Order picking operations play a critical role in the order fulfillment process of distribution centers (DCs). Picking a batch of orders is often favored when customers’ demands create a large number of small orders, since the traditional single-order picking process results in low utilization of order pickers and significant operational costs. Specifically, batch picking improves order picking performance by consolidating multiple orders in a "batch" to reduce the number of trips and total travel distance required to retrieve the items. As more pickers are added to meet increased demand, order picking performance is likely to decline due to significant picker blocking. However, in batch picking, the process of assigning orders to particular batches allows additional flexibility to reduce picker blocking. This dissertation aims to identify, analyze, and control, or mitigate, picker blocking while batch picking in picker-to-part systems. We first develop a large-scale proximity-batching procedure that can enhance the solution quality of traditional batching models to near-optimality as measured by travel distance. Through simulation studies, picker blocking is quantified. The results illustrate: a) a complex relationship between picker blocking and batch formation; and b) a significant productivity loss due to picker blocking. Based on our analysis, we develop additional analytical and simulation models to investigate the effects of picker blocking in batch picking and to identify the picking, batching, and sorting strategies that reduce congestion. A new batching model (called Indexed order Batching Model (IBM)) is proposed to consider both order proximity and picker blocking to optimize the total order picking time. We also apply the proposed approach to bucket brigade picking systems where hand-off delay as well as picker blocking must be considered. The research offers new insights about picker blocking in batch picking operations, develops batch picking models, and provides complete control procedures for large-scale, dynamic batch picking situations. The twin goals of added flexibility and reduced costs are highlighted throughout the analysis.

The present work consists of three parts. In the first part (chapters III and IV), the dynamics of Lorentz lattice gases (LLG) on graphs is analyzed. We study the fixed scatterer model on finite graphs. A tight bound is established on the size of the orbit for arbitrary graphs, and the model is shown to perform a depth-first search on trees. Rigidity models on trees are also considered, and the size of the resulting orbit is established. In the second part (chapter V), we give a complete description of dynamics for LLG on the one-dimensional integer lattice, with a particular interest in showing that these models are not capable of universal computation. Some statistical properties of these models are also analyzed. In the third part (chapter VI) we attempt to partition a pool of workers into teams that will function as independent TSS lines. Such partitioning may be aimed to make sure that all groups work at approximately the same rate. Alternatively, we may seek to maximize the rate of convergence of the corresponding dynamical systems to their fixed points with optimal production at the fastest rate. The first problem is shown to be NP-hard. For the second problem, a solution for splitting into pairs is given, and it is also shown that this solution is not valid for partitioning into teams composed of more than two workers.

A fascinating feature of bucket brigade assembly lines is that work load on workers is balanced spontaneously as workers follow some simple rules in the assembly process. This self-organizing property significantly reduces the management effort on an assembly line. We generalize this idea in several directions. These include an adapted bucket brigade protocol for complex assembly networks, a generalized model that permits chaotic behavior, and a more detailed model for a flow line in which jobs arrive arbitrarily in time and are introduced into the system at several points on the line.