Byran J. Smucker

Scheduling unrelated parallel machines with sequence-dependent setups

A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented in this paper. To comply with industrial situations, the dynamic release of jobs and dynamic availability of machines are assumed. Recognizing the inherent difficulty in solving industrial-size problems efficiently, six different search algorithms based on tabu search are developed to identify the best schedule that gives the minimum weighted tardiness. To enhance both the efficiency and efficacy of the search algorithms, four different initial solution finding mechanisms, based on dispatching rules, are developed. While there is no evidence of identifying solutions of better quality by employing a specific initial solution finding mechanism, the use of a specific search algorithm led to identifying solutions of better quality or that required lower computation time, but not both. Based on the extensive statistical analysis performed, the search algorithm with short-term memory and fixed tabu list size is recommended for solving small size problems, while that with long-term memory and minimum frequency for solving medium and large size problems, combined with fixed tabu list size for the former and variable tabu list size for the latter.

Exchange Algorithms for Constructing Model-Robust Experimental Designs

Optimal experimental design procedures, utilizing criteria such as D-optimality, are useful for producing designs for quantitative responses, often under nonstandard conditions such as constrained design spaces. However, these methods require a priori knowledge of the exact form of the response function, an often unrealistic assumption. Model-robust designs are those that, from our perspective, are efficient with respect to a set of possible models. In this paper, we develop a model-robust technique motivated by a connection to multiresponse D-optimal design. This link spawns a generalization of the modified Fedorov exchange algorithm, which is then used to construct exact model-robust designs. We also study the effectiveness of designs robust for a small set of models compared with designs that account for much larger sets. We give several examples and compare our designs with two model-robust procedures in the literature.

Beyond Normal: Preparing Undergraduates for the Work Force in a Statistical Consulting Capstone

In this article we chronicle the development of the undergraduate statistical consulting course at Miami University, from canned to client-based projects, and argue that if the course is well designed with suitable mentoring, students can perform remarkably sophisticated analyses of real-world data problems that require solutions beyond the methods encountered in previous classes. We review the historical context in which the consulting class evolved, describe the logistics of implementing it, and review assessment and student reaction to the course. We also illustrate the types of challenging projects the students are confronted with via two case studies and relate the skills learned and reinforced in this consulting class model to the skills demanded in the modern statistical work force. This course also provides an opportunity to strengthen and nurture key points from the new American Statistical Association guidelines for undergraduate programs: namely, communicating analyses of real and complex data that require the application of diverse statistical models and approaches. Supplementary materials for this article are available online. [Received December 2014. Revised July 2015.]

Model-Robust Two-Level Designs Using Coordinate Exchange Algorithms and a Maximin Criterion

We propose a candidate-list-free exchange algorithm that facilitates construction of exact, model-robust, two-level experiment designs. In particular, we investigate two model spaces previously considered in the literature. The first assumes that all main effects and an unknown subset of two-factor interactions are active, but that the experimenter knows the number of active interactions. The second assumes that an unknown subset of the main effects, and all associated two-factor interactions, are active. Previous literature uses two criteria for design construction: first, maximize the number of estimable models; then, differentiate between designs equivalent in estimability by choosing the design with the highest average -efficiency. We adopt a similar strategy, but (1) do not impose orthogonality or factor level balance constraints, resulting in generally equal or larger numbers of estimable models, and (2) use a flexible secondary criterion that maximizes the minimum -efficiency. We provide results for many situations of interest. We also provide online supplementary material that includes algorithmic details, designs, and MATLAB code.

Correcting Bias Introduced by Aerial Counts in Angler Effort Estimation

Abstract A critical part of most any roving angler survey is angler effort estimation. Various methods have been proposed and implemented to calculate this important parameter, and one of the most effective methods for estimation over large areas utilizes aerial counts of anglers. In this paper, we describe effort estimation methodology used for a creel survey conducted by the Pennsylvania Fish and Boat Commission in the lower Juniata River and lower and middle Susquehanna River during 2007. Daytime angler effort estimates were calculated using an augmented aerial survey, which includes both aerial counts and data collected by creel agents on the ground. Interview angler effort data obtained via a modified roving ground survey were used to produce estimates of daily effort distributions, which were then used to expand instantaneous aerial counts to daily effort estimates. We present two ratios that ameliorate biases introduced by the aerial survey. An angler-to-people ratio calculated from the ground data...

Cell Bounds in Two-Way Contingency Tables Based on Conditional Frequencies

Statistical methods for disclosure limitation (or control) have seen coupling of tools from statistical methodologies and operations research. For the summary and release of data in the form of a contingency table some methods have focused on evaluation of bounds on cell entries in k-way tables given the sets of marginal totals, with less focus on evaluation of disclosure risk given other summaries such as conditional probabilities, that is, tables of rates derived from the observed contingency tables. Narrow intervals - especially for cells with low counts - could pose a privacy risk. In this paper we derive the closed-form solutions for the linear relaxation bounds on cell counts of a two-way contingency table given observed conditional probabilities. We also compute the corresponding sharp integer bounds via integer programming and show that there can be large differences in the width of these bounds, suggesting that using the linear relaxation is often an unacceptable shortcut to estimating the sharp bounds and the disclosure risk.

Model-robust designs for split-plot experiments

Split-plot experiments are appropriate when some factors are more difficult and/or expensive to change than others. They require two levels of randomization resulting in a non-independent error structure. The design of such experiments has garnered much recent attention, including work on exact D-optimal split-plot designs. However, many of these procedures rely on the a priori assumption that the form of the regression function is known. We relax this assumption by allowing a set of model forms to be specified, and use a scaled product criterion along with an exchange algorithm to produce designs that account for all models in the set. We include also a generalization which allows weights to be assigned to each model, though they appear to have only a slight effect. We present two examples from the literature, and compare the scaled product designs with designs optimal for a single model. We also discuss a maximin alternative.

Validation of scaffold design optimization in bone tissue engineering: finite element modeling versus designed experiments

This study reports the development of biological/synthetic scaffolds for bone tissue engineering (TE) via 3D bioplotting. These scaffolds were composed of poly(L-lactic-co-glycolic acid) (PLGA), type I collagen, and nano-hydroxyapatite (nHA) in an attempt to mimic the extracellular matrix of bone. The solvent used for processing the scaffolds was 1,1,1,3,3,3-hexafluoro-2-propanol. The produced scaffolds were characterized by scanning electron microscopy, microcomputed tomography, thermogravimetric analysis, and unconfined compression test. This study also sought to validate the use of finite-element optimization in COMSOL Multiphysics for scaffold design. Scaffold topology was simplified to three factors: nHA content, strand diameter, and strand spacing. These factors affect the ability of the scaffold to bear mechanical loads and how porous the structure can be. Twenty four scaffolds were constructed according to an I-optimal, split-plot designed experiment (DE) in order to generate experimental models of the factor-response relationships. Within the design region, the DE and COMSOL models agreed in their recommended optimal nHA (30%) and strand diameter (460 μm). However, the two methods disagreed by more than 30% in strand spacing (908 μm for DE; 601 μm for COMSOL). Seven scaffolds were 3D-bioplotted to validate the predictions of DE and COMSOL models (4.5-9.9 MPa measured moduli). The predictions for these scaffolds showed relative agreement for scaffold porosity (mean absolute percentage error of 4% for DE and 13% for COMSOL), but were substantially poorer for scaffold modulus (51% for DE; 21% for COMSOL), partly due to some simplifying assumptions made by the models. Expanding the design region in future experiments (e.g., higher nHA content and strand diameter), developing an efficient solvent evaporation method, and exerting a greater control over layer overlap could allow developing PLGA-nHA-collagen scaffolds to meet the mechanical requirements for bone TE.

Approximate Model Spaces for Model-Robust Experiment Design

Optimal designs depend upon a prespecified model form. A popular and effective model-robust alternative is to design with respect to a set of models instead of just one. However, model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible. Here, we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set. We build our procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, we find that the designs constructed with the new method compare favorably with robust designs that use the full model space, with construction times reduced by orders of magnitude. We also construct designs that heretofore have been unobtainable due to the size of their model spaces. Supplementary material (available online) includes code, designs, and additional results.

Robustness of classical and optimal designs to missing observations

Missing observations are not uncommon in real-world experiments. Consequently, the robustness of an experimental design to one or more missing runs is an important characteristic of the design. Results of an evaluation of the robustness of classical and optimal designs to missing observations are presented, and optimal designs fare relatively well in terms of robustness compared to classical designs. Additionally, a modified version of an existing robustness criterion is used to construct designs that are robust to missing observations.