Mathematical Programming for the Design and Analysis of a Biologics Facility-Part 2

An algorithmic approach to fine tune facility design and predict capacity.
Mar 01, 2010
Volume 23, Issue 3


In this paper, we describe the use of mathematical programming methods for automated schedule generation. In part 1 of the article, we described the process and results of a study using large-scale mathematical programming in the design and analysis of a biologics facility. In part 2, we summarize the formulation, compare our approach to discrete event simulation, and discuss the algorithmic methods used to produce high quality production schedules.

Bristol-Myers Squibb, Inc.
In part 1 of this paper, we presented the results of a study using large-scale mathematical programming in the design and analysis of a biologics facility.1 Here, in part 2, we describe the solution methodology used in that study. First we define a basic modeling framework that describes process physics in terms of materials, equipment, and tasks. Then we provide a detailed description of how this framework is translated into a mathematical formulation that models the overall scheduling problem. Our solution uses a core solver with a customized outer layer, specifically designed to handle biologics processes. We discuss the importance of explicit consideration of intermediate material storage and also the challenges that this presents in solving scheduling problems in the process industry as opposed to discrete parts manufacturing. Finally, we contrast our approach with traditional methods of discrete event simulation, discussing the differences and relative strengths of both.


The mathematical programming approach described in this article uses process-specific information in two ways. A resource task network (RTN) description is used to provide a structured description of process details.2 The solution algorithm also is customized to accelerate the search of combinatorial alternatives and to address nuanced preferences concerning selection among degenerate solutions. A customized solution algorithm can select degenerate solutions that are most natural to accommodate the unmodeled constraints and adhere to desired patterns. For example, operators may prefer solutions that use the same equipment over and over for the same activity, even though many other patterns are mathematically equivalent. Under exceptional circumstances, operators will forgo preferences to achieve business objectives. A customized solution algorithm can address this reality. The RTN framework used here explicitly considers materials, equipment, and renewable resources, instead of using the more abstract versions that treat equipment as a renewable resource.3 This approach simplifies algorithm engineering and makes the development of theoretical properties for pruning the search space more straightforward. In intuitive terms, the RTN captures recipe information about a process. Developing the RTN as part of a prospective design analysis provides a way for development personnel to specify the important aspects of a process and helps translate research and development information to practice. In the approach considered here, an RTN instance is translated into a formulation automatically. This automatic translation formulates all necessary variable and constraint objects and constructs the supporting algorithm data structures.