Model (2)

Assumptions

This model makes the same assumptions as in the first model with a few additions and exceptions. The parking lot now has dimensions measured in feet instead of using a grid-like mechanism. We also assumed that we would want two cars to be able to pass each other in an aisle

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

LASTI the last row in a lot - 8

AISLEWIDTH the width of the driving aisle -16 feet

LENGTHI the length of the parking lot - 128 feet

WIDTHJ the width of the parking lot - 64 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:

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

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

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

-Aisles 1-2: ensure that there is a full driving aisle on all sides of the parking lot.

Assessment of Solution Validity

This solution is more valid than the previous model since an actual measurement system is used. The measurements used are representative of a real parking lot to ensure a "real life" answer. However, the parking space measures used would only fit small to medium-sized vehicles. The model also allows sufficient space for cars to turn into stalls. Vehicles can now turn corners in aisles wide enough for two cars to pass. These aisles are placed vertically alongside a column of stalls. The optimum solution for the chosen measurements is 28 parking stalls.

Critique of Model Choice and Assumptions

We are aware that our model is still not quite adequate for a real world application. The issue of accessibility of all vehicles to an aisle needs to be addressed as well as the need for an entrance to the parking lot. One major drawback of this model is that aisle widths are multiples of the parking stall length and width. A more realistic model would allow for any width of driving aisles. However, we chose to bypass this issue due to its complexity.

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

Solution Summary, Sensitivity Analysis, Parking Lot B, Acknowledgements