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Time (h)
Figure 10. The detailed schedule of charging tank filling.

the "Refining Scheduling" section is applied to obtain a refining
schedule. We solve the formulated model for problem P1 and
yield f10 = f11 = 375 tons/h, f20 = f21 = 230 tons/h, and
f30 = f31 = 500 tons/h. Notice that, by using this result, the
maximum production rate is reached. Then, with the production rate decided for each distiller during each bucket, the
amount of crude oil to be processed by each distiller is calculated
as shown in Table 4.
Based on the results obtained from Stage 1, the transportation problem model at Stage 2 can be easily formed and solved,
and a number of oil parcels are obtained for each distiller. The
oil parcels that have the same oil type are then merged at
Stage 3, yielding a refining schedule as shown in Figure 6.
With the obtained refining schedule and the schedulability
conditions, we use the method presented in the "Detailed
Scheduling" section and the heuristic given in [36] to find a
detailed schedule. For this schedule, the ODFs for distiller
feeding and the ODTs for charging tank filling are shown by
Gant charts in Figures 9 and 10, respectively. By observing the
obtained schedule, one can conclude that all the constraints,
including crude-oil residency time and charging-tank-switchoverlap constraints, are satisfied. Notice that, for the refining
scheduling problem, we aim at maximizing the productivity
using a linear programming formulation presented in the
"Refining Scheduling" section. Hence, for the obtained schedule, the production rate is maximal [27], [28]. In addition,
from the obtained result, when a charging tank is charged
according to an ODT, it is charged to capacity. By doing so, the
number of oil-type switches in performing ODTs for oil transportation and the number of charging tank switches in performing ODFs for distiller feeding are minimized.

mathematical programming methods, this article proposes a
control-theoretic approach to the STSP of crude-oil operations.
Using the proposed method, a hybrid PN is developed to model
the system. Based on this model, schedulability conditions are
derived by analyzing the schedulabilty of the process in the view
of control theory. After obtaining the schedulability conditions,
we successfully decompose the problem into tractable subproblems and solve them in a hierarchical way. By doing so, the interaction of discrete-event and continuous variables is decoupled
with each subproblem having either continuous or discrete variables but not both. For subproblems with continuous variables,
linear programming-based techniques can be used; however, for
those with discrete variables, heuristics can be applied. Thus, the
problem can be efficiently solved and the proposed approach is
applicable to solve real-life problems. This is the first time such
an efficient method for this problem has existed to the best
knowledge of the authors.
There are several promising future research directions: to
extend the proposed approach to other scheduling problems
in the process industry, e.g., steel production and food processing; to develop software tools like Process Industry Modeling System at the planning level for the commercialization
of the proposed methodology; and to incorporate some
recent developments from big data and sustainable production into the proposed method.

Conclusions
A refinery is a large-scale and complex system containing both
discrete-event and continuous operations. Its scheduling problem is essentially combinatorial and extremely challenging. Due
to its continuous processes, the jobs to be scheduled are not defined and unknown at the beginning of the process. Therefore,
they need to be defined and sequenced during a scheduling process. Such a feature disables heuristics and metaheuristics methods that are widely used to schedule discrete manufacturing
processes. Prior studies attempted mathematical programming
methods to study its STSP. However, because of the huge computation requirement, they are not applicable to real-life applications. To solve this challenging problem, instead of using

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[5] Y. He and C.-W. Hui, "A binary coding genetic algorithm for multi-purpose process scheduling: A case study," Chem. Eng. Sci., vol. 65, no. 16, pp. 4816−4828, 2010.

Acknowledgments
This work is supported in part by the FCDT of Macau under
grants 065/2013/A2 and 066/2013/A2, and the NSF of China
under grant 61273036.
References

JUNE 2015

IEEE ROBOTICS & AUTOMATION MAGAZINE

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