Evaluation and Optimization of Scheduling Operations with Uncertain Task Durations

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Abstract - Grossmann - 9810182 Supply chain management, and consequently process scheduling, are receiving increased attention. A major limitation of present scheduling models, however, is that they are deterministic in nature. These models assume that data such as processing times, costs, availability of equipment, and product demands are known. In practice, it is often the case that there will be considerable uncertainty in these items. This means that solutions that are predicted from existing deterministic models may not be very useful. The PI plans to build upon deterministic model and extend them in a meaningful way, so as to effectively handle the uncertainties. This project is concerned with the evaluation of scheduling operations that arise in multiproduct batch and continuous process manufacturing, in new product development, and in any scheduling situation which exhibits uncertainties in the task duration. These could correspond to inexact process times, lots whose processing must be repeated due to failures, and conditional tasks that may or may not be performed. The PI plans to investigate a largely symbolic procedure that consists of translating a proposed schedule into a directed acyclic graph on which piecewise polynomial distributions are considered with Dirac delta functions. To obtain the probability distribution function of the completion time of the schedule, a multiple integral is evaluated over all paths, which requires analytical integration over a polytope. The dimensionality of this integral is reduced with graph decomposition methods. The procedure should allow fast evaluation of uncertainties in a large variety of process scheduling problems. The integration of this evaluation technique in optimization methods is also planned, for both direct search and mathematical programming methods.