Scheduling Under Uncertainty

It is evident that uncertainties in batch operations may arise from different sources (i.e., external demand, prices of raw and final products, processing times, and equipment availability) causing that programmed schedules become nonoptimal and in some cases infeasible. Despite the uncertain nature of scheduling problems, research efforts over last decades have primarily focused on deterministic formulations, which assume that all parameters are precisely known in advance. 

Lafnez-Aguirre and L. Puigjaner, Advances in Integrated and Sustainable Supply Chain Planning, DOl 10.1007/978-3-319-10220-7 8 

8 Using S-Graph to Address Exogenous Uncertainty in Processes Scheduling 

Frameworks that reduce the computational complexity of scheduling problems are crucial for the eventual integration of the SC hierarchical decision levels. As mentioned before, that integration permits to find more realistic and feasible solutions for the SC design and planning. What is more, its consideration may improve the resolution of SC incidences and SC visibility. These topics will be further discussed in Chap. 9. 

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Scheduling Under Uncertainty Using a Moving Horizon Approach 187 9.2... 

Janak, S.L., Tin, X., and Floudas, C.A. (2007) A new robust optimization approach for scheduling under uncertainty II. Uncertainty with known probability distribution. Computers Chemical Engineering, 31, 171. 

Ryu, J.-H., Dua, V., Pistikopoulos, E.N. (2007) Proactive scheduling under uncertainty A parametric optimization approach. Industrial Engineering Chemistry Research, 46, 8044-8049. 

Enhancing S-Graph Framework to Address Scheduling Under Uncertainty... 

Finally, note that this approach for scheduling under uncertainty can be integrated with the control strategy proposed in Chap. 9. Nevertheless, further work is needed so that other kind of objective function can be considered. 

Blau et al. [22] have applied probabilistic network models to model resource needs and success probabilities in pharmaceutical and agrochemical development, through Monte Carlo analysis. This requires solving the problem of scheduling a portfolio of projects under uncertainty about progression. This approach is tractable for drug development. However, the inherent complex-... 

The scheduling problem is subject to uncertainties in the demands. The demands di in period i are only known precisely after the period i. Thus, the production decision %s has to be made under uncertainty without knowing the demand exactly for the current and for later periods. Table 9.1 provides a model of the uncertain demands. The model consists of two possible outcomes of the demands for each period i d- and df. We assume a probability distribution with equal probabilities pj and pj for all outcomes. 

In this section, the hybrid evolutionary algorithm described above is applied to a real-world scheduling problem under uncertainty. The performance of this algorithm is compared to that of the state-of-the-art MILP solver CPLEX and to that of... 

I. (2004) Approximation to multi-stage stochastic optimization in multi-period batch plant scheduling under demand uncertainty. Industrial and Engineering Chemistry Research, 43, 3695—3713. 

Tang O, Grubbstrom RW (2002) Planning and replanning the master production schedule under demand uncertainty. International Journal of Production Economics 78 (3) 323-334... 

In last decade, many authors have recognized that it is unlikely to apply deterministic schedules in real scenarios without significantly reducing their performance, and have made efforts to expand the deterministic approaches to situations with uncertainty, in order to obtain better results when their solutions are deployed in real scenarios. Here, the S-graph deterministic framework is extended for solving production scheduling problems under uncertainty in demand. 

In most chemical batch scheduling problems the underlying data is not exactly known at the time the schedule has to be generated. Typical sources of uncertainties are (1) failures of reactors, equipment, and resources, (2) varying processing times, (3) varying product qualities, and (4) varying customer s demands. 

Reactive scheduling is an online procedure which modifies nominal schedules in reaction to the occurrence of an unexpected event. Reactive scheduling is traditionally used to handle short-term uncertainties in parameters as, e.g., processing times, or equipment failures. The underlying-models themselves usually do not incorporate information on the uncertainty. 

In order to investigate the performance of a deterministic online scheduler, we apply it to the example problem under demand uncertainty for three periods. The model of the scheduling problem used in the scheduler considers a prediction horizon of H = 2 periods. Only the current production decision Xi(ti) is applied... 

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