(186b) Planuling: A Hybrid Planning and Scheduling Optimization to Schedule Slow and Plan Fast Processes

Planuling
is our term for combining planning and scheduling together within the same
future time-horizon. It is a portmanteau of planning and scheduling and may
also be classified as hybrid planning and scheduling given that within the same
time-horizon some units, machines or equipment are planned and others are scheduled.
This typically occurs when units with long run-lengths or time-constants are
optimized together with units with short run-lengths whereby determining a
greatest common factor would result in many small time-periods. This also
occurs when numerically integrating ordinary differential equations (ODE) and
is the phenomenon known as stiff-systems. Our novel approach to reduce the
number of time-periods and hence decrease the time to find good solutions is to
schedule the slow processes and to plan the fast processes with the
understanding or assumption that planning the short processes makes sense or is
appropriate. These types of situations are common in industry and occur when
large amounts of materials are produced in bulk operations and then need to be
packed into smaller amounts where the packing processes are much faster than
the bulking or batching operations. A specific example can also be found in
oil-refining when crude-oils are distilled and converted (refined) into many
diverse intermediate products in slower major processing units but are blended
into finished products such as gasoline, diesel and heating oil in faster
blending operations. From a mathematical formulation
perspective, we essentially allow the planuling model to contain both big-buckets
or planning time-periods (with a pile of production orders to be disaggregated) and small-buckets or scheduling time-periods.
Big-buckets are used for the fast unit-operations and small-buckets are used
for the slow unit-operations. Other examples of planuling other than bulking
to packing or refining to blending is smelting to casting, fermenting to
purifying, rolling to sheeting and batching to dispensing.

Figure 1 depicts a sample
flowsheet problem with a batch-process unit (BatchUnit), a continuous-process
unit (PackUnit) and three storage units (Tank1, Tank2, Tank3) drawn using the
unit-operation-port-state superstructure (UOPSS) [1], [2] and [3].

Figure 1.
Planuling UOPSS Flowsheet.

Based on the above planuling
discussion, the greatest common denominator is 1-hour and would require 24
times the matrix elements compared to our current implementation using 120
24-hour time-periods and enhancing the modeling to include our new planuling
formulation. The current matrix has approximately 11000 rows, 8000 columns of
which 4000 are binary, 30000 non-zeros. If we used a 1-hour time-period this
would require 120 * 24 = 2880 time-periods where the larger matrix would have
264000 rows, 192000 columns, 96000 binaries and 720000 non-zeros. Obviously,
planuling is able to drastically reduce the size of the problem provided that
planning and not scheduling of the fast unit-operations is sufficient for the
decision-making at hand.

Our new concept of planuling
is definitely novel and to our knowledge has not been presented previously. It
is a pragmatic procedure in the sense that for some faster units, they can be
planned instead of being scheduled with little loss in decision-making accuracy
or capability. It has the benefit of requiring significantly less matrix
elements and will translate into quicker solutions for what would previously be
intractable or insolvable APS problems. If necessary, as used in the example
below, a second level of scheduling can be performed to find the schedule of
the fast processes defined as planning inside the planuling optimization. In
this case, the total amount from the planning time-step containing the pile
of production orders are disaggregated within the faster or shorter time-grid
scheduling.

Figure 2 below is the Gantt
chart of the flowsheet found in Figure 1 configured in IMPL's IML file and
computed using GUROBI in about 3-seconds using 1-day time-periods. There is a
3-day past horizon where Batch2 starts 2-days before the start of the 120-day
future time-horizon. The batch-sizes and batch-times of the BatchUnit for
Batch1 are 2000 m³ and 2-days, Batch2 are 4000 m³ and
4-days and Batch3 are 5000 m³ and 5-days. The three tanks or pools
each have a capacity of 4000 m³ and open inventories of 2000 m³
each. The PackUnit has six operations Batch1Pack1, Batch1Pack2, Batch2Pack1,
Batch2Pack2, Batch3Pack1 and Batch3Pack2 with charge-sizes of 1200, 1200, 2400,
2400, 2400 and 2400 m³ respectively. These operations have a minimum
run-length of 11-hours and must not exceed 24-hours of continuous operation
i.e., they have a maximum run-length of 24-hours.

Figure 2. Gantt
Chart with 3-day and 120-day Past and Future Horizons.

[1] Kelly,
J.D., "Production modeling for multimodal operations", Chemical
Engineering Progress, February, 44, (2004).

[2] Kelly, J.D., "The
unit-operation-stock superstructure (UOSS) and the quantity-logic-quality
paradigm (QLQP) for production scheduling in the process industries", In:
MISTA 2005 Conference Proceedings, 327, (2005).

[3] Zyngier, D., Kelly,
J.D., "UOPSS: a new paradigm for modeling production planning and
scheduling systems", ESCAPE 22, June, (2012).