ABSTRACT
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.
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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 RESOURCE TASK NETWORK
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.
