SIMULATION

OPERATIONS RESEARCH

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QUESTIONS

1. Formulate and solve a linear program for this problem. Please provide all your model formulations and solutions.

2. What is your resulting recommendation to the school board? Prepare a managerial report to the EG.

3. Do sensitivity analysis, please include your sensitivity analysis.

The education department of Gauteng (EG) has to place learners into schools. They always have a problem with grade one learners. They have to place learners into the three available schools. The department provides transport for all learners who must travel more than approximately a kilometre, so the department wants a plan for reassigning the students that will minimize the total transportation cost. The monthly cost per student for transport from each of the six residential areas of the city to each of the schools is shown in the following table (along with other basic data for next year), where 0 indicates that transport is not needed and a dash indicates an infeasible assignment. Transportation Cost per Student in School 1 School 2 School 3 Area 300 Number in 1 st Grade 145 222 165 98 195 153 1 2 3 4 5 6 School capacity: 700 500 200 400 300 500 600 200 0 500 1 400 300 1 600 400 0 2 000 The education department also has imposed the restriction that each grade must constitute between 17 and 23 percent of each school population. The above table shows the number of learners in each area that needs to be placed in grade 1.. You have been hired as a decision analyst /operations research consultant to assist the board in deciding how many students in each area should be assigned to each school