Model (3)

Assumptions

This model makes the same assumptions as in the first two models. This model ensures that all vehicles have access to aisles by disallowing parking in the corners of the lot. This extension runs separately from the previous two, but works in conjunction with the second model in a two- stage approach. The second model is used to optimize the problem as a whole, and this model is used to address certain other considerations. These considerations include the need to disallow parking in corners to ensure access for cars parking at the ends of the edges of the lot. This method was chosen to make sensitivity analysis more efficient and to minimize the amount of processing time, due to the reduction in constraints. Simultaneously incorporating all of these assumptions into a model would have been overcomplicated and inefficient.

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 in the lot is empty.

Assessment of Solution Validity

This solution, in conjunction with the solution from the previous model, is the most valid so far. 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. As well, the current solution only allows for small cars. This is inappropriate since we must allow for spaces for larger vehicles.

Critique of Model Choice and Assumptions

Our two stage model is one step closer to our goal of a sufficient abstraction of the real world. However, as stated above, our model remains very relaxed. Assumptions greatly relax the model but are necessary to be able to model and solve the problem efficiently. An issue that still needs to be addressed is the need for an entrance to the parking lot. Other issues not addressed include angle parking, different stall sizes, and differing driving aisle width requirements.

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

Solution Summary, Sensitivity Analysis, Parking Lot B, Acknowledgements