Business and Technology Consulting

Stochastic Ruminations: Is Modeling in Your Future?

We build models for a variety of reasons, including:

  1. to gain a better understanding of a process, structure, or operation
  2. to identify how a change might affect the real world by observing changes in the model.
  3. to predict a future behavior based on a priori data

Consider the classic problem of fitting the piano in the right place in the living room. An appropriate model may be a scale drawing or even a three-dimensional prototype of the room and all its furniture. It's a lot easier to move the paper or cardboard piano than the real thing.

While models can be constructed in many different ways, mathematical models are efficient  tools for decision-making processes. In one project, the manager of a manufacturing plant was insistent on needing a significant capital investment for a new piece of equipment. The CFO questioned why he needed yet another one when he already had ten and the overall demand had not changed significantly.

While the overall demand had not changed, the demand patterns had changed dramatically. The plant manager argued that this would require additional machine setups during each shift in order to accommodate the change. As the setups were time-consuming, they reduced both throughput and efficiency.

Enter the mathematical model: we developed a set of equations that described the production time required to process the daily demand. The total production time to meet the daily demand exceeded the 10 machine-days due to the large setup time between major product lines. Then we adjusted the model to try alternate configurations. Using linear programming techniques, we varied the configuration parameters and solved multiple simultaneous equations to maximize throughput. 

The result is that the plant manager can meet the demand requirements with the existing equipment by pre-configuring certain machines for specific product lines. It was a lot easier to use a mathematical model than to change configurations and experiment in a trial and error fashion.

(C)Copyright 2005, James T. Moran & Associates. All rights reserved.