming problem in two stage hybrid flow shop and its inverse are equivalent. Efficient optimal solutions are obtained for some special cases. The general case is formulated using a mixed integer linear programming (MILP) model. Two heuristic algorithms are then proposed and compared with the optimal solution. Computational experiments show that the first heuristic algorithm performs well with mean error of less than 1.6% while the second one finds the optimal solutions for all the tested problems.

The work is then extended to multi-job cases in the same machine environment. Given the NP-completeness, we formulate the problem using MILP model and derive a lower bound from the MILP model to operate jointly with other two lower bounds. Two heuristic algorithms are proposed based on equal sublot and balanced sublot ideas respectively. Extensive computational experiments on a large set of randomly generated test problems show that the heuristics are both computationally efficient and generate solutions only 3.9% and 2.6% away from the lower bounds, respectively.

Finally, we study multi-job lot streaming in the general two-stage hybrid flow shop with both stages having multiple identical machines. Two heuristic procedures are proposed and real production data from industry are collected and applied to test the heuristics. Results show that the solutions of the proposed heuristic procedures significantly outperform the results of current method in reducing mean completion time.