Many high-volume warehouses for small parts such as pharmaceuticals, cosmetics and office supplies seek to improve efficiency by creating forward pick areas in which many popular products are stored in a small area that is replenished from reserve storage. This thesis addresses the question of how to stock forward pick areas to maximum benefit by answering two key, inter-related decisions that have been called Assignment-Allocation. The assignment question asks which SKUs should be stored in the forward pick area? And the allocation question asks how much space should be allocated to each SKU? We show fast, simple, near-optimal algorithms to answer these questions in a variety of circumstances. To allocate space to SKUS, we introduce a Powers of Two allocation scheme designed to simplify shelf management. In addition, we present a ranking-based algorithm to assign SKUs and allocate space among multiple forward pick areas. We show that a similar algorithm that accounts for constraints on congestion and workload within the forward pick area. We also show how to determine the optimal assignment for warehouses with one or more forward pick areas that allocate space in ways that are common in practice. Warehouses frequently use the 80-20 rule to manage SKUs based on their popularity. We examine empirical data from thirty warehouses and analyze whether the power law distribution is a suitable fit. We test the hypothesis that the power law fits of warehouses in similar industries are themselves similar. We review explanations for why power laws arise in other settings and identify those that are plausible in the warehouse setting.

This research investigates analytical models that might serve to support decisions in the early stages of designing high volume small parts order picking systems. Because the development of analytical closed-forms is challenging, a common approach is to use simulation models for detailed design performance assessment. However, simulation is not suitable for early stage design purposes; because simulation models are time-consuming (thus expensive) to construct and execute, especially when the number of alternatives to evaluate is large. If available, analytical models are computationally cheaper. They provide faster and more flexible solutions and though usually less detailed, may be adequate to support early stages of design. The challenge is to develop generic analytic models providing useful results for a class of problems. This research focuses on a class of problems in high volume small parts order picking systems with pick-to-buffer technology. This is a new technology, and not yet in widespread use. The novelty in the modeling approach is the distinct separation of item-picking and order assembly operations which permits the development of performance models for both throughput and service level. Essentially the system is modeled as a tandem queue, and the two detailed models for the picking and assembly subsystems are developed based on detailed description of the operations. Solving the model provides estimates for performance measures, such as order cycle time and system throughput, which are essential in design. The approximation method requires estimating the squared coefficient of interdeparture times from the classical GX/G/1 queuing model, and a suitable approximation is derived in this thesis. Computational tests show the model to provide reasonably accurate estimates of system performance, with minimal computational overhead. To support the proposed queuing model, new models are developed for estimating mean and squared coefficient of variation for pick and assembly operation times. These models include the variability of order contents and the picking process, along with the physical layout. Results of the estimation compare very well with that of simulation.

Wire Electric Discharge Machining (wire-EDM) is a non-traditional machining process. Controlled electric sparks are successively used to vaporize part of a workpiece along a programmed path in order to machine a desired part. Because there is no tool that comes in direct contact with the workpiece, it is possible to machine thin, delicate parts. This thesis was designed to observe and analyze the differences in cutting capabilities for a conventional wire-EDM machine when cutting thin-walled sections from five commonly used metals utilizing a variation of roughing and finishing passes. The five metals that were used in this study are: Aluminum 6061 T6, Yellow Brass SS360, 420 Stainless Steel, D2 Tool Steel at 25 to 30 RC, and D2 Tool Steel at 60 to 65 RC. The thin-walled sections were constrained on each end by the parent material to which they remained attached, and they ranged in thickness from 0.05 millimeters (0.002 inches) increasing incrementally by 0.05 millimeters (0.002 inches) until they reached a thickness of 0.30 millimeters (0.012 inches). A Sodick AQ325L wire-EDM machine was employed to perform the machining. It was observed that differences exist in the capabilities of cutting thin-walled sections from the five different metals. This could be both observed visually through inspection and statistically through the analysis of each data set obtained by measuring the resultant thickness of each section. It was also observed that differences exist for the same material while utilizing the variations of cutting parameters: a roughing with no finishing passes, a roughing with one finishing pass, and a roughing with three finishing passes. Thus both the material properties and the cutting parameters play a significant role in determining the capability of cutting thin-walled sections with a wire-EDM machine.