(385c) A Multi-Grid Scheduling Model for Integrated Gasoline Blending Operations

Optimal scheduling of various
operations in a refinery offers significant opportunities for saving costs and
increasing profits. The overall refinery operations (Pinto et al. 2000) involve
three main segments, namely crude oil storage and processing, intermediate
processing, and product blending. Scheduling of crude oil operations has
received the most attention so far, but limited work exists on the scheduling
of product blending operations.

Gasoline is one of the most
profitable products of a refinery and can account for as much as 60-70% of
total profit. A refinery typically blends several gasoline cuts or fractions
from various processes to meet its customer orders of varying specifications. The
large numbers of orders, delivery dates, blenders, blend components, tanks,
quality specifications, etc. make this problem of blending and scheduling highly
complex and nonlinear. A heuristic treatment of the nonlinear blending and
complex combinatorics can lead to inferior schedules and costly quality
give-aways. Thus, scheduling using advanced techniques of mixed-integer
programming are imperative for avoiding ship demurrage, improving order
delivery and customer satisfaction, minimizing quality give-aways, reducing
transitions and slop generation, exploiting low-quality cuts, and reducing
inventory costs.

The early work on
this problem focused mainly on gasoline-blending planning rather than
scheduling. Some other work (Pinto et al., 2000) considered blending operations
in general. Jia and Ierapetritou (2003) proposed a continuous-time
event-based MILP formulation for scheduling gasoline-blending and distribution
operations simultaneously for fixed recipes. Mendez et al. (2006) presented both
discrete-time and continuous-time models for the simultaneous optimization of
blending and short-term scheduling. However, most past work considered
only select aspects of the full gasoline-blending problem. Recently, Li et
al. (2009) developed a single-grid slot-based continuous-time formulation for the
simultaneous treatment of recipe, blending, and scheduling. They incorporated several
problem features such as multi-purpose product tanks, non-identical parallel blenders,
one blender charging at most one tank at a time, etc. They also ensured the continuity
of blending rate during a run and developed a schedule adjustment procedure to
avoid solving nonconvex MINLP. However, their model proved inadequate for
solving large-scale practical problems, as it needs large computation time just
to obtain a feasible solution with large integrality gap. In addition, they
assumed unlimited component inventories during the scheduling horizon.

This paper
presents a new model for the integrated treatment of recipe, blending, and scheduling
of gasoline operations. Its main feature is the use of multiple partially
independent time-grids with unit-slots instead of a single common grid with
process-slots. While Susarla et al. (2008) have successfully demonstrated the
use of multiple grids without any mass balance error for multi-purpose batch
plants, the present problem involves continuous operations and changeovers in
multi-purpose product tanks. Our proposed model addresses these additional
complexities in a multi-grid framework and shows improved MILP relaxation. This
allows us to solve the larger problems much quicker than the model of Li et al.
(2009). In addition to all the problem features of Li et al. (2009), we also relax
the assumption of unlimited component inventories during the scheduling
horizon, and extend the schedule adjustment procedure of Li et al. (2009) to
avoid solving nonconvex MINLP problem. Lastly, we use the fourteen examples
from Li et al. (2009) to evaluate the performance of our new blending scheduling
model.

Keywords: gasoline;
blending; unit slots; scheduling; non-convex; mixed integer nonlinear
programming (MINLP)

References

Jia, Z. Y., Ierapetritou,
M., Mixed-integer linear programming model for gasoline blending and
distribution scheduling,  Ind Eng Chem Res, 2003, 42, 825-835.

Li, J., Karimi I.
A., Srinivasan, R., Recipe determination and scheduling of gasoline blending
operations, in print, AIChE J., 2009.

Mendez, C. A., Grossmann,
I. E., Harjunkoski, I., Kabore, P., A simultaneous optimization approach for
off-line blending and scheduling of oil-refinery operations, Comput Chem Eng,
2006, 30, 614-634.

Pinto J. M., Joly
M., Moro, L. F. L., Planning and scheduling models for refinery operations, Comput
Chem Eng, 2000, 24, 2259-2276.

Susarla, N., Li,
J., Karimi, I. A., A Novel Approach to Scheduling Multipurpose Batch Plants
using Unit-Slots, submitted to AIChE J., 2008.