2025 AIChE Annual Meeting

(392bm) Optimal Production Scheduling Software Implementation Based on a Novel Representation of Batch Processes

Authors

Georgios Georgiadis, Intelligen Europe
Charles Siletti, INTELLIGEN, INC.
Demetri Petrides, INTELLIGEN, INC.
The gap between academic research and industrial implementation of production scheduling methodologies is well-known and well-documented. One of the reasons for this gap is that, in an attempt to reduce computational complexity, traditional production scheduling schemes are often built on top of simplified process representations. Also, they often assume very flexible task execution with the start and end of different tasks considered, in principle, independent of each other and only tied through constraints entered at the mathematical formulation stage. In reality, however, batch processing in pharmaceutical, biotech, food and other areas of industry is composed of tasks with complex internal structure and very firm processing rules that impose a strict order with no delays and only limited flexibility in their execution. The objective of this paper is to introduce a modeling framework that captures the complexity and firmness of actual batch processing while, at the same time, providing a way to automatically “translate” this representation into its mathematical description that can be used for optimal scheduling.

Unlike established approaches that treat processes as monolithic blocks, batch processing steps executed in some equipment (we will call them procedures) are, in reality, composed of subtasks (operations) that have a significant role in determining how the process is executed. More specifically, operations can be used to determine:

  • the start/end and duration of other procedures/operations (e.g. the start of material transfer operation from one tank signals the start of the receiving of the material in another tank)
  • the duration of procedures and, therefore, the equipment occupancy time.
  • the timing in the use of additional (auxiliary) equipment for operations (e.g. the use of a CIP-skid for a cleaning operation). In many cases, the operation (and, consequently, the procedure) duration is dependent on the auxiliary equipment used.
  • the amount and timing of material consumption/generation and the consumption of other resources (e.g. labor, utilities).

In this paper, a novel representation of a batch production process (recipe) is proposed that relies on the identification of procedures and operations as separate entities that need to be considered in the recipe formulation and, at the same time, enforces, a priori, the constraints that exist in their time execution while recognizing the limited flexibility that may exist in some operations.

More specifically, operations within the same or across procedures obey strict sequencing rules with respect to their start or end. These are:

  • finish_to_start (FS): Operation A starts at the end of operation B
  • start_to_start (SS): Operation A starts with the start of operation B
  • start_to_finish (SF): Operation A finishes at the start of operation B
  • finish_to_finish (FF): Operation A finishes at the end of operation B

In these relations, some fixed or flexible time shift may be applied. A flexible shift can be used to represent the freedom (where applicable) to move the start or end of an operation from its nominal time if the resources it requires are not available. For example, a flexible shift in a CIP operation may be applied to delay the tank cleaning until a CIP-skid becomes available. In the proposed formulation and in order to maintain uniformity in the representation, a flexible shift is represented as a “dummy” operation with fixed timing links but undefined duration; when the schedule is constructed, the scheduling algorithm can decide on the optimal duration of these dummy operations.

With the exception of flexible shifts, all operations are considered in this framework as having strict, inter-dependent starts and ends. This means that if we define a triplet of variables for each operation, start, end and duration, we can then construct linear relationships between them and, if these timing elements are ordered hierarchically based on dependency, a lower-triangular matrix capturing all dependencies will emerge. The only decisions that need to be made at scheduling time are the selection of resources for each task (which may also affect its duration) and the duration of the ‘dummy’ operations representing flexible shifts. For given equipment assignment and flexible shift specifications, the start, end and duration of all tasks in a batch can be calculated in a direct and unequivocal way. The paper will present the complete mathematical formulation which is a mixed-integer linear programming (MILP) model, specifically within the general precedence framework. It is also a continuous time framework known for its fine-grained control over resource allocation, sequencing, timing and ability to accommodate real-life industrial constraints.

With the use of the above formulation, the software implementation of any batch process scheduling problem in any level of detail is possible. The process representation through operations and procedures interlinked in their durations and timings matches exactly the way the process would be described by a practitioner in an industrial setting. Once the process is laid out, its representation can be easily translated into the mathematical formulation that, in turn, can be embedded in a MILP optimization problem to be solved for different objective functions. Additional constraints such as equipment-dependent operation durations, equipment compatibility or connectivity constraints etc. can be easily incorporated in this framework.

Such an approach has been implemented in the scheduling software SchedulePro. Starting with a user-defined process description (the recipe), SchedulePro generates automatically the mathematical model which can then be fed to different optimization solvers (such as SCIP, CPLEX or Gurobi) in order to produce the optimal schedule based on user-defined objective criteria (e.g. minimization of cycle time for periodic scheduling, minimization of makespan etc.) The results are read back into SchedulePro and are visualized through tables and interactive Gantt charts. Case studies motivated by industrial scheduling problems will be used to demonstrate the approach.

The results demonstrate the practicality, flexibility, and computational efficiency of the proposed framework. By using a representation that closely mirrors the actual structure and logic of industrial recipes, the method enables direct translation from process description to an optimization problem. It also reduces the modeling effort typically required by engineers and ensures that the generated schedules are both realistic and implementable. The approach bridges the gap between industrial needs and mathematical rigor, while the integration into a commercial software platform further supports its applicability and facilitates its adoption in real-world settings.