Journal of Food Engineering 70 (2005) 333–339
www.elsevier.com/locate/jfoodeng
Batch dispersion model to optimise traceability in food industry
C. Dupuy *, V. Botta-Genoulaz, A. Guinet
PRISMa laboratory, Institut National des sciences appliquées de Lyon, PRISMa––Bâtiment Blaise Pascal,
7 avenue Jean Capelle, 69621 Villeurbanne Cedex, France
Received 5 October 2003; received in revised form 4 April 2004; accepted 6 May 2004
Available online 15 December 2004
Abstract
Facing many food safety crises, like BSE or foot-and-mouth disease, food companies try to limit incurred risk and to reassure
consumers. So today, the point is not only to trace the products efficiently but also to minimize recalls and the number of batches
constituting a given finished product. The problem studied concerns a sausage manufacturing process in a French food company. It
tries to minimize the quantity of recalls when products are characterized by a 3-level ‘‘disassembling and assembling’’ bill of
material.
Such a ‘‘dispersion problem’’, encountered in the food industry, has been modelled, solved and experimented. A mathematical
MILP model is proposed and the results of experiments obtained with LINGO software are presented.
2004 Elsevier Ltd. All rights reserved.
Keywords: Traceability; Food industry; Batch dispersion; MILP model; Food safety
1. Introduction
Facing many food safety crises, like Bovine Spongiform Encephalopathy (BSE) or foot-and-mouth disease,
food companies try to limit incurred risk and to reassure
consumers. A good traceability system establishes precisely the history of composition and location of products all along the supply chain. But such a system does
not decrease the amount of products recalled in case
of production batch mixing. Many papers in literature
approach traceability in a quality, modelling or information system point of view. We propose a new approach
by improving traceability.
The problem under study tries to control the mixing
of production batches in order to limit the size, and consequently the cost and the media impact of batches
*
Corresponding author. Fax: +33 4 72 43 85 18.
E-mail address: [email protected] (C. Dupuy).
0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfoodeng.2004.05.074
recalled in case of problem. Given a 3-level bill of materials (raw materials split into components assembled
into recipes), the objective is to minimize the manufacturing batch dispersion in order to optimize traceability.
A mathematical model is proposed and the results of
experiments obtained with LINGO software are
presented.
Such a ‘‘dispersion problem’’ has been encountered in
sausage industry. Companies working with meat are
particularly concerned with traceability and interested
in reducing some possible recalls, as we saw during the
mad cow disease. Our model has been used to optimize
traceability of this particular industrial case.
Traceability and batch dispersion stakes in food
industry are presented in Section 2. In Section 3, we detail and illustrate the ‘‘batch dispersion problem’’, using
industrial examples. In Section 4, we propose a mixed
integer linear programming model. The criterion to be
minimized is the sum of tracing and tracking dispersions
of all the raw material batches and all the recipe batches.
Finally, we present and comment the results obtained
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C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339
with this model and discuss its use and implementation
in the food industry in Section 5. Sample data used come
from a French cooked pork meat producer.
If a TRU is split up, the separated parts keep the
identification of the parent TRU.
If some TRUs are assembled, the identification of the
new TRU is different from the identifications of parent
TRUs.
2. Definitions and fundamentals
2.1. Traceability definitions
The ISO 8402 norm defines traceability as ‘‘the ability
to trace the history, application or location of an entity,
by means of recorded identifications’’ (ISO, 1995). Moe
(1998) proposes an interesting definition for traceability
in the batch production industry: he introduces in this
definition the notions of chain and internal traceability.
‘‘Traceability is the ability to track a product batch and
its history through the whole, or part, of a production
chain from harvest through transport, storage, processing, distribution and sales (hereafter called chain traceability) or internally in one of the steps in the chain
for example the production step (hereafter called internal traceability)’’.
Two types of product traceability can be distinguished. Tracing is the ability, in every point of the supply chain, to find origin and characteristics of a product
from one or several given criteria. It is used to find the
source of a quality problem (Gencod EAN France,
2001). Tracking is the ability, in every point of the supply chain, to find the localization of products from one
or several given criteria. It is used in case of product recall (Gencod EAN France, 2001). The distinction between these two traceabilities is important. Indeed, an
effective information system for one of these traceabilities is not necessarily effective for the other.
Kim, Fox, and Gruninger (1995) propose a quality
ontology where two fundamental concepts, Traceable
Resource Unit (TRU) and primitive activity, are
introduced.
TOVE quality ontology defines a primitive activity as
an activity which is not constituted of sub-activities.
Therefore, this is a basic operation (storage, transformation. . .).
A TRU is defined as a homogeneous collection of one
resource class that is used/consumed/produced/released
by a primitive activity in a finite, non-zero quantity of
that resource class. The TRU is a unique unit that is
to say that no other unit can have the same (or comparable) characteristic from the traceability point of view.
More concretely, a TRU corresponds to an identified
type of production batch. In the case of discrete processes, the batch identification is generally easy.
For Kim et al. (1995), a traceability system must be
able to trace the historic of products and activities, that
is to say TRU and primary activities. Using the semantic
model of their ontology and first order logic, they define
some fundamental rules for traceability:
2.2. Definition of batch dispersion
In order to evaluate the accuracy of the traceability in
the production process, we introduce new measures:
downward dispersion, upward dispersion and batch dispersion (Dupuy, Botta-Genoulaz, & Guinet, 2002).
The downward dispersion of a raw material batch is
the number of finished product batches which contain
parts of this raw material batch. For example, if a
reception batch of ham is used in x batches of sausages, then the downward dispersion will be equal
to x.
The upward dispersion of a finished product batch is
the number of different raw material batches used to
produce this batch. For example, salami produced with
components of two different batches of pork shoulder
and three different batches of pork side will have an upward dispersion equal to 5.
Finally, the batch dispersion of a system is equal to
the sum of all raw material downward dispersion and
all finished products upward dispersion.
2.3. Interests of traceability in food industry
In view of the numerous food safety crises, traceability has become a very important issue for most food
companies (Latouche, Rainelli, & Vermesch, 1999).
The setting up of an effective traceability system in the
food industry presents many interests. Traceability has
an obvious marketing interest in reassuring the consumer with quality-labels obtained with an effective
traceability system. Moreover, nowadays many food
companies produce products sold with a retailer brand
name. Then, a good traceability system becomes an
important advantage for winning contracts by reinforcing the credibility of the producer (speed of reaction,
precise identification of products).
Even when a good traceability system does not improve the quality of products, it establishes the quality
of the company by tracing products, production processes and quality controls. A traceability system may
also help to respect the legislation and to be reactive
to future laws. Finally, an efficient traceability system
should help to avoid unnecessary repetitions of measures on products. Measures made on components are
not necessary made for sub-products if production
batches are traced efficiently.
Moe (1998) also presents benefits of the setting up of
internal traceability in production companies:
C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339
• Possibility to increase production control.
• Indications to find relation of cause and effect in case
of non-compliant products.
• Limitation of the cost in case of mixture of good and
bad quality products.
• Ease of finding information for a quality audit.
• Ease of setting up information systems (production
management, stocks, quality. . .).
Even if a traceability system presents many interests,
it is often difficult to evaluate its return on investment.
Actually, the setting up of an efficient traceability system
takes all its interest in case of food safety crisis. A good
traceability system does not reduce the probability of a
food safety crisis but it should reduce its consequences.
In case of crisis, the company must react quickly, accurately and reliably. These are the three principal qualities of a good traceability system. This is a vital issue:
some food companies went bankrupt because of food
safety crises.
We can identify many interests of a good traceability
system in the case of a food safety crisis:
• Cost reduction (of time and staff) to search historic
and localization of products in case of problems.
• Cost reduction of product recall: there are fewer
products to recall if they are identified, the need to
recall already processed products (or even worse, distributed to the customer) is eventually reduced, and
the number of customers concerned decreases.
• Reduction of the number of brands or production
sites concerned by a recall for a multi-site or multibrand company.
• Reduction of the loss of consumer confidence in the
case of a serious food safety problem, showing that
the problem is under control.
2.4. New relevance of traceability
Nowadays, consumers constantly demand more in
terms of food safety. For example, they worry about
BSE (Bovine Spongiform Encephalopathy or mad cow
disease), dioxin or transgenic food. Today, the point is
not only to trace the products efficiently but also to decrease recalls and the number of batches constituting a
given finished product.
For example, a French producer of minced beef had
to call back products because a case of BSE was found
in raw materials. The company had to call back 37 tons
of finished products in the supermarkets because of only
3 tons of contaminated meat. After this food safety
problem, the company not only improved the accuracy
of the traceability system but also decreased the number
of mixed batches of meat in one batch of minced beef
(Gattegno, 2001).
335
The problem studied here aims to minimize the quantity of products recalled in the case of a problem in a
particular situation: with a 3-level ‘‘disassembling and
assembling’’ bill of material.
3. The batch dispersion problem
3.1. An industrial issue: the sausage industry
The problem under study comes from a sausage manufacturing process in a French food company. Pork
meat industry is particularly interested in improving its
traceability (Liddell & Bailey, 2001). In order to produce
sausage, this company cut pork meat in components like
ham, belly, loin, trimmings. . . Further in the production
process, these meat components are minced and mixed
to create minced meat batches. These minced meat
batches will be used to produce different types of sausages (see Fig. 1).
Each type of raw material gives components in fixed
proportions. This is the disassembling (or cutting) bill of
material. A component can also come from different raw
material types. The finished products (sausages) are
composed of several components in given proportions.
This is the assembling (or mixing) bill of material. During a working day, the company receives several batches
of different types of raw material (ham, side of pork,
shoulder. . .). So, many batches of component will be
created and also many finished product batches.
The purpose of the company is to minimize the cost
due to a food safety crisis. If the food safety problem
comes from a raw material batch, the company will
identify (tracing) and recall all products which contain
the raw material. If it concerns a finished product, the
company will identify (tracking) the raw material
batches and then recall all concerned finished products.
So, in order to minimize the cost of a food safety crisis,
the company have to minimize the number of recalled
products. In the case of sausage production, batch size
should be reduced but also batch mixing. The more
raw material batches are mixed in finished products
batches, the bigger the recall, and the cost.
The company tries to use the highest capacity of the
cutting production process: all received batches are cut
in components. But already cut components can be
bought from external suppliers.
3.2. A graphical model for dispersion problems
The batch dispersion problem does not concern only
the sausage production process. It may concern all the
production processes which associate disassembling
and assembling processes and in which traceability optimization is an important factor.
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C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339
Fig. 1. Industrial case, meat cut and sausage production.
We propose a graphical model to the dispersion problem (see Fig. 2) based on Gozinto graphs (Dorp, 2003;
Loos, 2001). Each node represents a batch and each
edge represents a link between two batches, if one batch
contains material coming from the other batch. The dispersion problem under study presents three levels: raw
materials (meat), components (cut meat) and finished
products (minced meat). This model allows easy visualization of downward and upward dispersions.
An analogy could be made between our problem and
a transhipment problem with fixed costs. The sources
represent the raw material batches, the transient nodes
the component batches and the destinations the finished
product batches. An arc models a disassembling or an
assembling link of a bill of materials. A cost is assigned
to each arc use. It is independent of the arc flow i.e. it is
fixed. The sum of links between raw material batches
and finished product batches (i.e. the sum of fixed costs)
is sought to be minimised. Such an analogy allows us to
conclude our problem is at least as complex as the transportation problem with fixed costs i.e. NP hard (Palekar
& Karwan, 1990).
Fig. 2. Graphical model of the dispersion problem.
4. Mathematical model
We propose a mathematical model to the dispersion
problem. Data and variables are presented in Table 1
and the model in Table 2. i, j, k and l are indexes of
respectively raw material batches, component batches,
finished product batches and bought components
batches.
The objective function (1) allows calculating the minimum batch dispersion. It is the sum of links between the
raw material batches and the finished product batches
given by Y(i, k) and the dispersion due to the bought
components xBF(l, k).
Disassembling bill of materials and assembling bill of
materials are given by Eqs. (2) and (3) respectively.
In the manufacturing process, quantity must be conserved. Constraints (7) express that the limited total
quantity of a raw material batch is used in component
batches, when constraints (4) state that the quantity of
a component batch comes only from raw material
batches.
Each finished product batch comes from component
batches and/or bought component batches; their quantities must also be kept (5). And each component batch is
entirely assembled in finished product batches (4).
Eqs. (8)–(10) express that the binary variables xRC,
xCF and xBF are equal to 1 if respectively QRC, QCF
and QBF are not null.
Eqs. (11) are used to determine Y(i, k) which is equal
to 1 if the raw material batch i is used in the finished
product batch k. Y(i, k) is not defined as a binary variable because it is minimized in the objective function
so it will automatically take the value 1 or 0. If both
xRC and xCF are equal to 1, the only possible value of
C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339
337
Table 1
Nomenclature
Data
BoMRC(a, b)
BoMCF(b, c)
TRM(i)
TFP(k)
QRM(i)
QFP(k)
TCOMP(j)
M
N
P
Q
S
Vhv
proportion of component of type b given by a raw material of type a: this is the disassembling bill of materials
proportion of component of type b used in a finished product of type c: this is the assembling bill of materials
type of the raw material batch i
type of the finished product batch k
quantity of the raw material batch i
quantity of the finished product batch k
type of the component batch j
number of raw material batches
number of component batches
number of finished product batches
number of bought component batches
number of different types of components
Very high value
Variables
Y(i, k)
xBF(l, k)
xRC(i, j)
xCF(j, k)
QRC(i, j)
QBF(l, k)
QCF(j, k)
QCOMP(j)
variable equal to 1 if the raw material batch i is used in the finished product batch k and 0 otherwise
binary variable equal to 1 if the bought component batch l is used in the finished product batch k and 0 otherwise
binary variable equal to 1 if the raw material batch i is used in the component batch j and 0 otherwise
binary variable equal to 1 if the component batch j is used in the finished product batch k and 0 otherwise
variable which is the quantity of the raw material batch i used in the component batch j
variable which is the quantity of the bought components batch l used in the finished product batch k
variable which is the quantity of the components batch j used in the finished product batch k
variable which is the quantity of the component batch j
Table 2
Mathematical model
Minimize Z ¼
M X
P
X
i¼1
Y ði; kÞ þ
Q X
P
X
l¼1
k¼1
xBF ðl; kÞ
N
X
BoMRC ðT RM ðiÞ; bÞ QRM ðiÞ ¼
ð1Þ
k¼1
QRC ði; jÞ
8i ¼ 1; . . . ; M; 8b ¼ 1; . . . ; S;
ð2Þ
j¼1jT COMP ðjÞ¼b
N
X
BoMCF ðb; T FP ðkÞÞ QFP ðkÞ ¼
QCF ðj; kÞ þ
j¼1jT COMP ðjÞ¼b
QCOMP ðjÞ ¼
M
X
Q
X
QBF ðl; kÞ
8k ¼ 1; . . . ; P ; 8b ¼ 1; . . . ; S
ð3Þ
l¼1jT BCOMP ðlÞ¼b
QRC ði; jÞ 8j ¼ 1; . . . ; N
ð4Þ
i¼1
QFP ðkÞ ¼
N
X
QCF ðj; kÞ þ
j¼1
P
X
Q
X
QBF ðl; kÞ 8k ¼ 1; . . . ; P
ð5Þ
l¼1
QCF ðj; kÞ ¼ QCOMP ðjÞ 8j ¼ 1; . . . ; N
ð6Þ
QRC ði; jÞ ¼ QRM ðiÞ
ð7Þ
k¼1
N
X
8i ¼ 1; . . . ; M
j¼1
xRC ði; jÞ 6 QRC ði; jÞ
QRC ði; jÞ 6 xRC ði; jÞ Vhv
xCF ðj; kÞ 6 QCF ðj; kÞ
QCF ðj; kÞ 6 xCF ðj; kÞ Vhv
xBF ðl; kÞ 6 QBF ðl; kÞ
QBF ðl; kÞ 6 xBF ðl; kÞ Vhv
8i ¼ 1; . . . ; M; 8j ¼ 1; . . . ; N
ð8Þ
8k ¼ 1; . . . ; P ; 8j ¼ 1; . . . ; N
ð9Þ
8l ¼ 1; . . . ; Q; 8k ¼ 1; . . . ; P
ð10Þ
xRC ði; jÞ þ xCF ðj; kÞ 6 Y ði; kÞ þ 1
8i ¼ 1; . . . ; M; 8j ¼ 1; . . . ; N ; 8k ¼ 1; . . . ; P
ð11Þ
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C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339
Y(i, k) is 1. If not, the value of Y(i, k) will be set to 0, due
to objective function.
With the proposed mathematical model, it becomes
easy to determine the downward dispersion of a raw
material batch or the upward dispersion of a finished
product batch by Eqs. (12) and (13). It could be interesting to know the downward dispersion of a given raw
material batch if for example this raw material presents
a high frequency of quality problems.
D DISPðiÞ ¼
P
X
Y ði; kÞ
ð12Þ
k¼1
U DISPðkÞ ¼
M
X
Y ði; kÞ þ
i¼1
Q
X
xBF ðl; kÞ
ð13Þ
l¼1
5. Results and comments
With M as the number of raw material batches, N as
the number of component batches, P as the number of
finished products batches, Q the number of bought component batches and S the number of different types of
components, the number of equations can be calculated:
M + 2N + P + MS + PS + 2MN + 2PN + 2PQ + MNP.
The number of binary variables is equal to QP +
MN + NP.
LINGO 6.0 software was used to solve the MILP
model. First, a sample of four raw material batches,
six component batches, four finished product batches
and two bought component batches has been used. This
sample generated 142 variables (56 integers) and 244
constraints. It took about 30 s to find the global optimum for this sample with a 1.2 GHz Pentium III PC
computer.
An other sample of eight raw material batches, 24
component batches, 12 finished product batches and
eight bought component batches has been processed.
It generated 1292 variables (576 integers) and 3684 constraints. Calculation has been stopped after 12 h before
finding a global optimum (about 50,000,000 iterations).
The best local objective found was equal to 73 with an
objective lower bound equal to 58 (the gap regarding
the lower bound is equal to 25.9%).
Actually, the industrial case presents even more variables. A real industrial sample, in a period of one day,
presents at least 20 raw material batches, 30 component
batches, 30 finished product batches and 10 bought
component batches, that is to say 1800 integer variables
and 22,211 constraints. Industrial case cannot be processed in a reasonable time: heuristics methods should
be foreseen. A simplified linear model with less characteristics is under study.
Our problem is at least as complex as a transportation problem with fixed costs. The transportation prob-
lem with variable costs is polynomial solvable. Very few
heuristics have been developed for transportation problem with fixed costs. Branch and bound methods and
dynamic programming are generally used.
The proposed MILP model cannot be used to schedule or plan production. Quantities of raw materials
and finished products are fixed and there is no time
variable. But the batch dispersion optimisation may be
useful for both operational and strategic decision
making processes.
On the operational point of view, the model can be
used after a production order planning. Given a sample
of raw material and finished product batches, our model
can estimate the best way to constitute component
batches with a minimum dispersion. In this way, the
sample of data could represent one day or one week of
production.
The model can also be used on a strategic level. New
finished product recipes can be tested on a traceability
point of view. Then, it becomes easier to determinate
if a given recipe induces high or low batch dispersion.
For example, for the case under study, a sausage production company, the MILP model showed that it is
better to concentrate the bought components in few finished products. New disassembling bill of material can
also be tested: this functionality was experimented and
used to determine new ways to cut meat or to group
different trimmings.
6. Conclusion and perspectives
As we showed in Section 2, the main interest of traceability is to manage food crisis. Food companies aim to
reduce the cost of recalls, in term of products quantity
and media impact. A way to reduce this cost is to reduce
batch size and batch mixing in order to reduce recalled
batch size. In the particular case of a 3-level ‘‘disassembling and assembling’’ bill of material, it becomes hard
to reduce batch dispersion. This particular case has been
encountered in the sausage industry. We propose a
mathematical model to reduce batch dispersion. Unfortunately such a model is too huge to be used daily in the
industry. However, it can be used with simplified
models. The model is also a base to compare results of
future heuristics.
Further researches can be undertaken:
• As we already discussed, the model is limited
because when the problem size increases it
becomes impossible to use it. One possible direction
for future research is to develop a heuristic algorithm
that could solve the problem in a reasonable time.
Then, the presented business case could be solved
without the necessity to reduce the number of
variables.
C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339
• The studied industrial case under study is characterised by a 3-level bill of material (raw materials, components and finished products). The dispersion model
proposed could be completed by adding a fourth
level, considering the packaging process. A given
product batch can be packaged in many different
ways. Further, a given packaged product can be composed of various product batches as, for example,
sausages with different meats or seasonings in the
same package. We can wonder if the model and the
results would be very different with a 4-layer dispersion model.
• The MILP formulation aims minimizing the batch
dispersion. As we mentioned in Section 3, the purpose
of the problem is to minimize the size of batch recalls
in case of food safety crisis. So the quantities of raw
materials and finished products could appear in the
objective function using upward and downward dispersions (12) and (13). It could be interesting to study
such a model.
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