A Systematic Methodology for Analysing Zoning Options for a Building Using Dynamic Programming

In the designing phase of a building, the number of lifts, their capacities and nominal speeds are selected. In case of high-rise buildings, it is a common practice to divide the building into fixed contiguous floor segments called zones to save core area taken by lifts. Typically, each zone is served by a group of lifts, and zones do not have common floors except the entrance floor. The zoning design aims at similar service quantity and quality among all zones. Each lift group should satisfy the traditional design criteria related to handling capacity, interval, and nominal travel time. Finding a good zoning solution is not an easy task since, in general, the number of different zonings increases exponentially as a function of the number of served floors. Current practice in the lift industry is more or less based on rules of thumb, duty table calculations, and the designer’s expertise. This paper introduces a dynamic programming program for finding an optimal solution for the static zoning problem. It assumes the uppeak traffic condition. The developed method is an extension of Powell’s work carried out almost 50 years ago. The solution to the optimization problem divides the upper floors of the building into fixed disjoint zones and, for each zone, specifies the number of lifts as well as their sizes and rated speeds. Optimal zonings with respect to uppeak filling time, core area occupied by all lifts in all floors, and the total number of lifts over all zones objectives are analysed for a large set of hypothetical office buildings. The results show in general how many zones and lifts per zone are needed, what is the impact of different objective functions on optimal zones and how much zoning decreases core area occupied by the lifts.