A Mixed Integer Linear Program for Operational Planning in a Meat

Packing Plant

ıctor M. Albornoz

, Marcela Gonz

alez-Araya

, Mat

ıas C. Gripe

and Sara V. Rodr

ıguez

Departamento de Industrias, UTFSM, Avda. Santa Mar

ıa 6400, Santiago, Chile

Departamento de Modelaci

on y Gesti

on Industrial, Universidad de Talca, Talca, Chile

Facultad de Ing. Mec

anica y El

ectrica, Universidad Aut

onoma de Nuevo Le

on, San Nicol

as de los Garza, M

exico

Keywords:

Production Planning, Meat Industry, Mixed-Integer Linear Program, Product Perishability, Meat Supply

Chain.

Abstract:

This paper reports a mixed integer linear programming model to support the planning at an operational level in

a meat packing plant. The deterministic formulation considers multi-products (yielded from different cutting

patterns applied to the carcasses), multi-periods, a batch quality distribution on carcasses and perishability.

The perishability of the product is modeled by the inclusion of disaggregated inventory decision variables that

take into account a given maximum number of days for fresh product. The main contribution of the present

work is to develop an optimization model in a real tactical planning problem. Also we develop a sensitivity

analysis on the quality of the carcasses, subject to large variability. We present here two different scenarios,

comparing them to asses their economical impact.

1 INTRODUCTION

Pork is the most produced and consumed meat world-

wide. In 2012, with a global production of approxi-

mately 109 millions of tonnes, pork continues to be

the most important protein source for humans (FAO,

2014). In recent years it has been observed that

most pork production is starting to be produced un-

der larger productive structures called Pork Supply

Chains. Inside these structures several complex prob-

lems are faced by the chain manager, who needs to

integrate the stakeholder operations in order to coor-

dinate the ﬂow of product through the chain. One of

the most challenging problems is that related to the

planning and scheduling of operations for processing

the carcass (body of the animal gutted and bloodless)

into pork and by-products, taking into account verti-

cal integration links.

Operations Research is one of the most important

disciplines that deal with advanced analytical meth-

ods for decision making. It is applied to a wide

range of problems arising in different areas and their

ﬁelds of application involve the operations manage-

ment of the agriculture and food industry. There are

several works related to these topics, see (Ahumada

and Villalobos, 2009) for a review of agricultural sup-

ply chains; see (Bjørndal et al., 2012) for a review of

operations research applications in agriculture, ﬁsh-

eries, forestry and mining; see (Higgins et al., 2010)

for an application of agricultural value chains using

network analysis, agent-based modeling and dynam-

ical systems modeling; In (Pl et al., 2014) the au-

thors draw insights for new opportunities regarding

OR for the agricultural industries; (Rodrguez et al.,

2014) presents a key description of the pork supply

chain and points out the existing gaps in this topics.

In particular, there are numerous references that

consider models and strategies using methodologies

such as linear optimization models, see e.g. (Ro-

drguez et al., 2012); integer programming, see e.g.

(Jena and Poggi, 2013); nonlinear, see e.g. (Henseler

et al., 2009) multiobjective, see e.g. (Annets and Aud-

sley, 2002); dynamic programming, see e.g. (Gigler

et al., 2002); stochastic programs, see e.g. (Ahumada

et al., 2012); robust, fuzzy, see e.g. (Biswas and Pal,

2005); optimum control models, see e.g. (Dong et al.,

2013); decision theory models, see e.g. (Zangeneh

et al., 2002). For more details about the listed pre-

vious methodologies see e.g. (Pardalos and Resende,

2002).

In this paper, we present a mathematical optimiza-

tion model to support the decision making process

that focuses on the processing phase of the pork pro-

duction process, taking into account a supply chain

254

M. Albornoz V., González-Araya M., C. Gripe M. and V. Rodríguez S..

A Mixed Integer Linear Program for Operational Planning in a Meat Packing Plant.

DOI: 10.5220/0005211102540261

In Proceedings of the International Conference on Operations Research and Enterprise Systems (ICORES-2015), pages 254-261

ISBN: 978-989-758-075-8

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

context. Regarding agricultural supply chains (ASC),

authors in (Ahumada and Villalobos, 2009) identiﬁed

four main functional areas: production, harvest, stor-

age and distribution. In this work, we want to handle

the production and storage ﬁrst, leaving distribution

for future work. For ”harvest” models especiﬁcally

applied to pork supply chains, see (Rodrguez et al.,

2009), regarding sow farms. In particular, we for-

mulate a linear mixed integer program (MILP) that

addresses decisions at the operative level of the pro-

cessing phase in a meat packing plant. In Section 2,

we outline some background information on the pork

industry through a literature review to frame and mo-

tivate our work. In Section 3 we describe the details

of the problem. Section 4 describes the mixed integer

linear programming formulation that, indicates how

often a cutting pattern is applied and on which type of

carcase, in order to keep a certain level of inventory,

meeting demand requirements and other storage ca-

pacities. Section 5 summarizes the computational re-

sults and ﬁnishes with a sensitivity analysis on some

stochastic parameters. Section 6 summarizes the main

conclusions and discusses future work.

2 LITERATURE REVIEW

The planning in a meat packing plant has been stud-

ied by several authors. Although most of the exist-

ing literature targets beef production, these contribu-

tions can also be applied to pork production as we

will show later. To the best of our knowledge, the

ﬁrst contribution was done by (Whitaker and Cam-

mel, 1990), who presented a linear programming for-

mulation of a partitioned cutting stock problem ap-

plied in a meat industry. The main feature of their for-

mulation is the partitioning of cutting patterns among

carcass sections that vastly reduces the number of cut-

ting patterns in the formulation. However, such model

was devoted to market planning purposes, and con-

sequently lacks elements that support the production

planning, such as inventory and time horizon, among

others.

Years later (Stokes et al., 1998) presents a contri-

bution for a Meat Packing Plant production plan, us-

ing a Mixed Integer Goal Programming formulation

to pursue multiple objectives, however such a model

does not take into account that in a given batch there

may be different types of carcasses, and variations in

some parameters. (Bixby et al., 2006) presents an in-

tegrated system of 45 linear programming models to

schedule operations in a real case for Swift & Com-

pany, a beef meat packing plant. Several thesis dis-

sertations have also been found in the literature. One

of these (Wikborg, 2008) develops online optimiza-

tion techniques for determining which cutting pattern

to use in each carcass according to both carcass at-

tributes and demand. (Reynisdottir, 2012) presents

a linear programming formulation to maximize the

value of pork products. (S

anchez, 2011) develops a

DEA study on some parameters and uses a planning

model to determine the levels of pork production by

product. (Sanabria, 2012) develops a planning pro-

duction model for a beef meat packing plant but with-

out including multi-periods.

Unlike the approaches existing in the literature,

the proposed model takes into consideration a plan-

ning horizon, different type of products, raw material

availability, and regards the quality and availability of

carcasses from pigs supplied. Also, our approach con-

siders the perishability issue through the modeling of

a speciﬁc variable that manages the freshness of meat,

and more importantly, we realize and consider the ex-

istence of different types of carcasses in a batch of

pigs. On the other hand, biological and economical

parameters in pork production systems are subject to

large variations (like the weight of the animal or its

fat content), but no previous study has assessed the

economic impact of these variations. Hence, our ap-

proach aims to cover some of the gaps found in the

literature related to the animal’s yield and its impor-

tance.

3 PROBLEM DESCRIPTION

The pork supply chain involves several operations for

producing pork and by-products from pigs. Usually

in an integrated structure each chain echelon is spe-

cialized in one or two productive operations. The fat-

tening farms are in charge of producing fattened pigs

ready to be slaughtered. Slaughter and packing op-

erations are usually developed in two facilities: the

Slaughterhouse and the Meat Packing Plant (MPP).

For our formulation lets assume that they are located

close to one another and are both part of a MPP. Every

day, a batch of fattened pigs arrive at the MPP facility

by truck. The truck is unloaded and the pigs are kept

in a pen waiting for the slaughtering time. Slaughter-

ing operations are straightforward; slaughter the en-

tire batch of pigs because inventory of pigs is not pos-

sible. Once the entire batch of pigs is slaughtered,

the carcasses (carcass means body of the slaughtered

animal with the head, limbs, blood and entrails re-

moved) are sent to a freezing storing room where the

carcasses are kept for a period of time in order to de-

crease carcass temperature. The carcasses are pro-

cessed forward to obtain several pork products and

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255

sub-products.

Pork production planning at operative levels in-

volves determining the production levels of each

product and its level of inventory. These decisions

depend on how to cut up the carcasses in order to sat-

isfy consumer demand. Several cutting patterns exist

in the market; each cutting pattern entails its corre-

sponding set of products, speciﬁc rewards and operat-

ing costs. It can be possible that different cutting pat-

terns share a common product, that means a speciﬁc

product can be obtained through different cutting pat-

terns, but the yield per product obtained is related to

the cutting pattern used. However, the yield per prod-

uct depends not only on the cutting pattern applied on

the carcass but also on the quality of the carcass (raw

material). Hence, it is important to select the right

cutting pattern for each type of carcass. This prob-

lem in an isolated way could be tackled through data

analysis, but in practical implementation, its interac-

tion with the demand makes it much more complex

to solve. In the production planning at the operative

level the chain manager must consider not only the

yield of products, and carcass availability, but also

the demand behavior. Demand behavior is not con-

stant through time, and moreover it is not homoge-

neous among all pork products, each product has its

own level of demand. Such issues are particularly rel-

evant in a disassemble problem like the production of

pork. There exists a set of pork products (from the en-

tire carcass) with a large demand while other products

have small or no market at all. Hence, the major dif-

ﬁculty is to balance the beneﬁts between demand and

production, while managing inventories of perishable

products. The main concern here is to determine the

number of times each cutting pattern is applied to the

available carcasses, and the levels of production ob-

tained for the entire list of products.

Large variability, uncertainty, perishability, large

scale of operations and large lead times are some is-

sues that most pork supply chain managers must face

at the operational level.

4 MATHEMATICAL

FORMULATION

This section provides a detailed description of the

mathematical formulation designed to solve the

described problem and also to support the decision

making at an operative level. Major decisions of

this model include the number of times each cutting

pattern must be applied on the available carcasses in

each period of time, the total yield per product and

its corresponding levels of inventory. It is assumed

that the company is willing to allow unsatisﬁed

demand, and it is this unsatisﬁed demand which

measures the level of demand to be covered by other

stakeholders (meaning the company must buy those

products from its competitors). The model addresses

these decisions using an objective function that seeks

to maximize the revenue of the producer, taking

into consideration different constraints to represent

demand requirements, inventory balance, cutting

pattern yields, shelf life of fresh products, balance

between the section of the animal, warehouse capaci-

ties and labor availability in the production process.

The proposed model considers the following notation:

Sets and indexes:

t ∈ T : Planning horizon (days).

j ∈ J

: Set of cutting patterns per sections.

j ∈ J: Set of the whole cutting patterns.

i ∈ P: Set of Products.

k ∈ K: Set of sections per carcass.

l ∈ L: Shelf life for fresh products.

: Selling price per fresh product i .

: Selling price per frozen product i.

: Operational cost of pattern j .

: Operational cost of pattern j in overtime.

: Freezing cost per kilogram.

: Holding cost of fresh product.

: Holding cost of frozen product.

CME: Holding cost by outsourcing.

: Penalization for unsatisﬁed-demand.

of fresh product

: Penalization for unsatisﬁed-demand.

of frozen product

: Freezing tunnel capacity at period t.

: Demand of fresh product i in period t.

: Demand of frozen product i in period t.

: Warehouse capacity for fresh products.

: Warehouse capacity for frozen products.

: Cutting-operation time for pattern j.

: Available work hours.

E: Available overtime hours.

i j

: Yield of product i in cutting patern j.

τ: Minimun period of time that a product.

must stay in the warehouse before sale.

: Carcasses available to process in each period.

Decision Variables:

: Number of times to perform the cutting

pattern j in period t in normal work hours.

: Number of times to perform the cutting

pattern j in period t, in overtime.

it(t+l)

: Quantity of fresh product i to process.

in period t to be sold at t + l

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: Quantity of frozen product i to

process in t.

: Quantity of fresh product i to be sold in t.

: Quantity of frozen product i to be

: Quantity of frozen product i to hold in t.

: Frozen capacity to outsource in period t.

: Total quantity of product i to be

processed in period t.

: Unsatisﬁed-demand of fresh product i in t.

: Unsatisﬁed-demand of frozen product i in t.

The objective of the mixed integer linear pro-

gramming presented here is oriented to maximize the

net proﬁt. The net proﬁt is obtained by calculating

the difference between the incomes from selling the

products yielded by the cutting patterns, minus the

operational costs incurred. These operational costs

involve inventory, freezing costs, unsatisﬁed-demand

penalties and labor costs to perform the cutting-

patterns. Final output includes fresh and frozen

products.

max

∑

+ p

− u

−CM

) −

∑

+ s

) −

∑

t j

+ c

) − (1)

∑

itl

(CM

it(t+l)

) −

∑

CMEc

The optimal solution of the model satisﬁes a

different set of constraints described next.

Carcass Availability. Cutting patterns are parti-

tioned into sections in order to reduce the number

of different patterns, as explained by (Whitaker and

Cammel, 1990). Thereby, the carcass can be cut in

different sections, and for each section a different cut-

ting pattern can be applied. These constraints ensure

a balance between cutting patterns and the number of

carcasses. Equality is forced because of the infea-

sibility of leaving unprocessed raw material, due to

perishability issues.

∑

j∈J



+ z



∀t ∈ T, ∀k ∈ K, (2)

Cutting Patterns Yield. In the pork industry, dif-

ferent cutting patterns can be applied on the carcass to

make different products. A cutting pattern is therefore

deﬁned by a combination of a set of products and their

respective yields. It is assumed that a speciﬁc product

can be obtained from different cutting patterns, but

not from different sections. In reality, this might not

be the case in some speciﬁc products, such as skin,

bones, and trimming. The following constraint calcu-

lates the total number of products, retrieved from all

the cutting patterns applied in each period.

∑

j∈J

i j



+ z



∀i ∈ P, ∀t ∈ T, (3)

Available Daily Work Hours. These constraints

ensure that the labor time does not exceed the viable

working hours.

∑

j∈J

≤ T

∀t ∈ T (4)

∑

j∈J

≤ T

∀t ∈ T (5)

It is recognized that the pork industry works with

perishable products subject to spoilage. In order to

extend the life of the product, it undergoes a freezing

process. Thereby, a product can be sold in two pre-

sentations, fresh and frozen. A product is considered

fresh if it is sold within 4 days after elaboration. On

the other hand, frozen products can be kept for almost

2 years. However, the proﬁt of selling frozen products

decays considerably.

Fresh and Frozen Balance: This constraint de-

termines the amount of product to be frozen and the

amount to keep fresh to be sold in the next period.

∑

l∈L

it(t+l)

+ x

∀i ∈ P, ∀t ∈ T (6)

Fresh Product to be Sold. As mentioned, fresh

products are not allowed to be kept for more than 4

days. Constraint (7) calculates the total amount of

fresh products that can be sold in a period t, but were

produced in previous periods.

∑

l∈L

i(t−l)t

∀i ∈ P, ∀t ∈ T (7)

Frozen Product to be Sold. Fresh products need

to stay at least 2 days in the freezing tunnel, to be

considered frozen. The following constraint balance

the inventory of frozen products for each period.

= I

i(t−1)

+ x

i(t−τ)

− I

∀i ∈ P, ∀t ∈ T (8)

Demand of Frozen Products. Ensures that the

requested level of each frozen product is adressed, al-

lowing the existence of unsatisﬁed-demand if the raw

materials are insufﬁcient.

+ d

= D

∀i ∈ P, ∀t ∈ T (9)

Demand of Fresh Products. Ensures that the

requested level of each fresh product is adressed,

allowing the existence of unsatisﬁed-demand if the

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raw materials are insufﬁcient.

+ d

= D

∀i ∈ P, ∀t ∈ T (10)

Freezing Tunnel Capacity. Fresh products need

to be processed in a freezing tunnel in order to be-

come frozen. The following constraint ensures that

the capacity of this tunnel is never exceeded.

∑

i∈P



i(t−1)

+ x



≤ CT

∀t ∈ T (11)

Fresh Products Warehouse Capacity. Ensures

that the capacity for holding fresh products is never

exceeded.







∑

l=1

∑

+l≤L

i(t−l)(t+l)

∑

i∈P

∑

l=1

it(t+l)







≤ CI

∀t ∈ T

(12)

Frozen Products Warehouse Capacity. Ensures

that the capacity for holding frozen products is never

exceeded.

∑

i∈P

≤ O

+CI

∀t ∈ T (13)

Decision Variables Nature. z

≥ 0 and z

≥

0 are integer variables. The rest of the decision

variables are all continuous and non-negative i.e.

it(t+l)

≥ 0, x

≥ 0, v

≥ 0, I

≥ 0, c

≥ 0,

≥ 0, d

≥ 0.

We now explore the proposed model described by

developing experiments, in order to gain knowledge

about its sensitivity when changing some parameters.

5 COMPUTATIONAL RESULTS

In this section a case study is presented in order to il-

lustrate the suitability and advantages of the proposed

optimization model. Instances solved consider 17 dif-

ferent types of pattern, 10 planning periods and a to-

tal of 40 products. This results in a model with 4351

variables, 340 of them integer and 2550 constraints.

All instances of this case were solved using a PC

with Windows 7, i5-3210M CPU @ 2.5GHz and 8Gb

RAM. The modeling software used was IBM ILOG

CPLEX Optimization Studio 12.2 with an academic

license.

Basic parameters were created using market infor-

mation gathered from different pork producers, such

as prices, costs and capacities. Most countries use dif-

ferent patterns producing various products according

to their history and gastronomic culture. In this case,

we opted to use the patterns used by a given Mex-

ican pork ﬁrm. Pork carcasses were split up into 5

sections, and for each section a set of cutting patterns

was assigned. In total, the company operates with 17

cutting patterns, and manages 40 pork products with-

out taking into account the products derived from the

skin, head, trotters, tongue and visceras.

The ﬁrst instance represents a batch of 300 fat-

tened pigs arriving everyday to the meat packing plant

during a horizon period of 10 days.The labor capacity

is considered as 8 hours per day. Moreover, it is also

assumed that the demand is given, and the available

amount of carcasses is ﬁxed and known. One of the

most important and relevant aspects of the model is

that it gives the option to operate with different types

of carcasses. It is assumed that the company oper-

ates with a batch of homogeneous carcasses with av-

erage yield and average fat content. Table 1 considers

5 different types of carcasses, where instance C corre-

sponds to the most common type of carcass, and the

rest are modiﬁcations of the previous with a greater

or lower fat content. Each case has a different group

of possible cutting patterns, according to their quality,

and different sets of possible products.

Table 1: Instance composition.

Cases Description Fat Content

A Excellent meat 1.44%

B Exc-Average meat 3.78%

C Average meat 6.05%

D Ave-low yield meat 8.264%

E Low meat 10.44%

In the current work we will focus on the possi-

ble variations of the carcasses. Different types of car-

casses can be deﬁned by a combination of quality (fat

content) and total yield. Table 2 lists the results of the

instances deﬁned above; the ﬁrst column shows the

optimal value achieved, the second column represents

the percentage of demand met. The third column rep-

resents the percentage of utilization of the warehouses

for frozen and fresh products. And the fourth repre-

sents the labor usage of work hours. The results show

that the rewards increase as the quality of the carcass

increases, as we expected, but also the facilities and

labor capacity have better usage. In Europe and the

USA, fattened pig producers receive a bonus for better

quality of carcasses, but there are some Latin Amer-

ican countries that don’t even evaluate their raw ma-

terial quality. This study suggests that pork producers

can have a bigger beneﬁt if they process high quality

carcasses. The difference between the objective value

of instance A and the objective value of instance E is

around 10%, thus showing a great ﬁnancial increase

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by having carcasses with better yields. These results

suggest that the model responds to changes in the

quality. Processing higher quality carcasses not only

increases the meat yield, but also gives the producer

the chance to sell high quality lean products, mak-

ing them more competitive in the market and giving

them access to different markets. The increments in

the objective functions are explained because higher

quality carcasses give more revenue to the producer

as he spends less time cutting to produce more quan-

tity of meat, and thus he can fulﬁll demand require-

ments more efﬁciently. It is shown that better quality

can give differences up to 10% more proﬁt. Labor

is equal to employment but the use of facilities is re-

duced by 10%. Table 3 lists the results for the number

of times the cutting patterns are applied, in each case.

In the low quality cases, E and D, some patterns tend

to disappear completely, 4 and 5 respectively, while

other patterns reach their peak of usage, for exam-

ple pattern number 11. This clearly shows that some

patterns are better ﬁtted to a certain type of carcasses

than another.

Table 2: Results.

Instance Opt.Value Demand Facilities Labor

A +2.5% +3.6% -9% +0%

B +2.5% +1.2% -4% +0.1%

C 5,875,821 83% 91% 91%

D -3% -1% +2% +0%

E -7% -3% +2% +0%

Table 3: Applied number of patterns for the ﬁrst instance.

Pattern A B C D E

1 654 536 492 502 517

2 1012 1133 1250 1250 1239

3 834 831 758 748 744

4 45 21 12 0 0

5 807 851 884 930 994

6 1648 1628 1604 1570 1506

7 65 66 68 62 55

8 753 758 768 468 451

9 171 143 159 177 197

10 1511 1533 1505 1793 1797

11 2435 2458 2500 2451 2500

12 65 42 0 49 0

13 1856 1852 1844 1830 1813

14 644 648 656 670 687

15 1266 1266 1266 1317 1400

16 2683 2682 2682 2617 2151

17 1006 1006 1005 1006 1005

Next, a second set of experiments is developed.

In reality the batch of pigs arriving at the meat pack-

ing plant facilities is not composed of homogeneous

pigs. This is so, because the fattening process of a

pig is very variable, pigs dont grow at the same rate

and they have different feed conversion rates. Phys-

ically, these issues are reﬂected by the presence of

heterogeneous pigs in the fattening batch, those pigs

have different weight and carcass compositions. Al-

though homogeneity is a highly demanded aspect by

the chain manager for better control production, most

producers just rely on the weight of the animals as a

reference to calculate their proﬁts, though the hetero-

geneity in the quality of carcasses in the batch can not

be denied. Carcass composition is only known after

slaughter, and even if pigs do have similar weights

they may present different carcass composition. The

meat yield per product depends on the carcass com-

position. Hence, it is important to study the impact

of different distributions of carcass composition and

which cutting pattern is more worthwhile for each

type of carcass. One of the most important and rel-

evant aspects of the model is that it gives the option

of operating with different types of carcasses. Work-

ing with different types of carcasses at the same time

seems to add complexity to the model, as the reso-

lution time for these cases rises up to a max of 10

seconds in average.

Table 4: Composition of pattern yield for the 2nd instance.

Instance Description

F 50% A and 50% C

G 50% E and 50% C

H 33% A 34% C 33% E

I 20%A 20%B 20%C 20%D 20%E

Table 4 lists a set of instances based on different

distribution of carcasses, while table 5 lists the set of

corresponding results. The results for these instances

are similar to the ﬁrst set; the instances with better

quality of carcasses always have the highest values

for the objective function, and better operational indi-

cators, showing that in fact the quality of carcasses is

very important to the revenue of these types of pro-

ducers.

Table 5: Results for the 2nd instance.

Instance Obj.Value Demand Facilities Labor

F 5.917.113 82% 86% 61%

G 5.589.634 81% 87% 60%

H 5.746.693 81% 85% 43%

I 5.909.373 81% 95% 28%

Finally, we develop some sensitivity analysis on

critical parameters, such as the number of processed

animals, in order to observe the economic and tech-

nical impact of having the ﬂexibility to choose the

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number of raw materials to process. To study this,

we changed the ﬁxed number of carcasses in each pe-

riod to a decision variable, so the model could choose

the optimal number of raw materials for each time pe-

riod. This analysis is raised regarding the parameter

. Model (1) - (13) assumes that H

is given and

known for every period. Now, we consider H

as a

decision variable and we add a new constraint impos-

ing that the sum of this variable does not exceed the

original amount of available carcasses throughout the

time horizon.

Table 6: Value of H in each period of time.

Horizon H

1 461

2 309

3 262

4 398

5 374

6 360

7 188

8 272

9 73

10 169

Results in table 6 show that variable H

is mainly

inﬂuenced by the demand, and only orders the number

of pigs that are really needed. The optimal value of

this instance increases the economic reward by 10%

with respect to the most common case (Instance C).

Also, the inventory level of ready to sell products de-

creases by 12%, due to a better usage of the different

warehouses capacities, because here the producer is

not forced to use all the material coming to the slaugh-

ter house, so the model can make a better ﬁt of the

demand and sales.

6 CONCLUSIONS AND FUTURE

RESEARCH

In this paper we proposed and validated a mixed inte-

ger model for production planning in the meat indus-

try. The objective of this paper, besides developing a

model that incorporates aspects that were not present

in the current literature, was to extrapolate some op-

erational policies and advices for producers and farm

growers. We accomplish this through the interpre-

tation of the results obtained from the presented in-

stances.

The results explained in the previous sections

show that the formulated model is highly applicable

due to low resolution times (it can be solved using

commercial software) and the easy valuable informa-

tion an employee can extract from it, making the pro-

duction planning more efﬁcient. However, for larger

instances of the model, ones with more periods, prod-

ucts and patterns, we can’t assure yet that it will be

solvable, because of the exponential growth of the in-

teger variables. Although the instances tested here

were developed to ﬁt the reality of the industry, larger

cases can exist in reality, due to the variable size of

the patterns available across different countries.

According to the results obtained from the experi-

ments with different quality carcasses, our suggestion

is that producers and farmers should develop a quality

system to guarantee the yields (more than the weight)

of the raw material that they sell/work with, to ensure

satisfying levels of revenue for both. The difference

between the objective function and the other opera-

tional indicators are signiﬁcant enough to make ef-

forts towards this area, obtaining better usage of their

machinery, man-labor, time available and demand ful-

ﬁllment.

Future research in this area should go towards

the development of a stochastic model that takes into

account probabilites for different types of arriving

batches, to make the production planning more ro-

bust. Also, efforts should be made to test the com-

plexity of the model as available cutting patterns

grow.

ACKNOWLEDGEMENTS

This research was partially supported by CONICYT,

Departamento de Relaciones Internacionales ”Pro-

grama de cooperacin Cientﬁca Internacional (Grant

PPCI 12041), DGIP of Universidad Tcnica Federico

Santa Mara (Grant USM 28.13.69) and CIDIEN of

the Departamento de Industrias, Universidad Tcnica

Federico Santa Mara. Matas C. Gripe wishes to ac-

knowledge Graduate Scholarship from DGIP.

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