Scheduling under process uncertainty: A batch serial line study

Derrick Paul Schertz, Purdue University

Abstract

This work examines an n-stage batch serial production line with intermediate storage between stages. Each stage consists of a train of process equipment which operates under its own characteristic minimum cycle time. The line is subject to two types of uncertainties: failure of a batch of intermediate material to meet specifications, and batch processing time and yield variability. Ultimately, failed batches can only be compensated by initiating new batches. However, because of the significant processing times, replenishment in time to meet customer demands is not feasible. For this reason and also to accommodate time and yield variability, in practice significant inventories of intermediate materials are maintained between each stage. Since such inventories represent a considerable expense, especially in the pharmaceuticals industry, the objective of this work is to develop an approach for minimizing interstage inventory levels while still meeting customer demands with sufficiently high confidence. Two operating policies are used to schedule the line. First, a regular operating policy is created based on a time-averaged material balance for the line, assuming no batch failures. Second, batch failures are immediately addressed by a reactive scheduling algorithm which seeks to recover the original material balance. To evaluate the performance of a particular set of inventory control parameters, the policies are implemented in a detailed Monte Carlo simulation. Optimization of these parameters is performed on a simplified simulation model, decreasing the computational burden. Work is also economized by using need-based evaluation where only promising candidates, based on their proximity to successful points, are evaluated. Optimal solutions for a range of costs are preserved allowing cost-confidence tradeoffs to be examined. The method is applied to an example derived from an existing production facility. The effects of process variability on operating costs and the ability to meet demands with satisfactory confidence are demonstrated. Batch failures, especially those on the final stage, dominate the performance of the line. Process timing and yield variations have a significant but secondary effect. By quantifying the cost-confidence tradeoff curve, the method allows one to choose the optimal inventory distribution for a desired confidence level.

Degree

Ph.D.

Advisors

Reklaitis, Purdue University.

Subject Area

Chemical engineering|Operations research

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