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Sheldon Epstein

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Papers

Truth : Elusive or Illusive ? An Historical Example

How should one react when "reality," based on observations and scientific proofs, appea... more How should one react when "reality," based on observations and scientific proofs, appears to be at odds with the teachings of the Torah? Some critical observers have noted that it is common for people to accept "reality" as fact and attempt to reconcile the Torah with the "facts," regardless of how tortured and convoluted the solution may be. Rather than accepting this apologetic approach, these observers argue that it is "reality," not the Torah, which is amiss.

Pooled Testing: Determining The Optimum Pool Size To Minimize The Total Number Of Tests

Journal of Applied Business Research (JABR)

In light of the rapidly spreading COVID-19 virus, the FDA has suggested pooling of samples in ord... more In light of the rapidly spreading COVID-19 virus, the FDA has suggested pooling of samples in order to reduce the cost of testing a large population. Under this approach, several samples are pooled, and the pooled samples are first tested. If the pool tests negative, then the lab would have successfully tested many samples while consuming only the resources needed for a single test. If the pooled sample tests positive, then each sample that comprised the pool is individually tested. In this context, an important question for people in the field is “Given a certain overall infection rate among the population, what is the optimum pool size so that we can minimize the overall number of tests for a given number of individual samples?” In this paper, we derive this number both empirically and analytically. We also address the related question “Given a certain pool size, what is the maximum infection rate for which we can still gain in terms of the number of tests?”

Case Study: Structured Settlements

Journal of College Teaching & Learning (TLC), 2011

Students are presented with a report that offers a present value analysis of a Structured Settlem... more Students are presented with a report that offers a present value analysis of a Structured Settlement and asked to decide whether they agree with its conclusions. The case tests quantitative, financial and spreadsheet skills, exposes students to the world of law and legal statutes, and requires value judgments about fairness. The case is appropriate for senior-level undergraduate business majors and MBAs, in courses that involve decision-making.

The PBA vs Piscataway: A Case Study Statistics In The Workplace

Journal of Business Case Studies (JBCS), 2011

The State of New Jersey Public Relations Employment Commission recently rendered a decision in a ... more The State of New Jersey Public Relations Employment Commission recently rendered a decision in a dispute over the Piscataway Police Department’s procedure for promoting individuals to the rank of sergeant. One important component of the case was how to properly interpret the results of a 1999 sergeant’s promotion exam. This paper gives a brief history of the promotional process and offers the data and statistical analysis submitted by both the Plaintiff (Patrolmen’s Benevolent Association- PBA) and the Police Administration. The case provides an excellent tutorial for beginners and practitioners on how to properly apply some elementary, but powerful, statistical concepts.

Developing Transparent Health Care Reimbursement Auditing Procedures

Journal of Business Case Studies (JBCS), 2013

The continued computerization of health care records has enabled easier sampling and analysis of ... more The continued computerization of health care records has enabled easier sampling and analysis of large sets of medical records, making it easier than ever for Medicare, Medicaid and other private insurers to use statistical audits to determine and demand return of alleged overpayments to health care providers. However, there are sometimes statistical difficulties with the audits, and there is frequently not sufficient transparency in the procedures or their application to reproduce the results in order to determine whether they have been carried out correctly. This paper addresses concerns in sampling and analysis of data records by looking at the case of a specific audit of a medical practice carried out by a private insurer. If done properly, statistical audits can be a very useful tool, but often the methodologies are vague and the implementation is either wrong or not explained fully enough to reproduce and analyze.

Auditing The Auditors In Medicare And Medicaid

Journal of Business Case Studies (JBCS), 2011

Baker Surgical Supplies, a small company, went bankrupt after it could not repay a significant ov... more Baker Surgical Supplies, a small company, went bankrupt after it could not repay a significant overpayment charge demanded by Medicare based on a statistical extrapolation of claims of overpayment. The case centered on whether the extrapolation process was justifiable and whether it was properly implemented. This paper provides a description of the extrapolation process used by Medicare and Medicaid and presents the data and sampling procedure offered by Medicare and the statistical arguments offered by Baker. The case demonstrates some potential misuses of statistics in the auditing process. In shedding light on this issue, the analysis in this paper could prove to be instrumental in prompting significant improvements to the auditing process of Medicare and Medicaid.

How the oldest recorded multiple facility location problem was solved

Location Science, 1995

Multiple common due dates

Naval Research Logistics, 2001

Abstract Common due date problems have been extensively discussed in the scheduling literature. I... more

Deterministic multiprocessor scheduling with multiple objectives

Computers & Operations Research, 1992

Abstract One common job scheduling objective is to minimize makespan. The problem can be modeled ... more

Optimal common due-date with completion time tolerance

Computers & Operations Research, 1996

The common due-date problem involves minimizing the absolute deviation around a common due-date. ... more

Optimization in Multiple-Objective Linear Programming Problems with Pre-Emptive Priorities

The Journal of the Operational Research Society, 1990

The Effect Of Plus/Minus Grading On The GPA

Journal of College Teaching & Learning (TLC), 2011

In recent years, an increasing number of colleges and universities have been turning away from tr... more In recent years, an increasing number of colleges and universities have been turning away from traditional letter grading systems that limit student grades to A, B, C, D, and F based on the presumption that grading systems with more flexibility are advantageous to both teachers and students. However, as with any rating system, before opting for a new grading system it is important to recognize that modifications may result in some, possibly unintended, consequences as well. In this paper, we discuss theoretical effects that including plus and/or minus grades may have on Grade Point Average (GPA) and analyze data from a School that implemented such a change.

Modeling Deterministic Opportunistic Replacement as an Integer Programming Problem

American Journal of Mathematical and Management Sciences, 1990

ABSTRACT The field of opportunistic replacement deals with the benefits of performing maintenance... more ABSTRACT The field of opportunistic replacement deals with the benefits of performing maintenance on equipment prior to failure in order to avoid prohibitively high costs associated with failure. Problems of a deterministic nature, i.e., where the exact times of both mandatory replacement and maintenance opportunities are known at the outset, with infinite time horizons have been solved for the two component case using a specialized algorithm. This paper presents a more general integer programming formulation of the problem that will work for any specified time frame. The results are of theoretical as well as practical significance in solving problems such as maintenance scheduling in fusion power plants.

A Historical Note On The Proof Of The Area Of A Circle

Journal of College Teaching & Learning (TLC), Mar 15, 2011

An optimal replacement policy for life limited parts

A replacement schedule for multicomponent life-limited parts

Naval Research Logistics Quarterly, 1982

ABSTRACT In previous papers [1], [2] the authors developed a maintenance policy for a single life... more ABSTRACT In previous papers [1], [2] the authors developed a maintenance policy for a single life-limited part. Using an opportunistic replacement approach a scheme was devised which utilized early replacement of equipment to offset more costly future expenditures. This paper will extend the results to the multicomponent case. Examples are given illustrating the benefits of this new technique.

Opportunistic replacement in a deterministic environment

Computers & Operations Research, 1985

ABSTRACT An opportunistic replacement problem dealing with life-limited parts is analyzed. Becaus... more ABSTRACT An opportunistic replacement problem dealing with life-limited parts is analyzed. Because of prohibitively high costs of unscheduled breakdowns, life-limits on system components, e.g. nuclear fusion power systems, may be set so low as to insure performance during allotted life span. If two components with different life-limits are present, each individual scheduled replacement point offers potential opportunity for monetary savings. It is proved that in this deterministic situation only a limited number of the possible replacement points need be considered. An algorithm to generate these points is given and the computational requirements are discussed.

A Historical Note On The Proof Of The Area Of A Circle

by Sheldon Epstein and Yonah Wilamowsky

Journal of College Teaching & Learning (TLC), 2011

Abstract Proofs that the area of a circle is πr 2 can be found in mathematical literature dating ... more

The Effect Of Plus/Minus Grading On The GPA

by Sheldon Epstein and Yonah Wilamowsky

Journal of College Teaching & Learning (TLC), 2011

Page 1. Journal of College Teaching &amp; Learning September 2008 Volume 5, Number 9 1 The ... more

Case Study: Structured Settlements

by Sheldon Epstein and Yonah Wilamowsky

Journal of College Teaching & Learning (TLC), 2011

Abstract Students are presented with a report that offers a present value analysis of a Structure... more

Truth : Elusive or Illusive ? An Historical Example

How should one react when "reality," based on observations and scientific proofs, appea... more How should one react when "reality," based on observations and scientific proofs, appears to be at odds with the teachings of the Torah? Some critical observers have noted that it is common for people to accept "reality" as fact and attempt to reconcile the Torah with the "facts," regardless of how tortured and convoluted the solution may be. Rather than accepting this apologetic approach, these observers argue that it is "reality," not the Torah, which is amiss.

Pooled Testing: Determining The Optimum Pool Size To Minimize The Total Number Of Tests

Journal of Applied Business Research (JABR)

In light of the rapidly spreading COVID-19 virus, the FDA has suggested pooling of samples in ord... more In light of the rapidly spreading COVID-19 virus, the FDA has suggested pooling of samples in order to reduce the cost of testing a large population. Under this approach, several samples are pooled, and the pooled samples are first tested. If the pool tests negative, then the lab would have successfully tested many samples while consuming only the resources needed for a single test. If the pooled sample tests positive, then each sample that comprised the pool is individually tested. In this context, an important question for people in the field is “Given a certain overall infection rate among the population, what is the optimum pool size so that we can minimize the overall number of tests for a given number of individual samples?” In this paper, we derive this number both empirically and analytically. We also address the related question “Given a certain pool size, what is the maximum infection rate for which we can still gain in terms of the number of tests?”

Case Study: Structured Settlements

Journal of College Teaching & Learning (TLC), 2011

Students are presented with a report that offers a present value analysis of a Structured Settlem... more Students are presented with a report that offers a present value analysis of a Structured Settlement and asked to decide whether they agree with its conclusions. The case tests quantitative, financial and spreadsheet skills, exposes students to the world of law and legal statutes, and requires value judgments about fairness. The case is appropriate for senior-level undergraduate business majors and MBAs, in courses that involve decision-making.

The PBA vs Piscataway: A Case Study Statistics In The Workplace

Journal of Business Case Studies (JBCS), 2011

The State of New Jersey Public Relations Employment Commission recently rendered a decision in a ... more The State of New Jersey Public Relations Employment Commission recently rendered a decision in a dispute over the Piscataway Police Department’s procedure for promoting individuals to the rank of sergeant. One important component of the case was how to properly interpret the results of a 1999 sergeant’s promotion exam. This paper gives a brief history of the promotional process and offers the data and statistical analysis submitted by both the Plaintiff (Patrolmen’s Benevolent Association- PBA) and the Police Administration. The case provides an excellent tutorial for beginners and practitioners on how to properly apply some elementary, but powerful, statistical concepts.

Developing Transparent Health Care Reimbursement Auditing Procedures

Journal of Business Case Studies (JBCS), 2013

The continued computerization of health care records has enabled easier sampling and analysis of ... more The continued computerization of health care records has enabled easier sampling and analysis of large sets of medical records, making it easier than ever for Medicare, Medicaid and other private insurers to use statistical audits to determine and demand return of alleged overpayments to health care providers. However, there are sometimes statistical difficulties with the audits, and there is frequently not sufficient transparency in the procedures or their application to reproduce the results in order to determine whether they have been carried out correctly. This paper addresses concerns in sampling and analysis of data records by looking at the case of a specific audit of a medical practice carried out by a private insurer. If done properly, statistical audits can be a very useful tool, but often the methodologies are vague and the implementation is either wrong or not explained fully enough to reproduce and analyze.

Auditing The Auditors In Medicare And Medicaid

Journal of Business Case Studies (JBCS), 2011

Baker Surgical Supplies, a small company, went bankrupt after it could not repay a significant ov... more Baker Surgical Supplies, a small company, went bankrupt after it could not repay a significant overpayment charge demanded by Medicare based on a statistical extrapolation of claims of overpayment. The case centered on whether the extrapolation process was justifiable and whether it was properly implemented. This paper provides a description of the extrapolation process used by Medicare and Medicaid and presents the data and sampling procedure offered by Medicare and the statistical arguments offered by Baker. The case demonstrates some potential misuses of statistics in the auditing process. In shedding light on this issue, the analysis in this paper could prove to be instrumental in prompting significant improvements to the auditing process of Medicare and Medicaid.

How the oldest recorded multiple facility location problem was solved

Location Science, 1995

Multiple common due dates

Naval Research Logistics, 2001

Abstract Common due date problems have been extensively discussed in the scheduling literature. I... more

Deterministic multiprocessor scheduling with multiple objectives

Computers & Operations Research, 1992

Abstract One common job scheduling objective is to minimize makespan. The problem can be modeled ... more

Optimal common due-date with completion time tolerance

Computers & Operations Research, 1996

The common due-date problem involves minimizing the absolute deviation around a common due-date. ... more

Optimization in Multiple-Objective Linear Programming Problems with Pre-Emptive Priorities

The Journal of the Operational Research Society, 1990

The Effect Of Plus/Minus Grading On The GPA

Journal of College Teaching & Learning (TLC), 2011

In recent years, an increasing number of colleges and universities have been turning away from tr... more In recent years, an increasing number of colleges and universities have been turning away from traditional letter grading systems that limit student grades to A, B, C, D, and F based on the presumption that grading systems with more flexibility are advantageous to both teachers and students. However, as with any rating system, before opting for a new grading system it is important to recognize that modifications may result in some, possibly unintended, consequences as well. In this paper, we discuss theoretical effects that including plus and/or minus grades may have on Grade Point Average (GPA) and analyze data from a School that implemented such a change.

Modeling Deterministic Opportunistic Replacement as an Integer Programming Problem

American Journal of Mathematical and Management Sciences, 1990

ABSTRACT The field of opportunistic replacement deals with the benefits of performing maintenance... more ABSTRACT The field of opportunistic replacement deals with the benefits of performing maintenance on equipment prior to failure in order to avoid prohibitively high costs associated with failure. Problems of a deterministic nature, i.e., where the exact times of both mandatory replacement and maintenance opportunities are known at the outset, with infinite time horizons have been solved for the two component case using a specialized algorithm. This paper presents a more general integer programming formulation of the problem that will work for any specified time frame. The results are of theoretical as well as practical significance in solving problems such as maintenance scheduling in fusion power plants.

A Historical Note On The Proof Of The Area Of A Circle

Journal of College Teaching & Learning (TLC), Mar 15, 2011

An optimal replacement policy for life limited parts

A replacement schedule for multicomponent life-limited parts

Naval Research Logistics Quarterly, 1982

ABSTRACT In previous papers [1], [2] the authors developed a maintenance policy for a single life... more ABSTRACT In previous papers [1], [2] the authors developed a maintenance policy for a single life-limited part. Using an opportunistic replacement approach a scheme was devised which utilized early replacement of equipment to offset more costly future expenditures. This paper will extend the results to the multicomponent case. Examples are given illustrating the benefits of this new technique.

Opportunistic replacement in a deterministic environment

Computers & Operations Research, 1985

ABSTRACT An opportunistic replacement problem dealing with life-limited parts is analyzed. Becaus... more ABSTRACT An opportunistic replacement problem dealing with life-limited parts is analyzed. Because of prohibitively high costs of unscheduled breakdowns, life-limits on system components, e.g. nuclear fusion power systems, may be set so low as to insure performance during allotted life span. If two components with different life-limits are present, each individual scheduled replacement point offers potential opportunity for monetary savings. It is proved that in this deterministic situation only a limited number of the possible replacement points need be considered. An algorithm to generate these points is given and the computational requirements are discussed.

A Historical Note On The Proof Of The Area Of A Circle

by Sheldon Epstein and Yonah Wilamowsky

Journal of College Teaching & Learning (TLC), 2011

Abstract Proofs that the area of a circle is πr 2 can be found in mathematical literature dating ... more

The Effect Of Plus/Minus Grading On The GPA

by Sheldon Epstein and Yonah Wilamowsky

Journal of College Teaching & Learning (TLC), 2011

Page 1. Journal of College Teaching &amp; Learning September 2008 Volume 5, Number 9 1 The ... more

Case Study: Structured Settlements

by Sheldon Epstein and Yonah Wilamowsky

Journal of College Teaching & Learning (TLC), 2011

Abstract Students are presented with a report that offers a present value analysis of a Structure... more