Optimal and heuristic solutions for the single and multiple batch flow shop lot streaming problems with equal sublots

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Virginia Tech

This research is concerned with the development of efficient solutions to various problems that arise in the flow-shop environments which utilize lot-streaming. Lot streaming is a commonly used process of splitting production lots into sublots and, then, of scheduling the sublots in an overlapping fashion on the machines, so as to expedite the progress of orders in production and to improve the overall performance of the production system.

The different lot-streaming problems that arise in various flow-shop environments have been divided into two categories, single-lot problems and multiple-lot problems. Further classification of the multiple-lot problems into the lot streaming sequencing problem (LSSP) and the flow-shop lot-streaming (FSLS) problem is made in this work. This classification is motivated by the occurrence of these problems in the industry. Several variants of these problems are addressed in this research. In agreement with numerous practical applications, we assume sublots of equal sizes. It turns out that this restriction paves the way to the relaxation of several typical limitations of current lot-streaming models, such as assumption of negligible transfer and setup times or consideration of only the makespan criterion. For the single-lot problem, a goal programming (GP) approach is utilized to solve the problem for a unified cost objective function comprising of the makespan, the mean flow time, the average work-in-process (WIP), and the setup and handling related costs. A very fast optimal solution algorithm is proposed for finding the optimal number of sublots (and, consequently, the sublot size) for this unified cost objective function in a general m-machine flow shop.

For the more complicated multiple-lot problem, a near-optimal heuristic for the solution of the LSSP is developed. This proposed heuristic procedure, referred to as the Bottleneck Minimal Idleness (BMI) heuristic, identifies and employs certain properties of the problem that are irregular in traditional flow-shop problems, particularly the fact that the sublot sizes eminating from the same lot type and their processing times (on the same machines) are identical. The BMI heuristic attempts to maximize the time buffer prior to the bottleneck machine, thereby minimizing potential bottleneck idleness, while also looking-ahead to sequence the lots with large remaining process time earlier in the schedule. A detailed experimental study is performed to show that the BMI heuristic outperforms the Fast Insertion Heuristic (the best known heuristic for flow-shop scheduling), when modified for Lot Streaming (FIHLS) and applied to the problem on hand.

For the FSLS problem, several algorithms are developed. For the two-machine FSLS problem with an identical sublot-size for all the lots, an optimal pseudo-polynomial solution algorithm is proposed. For all practical purposes (i.e., even for very large lot sizes), this algorithm is very fast. For the case in which the sublot-sizes are lot-based, optimal and heuristic procedures are developed. The heuristic procedure is developed to reduce the complexity of the optimal solution algorithm. It consists of a construction phase and an improvement phase. In the construction phase, it attempts to find a near-optimal sequence for the lots and then, in the improvement phase, given the sequence, it attempts to optimize the lot-based sublot-sizes of each of the lots. Extensions of the solution procedures are proposed for the general m-machine FSLS problem.

A comprehensive simulation study of a flow shop system under lot streaming is conducted to support the validity of the results and to demonstrate the effectiveness of the heuristic procedures. This study clearly indicates that, even in dynamic practical situations, the BMI rule, which is based on the proposed BMI heuristic, outperforms existing WIP rules, commonly used in industry, in scheduling a flow-shop that utilizes lot streaming. With respect to the primary performance measure - cycle time (or MFT) - the BMI rule demonstrates a clear improvement over other WIP rules. It is further shown that it also outperforms other WIP rules with respect to the output variability measure, another important measure in flow-shop systems. The effects of several other factors, namely system randomness, system loading, and bottleneck-related (location and number), in a flow-shop under lot streaming, are also reported.

Simulation, BMI, lot sizing, equal sublots, Bottleneck Minimal Idleness, sequencing, Optimization, batch production, flow shop, lot streaming