Relaxed and Original Model

Relaxed Problem

Description

A simpler relaxation model, which does not take into account the requirement that each teacher must go to a different school in the morning and in the afternoon session. This simpler model is used to explain the transhipment theory behind the assignment problem.

Our goal is to develop a model which determine how to assign teachers to the different schools, subject to the following requirements:

each teacher is assigned to no more than one school

each of the 10 different schools is assigned to exactly one teacher.

In this case, our objective is to maximize the preferences of each parties expressed in terms of a scoring system.

Mathematical Model

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Original Problem

Verbal Formulation of the Mathematical Model

In the original problem, 10 teachers are assigned to two sessions at 10 different schools. Also, in this case, we take into account the requirement that each teacher must go to a different school in the morning and in the afternoon session. Our goal is to develop a model which determines how to assign teachers to the different sessions at different schools, subject to the following requirements:

each teacher is assigned to no more than one school in each session

each session at a particular school is taught by exactly one teacher

each each teacher must go to a different school in the morning and in the afternoon session

In this problem, a new index must be defined to indicate the two different sessions. Basically, we have a set of two sessions (am, pm) at 10 schools that must be assigned to 10 teachers. The objective is to maximize the preferences of each parties expressed in terms of a scoring system with addition condition of 10 teachers are assigned to two sessions at 10 different schools. Here is the mathematical model.

Mathematical Model

Sensitivity Anlaysis is also performed to determine the impact of changes in the data on the optmal assignment.

On the next page, we continue to extend our original problem. First extension will be on the next page, please click the right button to continue.

Background Extension 1