(26h) Poultry Production Planning with Batch-Lines in the Agriculture Industry

Production
planning applied in live-stock growth (of fish, poultry, pork, beef, etc.) consider
the number of male and female animals (from the hatchery) to be placed into appropriate
spaces or facilities (farms) for the animals to properly grow (see Figure 1).
It considers, as example, the limitation of the different cages or assigned
enclosures for their growth in general separated by gender. In the proposed
live-stock planning model applied to the poultry production case, the placed
animals in cages or free-range spaces are grown considering these assigned
units as batch-processes with limited capacity of males or females and with a
varying growing-time of the animal batches.

 Figure 1. A unitary livestock production
system.

The network in Figure 1, a
unitary livestock production system used in poultry planning example, is
constructed in the UOPSS [1], [2] network and its objects are defined as: a)
unit-operations m for sources and sinks (

),
tanks or inventories (

),
batch-processes (

)
and continuous-processes (

)
and b) the connectivity involving arrows (→), inlet-ports i (

)
and outlet-ports j (

).
Unit-operations and arrows have binary and continuous variables and the ports
hold the states as process yields or qualities. Brunaud et al. [3] showed that
the UOPSS formulation was computational superior to STN [4], [5] and RTN [6] in
complex scheduling cases tested from the chemical production industry using
batch processes. See examples of a complete UOPSS formulation in Menezes et al.
[7] and Kelly et al. [8].

In the proposed model,
although the average time of the live growth is known (considering the poultry
growth), the common practice in the field is to spread the time-of-growing of
the animals in different assigned places to reduce two issues. The primary
issue is to avoid bottlenecks in the management of animals during their
slaughtering and in the further steps of processing at the industrial
processing plants. The secondary issue is to scale down the impact of the
different animal genetics, given that within the same gender, there are animals
demanding lower time-of-growing (when compared to the average time) and are
those animals that need more time to grow. When planning the live-stock growth
by distributing its total time in the different cages or enclosures, the
uncertainties related to the production, from the management/processing and
from the hatchery (incubator or breeding locations), are reduced or mitigated.

With the evolution of the
manufacturing into the Industry 4.0 age, there will be novel technologies to
automatically re-position the animals considering its successive weighting
steps (monthly in general). This check-to-reposition engine can be performed by
selecting animals with bad genetics in terms of growing to be dispatched to the
same time-of-growing cages. The animals with a good response to the growing
stages, i.e., with a high-quality DNA considering the yielded weights with
respect to the same environment (feed, water, resources, etc.) may be
re-positioned to cages with higher time-of-growing since these live entities
can reach higher final weights.

In the example of the
live-stock planning model, the assigned units to place the animals as batch-process-cages
are considered with limited capacity of males or females and with a
growing-time of the animal batches as seen in Figure 2. In the figure, an
example of the poultry production planning is constructed considering the male
(toms) growing-time from 16 to 20-months and the female (hens) from 13 to
17-months.

Figure 2. Poultry production
planning for growth of animals considering toms (male) and hens (female).

The optimization for the
proposed MILP in Figure 2 for 52-weeks as time-horizon with 1-week time-step
gives 20,937 K USD of profit for the growth. The problem is solved in 80.4
seconds with GUROBI 8.1.0
and > 3600 seconds with CPLEX 12.8.0 both at 1.0% of MILP relaxation gap
using an Intel Core i7 machine at 3.4 GHz (8 threads) with 64 GB of RAM. There
are 16,888 constraints (4,613 equality) for 5,895 continuous variables and
4,704 binary variables with 5,986 degrees-of-freedom in the problem (variables
minus equality constraints).

The Gantt
chart in Figure 3 shows the startups of the toms and hens growth in cages
considering the different types of growing-time batches for toms (16 to
20-months) and hens (13 to 17-months). The batch-processes representing the
toms and hens types of cages can be started up
continuously since they are considered a pool of cages from where the growth
batch-time is initialized by using the available resource cages in the PoolCages inventories.  

Figure 3.
Startups of the toms and hens procreation cages
considering the types of time-of-growing batches

The Gantt
chart in Figure 4 shows the PoolCages object that
represents the inventory of cages to start the live-stock production. The
inventory upper bound is two (2) cages ready for the growth per week. The
formulation here uses inventories to control the resources of cages in the out-port of the PoolCages inventory that connects holdups for the batch
startups (see Figure 2 the PoolCages object). It may be considered as
the capacity of workers or machinery limits to be modeled in a problem.

Figure 4. Startups of the
toms and hens cages considering the types of
time-of-growing batches.

The Toms-20 growth started
in week 5 (see Figure 4) where its cage is used and then released back to the PoolCages structure in week 24 as seen in Figure 5, i.e.,
identical to a closed renewable resource.

Figure 5. Cage free again for
the next growth batch in week 24 from the PoolCages
object Toms-20.

[1] Kelly JD. (2005). The
Unit-Operation-Stock Superstructure (UOSS) and the Quantity-Logic-Quality
Paradigm (QLQP) for Production Scheduling in The Process Industries. In
Multidisciplinary International Scheduling Conference Proceedings: New York,
United States, 327.

[2] Kelly JD,
Menezes BC. (2019). Industrial Modeling and Programming Language (IMPL) for
Off- and On-Line Optimization and Estimation Applications. In Large
Scale Optimization in Supply Chain & Smart Manufacturing: Theory &
Application. Ed. Marzieh Khaifirooz, Mahdi Fathi, Jesus Velasquez: New York, United States.

[3] Brunaud B, Amaran S,
Bury S, Wassick J, Grossmann IE. (2019).
Batch scheduling with quality-based changeovers. Computer & Chemical
Engineering. Just Accepted.

[4] Kondili
E, Pantelides CC, Sargent RWH. (1993). A General
Algorithm for Short-Term Scheduling Of Batch
Operations – I MILP Formulation. Computers & Chemical Engineering, 17,
211-227.

[5] Shah N, Pantelides CC, Sargent R. (1993). A General Algorithm for
Short-Term Scheduling of Batch Operations – IΙ. Computational Issues.
Computers & Chemical Engineering, 17, 229-244.

[6] Pantelides
CC. Unified Frameworks for the Optimal Process Planning and Scheduling.
Proceedings on the Second Conference on Foundations of Computer Aided
Operations. 1994, 253-274.

[7]
Menezes BC, Kelly JD, Grossmann IE, Vazacopoulos A.
(2015). Generalized Capital Investment Planning of Oil-Refineries using MILP
and Sequence-Dependent Setups. Computer & Chemical Engineering,
80, 140-154.

[8]
Kelly JD, Menezes BC, Grossmann IE. (2018). Successive LP Approximation for
Non-Convex Blending in MILP Scheduling Optimization using Factors for Qualities
in the Process Industry. Industrial Engineering Chemistry Research, 57 (32),
11076-11093.