Mathematical Programming for the Design and Analysis of a Biologics Facility - The use of mathematical programming methods for automated schedule generation. - BioPharm International


Mathematical Programming for the Design and Analysis of a Biologics Facility
The use of mathematical programming methods for automated schedule generation.

BioPharm International
Volume 23, Issue 2

Figure 6. Peak and average labor requirements. A: labor pool levels (high); B: labor pool levels (low).
The profiles were smoothed somewhat before recording peak levels in an effort to account for the fact that many jobs can be done slightly earlier or later than dictated by the schedule. Figure 6 shows the peak and average labor requirement for the four labor pools for the high and low load scenarios. The disparity between peak and average levels indicates that a significant benefit can be gained by cross-training.

Figure 7. Quality control (QC) turnaround time for different staffing level cases
We also investigated the effect of staffing levels on QC turnaround time. Additional resource studies were designed to quantify the turnaround time by measuring how fast the laboratory processed different assays. The laboratory cycle time is measured from when the sample is taken to when the test (or set of tests) is complete. This includes any time the sample spends waiting to be processed plus the actual duration of the test, including any reprocessing required for failed tests. Completion of the release testing is key in particular because it is the final step of the process at the site. Four staffing scenarios were tested, with Case A being well-staffed and Case D being very lean.

Figure 8. Ten longest turnarounds contrasted with average turnaround by case
Figure 7 illustrates the behavior of QC turnaround time for these four cases. As the results indicate, the turnaround time initially decreases rapidly with increasing labor. With Case B, however, we have reached a point of diminishing returns, because the further increase in labor supply for Case A yields little improvement. Figure 8 shows data for the 10 longest turnarounds over any particular timeline, contrasted with the average turnaround time. As these data indicate, we see a marked improvement as labor availability is increased. In Case D, the minimum labor case, the outlying turnaround times can be significantly more than twice the average. In the other three cases, we see much better performance on average, with Cases A and B indicating significantly faster turnaround times only on about 20% of the timelines. Still, these data indicate that substantial variability in turnaround time may be expected on rare occasions.


We have described the results of a mathematical programming-based approach to modeling a large-scale biologics facility for design and analysis of the process. The method permits a Monte Carlo type treatment of stochastic parameters, even for very large problem sizes. As the results have shown, including many aspects of daily plant operation in the analysis allows the design to be fine tuned to increase capacity, anticipate and avoid operational difficulties, and provide insight into the required level of many critical support services, such as CIP and labor. The results for many different cadences show that because of process variability, notably in titers and cycle time, the optimum cadence must balance throughput with lots dropped because of excessive hold time. Furthermore, this mathematical programming approach permitted the analysis of other biologics products by industrial users, without any change to the customized algorithm.

Donald L. Miller is the co-founder and Derrick Schertz is a senior project engineer at Advanced Process Combinatorics, Inc., West Lafayette, IN. Christopher Stevens is an associate director of process support at Bristol-Myers Squibb, Inc., Devens, MA, 978.784.6413,
Joseph F. Pekny is a professor of chemical engineering and interim head of industrial engineering at Purdue University, West Lafayette, IN.


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3. Elkamel A. PhD thesis dissertation. Purdue University. West Lafayette, IN;1993.

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