Integer programming approach to staff scheduling of resource persons to a polytechnic: a case study of nbte’s accreditation team

Project Abstract

<p> </p><p>In this work,we applied an Integer Programmingapproach to schedulingof resource<br>persons on National Board for Technical Education (NBTE) accreditation team to a<br>Polytechnic. The level of compliance of the institution to national minimum benchmark<br>for academic standards with respect tostaff mix was deduced.The use of Integer<br>Programming approach and Lingo software in solving the model developed, resulted in<br>considerable drop in accreditation cost from four million, seven hundred and forty<br>thousand naira only (N4,740,000.00) to two million, eight hundred and seventy three<br>thousand, eighthundred and twenty seven naira only (2,873,827). The adoption of<br>Integer Linear programming has eliminated the bias and bottlenecks associated with the<br>current spreadsheet approach used by the Board. In view of her inherent advantage, we<br>recommend the use of Integer Linear programming approach using Lingo Software for<br>future scheduling of resource persons on accreditation visits by the NBTE.</p><p><strong>&nbsp;</strong></p> <br><p></p>

Project Overview

<p> </p><p>Introduction:<br>Workforce, labour, personnel scheduling or rostering is the process of designing work<br>timetables for employees to satisfy the demand requirements for its services as observed<br>by (Hillier and Lieberman, 2005). Different types of mathematical modelling approach<br>havebeen developed in order to help companies to solve the problemof staff scheduling.<br>The development of these mathematicalmodels and algorithms involves the following<br>steps according to Gabor(2004)<br>· a demand modelling study that collects and uses historical data to forecast<br>demand for services and converts these to the staffing levels needed to satisfy<br>service standards,<br>· consideration of techniques required for a personnel scheduling tool that satisfies<br>the constraints arising from workplace regulations while best meeting a range of<br>objectives including coverage of staff demand, minimum cost and maximum<br>employee satisfaction,<br>· Specificationof a reporting tool that displays solutions and provides<br>performancereports.<br>Effective staff scheduling takes into consideration the different peculiarities of various<br>staff needs for optimum performance. Scheduling has been applied to different facets of<br>life especially in the medical profession,police force, airline, transportation, telephone<br>companies,banksand hospitality industries, all these companies have an uphill task of<br>maintaining the delicate task of staff scheduling.<br>Following the advances and progress made in linear programming, we model<br>scheduling of resource persons that serve in National Board for Technical Education’s<br>(NBTE) ad-hoc programme accreditation team to Nigerian Polytechnics. The NBTE<br>currently uses a computer based spreadsheet for scheduling these resource persons for<br>accreditation visit; this approach has her draw backs and bottlenecks.Management has<br>expressed concern over the frequent use of some resource persons to the detriment of<br>others; this worry is shared by other stakeholders who felt that their not being featuredin<br>any accreditation exercise has a hidden undertone. In view of this, we assert that<br>adopting a mathematical based model will eliminate the question of bias and<br>favouritism. This model will provide an opportunity for every qualified resource person<br>on the Board’s database to participate in accreditation visit to Polytechnics that are due<br>for the exercise.<br>The National Board for Technical Education, Kaduna is a regulatory agency charged<br>with enforcing standards in all technical and technological based institutions outside the<br>university system. In performing these tasks, she carries out verification and<br>accreditation visits to institutions under her purview to ensure that standards are upheld<br>and maintained. When an institution prepares to run a programme either at the National<br>Diploma (ND) or Higher National Diploma (HND) level, she applies for license to<br>operate from the Board. The Board constitutes a verification team to ascertain the<br>resources on ground for the desired programme at the institution. Based on the team’s<br>satisfaction that the institution meets the minimal requirement to run such<br>programme(s), NBTE constitutes a team for an initial accreditation to the institution.<br>Accreditation visits are undertaken to these institutions either at the inception of the<br>institution or when they are mounting additional programmes in existing institution. If<br>successful, the NBTE conveys an interim accreditation status on the institution which<br>allows the institution to admit students for a period of two years only, and thereafter she<br>applies for final accreditation that is renewable after every five years. However, within<br>this period, application for new programmes can always be entertained, on the request<br>of the institution. Accreditation visits to institutions are at the National Diploma (ND)<br>or the Higher National Diploma (HND) levels or both for the respective programmes.<br>For every accreditation visits, a team is constituted comprising an NBTE staff (who is a<br>subject officer for the designated programme), member of a professional body/industry<br>and resource persons drawn from the academia who are conversant with programmes<br>that are due for verification or accreditation visits as resource persons. The Board<br>maintains an online database of resources persons in diverse discipline that she can<br>draw from for purposes of accreditation visits.<br>1.1 Statement of the Problem<br>· Determine effective means of selecting NBTE’s accreditation Team<br>· Determine the quality of assessors work<br>· Monitor the team’s performance at these institutions<br>· Determine minimum cost of accreditation exercise<br>1.2 Objective of the Study<br>· Develop a linear programming model for NBTE’s accreditation team that<br>minimizes the cost of accreditation.<br>· Develop a model for assessing the staff mix in the institution<br>1.3 Scope of the Study<br>This study covers accreditation team scheduling with particular reference to<br>National Board for Technical Education, Kaduna ad-hoc programme<br>accreditation team. Data of year 2014 from Delta State Polytechnic, Otefe-<br>Oghara, and the Board’s resource person database were used as case study.<br>CHAPTER TWO<br>LITERATURE REVIEW<br>2.1 NBTE accreditation framework and accreditation team<br>This Framework addresses the accreditation of Polytechnic programmes in Nigeria.<br>Accreditation is the primary assurance of quality in the preparation of students and<br>programmes in the respective institution across the country. The results of accreditation<br>exercise gives credence to quality assurance to all stake holders in the educational<br>sector and the general public.<br>2.2 The Purposes of Programme Accreditation<br>Programme accreditation is the process of verifying the quality of each programme<br>content, her staff, student and infrastructural requirement for the award of National<br>Diploma (ND) and Higher National Diploma (HND). The essence is to ascertain that<br>staff who teach, possess the requisite knowledge, skills and ability to impact knowledge<br>at the various programmes levels. It equally ensures that the institution conforms to the<br>set minimal standard for such programmes requiring accreditation.<br>The first primary purpose of programme accreditation is to ensure accountability to the<br>public, the students, the educational sector and the general public. The overall interest is<br>to establish that our various institutions are dynamic, conform to emerging trend in their<br>respective fields and are sensitive to her environmental needs by introducing<br>programmes with local content component into her curricula.<br>A second purpose of accreditation is to ensure that programmes are of high quality,<br>effective and provide experiences that are consistent with tertiary institution. The NBTE<br>has the statutory responsibility for adopting accreditation standards and benchmarks<br>which describe levels of quality that it deems necessary for quality assurance. The<br>accreditation team attempts to assess the assessor by ensuring that laid down standards<br>are followed in appointment, promotion and that evidence of requisite enhancement<br>training are undertaken for the purpose of growth and productivity.<br>The Accreditation system is oriented to issues of quality. During a review, reviewers<br>obtain evidence that relates to the educational quality of programmes and policies<br>governing the programmes. Through experience, expertise and training, the<br>accreditation team are skilled at discerning the important from the unimportant in<br>programme preparation. The findings and recommendations of accreditation team focus<br>on important matters of quality in the respective programmes. The findings of the team<br>are evidence based and afford the respective institution opportunities to rectify some of<br>the observed anomalies within a record time.<br>A third purpose of the accreditation team is to ensure adherence to standards. The<br>standards are designed to ensure that each programme is at tandem with current<br>curriculum in Nigeria. Through the accreditation process, sponsors of respective<br>institution’s programmes show evidence that their programmes conform to requisite<br>standards.<br>The fourth purpose of the accreditation programme is to support programme<br>development and enhancements. The NBTE accreditation team attempts to enforce<br>standards by harmonizing the various reviews and decisions of the various coordinators<br>that contributed to the preparation of programmes. Each institution strives to meet<br>NBTE’s minimal accreditation requirements. Where theirs is noticeable shortfalls,<br>appropriate suggestion are outlined, the essence is to ensure that respective institution<br>do the right thing always and not resort to cutting corners. When institutions fall short<br>of accreditation requirements, they are given opportunities to remedy such<br>shortcomings and invite the Board for verification.<br>2.3 Key Attributes of NBTE’s Accreditation team<br>These attributes pertain to the development of programme standards, the initial<br>accreditation, full accreditation and subsequent reviews.<br>First Attribute: The Character of Accreditation team.<br>Professional teachers drawn from respective tertiary institutions, professional bodies<br>and the industry should hold themselves and their peers accountable for the<br>enforcement of quality in any particular programme in the Polytechnic sector.<br>Practising professionals are involved in the entire accreditation process. They are<br>involved initially in the critique of curricula for the respective programmes before<br>adoption, at accreditation; they conduct reviews, and make accreditation decisions.<br>Participant in accreditation team have experience, expertise and training that are<br>appropriate for their specific roles in the team. During accreditation, decisions emerge<br>from consultative procedures that reflect the consensus of the professional participants<br>present for the exercise. The NBTE’s subject officer serves as a guide to the team and<br>takes custody of all emerging reports from the programme.<br>Second Attribute: Knowledgeable Participants.<br>The accreditation team relies on the quality of the decision making at each step in the<br>process by invited professional. Quality assurances are provided through the<br>participation of individuals who possess knowledge, skills and broad expertise and who<br>participate in the system in various roles, including policy development, policy<br>implementation, programme assessment, technical support, and professional<br>preparation. Periodically, the NBTE organises refresher workshops for resource persons<br>to keep them abreast of the Board’s requirement and policy adjustment in the<br>educational sector.<br>Third Attribute: Breadth and Flexibility.<br>For institution sponsors to be effective in a dynamic state, they must be creative and<br>responsive to the changing needs of prospective programmes, the communities and<br>students they serve. The NBTE seeks to enforce minimum standards in all her<br>programmes and encourages institution to develop local content that will meet the<br>peculiarity of their environment and further enrich her curricula. The Board encourages<br>innovation, expertise and ingenuity that are beneficial to students and the community.<br>Fourth Attribute: Intensity in Accreditation.<br>The Accreditation team focuses on educational quality and effectiveness. While<br>allowing and encouraging divergence, the process should also be exact in assembling<br>key information about critical aspects of educational quality and effectiveness. The<br>scope of accreditation team is comprehensive, the information generated by the review<br>processes should be sufficient to yield reliable judgments by policy makers in the<br>educational sector.<br>Accreditation team’s decisions are based on information that is sufficient in breadth and<br>depth for the results to be credible and dependable. Accreditation team understands the<br>components of the programme under review and the types of standards-based evidence<br>that substantiate its overall quality and effectiveness.<br>Fifth Attribute: Efficiency and Cost-Effectiveness.<br>The accreditation team seeks to fulfil its purposes efficiently and cost-effectively. She<br>reviews procedures, decision processes and reporting relationships are streamlined.<br>There are costs associated with establishing standards, training reviewers, assembling<br>information, preparing reports, conducting meetings and checking the accuracy of data<br>and the fairness of decisions. Minimizing these costs is an essential attribute of<br>accreditation exercise, but efficiency must not undermine the capacity of accreditors to<br>fulfil their responsibilities to the public and the Polytechnic sector. Accreditation costs<br>are borne by the institution and the regulatory body (NBTE). The stipends paid to<br>accreditation team members are reviewed periodically by Board in line the prevailing<br>Federal Ministry of Education guidelines.<br>Linear programming is a mathematical modelling technique designed for dealing<br>typically with problems of allocating limited resources among competing activities in<br>the best possible way in agriculture, engineering, social sciences, education, health<br>systems, military, industry, assignment, economics, government and transportation. It is<br>one of the techniques in the field of Operations Research developed for solving<br>problems that have a particular mathematical structure. In many of such problems in<br>Operations Research, the aim is either to maximize or minimize some objective<br>functions subject to certain constraints imposed on the resources available as observed<br>in (Sharma, 2009). For this study a special form of Linear Programming called integer<br>programming is applied, here all the decision variables are integers. We further consider<br>a special form of Integer Programming formulation called the binary integer<br>programming, where the values of the decision variables are zeros and one.<br>In this study we are looking at applying Linear Integer Proramming technique to<br>schedule staff to carry out specific assignment. We shall now review some related work<br>in the literature that will help us develop the model we plan to adopt in this study.<br>Gloyer (1986) studied a general employee scheduling problem using the technique of<br>management science and artificial intelligence. He generated solutions of exceedingly<br>high quality in very modest time. It is believed that similar gains may be possible for<br>other combinatorial zero-one applications.<br>Ipet al (2010) studied staff scheduling for airport service planning using integer<br>programming. Theydeveloped an optimization approach to improvethe manual<br>maintenance scheduling process in airport planning. They showed that planning and<br>scheduling can bring about a more efficient and effective process.<br>Sabet (2005) worked on web based staff scheduling, which demonstrated that online<br>web based scheduling involves assigning workers to task on a one-to-one basis; the<br>objective is to ensure that all jobs are completed at minimal cost within stipulated time.<br>Staff scheduling tools does a better job of balancing an organisation’s needs with staff<br>needs, gives staff greater access to scheduling, self-scheduling and staffing, and offer a<br>significant return on investment, while providing high level reporting and centralized<br>staffing for effective control.<br>Burke et al (2010) studied a hybrid model of Integer Programming (IP) and Variable<br>Neighbourhood Search (VNS) for highly-constrained nurse rostering problems in a<br>modern hospital environment. The basic variable neighbourhood search acted as a post<br>processing procedure to further improve the Integer Programme’s result solutions<br>obtained.Very promising results were reported compared with a commercial genetic<br>algorithm and the compared result demonstrates that our hybrid approach combines the<br>advantages of both the IP and the VNS to beat other approaches in solving this type of<br>problems.<br>Fernandez-Viagas and Framinan (2014) addressed the issue of simultaneously<br>scheduling tasks in a project and assigning staff to these tasks, taking into account that a<br>task can be performed only by employees with the requisite skills, and that the length of<br>each task depends on the number of employees assigned. They applied integer<br>programming model with extensions for the problem inquestion to cope with different<br>situations. Due to the complexity of the integrated model, a simple GRASP algorithm<br>is implemented in order to obtain good, approximate solutions in short computation<br>time.<br>Trilling et al (2006) studied Nurse scheduling using integer linear programming and<br>constraint programming, while trying to reduce cost and to optimize the use of<br>resources, hospitals were prompted to regroup facilities and human resources,<br>especially in the surgical suite. The team focuses on Anaesthesiology Nurse Scheduling<br>Problem(ANSP) which constitutes one of the most shared resources. The objective is to<br>maximize the fairness of the schedule.<br>Kassa and Tizazu (2013) In their work in hospitality industry applied integer<br>programming model that determines an optimal weekly shift schedule for the Hotel’s<br>engineering department personnel whichsatisfied several constraints including weekly<br>rest requirements per employee, rest requirements between working shifts per<br>employee, required number of personnel per shift, and other constraints.<br>The model was implemented on an excel solver routine that enabled the company’s<br>personnel department management to develop a fair personnel schedule as needed and<br>to effectively utilize personnel resources while satisfying several technical, legal and<br>economic requirements. These encouraging achievements showed the gains other<br>organizations can derive by introducing operations research approach in their<br>management planning and decision making systems.<br>Mohamad and Said (2013) used integer linear programming approach to scheduletoll<br>booth collectors’problem. Theydeveloped a general daily staff scheduling problem with<br>hourly requirement patterns with illustrative example for full and parttimers using<br>LINDO software.<br>Sigurðardóttir (2011) worked on near-optimal staff scheduling using mixed integer<br>programming, theyobserved that companies with employees working on irregular<br>schedules presents a challenge. They showed results from four Icelandic companies<br>and comparing it to a local-search based algorithm. The results showed that it was<br>possible to use mathematical programming techniques for staff schedules, though a bit<br>problematic with multiple and often changing objectives and goals.<br>Herowati (2005) worked on multi shifts and break windows in employees<br>scheduling.He utilized Integer Programming model for optimal shift scheduling with<br>multiple shifts and break windows to determine the optimal number of employees<br>needed in every shift and break assignment. Obtaining the optimal number of<br>employees helped the management in developing a recruitment plan.<br>Natashia (2010) studied the scheduling of maintenance for Hunter Valley Coal Chain.<br>Based on a network flow model of the system, a mixed integer programming<br>formulation was proposed for the planning task,the resulting large scale model obtained<br>could not be solved directly by a general purpose solver and they proposed two steps. A<br>reduction in the number of binary variables by choosing a representative subset of the<br>original variables of the problem and a rolling horizon approach that shortens the<br>problem.<br>Júdice et al (2005) studied workforce planning in a lotsizing mail processing<br>environment. Their work analysed a treatment area (registered mail) where mail objects<br>are treated in a chain production process. The objective is to minimize the costs with<br>human resources needed in the process, linked with the lot sizing production plan, by<br>matching staffto work requirements. An integer programming formulation was<br>proposed that considered small, average and high daily amounts of mails that arrived at<br>a particular treatment area.<br>Nissen (2009) worked on staff scheduling with Particle Swarm Optimisation (PSO) and<br>Evolution Strategies,he used a scenario from logistics to show that modern heuristics,<br>and in particular particle swarm optimization (PSO) can significantly add to the<br>improvement of staff scheduling in practice. Rapid, sub-daily planningwas the focus of<br>the research and it offered considerable productivity reserves for companies.<br>Davood (2015) studied the implementation of the theory of constraints (TOC) rules for<br>job-shop systems to advance the state of research on constraint scheduling. A number of<br>simulation scenarios were discussed providing insights into the master production<br>schedule (MPS), the drum–buffer–rope (DBR) scheduling method, the role of setup<br>times in scheduling, the impact of free products (those that do not use constraint<br>resources) on throughput and the effect of priority rules in resource assignment to free<br>products. Moreover, optimization techniques were used to find optimal and/or<br>satisfactory solutions for input variables in the simulation experiment. Their findings<br>suggested that the current rules of thumb should be modified for real-world applications<br>and complex job-shop systems.<br>Labidi et al. (2014) deployedscheduling to Information Technology Staff (IT) at a<br>Bank.Due to the large number of conflicting constraints, a multi-objective programming<br>model was proposed to automate the schedule generation process. The suggested<br>mathematical model was implemented using Lingo software. The results indicated that<br>high quality solutions can be obtained within a few seconds compared to the manually<br>prepared schedules.<br>Thomas (2013) based his work on scheduling algorithm with optimization of employee<br>satisfaction. He developed an algorithm for weekly workforce scheduling with 4-hour<br>discrete resolution that optimizes for employee satisfaction. Parameters of employee<br>availability, employee preference, required employees per shift, and employee weekly<br>hours were considered in a binary integer programming model designed for automated<br>schedule generation.<br>Beaulieu et al.(2000) while scheduling physicians in emergency room presented a<br>mathematical programming approach. They used multi-objective integer programming<br>theory to approach the problem. When the results of the mathematical models are<br>compared with schedules it produced and those generated by a human expert, the result<br>was remarkable. The mathematical programming approach accommodates more<br>variable and results turn out faster than previously obtained.<br>Sriram and Haghani (2003) showed that aircraft maintenance scheduling is an easily<br>understood but difficult to solve problem. Given a flight schedule with aircraft assigned<br>to it, the aircraft maintenance-scheduling problem is to determine which aircraft should<br>fly which segment and when and where each aircraft should undergo different levels of<br>maintenance checks as required law. The objective was to minimize the maintenance<br>cost and any costs incurred during the re-assignment of aircraft to the flight segments.<br>They opined that heuristic procedure provides good solutions in reasonable computation<br>time to the scheduling problem.<br>Christine(2013) noted that crew scheduling problem involves the process of assigning<br>crew to operate a designated route. They proposed a methodology to determine the most<br>efficient and least costly way of crew pairing optimization, using algorithm<br>optimization with Java programming language to solve the crew scheduling problems.<br>The algorithm was able to solve the main problem that is related to crew route<br>generation and balancing.<br>Chuin and Aldy (2012) worked on security patrol scheduling with the introduction of<br>elements of strategic randomness in the model on a mass rapid transit rail network.<br>Their mathematical model randomized the start – finish time, break time and frequency<br>of visits for improved efficiency.<br>Barnhart et al.(2003)showed that airline crew scheduling when delayed or has reached a<br>limit on its flying time for a duty or pairing would be highly desirable to have an<br>alternative crew available with which it could swap one or more flights. In addition to<br>the traditional objective of minimizing pairing costs, they introduced a new objective of<br>maximizing the number of opportunities for crew swapping. Thus, their model is a bicriteria<br>optimization model. Computational results showed that there are crew schedules<br>with only a slightly higher crew cost, it can be combined with stochastic models that<br>minimize expected cost or incorporate penalties.<br>In this work, we are adopting integer programming problem for finding the minimal<br>optimal amount of money that the NBTE will expend in recruiting resource persons for<br>accreditation exercise to Delta State Polytechnic, Otefe-Oghare.<br>Definition of terms<br>DECISION<br>VARIABLES<br>Decision variables are the known variables whose<br>values when determined influences the value of<br>the objective function and are used in making<br>viable decision on the problem in<br>question.Typically we will determine their<br>optimum values with an optimization method. In a<br>general model, decision variables are given<br>algebraic designations such as ıı, ıı, ıı,. . .ıı The<br>number of decision variables is n, and ı ıı is the<br>name of the jth variable. In a specific situation, it<br>is often convenient to use other names such<br>as ı ıı or ıı or ı(ı,ı) .<br>OBJECTIVE<br>FUNCTION<br>The objective function evaluates some<br>quantitative criterion of immediate importance<br>such as cost, profit, utility, or yield. The general<br>linear objective function can be written as<br>Here is the coefficient of the jth decision<br>variable. The criterion selected can be either<br>maximized or minimized.<br>CONSTRAINTS A constraint is an inequality or equality defining<br>limitations on decisions. Constraints arise from a<br>variety of sources such as limited resources,<br>contractual obligations, or physical laws. In<br>general, an LP is said to have m linear constraints<br>that can be stated as<br>One of the three relations shown in the large<br>brackets must be chosen for each constraint. The<br>number is called a “technological coefficient,”<br>and the number is called the “right-hand side”<br>value of the ith constraint. Strict inequalities (&lt;<br>and &gt;) are not permitted. When formulating a<br>model, it is good practice to give a name to each<br>constraint that reflects its purpose.<br>NONNEGATIVITY<br>RESTRICTIONS<br>In most practical problems the variables are<br>required to be nonnegative;<br>This special kind of constraint is called a nonnegativity<br>restriction. Sometimes variables are<br>required to be non-positive or, in fact, may be<br>unrestricted (allowing any real value).<br>LINEAR<br>PROGRAMMING<br>MODEL<br>Combining the aforementioned components into a<br>single statement gives:<br>The constraints, including non-negativity defines<br>the feasible region of a problem.<br>PARAMETERS The collection of coefficients for all<br>values of the indices i and j are called the<br>parameters of the model. For the model to be<br>completely determined all parameter values must<br>be known.</p><p>&nbsp;</p> <br><p></p>