Meta-Modeling for Capacity Buffer Optimization

Researchers: John Maleyeff, Mingxuan Zhang, Yuzhen Liang, and David Cadreact

Capacity management of hospitals, call centers, and other resources is an important challenge faced by a manager.  Because of the variation in service times and the inability to inventory services, capacity buffers are required to ensure reasonable waiting times for customers.  The nonlinear relationship between resource utilization and customer wait times makes it difficult to determine the optimal capacity buffer, called the knee.

This work expands on previous efforts to develop a decision support system using Python to determine optimal capacity buffers. This work expands on previous efforts to develop a decision support system using Python to determine optimal capacity buffers.  The original system used a Monte Carlo simulation and knee optimization model that allowed for flexibility in specifying uncertain arrival patterns and service times.  It showed users their current status and where changes need to be made to the service times or the number of servers to achieve optimal results.

This project attempts to eliminate the long processing times required to run the simulation by creating a meta-model of simulated results.  This approach, essentially creating a model of a model, can provide accurate results without length processing times.

Preliminary results show that a non-linear repression can be accurate in estimating power functions which are required to optimize service utilization.  The regression assumes that arrivals are random and includes variables such as the service time coefficient of variation, and the number of servers, and the server utilization.  The prediction equation is based on a 4th order estimation and the logs of other variables.  It appears to accurately estimate simulated results.  We are currently working with a large adhesives manufacturer who has provided operational data for their B2B call center.

Try our simplified version of the decision support tool by clicking here (beta version).

Photo Courtesy of Kaming Yip