Model (4)

Assumptions

This model makes the same assumptions as in the aforementioned models. The model creates an entrance to the parking lot by modifying the previous model. As in the previous model, this extension runs separately but works in conjunction with the second model in a two-stage approach. Again, the second model is used to optimize the complete problem and then this model is used to address the other considerations.

Index Sets and Variables

The sets used in this model were:

I, Number of rows in the parking lot

J, Number of spaces in each row in the parking lot

The variables used in this model were:

X(I,J) binary variable - 1 if a parking space, 0 otherwise

Z - total number of spots in the lot

Data

CENTRE the centre row in the parking lot - 4

C1 the number of spots in the corner - 2

LASTI the last row in a lot - 8

LENGTHI the length of the parking lot - 128 feet

SLENGTH the length of a parking spot - 16 feet

SWIDTH the width of a parking spot - 8 feet

Program

Objective Function - maximize the total number of spots in the parking lot.

Subject to the following constraints

-TotalI: observe the limit of the length of the parking lot;

-Corners 1-4: ensure that every corner of the lot is empty;

-Enter: allows for an entrance to the parking lot.

Assessment of Solution Validity

This solution, in conjunction with the solution from the previous model, is the most valid of all our solutions. However, it still ignores many real world factors such as angle parking and multiple sizes of parking spots. We should not ignore angle parking since studies have shown that angle parking at 60 degrees is the most effective. To model such a problem, one would declare a different variable for each type of parking angle. The problem would then be solved in a similar fashion to model (3), with each variable being one if such a parking stall existed, and zero, otherwise. As well, the current solution only allows for small cars. This is inappropriate since we must allow for spaces for larger vehicles. To model this issue, one would again use several binary variables, with each variable representing a different size of parking space.

Critique of Model Choice and Assumptions

Our model is now complete. However, it still ignores many important real world considerations such as angle parking, different types of parking spaces, and different driving aisle widths. However, we felt that the cost of modeling and solving the problem with these factors would outweigh the benefits, due to the complexity of the model and the time required to solve such a model.

Abstract, Introduction, Background, Summary of Results, Problem Statement,

Solution Summary, Sensitivity Analysis, Parking Lot B, Acknowledgements