## Building Space Allocation

On occasion, whatIf? Technologies is asked to use its mathematical expertise and software tools to help solve problems in the domain of operations research. According to Wikipedia, operations research is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems.

buildingspaceallocationOne such example is what might be called building space allocation problem. The problem involves a large organization that targets a reduction in the cost of providing building space for its employees. The organization owns or leases a portfolio of buildings, such that savings can be realized only when buildings are removed from the portfolio. The organization consists of a number of organizational units, each of which must be co-located in the same building. A new space entitlement standard reducing the space entitlement per employee is established such that, if units occupy the space to which they are entitled by the new standard, a sufficient amount of space may be saved to release the number of buildings from the inventory required to meet the targeted savings.

This seemed at first to be a straight forward problem of finding an allocation of space that minimized the cost of the portfolio, until it was realized that organizational units could not ‘shrink’ in situ. If an organizational unit is to meet the new standard, it must move into space that has been specially fitted for that purpose and the process of refitting space and moving takes time, typically 4 to 6 months, and incurs cost.

The problem could then be stated as follows: find the sequence of organizational unit moves that maximizes net savings, total savings from the reduced portfolio less costs of moving and fitting. As stated, there is no known solution for this problem. The number of possible move sequences is so large that all possible sequences cannot be evaluated and there is no known algorithm for finding the optimal pathway.

It was then necessary to restate the problem as follows: identify algorithms that will produce move sequences that will result in savings, explore a range of move sequences using different algorithms, then select the move sequence that produces the most savings. This is now a dynamic problem that may be sensitive to starting conditions. The starting condition reflects the current occupation of buildings by organizational units and the amount of vacant space in each building. The algorithm that produces the most savings for a particular starting condition may not be the one that produces the best result from alternative starting conditions. If there is little or no vacant space in the portfolio, it may be necessary to add ‘swing’ space to the inventory for some period of time.

A search of the literature revealed that this space allocation problem had been encountered by NASA and that the same conclusions had been reached.

In the course of the project, whatIf? Technologies created a family of algorithms, coded and tested one of them as an operator in the TOOL language, and implemented a model on the whatIf? platform that took as input the starting condition, the new standard, the savings target and produced as output a time sequence of moves, building occupancy at quarterly intervals over a five year period, and the net savings achieved over the five year interval.