Mathematical Programming for the Design and Analysis of a Biologics Facility-Part 2 - An algorithmic approach to fine tune facility design and predict capacity. - BioPharm International


Mathematical Programming for the Design and Analysis of a Biologics Facility-Part 2
An algorithmic approach to fine tune facility design and predict capacity.

BioPharm International
Volume 23, Issue 3

Another process-specific constraint handled in this way is the requirement that bioreactor batches enter the purification system within the required time after completion. If the most recent demand violates this condition, the core solver backtracks to the point before the demand was scheduled, and a demand is inserted for a discarded material. When this demand is considered, the core solver will manufacture the product up through the bioreactors, then use that material to feed to a disposal task, creating the demanded discarded material. This allows the solver to reproduce the effect of a bioreactor batch that is produced, but held too long and then discarded. Similar logic is used to accomplish the effect of batch failures that occur at a probability that may be specified by the user. Although some of these operations are possible using discrete event simulation, simulators are bound to the present time, so all decisions must be based on the state of the plant at tc. This makes developing logic difficult and the decisions tend to be myopic. There is no ability to view the entire timeline and make decisions based on the overall past, current, and a predicted future plan of activities. Also, programming the logic into a simulator devolves into a process of forming policies of the type: given state s, take action A. The programmer is left with the tedious exercise of trying to anticipate all possible relevant states and then decide on appropriate courses of action for each, using only the current state, or predictions of future state, as a decision basis. The simulation programmer takes on the responsibility that is fulfilled by the core solver in our approach.

A major advantage that our approach holds over discrete event simulation is that the process-specific outer algorithm is much less brittle. This means that the operational envelope over which the algorithm may be expected to work without alteration or human intervention is larger. The outer algorithm used here considers the process to be a sequence of stages, each of which has properties like preparation and process time. Each stage also has a list of parallel equipment on which its task can run. Adding more parallel equipment at a stage often is as easy as listing the new equipment in the input RTN file. Indeed, entire new stages may be added to the design without changing the solver customization. This reduces the time required for process engineers to explore major design changes.

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.


1. Miller D, Schertz D, Stevens C, Pekny JF. Results of a practical case study of the use of large scale mathematical programming for the design and analysis of a biologics facility. BioPharm Int. 2010;23(2):26–38.

2. Pantelides CC. Unified frameworks for the optimal process planning and scheduling. Proceedings of the Second Conference on Foundations of Computer aided Operations. 1994; New York.

3. Elkamel A. PhD thesis [dissertation]. Scheduling of process operations using mathematical programming techniques: towards a prototype decision support system. West Lafayette (IN): Purdue University; 1993.

4. Floudas CA, Lin X. Mixed integer linear programming in process scheduling: modeling, algorithms, and applications. Ann Oper Res. 2005:139:131–62.

5. Pekny JF. Algorithms architectures to support large-scale process systems engineering applications involving combinatorics, uncertainty, and risk management. Computers Chem Eng. 2002:26:239–67.

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