**On the Alleviation of Inventory Creep in Process Scheduling**

Jin Zhang and Donald J. Chmielewski

In the work of Lima et al., [1], the notion of inventory creep within a process scheduling context was introduced. In short, the inventory creep phenomenon is a gradual reduction of material inventory over time. To alleviate this myopic behavior, the authors of [1] advocate the use of larger prediction horizons, but quickly run into computational tractability issues. Recently, similar inventory creep phenomena have been observed in the context of Economic MPC, [2, 3, 4]. In [2] and [3], inventory creep was virtually eliminated by the use of a surrogate MPC objective function. This quadratic objective function was constructed to be inverse optimal with respect to an appropriately defined Economic Linear Optimal Control (ELOC) policy [5]. In [3], the original economic objective function is retained, but is appended by an ELOC derived final cost term. This final cost is an approximation of the original objective function (from the end of the prediction horizon to infinity) resulted in an approximate infinite-horizon EMPC policy.

In the current effort, the approximate infinite-horizon EMPC policy is applied to a simplified version of the long-term scheduling problem found in [1]. This example is distinct from those of [2-4] in that many of the decision variables of the scheduling problem are restricted to integer values. This fact has two implications. First, these integer restrictions will significantly increase the computational complexity of the original scheduling version of the EMPC problem, and create a much greater need for reductions in horizon size. The second issue is that ELOC is incapable of enforcing integer constraints. However, development of an ELOC policy with integer constraint relaxed, leads to a final cost term that sufficiently approximates the economic cost from the end of the horizon to infinity. The result is an approximate infinite-horizon policy that enforces integer constraints over the finite horizon, but due to the appropriately selected final cost term is able to employ much short prediction horizons (requiring much less computational effort) while observing virtually zero inventory creep.

[1] Lima, R. M.; Grossmann, I. E.; Jiao, Y. “Long-term scheduling of a single-unit multi-product continuous process to manufacture high performance glass.” Comput. Chem. Eng. 2011, 35 (3), 554−574.

[2] Omell, B.P.; D.J. Chmielewski, "IGCC Power Plant Dispatch using Infinite-Horizon Economic Model Predictive Control" Ind. Eng. Chem. Res., 52(9) pp 3151-3164 (2013).

[3] Mendoza-Serrano, D.I.; D. J. Chmielewski, "Smart Grid Coordination in Building HVAC Systems: Computational Efficiency of Constrained ELOC " Sci. Tech. Built Env., in press (2015)

[4] Omell, B.P.; D.J. Chmielewski, "On the Stability of Infinite Horizon Economic MPC," Annual Meeting of the AIChE, San Francisco, CA, 2013.

[5] Peng, J.K.; A.M. Manthanwar; D.J. Chmielewski, "On the Tuning of Predictive Controllers: The Minimally Backed-off Operating Point Selection Problem," Ind. Eng. Chem. Res., 44, pp 7814-7822, (2005).

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