(417f) Accounting for Uncertainty in Production Scheduling in the Presence of Feedback: Method Comparison, Paradoxes, and Guidelines

When a schedule is computed, disruptions or the arrival of new information can render the current schedule sub-optimal or even infeasible, thereby necessitating online (re)scheduling. Hence, the scheduling optimization problems are solved iteratively as the horizon is shifted forward, to determine the open-loop schedules. Based on feedback (i.e., injecting the decisions computed at the initial times of each open-loop schedule), the closed-loop schedule is generated. An important consideration when computing schedules is the incorporation of uncertainty in the online model. For this several methods exist: (i) deterministic optimization; (ii) robust optimization; and (iii) stochastic programming (Engell, 2009 and Gupta et al., 2020).

In this work, we focus on batch scheduling under demand uncertainty, wherein demand is modeled in the form of orders with the order sizes being drawn from a probability distribution. Demand uncertainty is composed of two aspects: (i) observation horizon (η), which is the length of the horizon within which demand is deterministically known and (ii) order size max-mean relative difference (ε), that captures the relative difference between the maximum and mean order size (Gupta et al., 2019). In deterministic optimization, the model does not incorporate information about the uncertainties and a mean order size is assumed for orders beyond . In robust optimization, an order size near the maximum order size value (from the given distribution) is assumed for orders beyond . Lastly, in stochastic programming, a moment matching technique is used to generate a discrete set of scenarios from the continuous probability distribution (Hoyland et al., 2001), for orders beyond .

We have found that the “load” (Λ) on the network used in the scheduling problem, calculated based on the production capacity of the network and the demand profile, plays an important role in differentiating the performance of the methods. On analyzing the closed-loop performance of the three methods across η, ε, and Λ for different networks, we conclude that at low and very high Λ or large η, all three methods perform similarly. At intermediate Λ and small η, the best choice of method depends on network characteristics. Furthermore, we draw interesting insights on how important it is to account for uncertainty apriori at high Λ and small η compared to feedback, since the stochastic programming model that is re-optimized infrequently performs much better than the deterministic model that is re-optimized frequently.

We explain why choosing the best method to mitigate demand uncertainty for any given network is non-trivial and expound on the paradoxes observed that depend on the network characteristics. To the best of our knowledge, our work is the first of its kind in understanding the importance of accounting for uncertainty apriori (i.e., using robust optimization, stochastic programming) compared to closed-loop batch scheduling based solely on feedback (i.e., using deterministic optimization).

References

1. Engell, S. (2009) Uncertainty, decomposition and feedback in batch production scheduling. Computer Aided Chemical Engineering, 26, 43-62.
2. Gupta, D., and Maravelias, C.T. (2020) Framework for studying online production scheduling under endogenous uncertainty. Computers & Chemical Engineering, 129, 106517.
3. Gupta, D., and Maravelias, C.T. (2019) On the design of online production scheduling algorithms. Computers & Chemical Engineering, 135, 106670.
4. Hoyland, K., and Wallace, S.W. (2001) Generating scenario trees for multistage decision problems. Management Science, 47(2), 295-307.