Use of Goal Programming Approach for Allocation of Teachers for Paper Correction

Neeta Jain¹*, Dr. Sanjay Jain²

¹Research Scholar, Ph.D Student, Pacific University, Udaipur, 313001

²Department of Mathematical Science, S.P.C Government College, Ajmer, 305001

*corresponding Author E-mail: v.neetajain@gmil.com

ABSTRACT:

Decision making about resource allocation is a problem that we face every day, resource allocation is a multi-criteria decision making problem and goal programming is a common technique for solving resource allocation problems with multiple objectives. One of the most difficult decision in conducting examination is preparation of timetable and completing paper correction timely so that the results can be declared within the stipulated time. The determination of the optimum allocation of teachers becomes difficult, because of the multiplicity of factors, complex relationship among the factors like various programmes, course, availability of teachers, Availability of computers for online correction, Availability of answer sheets, Technical system and support etc. is often beyond the ability to identify the optimum allocation alternative. Thus it has become important to understand the capabilities and applications of the various quantitative or management science techniques so that one can thoroughly evaluate its alternative allocation opportunities. Preparing a good time schedule of Exam for a university is a most difficult task. The term “good time schedule” is questionable, because there is always someone, who is not satisfied with the given timetable. Nevertheless we can find out some objective criteria that indicate the “good time schedule”. The teacher simultaneously cannot assess different course at the same time. Numbers of students in different course are not equal .Same teacher teaching in different course. The aim of this study is to propose a goal programming model to solve the allocation of teachers satisfying all the constraint.

KEY WORDS :Goal programming ,Time table ,teachers allocation for paper correction

LITERATURE REVIEW:

Goal programming, with its ability to handle multiple, conflicting criteria, has been used to model sustainability decisions in many contexts, e.g., education, budget, allocation of resources, agricultural planning.

Linear programming is the technique which formulate a linear objective function, then the linear objective function are optimized subjected to the limited resource called constraints. The Goal programming approach was given by Charenes(1965).He gave an algorithm in which objective function was prioritized rather than weighted.

In this method all resources are applied to first goal till it is satisfied, the process is repeated with second goal and so on.

Goal programming (GP) is an extension of Linear Programming (LP) which is a mathematical tool to handle multiple, normally conflicting objective. According to Ignizio (1978), Goal Programming is a tool that has been proposed as a model and approach for analysis of problems involving multiple conflicting objectives.

Institute of higher education requires Modelling for planning of human resources, financial and academic administration [01]-[03]. Course scheduling has been a subject of research for several decades. In the 1970s, Tillet [04] and Bristle [05] formulated the university course timetabling problem as a transportation model. Harwood and Lawless [06] created a linear model that integrates goal programming with 2 mixed-integer programming to solve the same type of problem.

INTRODUCTION:

In today’s complex organizational environment the decision maker is regarded as one who attempts to achieve a set of objective to extent of fullest under condition of different interest and conflicts and with a limited resources. The main advantage of Goal programming is it deals with real world problem in such a way that actually makes decision to a problem. It shows a substantial improvement in the modelling and analysis of the real life situation. Conducting examination and declaring the result is a real world scheduling problem on which every institute must put emphasis. Depending on the size of problem, institutional goals, this can require a large amount of human efforts and it is also a time consuming. Time table problem draw attention of research and many researchers has proposed a great variety of model .Teachers allocation for paper correction is equivalently important as time table for examination to be completed.

THE BASIC STEPS IN FORMULATING GOAL PROGRAMMING MODEL:

The basic steps in formulating a goal programming model are as follows:

(i) Determine the decision variables;

(ii) Specify goals including goal types (oneway or two-way goal) and their targets;

(iii) Determine the pre-emptive priorities;

(iv) Determine the relative weights;

(v) State the minimization objective functions of the deviation;

(vi) State other given requirements, example, technological constraints, nonnegativity (linear goal programming);

(vii) Finally, make sure that the model can exactly specify the decision maker’s preferences

THE OBJECTIVES OF THE STUDY:

To apply goal programming model to a make the timetable for teachers allocation for paper correction in such way that all papers are corrected on time and result are declared on time without any delay.

THE PROPOSED MODEL:

There certain assumption made for the model

1) There is only one exam for each course

2) More than one exam is possible on per day i.e there can be exam for two different course

3) One Examiner can assess more than one course but not on same day

4) Number of paper to be assessed per day cannot exceed certain limit may be 40paper per day.

5) Paper should be available for correction

This model requires scheduling of teachers for each course in prefixed period of time satisfying certain constraints.

Variables, Constants and Notations

Total no of student appeared for exam is N

Total number of course be R

I={1,2…..n} set of teachers

DI = {…}: These are the subsets of teachers. Each one refers to the group of teachers who are

Examiner to a course. For example, = {1,2,3,4} refers to the set of teachers who

areexaminer for course a

K=(1,2,3,…w) Days

S={represent the number of student in course For Example refers to number of student in course j

Total number of teachers can be assigned to a course

=This is sub set of Number of paper available for correction .For example total no of papers of course 1 .

mi Total number of course-section combinations that the teacher i can be assigned to.

tl(i) : load of paper correction of teacheri

Positive and negative deviations from teaching loads, i = 1,2,…,n..

Our model considers a number of hard constraints, which generally obey the common rules or follow

Constraints:

1 The first group of constraints ensures that teachers are assigned for all course- are assigned. This is a hard constraint.

2.The second group of constraint represent the paper correction load for teacher.One constraint should be written for each teacher.

3. The third group of constraints ensures that only one course- is assigned to a teacher for a certain time period. This is the second hard constraint.

4. The fourth group of constraint ensures that at least number of paper are corrected on given day.As No examiner can assess more than 40 paper

for all course j on day k

5.The number of required examiner required for correction depends on the number of student for the course. It is required that one examiner can correct 40 students paper otherwise we need more than one examiners. where is the number of teachers required for course j.Thisconstaints ensures required number of teachers are assigned for all course

6. It might be possible that certain teacher is not available for particular day

7 It is also possible is that teachers is correcting some course j hence not available for other course.

Objective Function:

The objective function has four priorities; two for teaching loads and two for teacher preferences. The administration is authorized to determine and assign the priorities.

CONCLUSION:

We offered a goal programming model to solve the allocation of teachers for paper correction.We used a non-preemptive approach. For future research, a user interface can be written to make the program more userfriendly. The efforts to find new solution processes that will lead toreach to better results in relatively shorter times should be continued. Since thesize of the problem is too big, more emphasis should be put on the use of heuristic approaches, and these methods should be investigated rather than mathematical ones.

CONFLICT OF INTEREST:

The authors declare no conflict of interest.

REFERENCES:

1. R.C. Dolan, and R.M. Schmidt, “Modelling institutional production of higher education,” Economics of Education Review, vol.13, no.3, pp. 197-213, 1994.

2. C. Joiner, “Academic planning through the goal programming model,” Interfaces, vol.10, no.4, pp. 86-92, 1980.

3. S. Lee, and E. Clayton, “A goal programming model for academic resource allocation,” Management Science, vol.18, no.8, pp.395-408, 1972.

4. Tillet, P., 1975, “An operations research approach to the assignment of teachers to courses”,SocioEconomic Planning Sciences, vol. 9, pp. 101-104.

5. Bristle, J., 1976, “A linear programming solution to the faculty assignment problem”, SocioEconomic Planning Sciences, vol. 10, pp. 227-230.

6. Harwood, G., and Lawless, R., 1975, “Optimizing organizational goals in assigning faculty teaching schedules”, Decision Science, vol. 6, pp. 513-524.

7. J. Bristle, “A linear programming solution to the faculty assignment problem,” Socio-Economic Planning Science, vol.10, pp. 227-230, 1976.

Received on 11.08.2017 Modified on 21.08.2017

Research J. Science and Tech. 2017; 9(3): 472-475.

DOI: 10.5958/2349-2988.2017.00082.1