www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 70 (2005) 333–339

Batch dispersion model to optimise traceability in food industry

C. Dupuy *, V. Botta-Genoulaz, A. Guinet

PRISMa laboratory, Institut National des sciences appliquees de Lyon, PRISMa––Batiment 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 Spongi-

form Encephalopathy (BSE) or foot-and-mouth disease,food companies try to limit incurred risk and to reassure

consumers. A good traceability system establishes pre-

cisely the history of composition and location of prod-

ucts 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 informa-

tion system point of view. We propose a new approachby improving traceability.

The problem under study tries to control the mixing

of production batches in order to limit the size, and con-

sequently the cost and the media impact of batches

0260-8774/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2004.05.074

* Corresponding author. Fax: +33 4 72 43 85 18.

E-mail address: cdupuy@prisma.insa-lyon.fr (C. Dupuy).

recalled in case of problem. Given a 3-level bill of mate-

rials (raw materials split into components assembled

into recipes), the objective is to minimize the manufac-

turing 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 optimizetraceability of this particular industrial case.

Traceability and batch dispersion stakes in food

industry are presented in Section 2. In Section 3, we de-

tail 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

334 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.

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 thisdefinition 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, process-

ing, distribution and sales (hereafter called chain trace-

ability) or internally in one of the steps in the chain

for example the production step (hereafter called inter-

nal traceability)’’.Two types of product traceability can be distin-

guished. Tracing is the ability, in every point of the sup-

ply 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 sup-

ply chain, to find the localization of products from one

or several given criteria. It is used in case of product re-call (Gencod EAN France, 2001). The distinction be-

tween these two traceabilities is important. Indeed, an

effective information system for one of these traceabili-

ties 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, trans-

formation. . .).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 isto say that no other unit can have the same (or compa-

rable) characteristic from the traceability point of view.

More concretely, a TRU corresponds to an identified

type of production batch. In the case of discrete pro-

cesses, 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 semanticmodel of their ontology and first order logic, they define

some fundamental rules for traceability:

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.

2.2. 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 disper-

sion (Dupuy, Botta-Genoulaz, & Guinet, 2002).

The downward dispersion of a raw material batch is

the number of finished product batches which containparts of this raw material batch. For example, if a

reception batch of ham is used in x batches of sau-

sages, 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 shoulderand three different batches of pork side will have an up-

ward 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, traceabil-

ity 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 con-

sumer with quality-labels obtained with an effective

traceability system. Moreover, nowadays many foodcompanies produce products sold with a retailer brand

name. Then, a good traceability system becomes an

important advantage for winning contracts by reinforc-

ing the credibility of the producer (speed of reaction,

precise identification of products).

Even when a good traceability system does not im-

prove the quality of products, it establishes the quality

of the company by tracing products, production pro-cesses 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 mea-

sures 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 ofinternal traceability in production companies:

C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339 335

• 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 afood safety crisis but it should reduce its consequences.

In case of crisis, the company must react quickly, accu-

rately and reliably. These are the three principal quali-

ties 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, dis-

tributed 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 multi-

brand 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 de-

crease recalls and the number of batches constituting agiven 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

3tons of contaminated meat. After this food safety

problem, the company not only improved the accuracy

of the traceability system but also decreased the numberof mixed batches of meat in one batch of minced beef

(Gattegno, 2001).

The problem studied here aims to minimize the quan-

tity 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 man-

ufacturing process in a French food company. Pork

meat industry is particularly interested in improving its

traceability (Liddell & Bailey, 2001). In order to producesausage, 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 sau-

sages (see Fig. 1).

Each type of raw material gives components in fixed

proportions. This is the disassembling (or cutting) bill ofmaterial. 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. Dur-

ing 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 bebought 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 opti-mization is an important factor.

Fig. 1. Industrial case, meat cut and sausage production.

336 C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339

We propose a graphical model to the dispersion prob-

lem (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 dis-persion problem under study presents three levels: raw

materials (meat), components (cut meat) and finished

products (minced meat). This model allows easy visual-

ization 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 finishedproduct 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 trans-

portation 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 ofrespectively raw material batches, component batches,

finished product batches and bought components

batches.

The objective function (1) allows calculating the min-

imum 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 con-

served. 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 quanti-

ties 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 equalto 1 if the raw material batch i is used in the finished

product batch k. Y(i,k) is not defined as a binary vari-

able 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

Table 2

Mathematical model

Minimize Z ¼XM

i¼1

XP

k¼1

Y ði; kÞ þXQ

l¼1

XP

k¼1

xBFðl; kÞ ð1Þ

BoMRCðTRMðiÞ; bÞ � QRMðiÞ ¼XN

j¼1jTCOMPðjÞ¼b

QRCði; jÞ 8i ¼ 1; . . . ;M ; 8b ¼ 1; . . . ; S; ð2Þ

BoMCFðb; T FPðkÞÞ � QFPðkÞ ¼XN

j¼1jTCOMPðjÞ¼b

QCFðj; kÞ þXQ

l¼1jTBCOMPðlÞ¼b

QBFðl; kÞ 8k ¼ 1; . . . ; P ; 8b ¼ 1; . . . ; S ð3Þ

QCOMPðjÞ ¼XM

i¼1

QRCði; jÞ 8j ¼ 1; . . . ;N ð4Þ

QFPðkÞ ¼XN

j¼1

QCFðj; kÞ þXQ

l¼1

QBFðl; kÞ 8k ¼ 1; . . . ; P ð5Þ

XP

k¼1

QCFðj; kÞ ¼ QCOMPðjÞ 8j ¼ 1; . . . ;N ð6Þ

XN

j¼1

QRCði; jÞ ¼ QRMðiÞ 8i ¼ 1; . . . ;M ð7Þ

xRCði; jÞ 6 QRCði; jÞQRCði; jÞ 6 xRCði; jÞ � Vhv

8i ¼ 1; . . . ;M ; 8j ¼ 1; . . . ;N ð8Þ

xCFðj; kÞ 6 QCFðj; kÞQCFðj; kÞ 6 xCFðj; kÞ � Vhv

8k ¼ 1; . . . ; P ; 8j ¼ 1; . . . ;N ð9Þ

xBFðl; kÞ 6 QBFðl; kÞQBFðl; kÞ 6 xBFðl; kÞ � Vhv

8l ¼ 1; . . . ;Q; 8k ¼ 1; . . . ; P ð10Þ

xRCði; jÞ þ xCFðj; kÞ 6 Y ði; kÞ þ 1 8i ¼ 1; . . . ;M ; 8j ¼ 1; . . . ;N ; 8k ¼ 1; . . . ; P ð11Þ

Table 1

Nomenclature

Data

BoMRC(a,b) proportion of component of type b given by a raw material of type a: this is the disassembling bill of materials

BoMCF(b,c) proportion of component of type b used in a finished product of type c: this is the assembling bill of materials

TRM(i) type of the raw material batch i

TFP(k) type of the finished product batch k

QRM(i) quantity of the raw material batch i

QFP(k) quantity of the finished product batch k

TCOMP(j) type of the component batch j

M number of raw material batches

N number of component batches

P number of finished product batches

Q number of bought component batches

S number of different types of components

Vhv Very high value

Variables

Y(i,k) variable equal to 1 if the raw material batch i is used in the finished product batch k and 0 otherwise

xBF(l,k) binary variable equal to 1 if the bought component batch l is used in the finished product batch k and 0 otherwise

xRC(i, j) binary variable equal to 1 if the raw material batch i is used in the component batch j and 0 otherwise

xCF(j,k) binary variable equal to 1 if the component batch j is used in the finished product batch k and 0 otherwise

QRC(i, j) variable which is the quantity of the raw material batch i used in the component batch j

QBF(l,k) variable which is the quantity of the bought components batch l used in the finished product batch k

QCF(j,k) variable which is the quantity of the components batch j used in the finished product batch k

QCOMP(j) variable which is the quantity of the component batch j

C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339 337

338 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 interest-ing 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 ¼XP

k¼1

Y ði; kÞ ð12Þ

U DISPðkÞ ¼XM

i¼1

Y ði; kÞ þXQ

l¼1

xBFðl; kÞ ð13Þ

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 com-

ponent 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 30s to find the global opti-mum for this sample with a 1.2GHz 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 con-

straints. Calculation has been stopped after 12h 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 vari-

ables. 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 variablesand 22,211 constraints. Industrial case cannot be pro-

cessed in a reasonable time: heuristics methods should

be foreseen. A simplified linear model with less charac-

teristics is under study.

Our problem is at least as complex as a transporta-

tion problem with fixed costs. The transportation prob-

lem with variable costs is polynomial solvable. Very few

heuristics have been developed for transportation prob-

lem with fixed costs. Branch and bound methods and

dynamic programming are generally used.

The proposed MILP model cannot be used to sche-

dule or plan production. Quantities of raw materialsand 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 componentbatches 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 pro-duction company, the MILP model showed that it is

better to concentrate the bought components in few fin-

ished 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 trace-

ability 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 ‘‘disassem-bling 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. Unfor-

tunately 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 solvedwithout the necessity to reduce the number of

variables.

C. Dupuy et al. / Journal of Food Engineering 70 (2005) 333–339 339

• The studied industrial case under study is character-

ised by a 3-level bill of material (raw materials, com-

ponents 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 differentways. Further, a given packaged product can be com-

posed 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 disper-

sion model.

• The MILP formulation aims minimizing the batch

dispersion. As we mentioned in Section 3, the purposeof 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 dis-

persions (12) and (13). It could be interesting to study

such a model.

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