Summary of Results

The first relaxation of the problem involved a 6x8 grid and assumed that the length and the width of the aisles and the parking stalls were the same. The optimum solution for this problem was 28 stalls, and indicated that the model was functioning. Other sized problems were also solved and verified manually to ensure that this starting model provided a strong foundation for further extensions.

In the first extension, (second relaxation) the dimensions of the parking lot and spots were taken into consideration. The lot size used was 128x64 feet, with a stall size of 8x16 feet. In addition, an aisle width of 16 feet was used to enable cars to turn around. Also, considerations were made so that vehicles could turn a corner, in that the aisles vertically alongside a column of stalls were made wide enough for two cars to pass. The optimum solution for the chosen measurements is 28 parking stalls.

The second extension involved designing a parking lot in a non-rectangular area. This meant cutting off the edges of the parking lot and breaking the lot into 2 problems: the centre rectangle, and the two edges. This also allowed vehicles to park along all edges of the parking lot while still permitting access to driving aisles. All other previous enhancements were maintained in this relaxation, but adjusted slightly to account for the new constraints. The extension runs separately but works in conjunction with the previous extension in that they are both needed to solve the parking lot problem, as a whole. This addressed the need to disallow parking in corners in order to ensure access for cars parking at the ends of all edges of the lot.

Finally, now that an optimum parking lot had been created, an entrance to this parking lot was constructed. The entrance provided access to one of the primary aisles which in turn allowed access to all parking stalls in the lot. This is essentially the same as the previous extension with the added constraint for an entrance. As before, this extension runs separately but works in conjunction with the first extension.

Abstract, Introduction, Background, Problem Statement,

Solution Summary, Sensitivity Analysis, Models, Parking Lot B, Acknowledgements