Model (1)

Assumptions

We assumed that the parking lot was of a standard shape, i.e., one rectangle. We assumed only one arrangement was allowed in the lot setup. For example, we did not allow for angle or parallel parking. Only one size of parking stall was required. Wheelchair parking was not necessary since there was no access from the parking lot to campus. This model involved a grid- like system that assumed that the length and the width of the aisles and the parking stalls were the same. No driveways, traffic aisle widths or sufficiency of aisle width for turns was taken into consideration.

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

LASTJ the last parking space in a row - 8 grid points

LASTI the last row in a lot - 6 grid points

Program

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

Subject to the following constraints:

-Lanes 1-3: ensure that there is a lane behind each parking row;

-IntLane 1-5: ensure that every driveway meets two other driveways;

-Corners 1-4: ensure only one spot in corners of lot.

Assessment of Solution Validity

The solution we have found using our model is valid, due to the assumptions made above. We did use integer programming to solve our model, therefore the number of spots in an aisle is an integer value. We realize that the solution would not be valid in a practical or real world application, as many of our assumptions would not hold, specifically there is no entrance to the parking lot.

Critique of Model Choice and Assumptions

We are aware that our model is not adequate for a real world application. However, given the assumptions that we made above, our model and solution are appropriate. Because this is a relaxed version of the problem, our model and assumptions are not realistic. That is, they do not model the real world sufficiently to make the model practical. This model will be adjusted to take into consideration many of the variables that we have disregarded to this point.

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

Solution Summary, Sensitivity Analysis, Parking Lot B, Acknowledgements