Allocation of Classroom Space Using Linear Programming (A Case Study: Premier Nurses Training College, Kumasi)

The use of linear programming to solve the problem of over-allocation and under-allocation of the scarce classroom space was considered with particular reference to the Premier Nurse’s Training College, Kumasi. Data was collected from the College on the classroom facilities and the number of students per programme. A linear programming model was formulated based on the data collected to maximize the usage of the limited classroom space. POM-QM for Windows 4 (Software for Quantitative Methods, Production and Operation Management by Howard J. Weiss) was used based on the simplex algorithm to obtain optimal solution.Analysis of the results showed that six (50%) of the twelve classrooms could be used to create a maximum classroom space of six hundred and forty.  It was also observed that the management could use two hundred and eighty (280) surplus spaces to increase its student’s intake from three hundred and sixty (360) to six hundred and forty (640) students, an increase of about 77.78% with only 50% of the total number of classrooms. Again management could cut down the number of classrooms used from twelve to six and reduce the cost of maintaining the classrooms by 50% and still have as many as six extra classrooms for other equally important purposes, hence maximize its profit margin. Keywords: Linear programming, Allocation, Optimal solution, Simplex Algorithm, Premier Nurse’s Training College.

Modelling Classroom Space Allocation at University of Rwanda-A Linear Programming Approach

Education and training play a key role as the human capital function. This is especially true for tertiary education. However, infrastructure and equipment limitations are some factors that limits levels of students\u27 enrollment in universities. This is moreso the case in developing countries where much of the infrastructure developments are donor-funded. For institutional managers and administrators, the allocating of the limited available classroom space is a constant problem that needs sophisticated approaches to deal with. Linear Optimization technique has shown promise in dealing with this problem. This research seeks to assess the Rwandan education system and highlight strides made to broaden access to tertiary education. Using data accessed from the College of Science and Technology for the 2019/2020 academic year, a linear programming model is formulated to assess the level of usage of the available classroom space at the College. The model is solved using the Dual Simplex algorithm via the Cplex solver implemented in AMPL. A solution analysis shows that, out of the 68 classrooms available on the Nyarugenge campus, only 18 with a seating capacity of 2,147 are being used to facilitate the learning of approximated 4,088 students, and that 50 classrooms with a seating capacity of 1,506 are being underutilized or not being used at all. Relevant recommendations including that the college explores the usage of virtual laboratory platforms to overcome space and material limitations associated with physical laboratories are presented