Integer Programming Approach to Staff Scheduling of Resource Persons to a Polytechnic

Integer Programming Approach to Staff Scheduling of Resource Persons to a Polytechnic: A Case Study of NBTA’s Accreditation Team

ABSTRACT

In this work, we applied an Integer Programming approach to scheduling of resource persons on National Board for Technical Education (NBTE) accreditation team to a Polytechnic. The level of compliance of the institution to national minimum benchmark for academic standards with respect to staff mix was deduced.

The use of Integer Programming approach and Lingo software in solving the model developed, resulted in considerable drop in accreditation cost from four million, seven hundred and forty thousand Naira only (N4,740,000.00) to two million, eight hundred and seventy three thousand, eight hundred and twenty seven Naira only (2,873,827).

The adoption of Integer Linear programming has eliminated the bias and bottlenecks associated with the current spreadsheet approach used by the Board. In view of her inherent advantage, we recommend the use of Integer Linear programming approach using Lingo Software for future scheduling of resource persons on accreditation visits by the NBTE.

TABLE OF CONTENTS

Certification ……………………………………………………………………………………………………. ii
Dedication ……………………………………………………………………………………………………… ii
Acknowledgement ………………………………………………………………………………………….. iv
Abstract …………………………………………………………………………………………………………. v
Table of Content …………………………………………………………………………………………….. vi
Chapter one …………………………………………………………… Error! Bookmark not defined.
1.0 Introduction …………………………………………………………………………………………. vii
1.1 Statement of the Problem ………………………………………………………………………. ix
1.2 Objective of the Study ……………………………………………………………………………. ix
1.3 Scope of the Study …………………………………………………………………………………. ix
Chapter Two …………………………………………………………………………………………………… x
Literature Review ……………………………………………………………………………………………. x
NBTE accreditation framework and accreditation team …………………………………………. x
The Purposes of Programme Accreditation………………………………………………………….. x
Key Attributes of NBTE’s Accreditation team ……………………………………………………… xii
Definition of terms ………………………………………………………………………………………… xx
Chapter Three……………………………………………………………………………………………… xxiv
3.0 Methodology: …………………………………………………………………………………….. xxiv
3.1 Model formulation and General solution ………………………………………………….xxv
3.2 An Integer programming model approach …………………………………………….. xxviii
Chapter Four ………………………………………………………………………………………. xxxv
Data Analysis ……………………………………………………………………………………………… xxxv
4.1 Analysis of Integer Programme results……………………………………………………… 25
5.1 Summary and conclusion ……………………………………………………………………….. 33
5.2 Recommendation …………………………………………………………………………………. 33
5.3 Future Work ………………………………………………………………………………………… 34
Appendix A: Programme Algorithm ………………………………………………………………….. 35
References ……………………………………………………………………………………………………. 38

CHAPTER ONE

Introduction:

Workforce, labour, personnel scheduling or rostering is the process of designing work timetables for employees to satisfy the demand requirements for its services as observed by (Hillier and Lieberman, 2005). Different types of mathematical modelling approach have been developed in order to help companies to solve the problemof staff scheduling.

The development of these mathematical models and algorithms involves the following steps according to Gabor(2004)
· a demand modelling study that collects and uses historical data to forecast demand for services and converts these to the staffing levels needed to satisfy service standards,

· consideration of techniques required for a personnel scheduling tool that satisfies the constraints arising from workplace regulations while best meeting a range of objectives including coverage of staff demand, minimum cost and maximum employee satisfaction,
· Specification of a reporting tool that displays solutions and provides performance reports.

Effective staff scheduling takes into consideration the different peculiarities of various staff needs for optimum performance. Scheduling has been applied to different facets of life especially in the medical profession, police force, airline, transportation, telephone companies, banks and hospitality industries, all these companies have an uphill task of maintaining the delicate task of staff scheduling.

Following the advances and progress made in linear programming, we model scheduling of resource persons that serve in National Board for Technical Education’s (NBTE) ad-hoc program accreditation team to Nigerian Polytechnics. The NBTE currently uses a computer based spreadsheet for scheduling these resource persons for accreditation visit; this approach has her draw backs and bottlenecks.

Management has expressed concern over the frequent use of some resource persons to the detriment of others; this worry is shared by other stakeholders who felt that their not being featured in any accreditation exercise has a hidden undertone.

In view of this, we assert that adopting a mathematical based model will eliminate the question of bias and favoritism. This model will provide an opportunity for every qualified resource person on the Board’s database to participate in accreditation visit to Polytechnics that are due
for the exercise.

The National Board for Technical Education, Kaduna is a regulatory agency charged with enforcing standards in all technical and technological based institutions outside the university system. In performing these tasks, she carries out verification and accreditation visits to institutions under her purview to ensure that standards are upheld and maintained.

When an institution prepares to run a program either at the National Diploma (ND) or Higher National Diploma (HND) level, she applies for license to operate from the Board. The Board constitutes a verification team to ascertain the resources on ground for the desired program at the institution. Based on the team’s satisfaction that the institution meets the minimal requirement to run such program(s), NBTE constitutes a team for an initial accreditation to the institution.

Accreditation visits are undertaken to these institutions either at the inception of the institution or when they are mounting additional programs in existing institution. If successful, the NBTE conveys an interim accreditation status on the institution which allows the institution to admit students for a period of two years only, and thereafter she applies for final accreditation that is renewable after every five years.

However, within this period, application for new programs can always be entertained, on the request of the institution. Accreditation visits to institutions are at the National Diploma (ND) or the Higher National Diploma (HND) levels or both for the respective programs.

For every accreditation visits, a team is constituted comprising an NBTE staff (who is a subject officer for the designated programme), member of a professional body/industry and resource persons drawn from the academia who are conversant with programs that are due for verification or accreditation visits as resource persons. The Board maintains an online database of resources persons in diverse discipline that she can draw from for purposes of accreditation visits.

1.1 Statement of the Problem

· Determine effective means of selecting NBTE’s accreditation Team

· Determine the quality of assessors work

· Monitor the team’s performance at these institutions

· Determine minimum cost of accreditation exercise

1.2 Objective of the Study

· Develop a linear programming model for NBTE’s accreditation team that minimizes the cost of accreditation.

· Develop a model for assessing the staff mix in the institution

1.3 Scope of the Study

This study covers accreditation team scheduling with particular reference to National Board for Technical Education, Kaduna ad-hoc program accreditation team. Data of year 2014 from Delta State Polytechnic, Otefe- Oghara, and the Board’s resource person database were used as case study.

CHAPTER TWO

LITERATURE REVIEW

2.1 NBTE accreditation framework and accreditation team

This Framework addresses the accreditation of Polytechnic programs in Nigeria. Accreditation is the primary assurance of quality in the preparation of students and programs in the respective institution across the country. The results of accreditation exercise gives credence to quality assurance to all stake holders in the educational
sector and the general public.

2.2 The Purposes of Programme Accreditation

Program accreditation is the process of verifying the quality of each program content, her staff, student and infrastructural requirement for the award of National Diploma (ND) and Higher National Diploma (HND). The essence is to ascertain that staff who teach, possess the requisite knowledge, skills and ability to impact knowledge at the various programs levels. It equally ensures that the institution conforms to the set minimal standard for such programs requiring accreditation.

The first primary purpose of program accreditation is to ensure accountability to the public, the students, the educational sector and the general public. The overall interest is to establish that our various institutions are dynamic, conform to emerging trend in their respective fields and are sensitive to her environmental needs by introducing programs with local content component into her curricula.

A second purpose of accreditation is to ensure that programs are of high quality, effective and provide experiences that are consistent with tertiary institution. The NBTE has the statutory responsibility for adopting accreditation standards and benchmarks which describe levels of quality that it deems necessary for quality assurance.

The accreditation team attempts to assess the assessor by ensuring that laid down standards are followed in appointment, promotion and that evidence of requisite enhancement training are undertaken for the purpose of growth and productivity.

The Accreditation system is oriented to issues of quality. During a review, reviewers obtain evidence that relates to the educational quality of programs and policies governing the programs. Through experience, expertise and training, the accreditation team are skilled at discerning the important from the unimportant in program preparation.

The findings and recommendations of accreditation team focus on important matters of quality in the respective programs. The findings of the team are evidence based and afford the respective institution opportunities to rectify some of the observed anomalies within a record time.

A third purpose of the accreditation team is to ensure adherence to standards. The standards are designed to ensure that each program is at tandem with current curriculum in Nigeria. Through the accreditation process, sponsors of respective institution’s programs show evidence that their programs conform to requisite standards.

The fourth purpose of the accreditation program is to support program development and enhancements. The NBTE accreditation team attempts to enforce standards by harmonizing the various reviews and decisions of the various coordinators that contributed to the preparation of programs.

Each institution strives to meet NBTE’s minimal accreditation requirements. Where theirs is noticeable shortfalls, appropriate suggestion are outlined, the essence is to ensure that respective institution do the right thing always and not resort to cutting corners. When institutions fall short of accreditation requirements, they are given opportunities to remedy such shortcomings and invite the Board for verification.

2.3 Key Attributes of NBTE’s Accreditation team

These attributes pertain to the development of program standards, the initial accreditation, full accreditation and subsequent reviews.

First Attribute: The Character of Accreditation team.

Professional teachers drawn from respective tertiary institutions, professional bodies and the industry should hold themselves and their peers accountable for the enforcement of quality in any particular program in the Polytechnic sector.

Practicing professionals are involved in the entire accreditation process. They are involved initially in the critique of curricula for the respective programs before adoption, at accreditation; they conduct reviews, and make accreditation decisions.

Participant in accreditation team have experience, expertise and training that are appropriate for their specific roles in the team. During accreditation, decisions emerge from consultative procedures that reflect the consensus of the professional participants present for the exercise. The NBTE’s subject officer serves as a guide to the team and takes custody of all emerging reports from the program.

Second Attribute: Knowledgeable Participants.

The accreditation team relies on the quality of the decision making at each step in the process by invited professional. Quality assurances are provided through the participation of individuals who possess knowledge, skills and

broad expertise and who participate in the system in various roles, including policy development, policy implementation, program assessment, technical support, and professional preparation. Periodically, the NBTE organizes refresher workshops for resource persons to keep them abreast of the Board’s requirement and policy adjustment in the educational sector.

Third Attribute: Breadth and Flexibility.

For institution sponsors to be effective in a dynamic state, they must be creative and responsive to the changing needs of prospective programs, the communities and students they serve. The NBTE seeks to enforce minimum standards in all her programs and encourages institution to develop local content that will meet the peculiarity of their environment and further enrich her curricula. The Board encourages innovation, expertise and ingenuity that are beneficial to students and the community.

Fourth Attribute: Intensity in Accreditation.

The Accreditation team focuses on educational quality and effectiveness. While allowing and encouraging divergence, the process should also be exact in assembling key information about critical aspects of educational quality and effectiveness. The scope of accreditation team is comprehensive, the information generated by the review processes should be sufficient to yield reliable judgments by policy makers in the educational sector.

Accreditation team’s decisions are based on information that is sufficient in breadth and depth for the results to be credible and dependable. Accreditation team understands the components of the program under review and the types of standards-based evidence that substantiate its overall quality and effectiveness.

Fifth Attribute: Efficiency and Cost-Effectiveness.

The accreditation team seeks to fulfill its purposes efficiently and cost-effectively. She reviews procedures, decision processes and reporting relationships are streamlined. There are costs associated with establishing standards, training reviewers, assembling information, preparing reports, conducting meetings and checking the accuracy of data and the fairness of decisions.

Minimizing these costs is an essential attribute of accreditation exercise, but efficiency must not undermine the capacity of accreditors to fulfill their responsibilities to the public and the Polytechnic sector. Accreditation costs are borne by the institution and the regulatory body (NBTE).

The stipends paid to accreditation team members are reviewed periodically by Board in line the prevailing
Federal Ministry of Education guidelines.

Linear programming is a mathematical modeling technique designed for dealing typically with problems of allocating limited resources among competing activities in the best possible way in agriculture, engineering, social sciences, education, health systems, military, industry, assignment, economics, government and transportation.

It is one of the techniques in the field of Operations Research developed for solving problems that have a particular mathematical structure. In many of such problems in Operations Research, the aim is either to maximize or minimize some objective

functions subject to certain constraints imposed on the resources available as observed in (Sharma, 2009). For this study a special form of Linear Programming called integer programming is applied, here all the decision variables are integers.

We further consider a special form of Integer Programming formulation called the binary integer programming, where the values of the decision variables are zeros and one.

In this study we are looking at applying Linear Integer Programming technique to schedule staff to carry out specific assignment. We shall now review some related work in the literature that will help us develop the model we plan to adopt in this study.

Gloyer (1986) studied a general employee scheduling problem using the technique of management science and artificial intelligence. He generated solutions of exceedingly high quality in very modest time. It is believed that similar gains may be possible for other combinatorial zero-one applications.

Ipet al (2010) studied staff scheduling for airport service planning using integer programming. They developed an optimization approach to improve the manual maintenance scheduling process in airport planning. They showed that planning and scheduling can bring about a more efficient and effective process.

Sabet (2005) worked on web based staff scheduling, which demonstrated that online web based scheduling involves assigning workers to task on a one-to-one basis; the objective is to ensure that all jobs are completed at minimal cost within stipulated time.

Staff scheduling tools does a better job of balancing an organisation’s needs with staff needs, gives staff greater access to scheduling, self-scheduling and staffing, and offer a significant return on investment, while providing high level reporting and centralized staffing for effective control.

Burke et al (2010) studied a hybrid model of Integer Programming (IP) and Variable Neighbourhood Search (VNS) for highly-constrained nurse rostering problems in a modern hospital environment. The basic variable neighborhood search acted as a post processing procedure to further improve the Integer Programme’s result solutions obtained.

Very promising results were reported compared with a commercial genetic algorithm and the compared result demonstrates that our hybrid approach combines the advantages of both the IP and the VNS to beat other approaches in solving this type of problems.

Fernandez-Viagas and Framinan (2014) addressed the issue of simultaneously scheduling tasks in a project and assigning staff to these tasks, taking into account that a task can be performed only by employees with the requisite skills, and that the length of each task depends on the number of employees assigned.

They applied integer programming model with extensions for the problem in question to cope with different situations. Due to the complexity of the integrated model, a simple GRASP algorithm is implemented in order to obtain good, approximate solutions in short computation time.

Trilling et al (2006) studied Nurse scheduling using integer linear programming and constraint programming, while trying to reduce cost and to optimize the use of resources, hospitals were prompted to regroup facilities and human resources, especially in the surgical suite.

The team focuses on Anesthesiology Nurse Scheduling Problem (ANSP) which constitutes one of the most shared resources. The objective is to maximize the fairness of the schedule.