Contractor Accreditation: A Probabilistic Model

The selection of competent contractors is a critical function in all business organizations. In contrast to other types of vendors (e.g., distributors, manufacturers, etc.), contractors are typically accredited before any business transaction takes place. In such situations, there is often a considerable amount of uncertainty associated with the accreditation process. This research presents a probabilistic model for accrediting contractors. We discuss a methodology in which probability measures are used to capture the uncertainty inherent in the decision process. These probabilities are estimated from data on (i) past applicants and (ii) their eventual performance, if accredited. Furthermore, these probabilities are used to determine when additional information about an applicant should be collected, as well as what kind of information would be most relevant for the vendor under consideration.     

Robust sure independence screening for nonpolynomial dimensional generalized linear models

We consider the problem of variable screening in ultra-high-dimensional generalized linear models (GLMs) of nonpolynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the marginal regression coefficients. Our proposed screening procedure performs well under pure and contaminated data scenarios. We provide a theoretical motivation for the use of marginal MDPDEs for variable screening from both population as well as sample aspects; in particular, we prove that the marginal MDPDEs are uniformly consistent leading to the sure screening property of our proposed algorithm. Finally, we propose an appropriate MDPDE-based extension for robust conditional screening in GLMs along with the derivation of its sure screening property. Our proposed methods are illustrated through extensive numerical studies along with an interesting real data application.     

Heuristic Estimation of the Efficient Frontier for a Bi-Criteria Scheduling Problem

We examine a single-machine scheduling problem where the objective is to minimize the mean and the variance of the job completion times simultaneously. We seek to identify the efficient frontier which is obtained by parametrically solving a weighted combination of the two criteria. The identification of the true efficient frontier for this problem is notoriously difficult. To estimate the frontier, we propose a heuristic procedure which is quite general and can be applied to other bi-criteria problems as well. It involves repeated applications of a relatively new technique called beam search in an adaptive manner. To evaluate the proposed procedure, we introduce two measures of performance and conduct a computational study. The results of the study indicate that the procedure is highly effective.     

Optimal Delivery Time Quotation and Order Sequencing

This paper examines the problem of quoting a common delivery time for several orders. The decision maker responsible for the quote must trade off the cost associated with a long delivery time against the cost of tardy orders that might be induced by a short delivery time. First, an aggregate cost model is investigated where it is assumed that some cost is incurred if the quoted delivery time exceeds a given threshold and the cost of order tardiness is dependent on the order. Both exact and heuristic solution procedures are proposed for this model. Finally, for the situation where the costs cannot be quantified, a bicriteria formulation of the problem is pursued and the set of nondominated solutions is identified.     

Assigning students to academic majors

We address here the problem of assigning undergraduate students to academic major areas at a Middle-Eastern business school, which is quite different from what one usually faces in the West. Our formulation considers the student's preference in the light of his/her performance in certain bellwether courses and various practical constraints in arriving at an initial solution. We present a linear program that maximizes the overall value of the assignments to the students as well as the academic units concerned. We show through a real example how this approach has been implemented as one step in the major-assignment process.     

Evaluation of missing data mechanisms in two and three dimensional incomplete tables

The analysis of incomplete contingency tables is a practical and an interesting problem. In this paper, we provide characterizations for the various missing mechanisms of a variable in terms of response and non-response odds for two and three dimensional incomplete tables. Log-linear parametrization and some distinctive properties of the missing data models for the above tables are discussed. All possible cases in which data on one, two or all variables may be missing are considered. We study the missingness of each variable in a model, which is more insightful for analyzing cross-classified data than the missingness of the outcome vector. For sensitivity analysis of the incomplete tables, we propose easily verifiable procedures to evaluate the missing at random (MAR), missing completely at random (MCAR) and not missing at random (NMAR) assumptions of the missing data models. These methods depend only on joint and marginal odds computed from fully and partially observed counts in the tables, respectively. Finally, some real-life datasets are analyzed to illustrate our results, which are confirmed based on simulation studies.