Jean-Antoine Désidéri

A quasi-Riemannian approach to constrained optimization

Keywords: differentiable parametric optimization, nonlinear constraints, Newton's method, BFGS method, Riemannian method optimisation paramétrique différentiable, contraintes nonlinéaires, méthode de Newton, méthode BFGS, méthode riemannienne

A quasi-Riemannian approach is developed for constrained optimization in which the retraction and transport operators are only approximate. If n is the dimension of the admissible domain, and p the number of scalar equality constraints, the iteration is expressed in terms of a vector of reduced dimension n -p lying in the subspace tangent to the constraint manifold as optimization variable, whereas the minimized function is evaluated at a point, after retraction, that is approximately on the constraint manifold. Precisely, if h is the norm of the tangent vector, the distance between the point of evaluation of the function to be minimized, after retraction, is in general O(h 4 ), while it would only be O(h 2 ) if retraction were not applied. The construction only requires evaluation procedures for constraint functions and their gradients to be provided, and eludes the necessity of curvature information.

Introduction

In differentiable optimization, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [START_REF] Fletcher | Practical methods of optimization[END_REF] is one of the most efficient methods for unconstrained problems. Besides function values, it only requires the specification of the gradient. An approximate Hessian is calculated by successive approximations as part of the iteration, using rank-1 correction matrices. As a result, the iteration has superlinear convergence rate: when minimizing a quadratic function in n variables, if the one-dimensional minimizations in the calculated directions of search are done exactly, the Hessian matrix approximation is exact after n iterations, and from this, the iteration identifies to Newton's iteration, and produces the exact local optimum in only one additional iteration (n + 1 in total). However the BFGS method does not extend to constrained problems very simply. Following Gabay [START_REF] Gabay | Minimizing a differentiable function over a differential manifold[END_REF] and other authors, Chunhong Qi et al [START_REF] Qi | Riemannian BFGS algorithm with applications[END_REF] have proposed a "Riemannian" variant, RBFGS that indeed incorporates equality constraints in the formulation and actually demonstrates superior convergence rates for problems with a large number of variables. However these Riemannian formulations are complicated to implement since they require procedures implementing non-trivial differential-geometry operators ("retraction" and "metric transport") to be developed. In their paper, they assume a formal expression of the constraint to be known. But, in PDE-constrained optimization, many constraints are functional, and it is not clear how can the metric transport operator in particular can be defined.

In this report, a quasi-Riemannian method is defined based on the sole provision of evaluation procedures for the constraint functions and their gradients. By condensing all the equality constraints in one, a purely-explicit approximate retraction operator is defined that yields a point whose distance to the constraint manifold is fourth-order at least. The associated transport operator is approximated. The evaluation of its formal order of accuracy will require further investigation.

Method construction

One considers the following constrained-optimization problem:

min x∈Ωa f (x) subject to: g(x) = 0 (1)
where Ω a ⊆ R n is an open admissible domain in which the function f to be minimized is smooth, say C 2 , as well as the p components of function g : Ω a → R p .

The constraint functions are assembled in one single "compound constraint function":

γ(x) = 1 2 g(x) t g(x) = 1 2 p j=1 g j (x) 2 (2)
The following notations are introduced:

x: starting point; this point is the kth iterate of an outer-loop iteration for the minimization of function f (not specified in this report) by some gradient-based optimization method, such as the BFGS method [START_REF] Fletcher | Practical methods of optimization[END_REF]; by assumption, at this point, the constraints are satisfied: g j (x) = 0 (j = 1, . . . , p);

N : subspace orthogonal to the constraint manifold at x; this subspace is spanned by the constraint gradients at x, {∇g j (x)} (j = 1, . . . , p); these vectors are assumed to be linearly independent ("constraint qualification"); through a Gram-Schmidt orthogonalization process, two-by-two orthogonal unit vectors, {ω n-p+1 , . . . , ω n } spanning the same subspace are calculated and the following n × p matrix is formed:

Ω N =      ω 1,n-p+1 . . . ω 1,n ω 2,n-p+1 . . . ω 2,n . . . . . . . . . ω n,n-p+1 . . . ω n,n      (3)
T : subspace tangent to the constraint manifold at x; T and N are supplementary subspaces; T is defined by completion of the orthonormal basis {ω j } (j = 1, . . . , n); the tangent subspace is the range of the following n × (n -p) matrix:

Ω T =      ω 1,1 . . . ω 1,n-p ω 2,1 . . . ω 2,n-p . . . . . . . . . ω n,1 . . . ω n,n-p      (4)
x = x + y; y ∈ T : search variable in the minimization procedure ;

x⊥ : orthogonal projection of x onto the constraint Riemannian manifold; this theoretical point is not actually calculated in practice;

xN : the result of one iteration of the (exact) Newton method for the minimization of function γ(x), initiated at x by using the Hessian matrix evaluated at x; also not calculated;

xQN : the result of one iteration of the (approximate) Newton method for the minimization of function γ(x) initiated at x by using an approximate Hessian matrix H evaluated at x.

These notations are illustrated in Figure 1. This figure has been drawn to scale in a particular case in which f depends on only 2 variables and g is scalar and quadratic.

Note that xN is a theoretical point that will not be computed in practice since the second derivatives of the constraint functions are not assumed to be available. The actual point of evaluation of f will be xQN . This point will be defined precisely by approximation of these second derivatives as follows.

At x, the constraint gradients are again evaluated, as well as N spanned by the local constraint gradients, {∇g j (x) }, and the supplementary subspace T is also identified.

We define the support of vector ------→ ( xQN , x) to be N , whereas vector ----→ (x ⊥ , x) is orthogonal to the constraint manifold at the theoretical point x⊥ ; point xN is situated in the neiborhood of point x⊥ ; however its exact location depends on the unknown first and second derivatives of the constraint functions at x, whereas the location of point xQN relatively to point x only depends on first derivatives.

Recall the following expressions for the gradient and Hessian of the compound constraint function at some arbitrary point:

∇γ = j g j ∇g j ∇ 2 γ = j ∇g j (∇g j ) t + g j ∇ 2 g j . (5)
Consequently, specifically at points x as well as x⊥ at which g = γ = 0, one has:

∇γ = 0 ∇ 2 γ = j ∇g j (∇g j ) t . (6)
Let: In what follows, an order-of-magnitude analysis is conducted in which h is considered as infinitesimally small.

h = x -x . (7) Inria (a) Overview y (x 1 ) T 1 x z (x 2 ) ∇g N g = γ = 0 • • x⊥ • x = x + y T N ∇g • xQN z • xN • ξ τ η (b) Zoom
To elaborate a Riemannian-type optimization method, one should reduce the optimization variable to an (n -p)-vector, denoted y T hereafter. In this reduction, one retains a vector tangent to the constraint manifold at x:

y = Ω T y T (8)
and the (n -p) components of vector

y T = (y 1 , y 2 , . . . , y n-p ) t (9)
are from now on new optimization variables in the course of one (or several) BFGStype iteration(s) devised to minimize f in an outer loop using x (at which y T = 0) as starting point.

One lets:

x = x + y (10)
and one considers the theoretical point xN , not calculated in practice, that would be obtained by application of one iteration of Newton's method for the minimization of the constraint compound function γ initiated at point x, by solving the following equation:

0 = ∇γ + ∇ 2 γ ( xN -x) (11)
where, and from now on, it is convened to indicate evaluations at x by overlined symbols. Recall that

∇ 2 γ = j ∇g j ∇g j t + ḡj ∇ 2 g j = H + O(h 2 ) (12)
where one has let:

H = j ∇g j ∇g j t . (13)
The effective calculation of xN would require the knowledge of the constraint Hessian at x, and we precisely exclude this. Instead, we calculate xQN from point x by one iteration of a "quasi-Newton's method" defined as follows:

0 = ∇γ + H ( xQN -x) . ( 14
)
This equation requires some precisions to be made, since matrix H is singular. At point x, the constraint gradients {∇g j } (j = 1, . . . , p) are assumed to be linearly-independent. They span the subspace N . Vector ∇γ belongs to this subspace. The range of the linear operator associated with matrix H itself lies in this subspace. By algorithmic choice, we force vector

z = xQN -x (15)
to belong to N . So to speak, one solves (14) in this subspace. For this, the orthogonal decomposition of R n = T ⊕ N is performed at x and the vectors {ω n-p+1 , . . . , ωn } spanning N are defined, and one lets:

z = p k=1 ζ k ωn-p+k = Ω N ζ (16)
where:

ζ = (ζ 1 , ζ 2 , . . . , ζ p ) t (17)
is the unknown vector. The definition of matrix H given in (13) implies that:

H ( xQN -x) = Hz = p j=1 p k=1 ∇g j t ωn-p+k ζ k ∇g j (18)
whereas the right-hand side vector in ( 14) is also expressed in the family of constraint gradients:

∇γ = p j=1 ḡj ∇g j . (19)
Hence ( 14) admits a unique solution in N given by the solution z N of the following linear system:

∀j : p k=1 ∇g j t ωn-p+k ζ k = -ḡ j (20)
or, equivalently:

C ζ = -ḡ (21)
in which matrix C is p × p and its elements are the following scalar products:

Cj,k = ∇g j t ωn-p+k . (22)
This completes the definition of point xQN , shortly denoted x hereafter, whose distance to the constraint manifold will be evaluated in terms of h subsequently. In this way, an approximate "retraction operator" x → x has been defined. To complete the definition of a Riemannian method, here an approximate one, one should also define a "metric transport operator" [START_REF] Gabay | Minimizing a differentiable function over a differential manifold[END_REF] to evaluate the gradients at x. A proposition for this is made below, but further investigation is still required to assess it precisely.

Matrix C and vector ḡ are evaluated at point x = x+y. These elements depend on y = Ω T y T . Hence, by differentiating with respect to y, one obtains:

Cy ζ + C ζ y = -ḡ y . (23)
In this report, and prior to further analysis, it is assumed that neglecting the first term in the above, which reflects the variation of the matrix, is legitimate. Accordingly:

C ζ y . = -ḡ y (24) that is, C dζ . = -∇g Ω T dy T ( 25
)
and finally:

C ζ y T . = -g Ω T ( 26
)
in which the Jacobian matrix ζ y T is, by definition, the following:

ζ y T =    ζ 1,y1 . . . ζ 1,yn-p . . . . . . . . . ζ p,y1 . . . ζ p,yn-p    (27)
and ζ i,yj = ∂ζ i /∂y j . Equation ( 26) provides an approximation of the "transported gradient".

Let us examine the dimensions of the various terms appearing in ( 21) and (26):

• matrix C: p × p;

• vector ζ: p × 1;

• vector y T : (n -p) × 1;

• Jacobian matrix ζ y T : p × (n -p);

• left-hand-side: p × (n -p);

• constraint vector g: p × 1;

• position vector x: n × 1;

• Jacobian matrix g = ∇g: p × n;

• matrix Ω T : n × (n -p);

• right-hand side: p × (n -p).

Thus, one solves a linear system defined by the p × p matrix C and one right-hand-side of dimension p in (21), and

-(n -p) right-hand-sides of dimension p in (26),
that is, a total of n -p + 1 right-hand side vectors.

We now dispose of the elements that are necessary to apply one iteration of the BFGS algorithm (or some other gradient-based algorithm) applied to the restricted function

φ(y T ) := f xQN = f x + y + z = f x + Ω T y T + Ω N ζ ( 28
)
whose gradient is calculated at xQN from:

dφ(y T ) = ∇f xQN t (dy + dz) = ∇f xQN t Ω T dy T + Ω N dζ = ∇f xQN t Ω T + Ω N ζ y T dy T ; (29)
then by transposition:

∇φ(y T ) . = Ω t T + ζ t y T Ω t N ∇f xQN ( 30
)
This gradient is of dimension (n -p). One easily checks that the dimensions are compatible. In this expression, the second term reflects the approximation that was made of the constraint manifold curvature.

Summary of algorithm

Starting from point x, the following steps are performed:

• Calculation of constraint gradients at x, Gram-Schmidt orthogonalization, orthogonal basis completion, definition of matrices Ω T and Ω N , definition of optimisation variables y T .

• Elaboration of a procedure that performs the following operations for an arbitrary y T :

-Setting x = x + Ω T y T -Calculation of the constraint gradients at x, Gram-Schmidt orthogonalization, orthogonal basis completion, definition of matrices Ω T and Ω N . -Calculation of matrix C, and values at x of constraint functions, ḡ, and gradient ∇g.

Inversion of the linear system (21)(26) involving a p × p matrix and n -p + 1 righthand-side vectors. -Calculation of the restricted function value φ(y T ) by ( 29), and its gradient approximation by (30).

Once this procedure is realized, it is possible to apply one or several iterations of the BFGS algorithm applied to the restricted function φ(y T ), in which the evaluation point remains very close to the constraint manifold as it will now be established.

Analysis of orders of magnitude

By Taylor's expansion to first oder of ∇γ about x, one obtains:

0 = ∇γ(x ⊥ ) = ∇γ(x) + ∇ 2 γ(x) x⊥ -x + O( x⊥ -x 2 ) O(h 4 ) (31)
to which ( 11) is subtracted to get:

∇ 2 γ(x) xN -x⊥ = O(h 4 ). (32)
The orders of magnitude of the terms appearing in ∇ 2 γ(x) are the following:

∇ 2 γ(x) = j   ∇gj ∇g j t O(1) + ḡj ∇ 2 g j O(h 2 )    (x) = H + O(h 2 ) = O(1) (33)
This matrix is singular in x, but invertible in the orthogonal direction N . It is admitted that (32) implies that:

xN -x⊥ = O(h 4 ) (34)
Besides, for (exact) Newton's method (11), (33) implies that:

0 = ∇γ(x) + H + O(h 2 ) ( xN -x) = ∇γ(x) + H ( xN -x) + O(h 4 ) (35)
whereas for the quasi-Newton method:

0 = ∇γ(x) + H ( xQN -x) (36)
Consequently:

H xQN -xN = O(h 4 ) ( 37
)
and we conclude that:

xQN -xN = O(h 4 ) (38)
since the inversion of H in the subspace N is well-posed.

By combining (34) and (38), the final conclusion is achieved:

xQN = x⊥ + O(h 4 ) (39)
in which, recall, x⊥ is a theoretical point (exactly) on the constraint manifold.

Application to a simple case

One considers the simplest case of an optimization in R 2 subject to one scalar constraint given by: g

(x) = ax α 1 + x 2 = 0 (40)
where a > 0, as in Figure 1 (drawn setting a = 1 2 , α = 2). The starting point is x = (0, 1) t . The general expression of the gradient is the following:

∇g = αax α-1 1 1 . (41)
One considers the following point on the tangent:

x = y 0 (42)
where the value of g is the following:

ḡ = ay α (43)
and the expression of the gradient the following::

∇g = αay α-1 1 . (44)
Here the subspace N is one-dimensionnal and spanned by the vector

ω2 = ∇g ∇g (45) so that z = ζ 1 ω2 (46)
and the unique component ζ 1 is the following equation to which (21) here reduces to:

ωt 2 ∇g ∇g ζ 1 = -ḡ. (47)
Hence:

z = - ḡ ∇g 2 ∇g (48)
and finally:

x = x + z = x1 x2 (49)
where:

       x1 = y - ay α 1 + α 2 a 2 y 2α-2 (αay α-1 ) x2 = 0 - ay α 1 + α 2 a 2 y 2α-2 (50)
and the value of g at this point is given by:

ḡ = a xα 1 + x2 = a y - ay α 1 + α 2 a 2 y 2α-2 (αay α-1 ) α - ay α 1 + α 2 a 2 y 2α-2 := ay α κ ( 51
)
where κ is expressed in terms of the infinitely-small parameter

= α 2 a 2 y 2α-2 = O(h 2α-2 ) (52)
as follows:

κ = 1 - 1 α 1 + α - 1 1 + . (53)
Then:

κ = 1 -α α(1 + ) + α(α -1) 2 α(1 + ) 2 + O( 3 ) -1 -+ 2 + O( 3 ) = α -1 2α 2 + O( 3 ) = O( 2 ) (54)
and finally:

ḡ = O(h 5α-4 ). (55)
This indicates a distance of x to the constraint manifold in h 6 in the case of a parabolic constraint (α = 2) and h 16 in the case of the quartic constraint (α = 4). These results have been confirmed by experiment, see Tables 1-2-3. They are more favorable than the general result given in (39), due to the simplified context of a scalar constraint and two variables.

Case of a parabola (α = 2): To simplify one lets a = 1 2 . For values of y = h i = 1/2 i (i = 1, . . . , 4), the coordinates of x are directly calculated from (50), as well as the corresponding value of g. We observe that the ratio of successive ḡ converges to 64 = 2 6 as it was established formally.

Case of a quartic constraint (α = 4): the experiment was repeated using this time a = 1 and y = h i = 0.75/1.5 i-1 . This time, we observe that the ratio of successive ḡ indicates evidence of convergence to 1.5 16 . = 657, which confirms the formal result of convergence in h 16 .

We now return to the case of a single scalar parabolic constraint and two variables for a closer examination of the unexpected higher convergence rate in h 6 . Another series of experiments of Table 3: Observed orders of magnitude in the parabolic case of two variables x = (x 1 , x 2 ) and one scalar constraint g(x) = 1 2 x 2 1 + x 2

As an example, below is the output for θ = 0 corresponding to the first random draw: In the above, the notations are straightforwardly understood: theta for θ, cost and sint for cos θ and sin θ, idraw =1 for first draw, Hmat for H 1 , hnorm for ||H 1 || ∞ , y for the 2 components of y, b3 for b 3 , xbar for x, gbar and gradgbar for ḡ1 and ∇g 1 , xbarbar_i for xi , gbarbar for g 1 ( x) := q.

theta = 0.
The second set of data corresponds to halved y, and the third to halved again. The estimated order of convergence is α = log 2 (q 0 -q 1 )/(q 1 -q 2 ).

The results of this experiment are collected in Table 4. They clearly indicate a 4th-order convergence rate. This conclusion confirms the general estimate even in case of a single scalar constraint when the number of variables is at least equal to 3. 4: Estimated order of convergence in case of a single scalar quadratic constraint and three variables (n = 3, p = 1). (For a given θ, the 10 values correspond to different random draws.)

Conclusions

The development of a quasi-Riemannian method made in this report will permit to study the application of the BFGS algorithm in case of equality constraints that are not necessarily defined explicitly in terms of the optimization variables, but only through procedures of evaluation of constraint functions and their gradients. This is the case in particular in a setting subject to the solution of a partial-differential equation when the constraints are functional, and evaluating accurate second derivatives is often considered as an unrealistic endeavor. In the present method, no curvature information on the constraint functions is necessary.

We also remark that the singular system, (14), was not found impossible since a particular solution was identified, but under-determined. Thus, it will be examined whether other solutions could yield a higher-order approximation of the constraints.

While the approximation of the retraction operator is considered well established, more analysis of the transport-operator proposed approximation remains necessary.

Figure 1 :

 1 Figure 1: Quasi-Riemannian approach.(This figure has been drawn to scale in the specific case of two optimization variables (x 1 , x 2 ) assuming a single quadratic constraint function g(x 1 , x 2 ) = 1 2 x 2 1 + x 2 , a starting point located at x = (0, 0), and the abscissa of the tangent vector y set to y = x1 = 123 128 so that the abscissa of point xQN is precisely 3 4 .)

  θ

Table 1 :

 1 Orders of magnitude estimations in the case of a parabolic constraint

	i h i	x1	x2	ḡi	ḡi-1 / ḡi
	1 0.5	0.45	-0.1000 0.0013
	2 0.25	0.2426 -0.0294 2.70 10 -5 48.1
	3 0.125	0.1240 -0.0017 4.66 10 -7 58.5
	4 0.0625 0.0624 -0.0019 7.39 10 -9 63.1

Table 2 :

 2 Orders of magnitude estimations in the case of a quartic constraint

	i h i	x1	x2	ḡi	ḡi-1 / ḡi
	1 0.75	0.6720	-0.1848 0.0191
	2 0.50	0.4926	-0.0588 0.0001	238
	3 0.3333 0.3329	-0.0123 1.38 10 -7	583
	4 0.2222 0.222195 -0.0024 2.13 10 -10 647

RR n°9007

Inria

Acknowledgement

This study was developed in cooperation with ONERA DAAP (Department of Applied Aerodynamics) Meudon. In particular, discussions with D. Bailly were extremely fruitful.

similar type have been conducted and reported in Table 3. Let us introduce a short notation for the vector

and denote ξ the projection of point xQN onto the direction of ∇g(x ⊥ ), η; let us split vector v in a component parallel to ∇g(x ⊥ ), η, and the orthogonal component, τ :

We have established that in general the following bound holds:

Here, we observe that:

The bound on η itself comes from the fact that the angle between vectors v and τ is O(h), while the angle between the support of vector ------→ ( xQN , x), i.e. ∇g(x), and the support of vector ----→ (x ⊥ , x), i.e. ∇g(x ⊥ ), is O(h 2 ) since the two gradients are evaluated at points that are O(h 2 ) distant. Consequently, the Taylor expansion to first-oder of g( xQN ) about x⊥ writes:

and produces the observed result. However this is a very particular case.

In order to perform a more general verification, the following procedure was developed to account for situations involving possibly more than two variables and more than one constraint:

-The starting point is x = 0.

-Each constraint is modeled as a quadratic form:

where {x i } are the components of vector x. In this way, the subspace tangent to the manifold at x = 0, T , is parameterized as follows (x 1 , . . . , x n-p , 0, . . . , 0). The n(n + 1)/2 distinct elements of the Hessian matrix H j and the algebraic value of the gradient along its axis, b n-j+1 , are drawn using a random generator whose output is transformed to produce a real number of arbitrary sign and absolute value.

-For each random draw defining a complete set of constraint functions, an initial value of h is chosen to be 10 -5 × max j ||H j || ∞ , and the tangent vector y (whose norm is h) is then completely defined by angular parameters; these angles are defined in several cases chosen to cover broadly all angular directions.

-Then, for each random draw, and each discretization of the angular parameters completing the definition of y, one computes the point x, and the corresponding value of the constraint

Then, the process is repeated for the same set of constraints but after y has been halved, yielding a compound constraint value q 1 ; and then y is halved again, yielding q 2 . From {q 0 , q 1 , q 2 } the order of convergence is estimated.

For the case of one constraint (p = 1) and three variables (n = 3), thus two in the tangent plane, in polar coordinates a single angular parameter θ is sufficient. This parameter was given 10 discrete values between 0 and π. For each one, 10 random draws were made of the 7 arbitrary coefficients.


Bruno A Rodrigues Filho
email: bafilho@inmetro.gov.br

Mauricio E Silva

Cláudio R Fogazzi

Marcelo B Araújo

Rodrigo F Gonçalves

Information System as a Tool to Decrease the Economic Distortion in Trade Metrology

Keywords: Economics, legal metrology, market asymmetry, information technology

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Legal metrology is a specific field in the science of measures, where regulations are applied on measurements, determining required characteristics and methods in measuring instruments that are relevant to a measure. Regulations change according to each country necessity however they are usually applied, in metrology, to instruments where trade, health and safety are involved [START_REF] De Silva | Development of metrology in developing economies[END_REF]. Specifically in trade, the consumers have no means to check the amount of goods that is being traded, leading to an unfair competition as well as to consumer's protection issues [START_REF] Sanders | Why do we regulate measuring instruments used for trade[END_REF], consequently leading to a lack of confidence undermining the relationship between consumers and suppliers. The impact of measuring instruments can be significant to a country, affecting a significant part of its Gross Domestic Product (GDP) [START_REF] Carstens | AFRIMETS (Intra-Africa Metrology System)[END_REF]. The economic impact of measuring in trade can be realized in studies carried out in USA in 1996 that showed that measures represent the amount of 54.5% of the GNP [START_REF] Ardianto | A way to stimulate public awareness[END_REF], and more recently in the United Kingdom where goods which value is based on a measure represented £ 622 billion in 2002 [START_REF] Sanders | Why do we regulate measuring instruments used for trade[END_REF]. Impact studies have also presented that an average of 0.1% error in measures would represent 0.05% of GDP [START_REF] Birch | Economic and Social Benefits of Legal Metrology[END_REF]. The substantial impact of measurements in the GDP of a country demonstrates the importance of developing tool to improve legal metrology control.

The legal control of measuring instruments is the tool used in legal metrology to maintain under control this asymmetry, using verifications and surveillance activities to keep these errors according to established in regulations.

This market asymmetry, i.e. the economic distortion between what is being traded and the measurement indicated by an instrument, indicates the monetary unit attached to an error in a measuring instrument [START_REF] Birch | Benefit of legal metrology for the economy and society -A study for the International Committee of Legal Metrology[END_REF]. In the macro economic scenario this indicator allows to obtain the amount of money under uncertainty due to measuring errors. This distortion is considerate one of the causes that can fail a market, where increasing accuracy of the metrology system increases the economic return [START_REF] Swann | The economics of metrology and measurement[END_REF], so an efficient way to decrease the economic distortion is vital to improve a nation economy. Moreover, the main aspect of the economic distortion indicator is to be a monetary representation of measuring errors, allowing comparisons among countries.

Repaired measuring instruments represent a significant number of instruments used in trade, as an example, in Brazil, 276,464 fuel dispensers were repaired in 2013, representing 64.8% of total and 21.1% of the 1,401,510 non-automatic weighing instruments in use [START_REF] Rodrigues Filho | Enhancements of the legal metrological control in Brazil due to after repair verification. 9th International Symposium[END_REF]. The repaired instrument is an important part of the legal metrology control because when an instrument in the marked is repaired, its metrological performance is affected and a complementary verification, defined as after repair verification is necessary to attest if the errors are according to regulations, keeping the market under control. The commercial relationship involving repaired measuring instruments involves impartiality and independence issues once a body responsible for the repair evaluates its own service.

In order to decrease the economic distortion in trade due to repaired measuring instruments the present study aims to implement an information system align strategically to be used as a tool to decrease this asymmetry in repaired measuring instruments under the legal metrology control.

The Control of Measures in Trade

In most countries, metrology is centralized in a National Metrology Institute (NMI), responsible for regulation in legal metrology and maintenance of the national standards and laboratorial infrastructure to dissemination of traceability [START_REF] De Silva | Development of metrology in developing economies[END_REF]. The activities to control the measuring instruments can be divided in three different levels [START_REF] Klenovsky | Legal metrological control over measuring instruments in use: current situation[END_REF]:

• Type approval an initial verification -Type approval comprehends the compliance of instrument features according to the regulations, before its production; and initial verification represents the assessment of the instrument, according to its legal requirements, after it is manufactured. Both are conducted before the instrument is put in the market.

• Periodic and after repair verification -Regulated measuring instruments are verified regularly in the market to attest the continuous attendance of the instrument to the legal requirements. After a repair, the instruments are also verified, once it may cause influence over its performance, affecting its reliability.

• Surveillance -This level represents the control of instrument in use in the market applied to identify frauds and misuses of regulated measuring instruments.

These actions in legal metrology are named as the legal metrological control activities and must be conducted in order to keep the reliability of measures in trade.

The NMI can delegate the verification and repair activities to notified bodies to either private or public bodies, as in France, where verifications are carried out by both public and private notified bodies [START_REF] Lagauterie | The evolution of the metrological control of measuring instruments in France[END_REF] and in Brazil where verifications are executed exclusively by public bodies [START_REF] Silva | The legal metrology Brazilian model[END_REF].

Another relevant aspect that must be pointed regards the repairs performed in measuring instruments by notified bodies. There are two approaches regarding a repair in a measuring instrument: the body responsible for the repair conducts the verification; or the NMI carries out the verification after the repair is executed. In the first case, there is a lack of impartiality once the body verifies its own repair. In the second situation despite after repair verification carried out by a third independent body, the measuring instrument is still in use right after the repair for an indeterminate period. This period depends on the infrastructure of the NMI to perform the after repair verification as soon as possible. Also, it is not possible to predict when or where a repair is going to be demanded. This aspect is vital to countries with large territories.

Information Systems

Information systems (IS) were introduced in organizations mainly to support managers [START_REF] Gupta | Management information systems planning: analysis and techniques[END_REF]. The concept of an information system involves not only technical aspects of a system as the software or hardware, but also all the information flow, i.e. data and human resources [START_REF] Alter | Information Systems: a management perspective[END_REF].

The aspects of developing an information system are wider than developing software or a platform as it also incorporates human, administrative and organization aspects [START_REF] Keen | Information Technology And The Management Theory: The Fusion Map[END_REF].

Strategy is also a significant component of success to implant an information system inside an organization. The misalignment between the organizations and IS strategies may lead to the inefficiency of the IS when compared to its full potential [START_REF] Henderson | Strategic Alignment: Leveraging Information Technology For Transforming Organizations[END_REF]. Consequently, to have full benefits of an efficient information system, the organization should be strategically aligned to the information system to be implemented [START_REF] Luftman | Transforming the enterprise: The alignment of business and information technology strategies[END_REF].

Regarding the insertion of IS inside an organization, development of data process can be divided into six stages: initiation (I); contagion (II); control (III); Integration (IV); data administration (V); maturity (VI). The managing action to the progress of the IS starts with the initiation of the system within the organization passing throw contagion, control, integration, data administration concluding in the maturity stage. According to this model, the first stage represents the initialization of the system inside the organization, the users are not concerned about the system and the control is considered lax. As the system evolves inside the firm, in stage three (control), the management moves from the computer management to data resources management. In the final stage of growth, the system application is considered mature and the managements are focused on information flow [START_REF] Nolan | Managing the Crises in Data Processing[END_REF].

In addition, the IS when properly lined up to the strategic requirements of the organization contributes to innovation [START_REF] Yang | The impact of quality of IS information and budget slack on innovation performance[END_REF].

Methodology

The system used to control repaired measuring instruments was incorporate in a specific website named PSIE -Portal de Serviços do Inmetro nos Estados (Platform of Services of Inmetro in States, literally). For simplicity, the system will be called hereinafter PSIE. The platform can be accessed in the link http://servicos.inmetro.rs.gov.br, and allowed to identify the location and the technical specifications of repaired measuring instruments. The authors were involved in establishing the requirements to the system according to legal metrology requirements in Brazil, coordinate the programmers' team, as well as to analyze the results in order to verify its impact in the after repair verifications.

In order to initiate a mandatory activity in legal metrology, a regulation development is necessary. Thus the project was divided into three well-defined steps:

• Step 1. Launching the system as voluntary for fuel dispensers in August 2012, in order to identify possible problems; • Step 2. Developing and implementing regulation for bodies that execute repairs in fuel dispensers, issued in January 2013; • Step 3. Expanding the regulation (to be issued in 2015) to notified bodies that provide repairs to measuring instruments used in trade (non-automatic weighting instruments, taximeters, length measuring instruments, and measuring systems for gaseous fuel).

The control of repaired fuel dispenser was set as a priority due to fraud events related to this instrument [START_REF] Brandão | Contramedidas de hardware y software sobre el fraude de alta tecnología al Surtidor de combustible bajo el alcance de Metrología Legal. 9th International Symposium[END_REF]. It would also be used as a test case to point out failures in the system, allowing improvements to the system to be applied to other instruments. Despite the regulation to be issued in 2015, the system is available since January 2013 as voluntary to non-automatic weighing instruments (NAWI).

No comparisons to other countries were conducted, once similar studies were not available, according to systematic literature review carried out in the legal metrology control [START_REF] Rodrigues Filho | Legal metrology, the economy and society: A systematic literature review[END_REF].

Strategy Alignment

In order to develop the system that will monitor repaired measuring instruments used in trade, the strategic alignment between Inmetro (National Institute of Metrology, Quality and Technology), the Brazilian NMI, and the system was explored. Inmet-ro strategic guidelines are available for consult in the link: http://www.inmetro.gov.br/english/institucional/index.asp.

According to Inmetro strategy, the system has been developed to meet the necessities in metrology regarding competitiveness, fair competition and consumers' protection since its main objective is to decrease the economic distortion due to increase of after repair verification.

Using the Platform

When a bodied is notified by the NMI to be responsible for repairs in measuring instruments, it gets, for each technician, a unique password to access the platform. After a repair, the technicians have a five days deadline to inform the specifications of the repair, measuring instrument information, and address in the platform (as serial number, ID, number of type approval certificate and sealing marks). This deadline period was chosen due to regional aspects of Brazil, once it is a continental country and internet connection problems may occurs in remote regions.

The bodies responsible for verifications conduct after repair verifications using the information provided by the notified body, as well as the surveillance over the usage of the platform by the notified bodies.

Results and Discussion

A three level curve was obtained, where first level (A) represents the understanding and initialization of the system followed by a fast growth (second level) as the use of the system becomes more frequent (B), and finally a stabilized behavior where the number of repair fluctuates around an average (C). According to the six stages of processing growth, first level (A) of curve in figure 1 can be interpreted as stage I, which means the initialization of the system.

Step two (B) is related to stage II and III as PSIE use proliferated and regulation was implemented. In step three (C), the curve stabilizes and integration of repairs and after repairs verification is implemented representing stage IV. Data managing and full use of the system, including not only repairs in fuel dispensers would represent stages V and VI, and are next step to be achieved by the PSIE. The organization in this case can be interpreted as a composition of the National Metrology Institute and bodies responsible for repairs.

Figure 1 shows the number of repairs informed to the PSIE for fuel dispensers. The first level (A) can be observed from August (2012) -February (2013), second level (B) from February-April (2013) and third level (C) after April (2013), where repairs float around an average of 25,050.

For NAWI, a fast growth of the curve is not observed, regarding its voluntary use until 2015. A Pearson correlation coefficient ρ = 0.6713 characterizes the curve as still in the first level (A). A fast growth, similar to fuel dispenser repair, is expected during 2015 due to mandatory aspects of the PSIE to NAWI.

In 2012 (August-December) 87,740 repairs in fuel dispensers were informed in PSIE, in 2013 276,464 (January-December) repairs were informed and finally in 2014 that number increased to 315,013. For non-automatic weighing instruments, 295,624 repairs were informed in 2013 (January-December) and from January to December 2014 it increased to 405,668. A superior number of repairs in NAWI are expected when compared to fuel dispenser since 1,384,825 verifications were executed in NAWI compared to 363,803 in fuel dispensers, in 2014. The number of after repair verifications in fuel dispensers and NAWI is exhibited in figure 2. For fuel dispensers, an increase from 57,598 to 71,913 (24.8%) comparing 2012 to 2011 and from 71,913 to 80,273 (11.6%) in after repair verifications comparing 2013 to 2012. In 2014 it decreased from 80,273 to 73,551 is observed due to external aspects, once periodic verifications decreases 17.22% as well. However, since the system implantation, comparing 2014 to 2011, an expansion from 57,598 to 73,551 (27.6%) is observed for after repair verifications for fuel dispensers.

Regarding after repair verification in NAWI, a growth from 23,432 to 43,515 (85.7%) comparing 2013 to 2012, and a growth to 47,999 (10.3%) comparing 2014 to 2013 However, as the PSIE was implemented as voluntary in 2013, an increase 104.8% from 2012 to 2014 is contemplated in NAWI.

As a consequence of after repair verifications, 6,300 fuel dispensers and 4,417 NAWI (considering accuracy class III and IV, up to 1,500 kg capacity) were rejected and were withdrawn of use in 2014.

Conclusions

The system presented in this study has shown an important tool to legal metrological control. After the implementation of PSIE, in 2012, an abrupt increase of 24.8% was observed in after repair verification in fuel dispensers comparing to 2011. And an increase of 27.6% is observed comparing 2014 to 2011.

Legal aspects were also a vital component to PSIE to succeed. It can be observed since the performance of the system has not shown the same efficacy to nonautomatic weighing instruments when compared to fuel dispensers mainly because the PSIE is not mandatory to NAWI however a significant growth of 104.8% in after repair verification in observed from 2012 to 2014.

The impact to the consumers can be realized in the 6,300 fuel dispensers and 4,417 NAWI rejected and withdrawn from market in 2014. Despite this significant result, a stable number of repairs to NAWI are still desirable. However, it can be interpreted that the system has been vital to this result.

Strategic alignment of PSIE to legal metrology, incorporating legal aspects in the regulation was also an important goal for the system, once three well-defined steps can be observed after the system implantation. Also, according to the six stages of growth of data processing in an organization, in this case an organization is composed of the NMI and bodies responsible for repairs, it can be conclude that the system is between stages III and IV, where proliferation and data processing are in course.

Finally, due to the increase of after repair verifications, inaccurate instruments are withdrawn from the market, consequently decreasing the economic distortion in the commerce. Once measuring instruments used in trade are according to regulation, they lead to fair competition, consumer's protection, contributing to the economic development.

It can be concluded that the PSIE has achieved its main objective since the increase of after repair verifications is responsible for decrease economic distortion once an abrupt growth is verified in after repair verifications for fuel dispensers. For NAWI this behavior has not been observed, mainly because of voluntary use of PSIE, However, a similar performance is expected after 2015.

Fig. 1 .

 1 Fig. 1. Repairs informed to the PSIE by notified bodies for fuel dispensers from August 2012 to December 2014.

Fig. 2 .

 2 Fig. 2. After repair verification for fuel dispensers and non-automatic weighing executes from 2011 to 2014.

B. A. Rodrigues Filho et al.

Acknowledgement

The authors acknowledge the support of INMETRO, which enabled us to carry out this research.


Teixeira Sivanilza

Irenilza Machado

Alencar De

João Gilberto Naas

Dos Mendes

Rodrigo Couto Reis

Fabiana Ribeiro Santos

Rodrigo Caldara

Garcia Garófallo

Sivanilza Teixeira Machado

Irenilza De Alencar Naas

João Gilberto Mendes Dos Reis

Rodrigo Couto Santos

Fabiana Ribeiro Caldara

Rodrigo Garófallo

Logistics Issues in the Brazilian Pig Industry: A Case-Study of the Transport Micro-Environment

Keywords: Pig transport logistic, hot weather, pre-slaughter management

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The key factor in a pre-slaughter logistics chain is the transportation system. The main links of the chain are the farm, transport and slaughterhouse plants. Transportation is essential throughout production. Typically, pigs are sent to the slaughterhouse plant by the farmer through some intermediaries not necessarily well trained in taking good care of the animals [START_REF] La Lama | Livestock transport from the perspective of the pre-slaughter logistic chain: a review[END_REF]. Maximizing the management between each supply chain component will help to minimized losses; therefore, reducing the weight loss in livestock transportation is an essential element in the meat supply chain. The pre-slaughter logistics scheme is presented in Figure 1.

The authors wish to thank the CAPES. High air temperatures and humidity impact negatively livestock production and animal welfare [START_REF] Naas | Impact of global warming on beef cattle production cost in Brazil[END_REF], [START_REF] Silva | Effects of dietary protein level and amino acid supplementation on performance of mixed-parity lactating sows in a tropical humid climate[END_REF]. The micro-climate inside the truck affects livestock production and animal welfare. Climate changing impact has led to global warming of approximately 1 • C in the last 30 years affecting regional hydrological systems and agribusiness including livestock production [START_REF] Naas | Impact of global warming on beef cattle production cost in Brazil[END_REF], [START_REF]Intergovernmental Panel on Climate Change: Climate change 2014: synthesis report. Tech. rep., Intergovernmental Panel on Climate Change[END_REF]. Brazil is the world fourth-largest pork producer and export [START_REF]Livestock and poultry: world markets and trade[END_REF] and the country is located in a tropical and sub-tropical region. The country swine herd is nearly 40 million heads, and approximately 80% of the production is concentrated in three main regions South, Southeast and Midwestern of Brazil [START_REF]Produção da pecuária municipal[END_REF]. High air temperatures and humidity impact negatively livestock production and animal welfare [START_REF] Naas | Impact of global warming on beef cattle production cost in Brazil[END_REF], [START_REF] Silva | Effects of dietary protein level and amino acid supplementation on performance of mixed-parity lactating sows in a tropical humid climate[END_REF]. Pre-slaughter logistics exceed the boundaries of the farm, and it involves mostly animal transportation [START_REF] Oliveira | Bioclimatic mapping of southern Brazilian region for animal and human thermal comfort[END_REF], [START_REF] Amaral | Boas práticas de produção de suínos[END_REF]. The thermal environment inside the truck lead to a loss in live weight, especially in large animals during long distances [START_REF] Silva | Ambiência animal e as perdas produtivas no manejo pré-abate: o caso da avicultura e corte brasileira[END_REF].

A major problem that farmers and slaughterhouse plants face is to determine the alignment between the slaughterhouse plant capacities with the pre-slaughter logistics, to comply with several issues, including animal welfare [START_REF] Oliveira | Bioclimatic mapping of southern Brazilian region for animal and human thermal comfort[END_REF], [START_REF] Kephart | Establishing sprinkling requirements on trailers transporting market weight pigs in warm and hot weather[END_REF]. Several slaughterhouse plants adopt the pigs transportation at night, due to the incidence of high temperatures during the day [START_REF] Bench | Welfare implication of pig transport journey duration: scientific background of current international standards[END_REF]. However, slaughterhouse plants production logistics usually imply in receiving the pig loads during the day, generally under the hot weather. At the slaughterhouse plant (final node of the chain), vehicles often have to queue while waiting to unload the pigs. Long queues at the slaughterhouses delivery point often cause problems for drivers and also negatively affect the animal welfare. Brazilian law required a total fasting time up to 24 h [START_REF] Brasil | Regulamento da inspeção industrial e sanitária de produtos de origem Animal[END_REF] and animals under fasting time after above 24 h must be fed. As this condition implies in the extra management of pre-slaughter logistics, it is avoided. Brazilian logistics performance adopts two different ways: (i) animals arrival at night are slaughtered in next morning; and (ii) animals arrival at morning are slaughtered in the afternoon.

Considering that while pigs are transported the truck microenvironment is a critical issue, this study aimed to assess the variation in the truck thermal conditions during two schedules in the afternoon.

Methodology

The present study used hybrids finishing pigs from a commercial farm located in Espírito Santo State, Brazil (6 • 20 4 S, 35 • 18 33 W ). The experiment was conducted in February 2015. Pigs were transported in open truck with 7 m long and 2.45 m wide, wood body, two floors and two compartments per floor with a capacity of 70 animals (Table 1). The pigs transportation from farm to slaughterhouse plant had a distance of 45 km. Two transportation schedules were monitored at 1 and 4 P.M. 2.1 Animals, pre-slaughter handling, and variables recorded A total of 140 finishing hybrid pigs (Landrace and Large White) had feed deprivation of six hours. During the loading process, the animals were moving in groups of six pigs. Pigs were moving from the pens to the truck on a hallway with a concrete floor until the wood dock that gave them access to the truck. The difference in the material of floor made the pigs stop in front of the dock. In this occasion, handlers used a kind of rattle to guide pigs inside the truck. The overall stocking density was 250 kg/m 2 [8], [START_REF] Kephart | Establishing sprinkling requirements on trailers transporting market weight pigs in warm and hot weather[END_REF]. Pigs were sprinkled with water before the truck started moving to the processing plants. In the slaughter plant, pigs were unloaded, moving from the truck to the waiting pens. In these pens, the pigs remain a minimum of eight-hour in rest until the slaughter. During the fasting time, the transportation process and the rest the pigs had access only to water for 15h. The variables ambient air temperature (AT), relative humidity (RH), wind speed (WS), truck speed (TS) and noise (N), and animals surface temperature (ST) were recorded. A data logger (Testo model 174H) recorded the variations in air temperature and humidity relative inside of truck during pigs transportation. The recording of wind speed and the noise was done using an anemometer (Krestel, Nielsen-Kellerman Co., US) and decibel meter (Testo model 815, Testo Co., Germany). The pigs surface temperature was assessed using a thermal infrared camera (Testo model 875, Testo Co., Germany). The measurements were taken every 5 min [START_REF] Mcglone | Temperature and relative humidity inside trailers during finishing pig loading and transport in cold and mild weather[END_REF], during the logistics of the pre-slaughter phase, except the surface temperature that took place during the loading and unloading of animals. The thermal images were taken from the lateral of the truck in randomly select pigs located on the first and second truck floors. The measurement of AT and RH started with loading of the first animal and finished with unloading of the last animal [START_REF] Kephart | Establishing sprinkling requirements on trailers transporting market weight pigs in warm and hot weather[END_REF]. The measurement of WS, TS and N were taken when the truck started moving from the farm to the slaughterhouse.

2.2 Thermal environment, surface temperature analysis, and statistical method THI (Eq. 1) allows the assessment of pigs thermal comfort during transportation. The wet bulb temperature was calculated using RH as input in the software Psicrom [START_REF] Roriz | Psicrom 1.0 software Relações Psicométricas[END_REF].

The temperature humidity index (THI) was calculated as suggested by [START_REF] Roller | Response of swine to acute heat exposure[END_REF].

T HI = 0.45W T + 1.35AT + 32 (1)
The average values of ST ( • C) were determined by selecting 40 points within the thermal image and using the software Testo Software IRSoft, Version 2.5 adopting the emissivity of the pig skin equal to 0.95.

Data from the data logger were transferred to Excel and analyzed using Statistical Analysis System, version 9.0 [16] by Means and General Linear Models procedures. The THI values were calculated for the region climatic condition and inside studied sites (farm, truck, and slaughterhouse). Means of THI and ST of pigs were tested using T-test adopting a confidence value of 95%.

Results and Discussion

No difference was found between the variables assessed during the pigs transportation process, except to RH (p = 0.018). According to the recommended by [START_REF] Leal | Ambiência animal[END_REF] the THI should be between > 57 and < 62. In the present study, the schedule of pigs transportation during the afternoon is unsuitable for the animals (Table 2). The truck micro-environment is determined by AT, RH and WS [START_REF] Mcglone | Temperature and relative humidity inside trailers during finishing pig loading and transport in cold and mild weather[END_REF]. However, other variables also affect the truck microenvironment during transportation, such as stocking density, size, weight and age of animals, and vehicle motion.

The monitoring procedure showed the variation in temperature and relative humidity during the transportation of pigs in three moments within two periods: loading, journey, and unloading (Fig. 2). Despite the variation be similar to both schedules of transportation, in the first transportation during the loading of animals, AT increased in 4.1 • C. With water sprinkling during loading AT values inside the truck decreased 8.2 • C. ST was not affected by sprinkling, but stress signs in pigs were observed [START_REF] Kephart | Establishing sprinkling requirements on trailers transporting market weight pigs in warm and hot weather[END_REF]. In the present study, during the pigs transportation process AT increased gradually 2.5 • C. During the unloading process AT increase 1 • C.

Throughout the second schedule of transportation, AT increased 1.9 • C during loading and 1.7 • C during the journey. AT inside the truck decreased 0.7 • C when water sprinkling of the animals was done before unloading at the slaughter plant. The thermal comfort varied 4.63 between farm and slaughter plant (p < 0.0489). The variation can be associated with the transportation process. No difference was found between the sites truck and slaughterhouse. However, truck and slaughter plant show different ambient THI values from the regional ones (Table 3). Such values indicate that both farm and meat processing industry should invest in environment control. AT and RH are variables responsible for the thermal comfort and welfare of livestock, and they may affect animals ST (p < 0.0001), Fig. 3. Finishing pigs have difficulty to dissipate sensible heat, and it worsens when pigs are in heat stress due warm weather. Some action needs to be adopted by the pig supply chain to minimize this issue such as water sprinkling, adoption of forced ventilation, and improvement in the thermal material in the construction of the truck body. Pigs surface temperature increased 0.7 • C in the first schedule of transportation and 1.7 • C in the second schedule (Table 4). Results agree with the threshold of surface temperature observed by [START_REF] Kephart | Establishing sprinkling requirements on trailers transporting market weight pigs in warm and hot weather[END_REF] in pigs transported during hot weather (30.1 -38.7 • C).

Loading activities are preceding transportation process and the pigs ST has been affected by region and farm THI. Unloading activities (p < 0.027) occurred after transportation, and pigs ST were mostly influenced by the variables microenvironment inside the truck, time of transportation and region climate [START_REF] Silva | Ambiência animal e as perdas produtivas no manejo pré-abate: o caso da avicultura e corte brasileira[END_REF], [START_REF] Bench | Welfare implication of pig transport journey duration: scientific background of current international standards[END_REF]. Also, pigs transported on the second floor of the truck (mean = 40.1) showed a difference of 1.2 • C when compare pigs located on the first floor (mean = 38.9). [START_REF] Mcglone | Temperature and relative humidity inside trailers during finishing pig loading and transport in cold and mild weather[END_REF] showed an increasing of dead pigs with increase the ST after transportation.

Conclusions

Transport of livestock requires special care, becoming a challenge logistic issue along the chain. In developing countries, the available transport infrastructure is relatively poor with inappropriate maintenance. Inadequate logistics services are associated not only with product loss but also with the spread of disease at different stages of food supply chain. Although logistics risk in livestock production covers a wider scope, this study focused on the element transportation from the node farm to the node slaughterhouse plant, with the focus on the truck microenvironment.

Adequate environmental control might reduce the effect of the temperature humidity index on pigs surface temperature, leading to increase the animal thermal comfort and welfare. The present study concludes that pigs farmers and pork industry should invest in the pre-slaughter logistics. Adopting the transport the livestock during the morning or at night is needed, as those operations during the afternoon might provide an inappropriate thermal comfort.

Fig. 1 .

 1 Fig. 1. Pre-slaughter logistics

Fig. 2 .

 2 Fig. 2. Monitoring of air temperature ( • C) and relative humidity (%) during pigs transportation from the farm to the slaughterhouse from 1:11 to 2:57 P.M. [A]; and from 3:45 to 5:18 P.M. [B].

Fig. 3 .

 3 Fig. 3. Effects of Temperature Humidity Index (THI) at pre-slaughter logistics on the surface temperature (ST) of pigs in two-schedules of transportation.

Table 1 .

 1 Characteristics of pigs transportation process from farm to slaughterhouse.

	Period	Weight of Pigs 1st Floor 2nd Floor Loading Journey Unloading
	(P.M.)	(kg)	(kg/m 2 ) (kg/m 2 )	(min)	(min)	(min)
	1:11 at 2:57	123	260.0	246.0	24	75	7
	3:45 at 5:18	120	254.1	240.0	18	60	15

Table 2 .

 2 Average values of temperature (AT), relative humidity (RH), temperature and humidity index (THI), wind speed (WS), truck speed (TS) and noise (N) during pre-slaughter logistics.

	Period	AT	RH	THI	WS	TS	N
	(P.M.)	( • C)	(%)		(m/s) (k/h) (dB)
	1 : 11 at 2 : 57 36.33 35.75 b 91.76 0.94	47.0 81.13
	3 : 45 at 5 : 18 36.03 41.05 a 91.85 0.76	40.6 84.46
	ab = Means with the same letter do not differ (p > 0.05).

Table 3 .

 3 Temperature Humidity Index (THI) values for the sites inside the farm, the truck and the slaughterhouse plant. 84.88 b 86.75 ab 90.92 a 91.38 a ab = Means with the same letter do not differ (p > 0.05).

	Regional	Farm	Truck Slaughterhouse
	THI

*

Table 4 .

 4 Average values of the surface temperature (ST) of pigs during loading and unloading. Number = total of animals assessed per activity. abc = Means with the same letter do not differ (p > 0.05).

	Period (P.M.) Number Activity Minimum Maximum Average THI
	1 : 11 at 2 : 57	34 26	Loading Unloading	35.1 36.5	39.6 40.0	37.5 c 38.2 c	95.06 a
	3 : 45 at 5 : 18	36 34	Loading Unloading	34.4 37.0	40.1 43.0	37.4 c 39.1 a	91.61 b


Volker Stich
email: volker.stich@fir.rwth-aachen.de

Matthias Blum
email: matthias.blum@fir.rwth-aachen.de

A Cybernetic Reference Model for Production Systems using the Viable System Model

Keywords: Cybernetic reference model, Manufacturing Execution, Production System, Supply Chain, Viable System Model

Designing viable and integrative production systems is challenging for big companies. Researchers often fail to holistically consider the production system. Thus, the aim of this paper is to propose a holistic approach how the supply chain, the production and shop floor planning intermesh. Hereby a Viable System Model was applied. Standardized communication channels were able to be defined among three entities. In conclusion this newly proposed approach enables companies to reduce necessary stocks, production lead times and manpower allocation. This proposed approach boosts the efficiency of all production planning processes. This in turn translates to decreased stocks, shorter lead times and to more efficient manpower allocation. This holistic approach is a key to success for companies, in particular, in high-wage countries.

Background

Today, manufacturing companies are increasingly confronted with the influences of a dynamic environment and the ensuing continuously increasing planning complexity [START_REF] Brecher | Integrative Production Technology for High-Wage Countries[END_REF]: Reduced time to markets, increasing product diversity, and increasingly complex multi-tier and world-spanning supply chains are faced with growing interconnectivity of production machinery, manufacturing execution systems, and enterprise resource planning systems under the term Industry 4.0. The Cluster of Excellence "Integrative Production Technology for High Wage Countries" at RWTH Aachen University addresses these opportunities and challenges and aims at resolving the "polylemma of production" which spans along two dilemmas plan-oriented vs. value-oriented production and scale vs. scope [START_REF] Brecher | Integrative Production Technology for High-Wage Countries[END_REF].

Within the Cluster of Excellence (CoE) on "Integrative Production Technology for High-Wage Countries" several institutes at RWTH Aachen University are conducting research on fundamentals of a sustainable production strategy. As part of the Cluster of Excellence on "Integrative Production Technology for High-Wage Countries" the sub-project D-1 aims at the goal of developing a self-optimizing production network. By applying instruments of self-optimization it leads to a quicker achievement of an optimal working point under changing input-parameters. A specific focus is on the consideration of human decisions during the production process when elaborating the cognitive model. To establish socio-technical control loops, it is necessary to understand how human decisions in diffuse working processes are made as well as how cognitive and affective abilities form the human factor within production processes. Thus a cybernetic based reference model of self-optimizing production management, addressing all levels from the supply chain management to the production cell control, has been developed and detailed building on these earlier results. The model has been concretized by individual elements. Introduction On a management level, companies are facing a wide range of challenges in the field of customer demand, dynamic environment conditions and quality problems [START_REF] Brosze | High Resolution Supply Chain Management: Resolution of the polylemma of production by information transparency and organizational integration[END_REF]. Companies have to adapt themselves and their processes to dynamic environment conditions like movements in customer demand, reschedules in supply as well as turbulences in networks [START_REF] Schuh | High resolution supply chain management[END_REF]. Nevertheless, a successful production management is characterized by high process efficiency and a high availability of information. The challenge is to manage negative consequences, such as wrong decisions in the planning processes, caused by poor communication and conventional solution approaches based on centralized planning methods. Conventional planning and control concepts try to tackle these problems by using highly sophisticated and centralized planning methods. These approaches constrain the ability of companies to react quickly and flexibly on internal and external disturbances [START_REF] Meyer | Wirtschaftliche Produktion in Hochlohnlndern durch High Resolution Supply Chain Management[END_REF]. This leads to a slower and more inflexible reaction of companies on internal and external disturbances and thus to an increasing gap between reality and intention [START_REF] Fleisch | High Resolution Production Management[END_REF]. To achieve a higher changeability and a better value-orientation of inter-and inner-company PPC processes, it is necessary to replace the present static arrangement of the central-controlled processes [START_REF] Beer | Brain of the firm : the managerial cybernetics of organization[END_REF].

Methodological Approach and Preconditions

The structure of the cybernetic reference model is derived from principles of the Viable System Model (VSM). The Viable System Model was evolved by STAFFORD BEER in the 1960s as a management model to support managers dealing with complex management processes. It is built on three main principles: viability, recursivity and autonomy. Viability means that a company must react to internal and external disturbances in an appropriate way, in order to sustain its existence. Recursivity is a principle to structure organizational systems in a self-similar way. Hence, a viable system is a composition of nested systems, which are viable systems, too [START_REF] Beer | Brain of the firm : the managerial cybernetics of organization[END_REF][START_REF] Malik | Strategie des Managements komplexer Systeme. Ein Beitrag zur Management-Kybernetik evolutionärer Systeme[END_REF]. In this context, autonomy means that a system can act independently as long as it is in accordance with its meta-systems' rules [START_REF] Beer | The heart of enterprise[END_REF][START_REF] Gomez | Die kybernetische Gestaltung des Operations Managements. eine Systemmethodik zur Entwicklung anpassungsfähiger Organisationsstrukturen[END_REF].

For realizing these principles, BEER introduced a System consisting of a topology with five subsystems (see figure 2). System 1 reacts to the development of the relevant operative unit´s environment and it coordinates itself with the other operative units with the objective of own stability and whole company´s stability. System 2 enables the units of System 1 to solve their own problems allowing decentralized decision-making and solve conflicts between those units. It also carries out the coordination of the operative units regulatory centers. It is an interface between Systems 1 and 3. System 3 has an overall model which is superior to all Systems 1 and their interactions. The operative overall management system ensures optimization of the whole system. By its direct connections with all subsystems it detects simultaneously and in real time everything that occurs in System 1. It is also notified about activities in System 2. System 3 passes on instructions directly to System 1 via the central command axis. The monitoring and validation of information from the operative units are functions of System 3*.

System 3 realizes the control of the orders that are taken in the current operations. It checks the strategic activities provided by System 4 and converts them into tactical operations. Systems 1, 2 and 3 constitute an autonomic system that regulates internal stability and tries to optimize performance within a given structure and criteria. System 4 does an analysis of the external environment and the internal ability to deal with it. It also makes strategic decisions. The internal stability has only sense if the external factors are considered. Reception, elaboration and transmission of information from the environment are tasks of System 4 in order to provide external stability. It is a set of activities, which feeds the highest level of decision making. It must contain a model that represents the idea of the firm in order to inform the top management about which type of firm they are running. System 5 represents the normative level that makes the balance between current operations (System 3) against future´s needs (System 4). When there is no balance, System 5 plays the role of judge. System 5 for the firm is the top management and it determines policies and establishes the goals to take decisions [START_REF] Beer | Brain of the firm : the managerial cybernetics of organization[END_REF][START_REF] Malik | Strategie des Managements komplexer Systeme. Ein Beitrag zur Management-Kybernetik evolutionärer Systeme[END_REF][START_REF] Gomez | Die kybernetische Gestaltung des Operations Managements. eine Systemmethodik zur Entwicklung anpassungsfähiger Organisationsstrukturen[END_REF].

Application of the Viable System Model to Cybernetic Production Management

The Viable System Model (VSM) is, as stated above, serving as a basis for the organizational structure view. It is conceived in analogy to the human nervous system, which has proven its reliability due to the evolutionary process of billions of years to be the most reliably organized and most adaptable system. The VSM specifies the necessary and sufficient constraints for the viability of complex organizations [START_REF] Beer | Brain of the firm : the managerial cybernetics of organization[END_REF][START_REF] Espejo | The viable system model. interpretations and applications of Stafford Beer's VSM[END_REF]. These constraints can be subsumed as completeness and recursiveness of the system structure. This leads to the requirements of the basic model.

To cope with the dynamic environment, a cybernetic production management reference model has been developed which integrates the different level of production and production management (see figure 2) [START_REF] Stich | Viable production system for adaptable and flexible production planning and control processes[END_REF][START_REF] Schuh | High resolution supply chain management[END_REF]. The main result which has been achieved in previous phases of the project is a cybernetic model structuring a selfoptimizing production management on its different levels, capable to cope with dynamics and to continuously adjust itself. In contrast to the international state of the art the developed model aims to integrate all levels and domains of production and production management. Based on the Viable System Model first developed by Stafford Beer it defines the necessary planning and control tasks as well as the required and sufficient information channels for a self-optimizing production management. It serves as a regulatory framework to allocate the planning and decision models within the overall production management context and to derive design requirements.

Based on these results the project addresses now the comprehensive application of self-optimizing planning and control. This implies the integration of self-optimizing control loops on cell level with those addressing the production planning and control (PPC) as well as supply chain and quality management aspects and will lead to an improvement of planning decisions on different levels of the production network. The Viable System Model provides an adequate structure for consistent integration of trans-disciplinary control loops and their alignment to a super-ordinate target system. It serves as a regulatory framework to allocate the planning and decision models within the overall production management context and to derive design requirements.

To incorporate the different levels of the production systems the levels have been specified. The following figure shows the application of the Viable System Model in production networks and provides an overview of the results of the different levels (see figure 2). As recursion levels the supply chain, the company, the shopfloor, the manufacturing cell and on the bottom the machine level have been defined for the model. The entire model takes on a recursive structure. Recursiveness means that the structure of the model is the same on each level of observation. Any Viable System Model contains and is contained in another viable system model.

Fig. 3. Recursive organizational level of the Viable System Model

The description of the function of these levels is the central goal of the article at hand and will be shown in the following (see figure 3). The figure shows the different levels within the production management and the function of each system in the context of the Viable System Model. To get a more detailed impression of the composition of such a cybernetic based production management model, exemplarily the process and information view for the Supply Chain are described in the following.

Fig. 4. Information transfer between the different levels

The policy function of a Supply Chain is defined by System 5 and in charge of giving a general respectively a legal framework for the whole Supply Chain. System 5 generates neither know-how nor takes direct action in the Supply Chain. It simply ensures that a balance is maintained between the Supply Chain Control Room (System 3 and 2) and for example the Market Analyses (System 4). When an imbalance develops, i.e. Systems 4 predicts high economic growth and System 3 is not capable to cope with this situation, System 5 will take measures (subsidies, laws etc). By this, System 5 has the power to design the way Supply Chains work without interacting in an operative way. Based on the information System 4 is providing, actions are taken to design the future framework of the Supply Chain.

There are different ways of how the Supply Chain can be affected by its environment or how the Supply Chain can influence it. On the one hand all companies (System 1) can interact with its environment, but only for its own professional expertise. On the other hand System 4 comprises the environments of the separate System 1 and the greater environment. System 4 identifies needs and potential for change, i.e. economic development, new technologies and new markets and transmits the information to System 3. It is also important that the information is exchanged between the separate Systems 4 in the recursion levels. In Supply Chains these tasks are fulfilled by lobbyists to influence the environment, or by Market researchers and associations to collect information. This information is then transferred to System 3 (Supply Chain Control Room) and to other Systems on other recursion levels.

The monitoring and optimization of the various actors in the supply chain is carried out by System 3 and System 2 which represent both together the Supply Chain Control Room. Although, the different companies in the supply chain (System 1) usually are in contact and interact among each other, their behavior is not synchronized. As part of the Supply Chain Control Room System 3 intervenes as necessary and solves conflicts between the companies. To achieve this aim System 3 transfers the infor- mation about the operations of the companies into an input-output-matrix and tries to optimize them. The relevant information provides System 2. The aim of System 2 is to coordinate the companies and to avoid oscillations between them. So, System 2 is a system of individual rules and behavior for coordinating operations of the companies. Typical activities of System 2 in the supply chain are for example the rules for joint purchases, the rules for the distribution of parts and the rules for logistical concepts. Furthermore, System 2 is collecting information of the activities such as inventory levels, point of sales data etc., compares the plans to standards and is informing System 3 about deviations to avoid for example the Bullwhip Effect. The gathered information arises from the companies (System 1). System 1 is directed by the meta-system (System 5-3) and reflects the different companies in the Supply Chain.

In addition, for the other levels of the model (company, shop floor, manufacturing cell and machine) also the functions inside the model have been specified. In order to generate a holistic framework including all levels in the Viable System Model the information transfer will be designed as a relationship model describing the connections between the targets on the different levels of the system.

Summary and further Research

In today's time companies are facing a wide range of challenges. In this paper, the application of Stafford Beer's Viable System Model (VSM) on the production management has been discussed as one way of handling these challenges. It has been used as a basis to build up a holistic framework for a changeable production management system. After introducing the preconditions of the model, we have derived the structural framework of the cybernetic production management from the Viable System Model and specified the functions of the system elements and their interactions.

Further research is needed to substantiate the presented solution principles for the different tasks in order to verify and validate the model's ability to support the design of control loops. Thereby a specific focus should be dedicated to the determination of the input and output values for each of the systems.

Fig. 1 .

 1 Fig. 1.: Structure of the Viable System Model (Source:Beer 1979, p. 319, Malik 2006, p. 84, Gomez 1978, p. 24, Espejo & Harnden 1989, p. 99)

Fig. 2 .

 2 Fig. 2. System structure of the CPM model derived from the VSM

Acknowledgements

The presented research is result of the Cluster of Excellence (CoE) on "Integrative Production Technology for High-Wage Countries" funded by Deutsche Forschungsgemeinschaft (DFG). Within the CoE "Integrative Production Technology for High-Wage Countries" several institutes at RWTH Aachen University are conducting research on fundamentals of a sustainable production strategy. The authors would like to thank the German Research Foundation DFG for the kind support within the Cluster of Excellence "Integrative Production Technology for High-Wage Countries".


Siavash H Khajavi
email: siavash.khajavi@aalto.fi

Jan Holmstrm
email: jan.holmstrom@aalto.fi

Manufacturing Digitalization and Its Effects on Production Planning and Control Practices

Keywords: Production planning and control, manufacturing digitalization, supply chain simplification

Advent of additive manufacturing (AM) as a final-parts production method has the capacity to impact the supply chains radically (The Economist, 2012). This effect extends from raw material procurement to production management and further towards distribution and the final customers. Digitalization of production as for the other industries such as automotive and aerospace reduces the operational complexity, while embedding the complexity in the digital components of the system. For instance, the production planning and control for an AMenabled manufacturing may be distinctly different compared to conventional production methods. Production routing, loading and scheduling can become simplified as steps of production are combined through AM utilization. Moreover, production dispatching, reporting, inspection and corrective actions require development of novel effective practices. In this paper we investigate the in-depth impact of digital production technologies (e.g. additive manufacturing) on the production management practices. Our methodology is based on conceptual modelling intertwined with case data.

Introduction

The development of production systems introduced batching methods, standardization of components and stock keeping units to improve the efficiency of the production systems, however the emergence of computers and digitalization of tasks, changed the production methods and visibility of operations by improving the data gathering and sharing methods [START_REF] Berry | Manufacturing planning and control for supply chain management[END_REF]. Now that the manufacturing machines becoming more and more software based and flexible, the question is do we still need the concepts previously set for the labor managed operations. We see a transition from a full human operated world towards a human-machine operated world within which machines are smarter and embed the know-how. In the new paradigm the order can be accomplished by an autonomous system to reach the outcome.

What we looked into throughout this research is the possible impact of direct digital manufacturing technologies (including additive manufacturing) on the conventional production practices. If the conventional shop floor concepts such as batching, SKUs, and other production planning and control tactics can be necessary for the new paradigm of digital smart production. The method is to review the conventional practices point out the costly ones then realize the possibility to omit them through the new tagging and other methods, while using available case studies.

The remainder of this paper is organized as follows: Section 2 presents a literature review; Section 3 explains the research methodology; and Section 4 presents the findings and results of our analysis. This paper ends with conclusions summarizing the research outcomes, and suggestions for future investigation are provided.

Literature Review

In this section we briefly review the literature on the two main subjects of this paper which are direct digital manufacturing and production planning and control.

Direct digital manufacturing

Direct Digital Manufacturing (DDM) technologies are a set of novel manufacturing techniques that produce the final parts from a computer aided design (CAD) file. These technologies which started to appear during the 1980s also have been known as additive manufacturing and 3D printing production techniques. In most of these technologies the computer software slices the three dimensional model of the part to very thing two dimensional cross sections and send them one at a time to the printing machines. The machine then utilized various technologies to produce these parts a layer at a time to reach the final geometrical form factor [START_REF] Khajavi | Additive manufacturing in the spare parts supply chain[END_REF][START_REF] Kruth | Progress in additive manufacturing and rapid prototyping[END_REF].

The application of these CAD based technologies in the beginning was focused on the production of design models and prototypes. However, as the material range expanded and production quality and precision increased the application shifted to functional prototypes and recently final parts. Still there are obstacles to overcome before this method of production can enter the mainstream use and realize a wide application. For instance the cost intensiveness of the production machines as well as raw material, low throughput of the processes, limited range of available material and labour intensiveness of the pre and post production steps are among the most notable issues that need to be addressed [START_REF] Gibson | Additive manufacturing technologies[END_REF].

However, DDM has a number of unique characteristics which makes it a very useful manufacturing method for a number of industries even at the current cost levels. DDM enables the production of very small batch size (as small as the batch of one in medical applications) while also removes the design for manufacturing limitations to a high extent. This means the production of very complex parts with moving parts is possible in a single run, which translates to designers freedom to take advantage of design for performance instead. This is very relevant especially to the aerospace industry which searches for any opportunity to cut weight from the components and increase the fuel efficiency of airplanes. The other important features of this production method are the significant reduction in the amount of raw material waste through the production, the nonexistence of economics of scale (no tooling) and high flexibility for modifications on the fly [START_REF] Khajavi | Additive manufacturing in the spare parts supply chain[END_REF][START_REF] Holmstrm | Guest editorial: Five steps towards exploring the future of operations management[END_REF].

As the DDM attracts more attention and investment the new advancements will emerge which may turn it to a common production method for small and medium volume production batches in distributed settings which also has the potential to enable on-shoring of the manufacturing to the worlds developed countries and cut the costs of transportation of goods significantly [START_REF] Khajavi | Additive manufacturing in the spare parts supply chain[END_REF]. Therefore we see the urge to study the impact of this technology on various aspect of production management to illustrate the potentials and refute the myths.

Production planning and control

Production planning and control (PPC) are a set of activities which have been designed to make the production and delivery of products more smooth and efficient both time and cost-wise. Planning sets the goals for the productions long, medium and short term goals with regard to product and processes, in order to satisfy the customers needs on time and uninterrupted. Production control is responsible to check the performance of the organization with regard to its production schedules and deliveries to alert any sign of derailment from the established plans. Moreover, the healthy functioning PPC can keep the inventories in check and customers satisfied through the optimum utilization of labor, material and machinery [START_REF] Berry | Manufacturing planning and control for supply chain management[END_REF][START_REF] Peterson | Decision systems for inventory management and production planning[END_REF].

Planning, routing, scheduling and loading are the main tasks in the production planning while, dispatching, follow up, inspection and corrective action are the production control practices. Planning is concerned with the processes which are required to be done to enable the production of the product, routing is the task of determining a path for the movement of the production lots in the factory while it is being made. Loading of the works on the machines is related to the capacity utilization of machines. Scheduling which is the last action in the production planning function, determines when and for how long a machine will be occupied with the production of specific parts or batches [START_REF] Peterson | Decision systems for inventory management and production planning[END_REF].

Dispatching deals with authorization of machine starts on various jobs based on the routing and scheduling. The action of controlling the start and stop of the works on the machines is called follow-up. Moreover, inspection of products acts as the problem detection method which will be fixed through the corrective actions on planning of the processes [START_REF] Berry | Manufacturing planning and control for supply chain management[END_REF].

Literature gap

The current literature on the impact of DDM on PPC is quite limited and mostly is focused on the utilization of PPC practices also on direct digital manufacturing technologies [START_REF] Gibson | Additive manufacturing technologies[END_REF]. However, there is no critical study of the PPC to evaluate the actual necessity of those concepts in the new production management [START_REF] Berry | Manufacturing planning and control for supply chain management[END_REF]. We tend to address this literature gap through this paper.

Method

The methodology chosen for this research is the literature review and use of case studies while available. By doing so we aim to locate and describe the potential changes that are required in the current production planning and control practices as the DDM evolves. The current challenge with studying the DDM technologies is the lack of case data in the low or medium volume production which makes it difficult to study this phenomenon fully. However, by finding cases in somehow similar and currently in use production technologies we can expand our understanding of what might be possible when the existing limitations are removed. However, the prospects are bright as the new wider applications for the DDM is starting to appear which makes it possible for our method to be tested and refined against the facts while they become available.

Results

In this section we utilize case analysis and literature to synthesize a potential impact of DDM on the current PPC practices. Cases will be explained and then analyzed for the potential efficiency improvements and lessons learned in production planning and control of the future.

Our first case is an example of a digitalized manufacturing system. The company which is active in the area of custom-made industrial hoses has developed a production system which can be assumed as a digital factory. When the company receives the orders, they directly go to a machine which holds different variants of hoses with various diameters. The machine reads the order and chooses the correct hose by reading the tag on it. Then the ordered length will be cut and the process continues until the whole order batch is ready. While the machine is cutting the hose it also tags it with the correct metal connection ordered for it, which after the completing of the cutting on the production batch will be installed by the operator. Throughout this process the production planning has a shorter routing, simpler scheduling and loading. Moreover in this plant the digitalization has also enabled the possibility of customization on product by product bases. The main advantage of this process also comes from this feature which eliminates the need for stock keeping units as the orders can be manufactured and stocked in single containers with the customers tags.

In this case the dispatching can also be out-sourced to the machine through the prioritization of each order before sending it to the machine. Then if the machine receives an order with a higher priority it can utilize its capacity to fulfill the newly received one and hold the previous batch until the completion of that. In our case the follow-up process can be done well in advance as the process time can be predicted right after the loading. However, at this point the inspection of the products should be done manually but in the future when the machine can also install the metal end connections to the hose; this can also be done by the digital system. All in all, the digitalization of manufacturing can significantly reduce the need for SKUs on the product bases and also improve order delivery and inventory levels.

In direct digital manufacturing where, the product is manufactured through a CAD file, most of the PPC information can be delivered to the machines and after the production is complete it can be directly delivered to the customer after packaging. The additional value of a direct digital manufacturing will be less complexity in the PPC operations while increases the possibility for customization.

In the second example which is the result of analyzing the Volvos Kalmar radical automobile assembly plant, as depicted in Figure 1. The company tried to revolutionize the production line and switch towards a more worker friendly and group oriented fixed position (the vehicles were carried on electric carriers on the plant floors in various directions reprogrammable by the assembly group). Moreover, by giving the workers a team and a single vehicle at each time, they also tried to make the workers skilled in multiple tasks and provide them with the feeling of responsibility for the product that they are completing. However, while the efficiency of production was improved as the workers got used to their tasks and become comparable with the production line concept, Volvo Company decided to close the Kalmar plant in 1994 [START_REF] Sandberg | Enriching production: Perspectives on Volvo's Uddevalla plant as an alternative to lean production[END_REF][START_REF] Sandberg | Volvo Kalmartwice a pioneer[END_REF]. Among the main reason was the fact that group assembly in a single location required kitting of the assembly parts and transferring them to the location of production and to the working team. This was quite a time consuming and complex task which in relatively simpler in the production line concept [START_REF] Sandberg | Volvo Kalmartwice a pioneer[END_REF][START_REF] Engstrm | Alternatives to line assembly: some Swedish examples[END_REF]. However, the kitting process in the future can be done by the autonomous robots, while the production plan is sent to the additive manufacturing machines, located in the plant to produce them according to the daily production plan. Then the robots similar to Kiva system which are in use by Amazon company can directly deliver the parts on a just in time bases to the assembly teams for the installation. In such scenario, the complexity of kitting and dispatching will be out sourced to the computers and DDM systems and the follow-up as well as the product inspections can be done more carefully and on a timely fashion. Such scenario requires a major leap in the development of additive manufacturing technologies to enable a reliable and repeatable production method that can also produce the parts quicker and more economically. However, currently AM is suitable for a number of low volume productions such as jet engine components and medical prosthesis production but the push towards more customized products in various industries will make AM necessary for other ones. Also as the level of implementation grows, bigger industrial players consider the potential improvements to their business from direct digital manufacturing technologies and potentially to build a competitive edge, invest in the advancement and finding new applications. This potentially realizes the impact of DDM on production planning and control practices.

Although the promise of DDM is strong and revolutionizing for the current manufacturing processes there is a need to understand the current limitations and possibilities. Although the DDM technologies are progressing rapidly, there still are sizable obstacles when it comes to the production throughput, reliability of parts, material range and costs. Having this in mind General Electric Company which is among the biggest and most advanced manufacturing companies in the world has started to manufacture the fuel nozzles of their CFM Leap jet engines using direct metal laser melting (DMLM) additive manufacturing process. And this is just the beginning as they and also other manufacturer of aerospace products are going to use this method for additional parts [START_REF] Zaleski | GEs bestsellnig jet engine makes 3-D printing a core component[END_REF].

In this research we tried to utilize the industrial example to carefully predict the impact of DDM technologies on the PPC practices. That is important because production planning and control practices are the ones which are responsible for the efficiency of the plants as well as the on time delivery of the products with acceptable quality to the customer. Therefore, we think it is essential for these practices to become updated and be as efficient as possible.

The main limitation of this research is rooted in the lack of real world cases in the area of DDM which makes it hard to assess the situation fully. However, we see a significant opportunity for researchers to speculate and spread the possibilities of improvement to the industrial managers that they become aware of the potential for savings and improvements through this novel digital production technology.

Fig. 1 .

 1 Fig. 1. Volvo Kalmar plant layout.