Florence Podwojewski

Mélanie Ottenio

Philippe Beillas

Gaëtan Guerin

Frédéric Turquier

David Mitton
email: david.mitton@ifsttar.fr

M Otténio

G Guérin

Mechanical response of human abdominal walls ex vivo: Effect of an incisional hernia and a mesh repair

Introduction

The treatment of incisional hernias by synthetic mesh implantation has contributed to the reduction of recurrence rates from 25-55% to 2-25% [START_REF] Korenkov | Classification and surgical treatment of incisional hernia[END_REF][START_REF] Heniford | Laparoscopic repair of ventral hernias: nine years' experience with 850 consecutive hernias[END_REF][START_REF] Cobb | Incisional herniorrhaphy with intraperitoneal composite mesh: a report of 95 cases[END_REF]. However, patients may still suffer from pain or limited mobility of the abdomen [START_REF] Mclanahan | Retrorectus prosthetic mesh repair of midline abdominal hernia[END_REF][START_REF] Müller | Abdominal wall compliance after Marlex mesh implantation for incisional hernia repair[END_REF]. To reduce pain in patients, it has been suggested that an abdominal wall with an implant will demonstrate similar behaviour to the intact abdominal wall [START_REF] Junge | Elasticity of the anterior abdominal wall and impact for reparation of incisional hernias using mesh implants[END_REF][START_REF] Hernández | Mechanical and histological characterization of the abdominal muscle. A previous step to modelling hernia surgery[END_REF][START_REF] Konerding | Maximum forces acting on the abdominal wall: experimental validation of a theoretical modeling in a human cadaver study[END_REF].

Thus, a better knowledge of the biomechanical response of the abdominal wall and how it is affected by the implant could be helpful to further improve the treatment of incisional hernias.

However, few studies considered the behaviour of an intact abdominal wall, and even fewer examine the behavior while interacting with an implant. Indeed, many studies only focused on the response of some components of the abdominal wall using an ex vivo sample testing approach. For example, [START_REF] Hwang | Passive mechanics of canine internal abdominal muscles[END_REF] and Hernandez et al. (2011) studied the behaviour of the abdominal muscles on animals. Some authors conducted tensile tests on the human linea alba and rectus sheath [START_REF] Rath | The sheath of the rectus abdominis muscle: an anatomical and biomechanical study[END_REF], [START_REF] Hollinsky | Measurement of the tensile strength of the ventral abdominal wall in comparison with scar tissue[END_REF], [START_REF] Förstemann | Forces and deformations of the abdominal wall -a mechanical and geometrical approach to the linea alba[END_REF], [START_REF] Martins | Mechanical characterization and constitutive modelling of the damage process in rectus sheath[END_REF], Ben [START_REF] Abdelounis | Effect of two loading rates on the elasticity of the human anterior rectus sheath[END_REF]). In addition, the mechanical tests are often far from physiological loading conditions. [START_REF] Junge | Elasticity of the anterior abdominal wall and impact for reparation of incisional hernias using mesh implants[END_REF] only considered uniaxial loading to study the abdominal wall elasticity (with skin and adipose tissue removed). [START_REF] Song | Elasticity of the living abdominal wall in laparoscopic surgery[END_REF], [START_REF] Van Ramshorst | Non invasive assessment of intra-abdominal pressure by measurement of abdominal wall tension[END_REF] and [START_REF] Szymczak | Investigation of abdomen surface deformation due to life excitation: Implications for implant selection and orientation in laparoscopic ventral hernia repair[END_REF] studied the complete human abdominal wall in vivo, which made the loading conditions more physiological, but limited the analysis to the skin surface of the abdominal wall. No data could be collected on the internal surface of the abdominal wall, which is where incisional hernias occurred and where meshes are typically implanted. Finally, few studies evaluated the influence of a mesh on the mechanical response of the abdominal wall and assessed the differences with the response of a healthy abdominal wall [START_REF] Müller | Abdominal wall compliance after Marlex mesh implantation for incisional hernia repair[END_REF][START_REF] Hernández-Gascón | Long-term anisotropic mechanical response of surgical meshes used to repair adbdominal wall defects[END_REF]). Müller et al. reported the effect of implanted meshes on the abdominal wall mobility measured noninvasively using three-dimensional stereography and compared with a non-operated healthy control group. However, this study is limited to external observations. Hernández-Gascón et al. tested ex vivo abdominal wall tissue specimens from rabbits (one group with meshes, one group as a control). The loading was limited to uniaxial loadings.

Finally, note that no information on an incisional hernia effect on the human abdominal wall behaviour is given in the literature.

A recent study from our group proposed a methodology to assess the behaviour of the abdominal wall under three states: intact, incised, and repaired with a mesh [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF]. However, the methodology was developed and applied on porcine abdominal walls. The objective of the current study is to characterize, for the first time, the mechanical behaviour of the human abdominal wall using this methodology. The internal surface of the abdominal wall (location of the incisional hernias) and the external surface of the abdominal wall (the only visible one in vivo) were studied simultaneously.

Materials and methods

Specimen & preparation

Six anterolateral abdominal walls were dissected from post-mortem human subjects (2 female and 4 male subjects, all 66 to 84 years old) obtained from the Department of Anatomy Rockefeller of the University of Lyon (Lyon, France) through the voluntary body donation to science program. The abdominal walls were first dissected along the xiphoid process, the costal margins, the pubic bones, and the iliac crests. The lateral incisions were made between the iliac spines and the lowest point of the rib cage. All layers of the abdominal wall were preserved: skin, adipose tissue, aponeuroses, muscles, and peritoneum. Specimens were collected over a period of 14 months and then kept frozen at -20°C. They were thawed at room temperature for 16 hours before the test. Just before testing, the external surface of the abdominal wall was shaved when necessary. The height, the width, and the average thickness of each abdominal wall were also measured and are reported in Table 1. At the beginning of the experiment, the specimens were sprayed with saline solution to prevent drying.

Table 1. Age and gender of the subjects. Dimensions (cm) and average thickness (mm) of the abdominal walls

Experimental setup

The experimental setup is based on the protocol described in [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF], using air pressure loading. The main steps and the specificity of this study on human specimens are given below. First, the edges of the abdominal wall were tightened between an aluminium plate and a rubber ring using custom designed clamps. The custom grips illustrated Figure 1 are composed of:

on one side, an aluminium plate (with an octagonal hole). The border of the hole is covered by a water resistant sandpaper and a plastic tube is inserted in a groove to strengthen the gripping effect. clamps to tighten the abdominal wall in between the plate and the ring (Figure 1.b).

Octagonal holes in the aluminium plate and in the rubber sheet enabled exposure of both surfaces of the abdominal wall (Figure 1). As human abdominal walls differed from porcine abdominal walls in size and shape, the shape of the hole was modified to an octagon. The octagonal shape was used to ensure that the largest area can be loaded for all the specimens considered.

Then the abdominal wall on its support plate was positioned on a custom-designed aluminium table. A Plexiglas plate was mounted on the top of the table in order to create a closed cavity above the internal surface of the abdominal wall. Compressed air and a manual valve were used to control the pressure in the cavity. The abdominal wall was then subjected to air pressure loading by applying in the cavity a pressure of 50 mmHg (loading in 9s and unloading in 12.5s in average), which is the average measured pressure during the Valsalva manoeuvre [START_REF] Cobb | Normal intraabdominal pressure in healthy adults[END_REF]. The pressure loading cycle was repeated six times to precondition the wall. Only the last cycle was analysed.

The six abdominal walls were successively loaded by pressure for three states: intact, incised, and repaired. For the incised state, a 4cm-long incision was made on the mid-sagittal line of the linea alba. The incision was left open, filled with Vaseline, and covered with a latex film to avoid air infiltrations between the layers of the abdominal wall. For the repaired state, the abdominal wall was repaired with Parietex TM Composite meshes (Covidien, Trévoux, France), whose dimensions were adjusted to 8 cm by 12 cm in order to let an overlap between the defect and the mesh of at least 3 cm. This is in agreement with the recommendation from [START_REF] Cobb | Incisional herniorrhaphy with intraperitoneal composite mesh: a report of 95 cases[END_REF] and [START_REF] Binnebösel | Biomechanical analyses of overlap and mesh dislocation in an incisional hernia model in vitro[END_REF] to reduce the risk of recurrence. The meshes were fixed on the wall with 16 tacks (AbsorbaTack TM , Covidien, Trévoux, France) that were positioned at one centimetre of the edge of the implant and spaced 2cm apart. The meshes were also covered with a soft plastic film (13cm by 17cm, thickness 10μm) to avoid air infiltration between the implant and the peritoneum. The plastic film was laid on the abdominal wall and left free to slide. It was maintained only by the applied pressure, and it was assumed that it had no mechanical effect.

Measurements

The pressure applied to the abdominal wall was measured by a pressure sensor (ENTRAN EPX-N02). During the deformation, videos of the internal and external surfaces of the abdominal wall were recorded with four synchronized SA3 PHOTRON black-and-white cameras (Tokyo, Japan). Two cameras equipped with 35mm Zeiss lenses (Oberkochen,

Germany) were set on the internal surface, and the two others (equipped with 24-70mm Sigma lenses (Tokyo, Japan) in 24mm position) were set on the external surface. The resolution of the cameras was 1024 by 1024 pixels, which allocated approximately 4 pixels per mm in the region of interest. The acquisition frequency was 10 frames per second. Both surfaces of the abdominal wall were covered with white makeup to create a uniform background, and a speckle pattern was applied with black spray paint (Figure 1c). The speckle was used to determine 3D surface displacements and strain fields by digital image correlation using the VIC3D ® stereo-correlation software (Correlated Solution, South Carolina, USA).

The Lagrange first principal strain fields were computed for the three states on the whole external surface of the abdominal wall. The strain fields on the internal surface could only be computed for the intact abdominal wall. For the incised and repaired states, the presence of a plastic film on the internal surface prevented image correlation on this surface. Strains along the longitudinal direction (parallel to the linea alba) as well as transverse (perpendicular to that direction) and oblique were also calculated on the external abdominal wall surface.

Statistical analysis

A statistical analysis was performed on strain results in order to assess the influence of the state (intact, incised, and repaired) of the abdominal wall. A Wilcoxon non-parametric test (Wilcoxon, 1945) for paired samples was used. A value of p < 0.05 was selected to indicate statistical significance. Statistical analysis was performed using the Unistat® software (London, England).

Results

The protocol was successfully applied on 6 specimens (duration: 4 h each).

Influence of a defect and mesh repair on the behaviour of the abdominal wall

For each abdominal wall and each state, profiles corresponding to a section of the external abdominal wall in the transverse plane in the umbilical area were plotted at the initial pressure and at 50mmHg pressure. For example, the profiles of the abdominal wall H1 are provided in For five abdominal walls, a concavity at the centre (i.e. near the linea alba) was observed for the intact state. The last wall (H3) had a smoother profile with no concavity (Figure 3) that was associated with a large thickness of adipose tissues and the highest thickness of the walls tested. After incision, the profiles of four abdominal walls (H1, H2, H4, H5) were immediately affected, even without pressure loading. The region in which the concavity was observed in the intact state became flat or even convex (H2, H5). With the increase of the pressure, a larger bump (from 1 to 5 mm high) comparable to what can be observed in the case of incisional hernia was observed. The repair with a mesh did not seem to reduce the bump.

Strains calculated at 50 mmHg are reported in Figure 4 for the three states (intact, incised and repaired). In the intact state, the average longitudinal and transverse strains at 50mmHg were 6.6 ± 2.4% and 5.0 ± 1.0%, respectively. Corresponding values in the incised state were 7.9 ± 1.2% and 7.0 ± 2.3%. Along the same orientations, the values for the repaired state are 6.8 ± 2.0% and 5.9 ± 2.1%. In all states, the elongation was on average higher in the longitudinal than in the transverse direction. Five abdominal walls (H1, H2, H4, H5, H6) exhibited an increase of the strains after incision of the linea alba while one (H3) did not. Four abdominal walls (H1, H2, H3, H6) exhibited a decrease of the strains after mesh repair; one had the same strain (H5), and one (H4) went from 7.6 to 8.3 %. Due to the low number of cases, these tendencies were not significant.

Relation between internal and external surface strains in the intact abdominal wall

The maximum locations in the strain field patterns are different in the internal and external surfaces of the abdominal wall. However, strain fields appeared to be symmetrical with respect to the median axis, corresponding anatomically to the linea alba (Figure 5) for the internal surfaces of four abdominal walls. For the two abdominal walls lacking this symmetry, the dissections performed by a visceral surgeon highlighted two issues (Figure 6). In the first case, there was an asymmetry in the positioning of the abdominal wall during tightening; i.e. the linea alba was not centred in the device (Figure 6). In the second case, there was an anatomical abnormality, namely a widening of the linea alba near the centre of the specimen of the abdominal wall (diastasis). Figure 6. Specific cases observed after dissection that may explain the lack of symmetry in the strain fields: the abdominal wall H3 showed an asymmetry related to its position in the experimental device; the abdominal wall H5 had a wider linea alba at the umbilical level.

The mean and standard deviations of the strain values in the longitudinal and transverse directions on the internal and external surfaces at 50 mmHg are summarized in Table 2. The strains on the external surface were about two times higher than the corresponding strains on the internal surface (p < 0.05) (the ratio (external/internal) is 1.9 ± 1.0 and 2.2 ± 1.0 for the longitudinal and transverse strains, respectively).

Discussion

In this study, the experimental protocol developed by [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF] on porcine specimens to characterize the mechanical response of passive abdominal wall in three states (intact, incised, and repaired) was applied to six human abdominal walls. The size and the shape of human abdominal walls after excision differed from the animal specimen and required slight modifications of the protocol. The shape of the hole in the experimental setup exposing the abdominal wall was hence changed to an octagonal shape.

The strains of the human abdominal wall were compared by calculating the mean strain of the abdominal wall along the linea alba, in the transverse, and oblique directions. Higher elongations were obtained along the linea alba than in the transverse direction, which is in agreement with the results obtained ex vivo by [START_REF] Junge | Elasticity of the anterior abdominal wall and impact for reparation of incisional hernias using mesh implants[END_REF] and in vivo by [START_REF] Song | Elasticity of the living abdominal wall in laparoscopic surgery[END_REF] and [START_REF] Szymczak | Investigation of abdomen surface deformation due to life excitation: Implications for implant selection and orientation in laparoscopic ventral hernia repair[END_REF]. These results confirm the anisotropic response of the abdominal wall and could be used for validation purpose of a finite element model of the abdominal wall.

During pressure loading, the edges of the incision moved away, and a bump was observed on the external surface of the abdominal wall. This protocol was designed to assess the effect of an incision and a mesh repair on the mechanical behaviour of the human abdominal wall. The limited number of specimens that could be tested prevented the study from reaching statistical significance using a Wilcoxon test, as changes between states affected 5 out of the 6 walls, and the presence of the effect on all walls would be required to reach significance. Results

should therefore be considered as preliminary tendencies. For the porcine specimen from [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF], the mean strains of the abdominal wall were increased by about 85% in longitudinal and transverse directions. The mesh repair was associated with mean strains reduction by about 18% of porcine specimens.

However, the shapes of the region exposed to pressure -triangular for the pig and octagonal for the human -could affect some of these results, and it could be interesting to test the abdominal walls of the two species using the same shape. This could facilitate the comparisons and possibly help determine a relationship between the mechanical responses of the porcine and human abdominal walls. Indeed, such a relationship would be helpful, since animal samples are more accessible than human samples. Moreover, ex vivo mechanical characterization of an abdominal wall repaired with mesh at different post-operative times, like that which was studied by [START_REF] Hernández-Gascón | Long-term anisotropic mechanical response of surgical meshes used to repair adbdominal wall defects[END_REF] and [START_REF] Konerding | Biomechanical and histological evaluation of abdominal wall compliance with intraperitoneal onlay mesh implants in rabbits: a comparison of six different state-of-the-art meshes[END_REF], can only be performed on animal samples. Further work could also include multiple pressure levels, which could facilitate the identification of material parameters in modelling studies, and other states that could be clinically relevant (e.g. add a state with repair by suture only without using a mesh).

This study also provides results on the strain fields measured simultaneously on the internal and external surfaces of an intact abdominal wall. Analyses showed that the strain patterns differed on the two surfaces. The location of the maximum strain on the internal surface did not correspond to the location of the maxima on the external surface. For the external surface, the strain patterns were homogeneous, while for the internal surface, the strain pattern appeared to be related to the underlying anatomy of the abdominal wall. This suggests that the strain pattern of the internal surface cannot solely be deduced from the strains on the external surface in in vivo studies and that shear or sliding may occur at or between anatomical layers.

However, the external strains were found statistically twice higher than the internal ones. In one case, the external strain was four times greater compared to the internal strain. This outlier might be due to the shape specificity of the external part (e.g. umbilicus, initial tension).

For the internal surface, the strain fields appeared to be symmetrical with respect to the longitudinal axis corresponding to the linea alba in 4 out of 6 cases. The lack of symmetry in the other two cases was attributed to positioning or anatomical issues.

Some limitations can be mentioned with regard to the protocol. The effect of the test protocol duration on the response and the effect of the dehydration and rigor mortis were not evaluated. Using a similar setup on the porcine abdominal wall, [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF] found less than 10% stiffness change between two tests performed at a 3 hours interval. This difference includes duration, and dehydration, among other parameters. While a limited effect was found on the porcine abdominal wall [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF], it can only be assumed that this result could be transferred to the human samples. The effect of the stiffness of the latex film was not assessed. However the latex film was free to slide on the internal surface.

So it can be assumed that its effect is limited. No statistical difference was observed regarding the influence of an incision and a mesh repair. The small number of samples and the presence of two atypical cases could explain this result. As for the animal study [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF], the effect of freezing was not considered. Furthermore, while attention was paid to attempt to minimize the initial stresses in the positioning and tightening, these stresses were not assessed.

In the current study an experimental protocol was applied to observe the effect of an incision and a mesh repair on the biomechanical behaviour of an abdominal wall. This protocol could also detect anomalies on the wall tested (problem of positioning or anatomical anomaly).

A perspective of this study is to perform in vivo experiments in order to characterize the abdominal wall in conditions closer to the physiological conditions. The use of imaging techniques should be considered to observe the internal behaviour of the abdominal wall and not only the external surface.

  Figure 1. a) Scheme of the custom test apparatus. b) View of the grips exposing the external surface (prior to the application of the speckle) with aluminium plate, rubber ring and clamps

Figure 2 .

 2 Figure 2.

Figure 3 .

 3 Figure 3. Position profiles of the abdominal wall H3 in the transversal plane for the three states at a pressure of 0 mmHg and 50 mmHg (external surface)

Figure 4 .

 4 Figure 4. Mean strain of the abdominal wall in longitudinal (L), transverse (T) and oblique (O1, O2) directions. N=6. Error bars indicate the standard deviation

Figure 5 .

 5 Figure 5. View of the internal surface of the abdominal walls with their strain fields at 50 mmHg -view of the left camera. The dotted lines represent approximately the edges of the linea alba. The dotted lines were placed after anatomical observation The linea alba appears tilted since in digital image correlation, the camera is slightly inclined.

Table 2 .

 2 Mean strains (%) in longitudinal and transverse directions computed on internal and external surfaces of each intact abdominal wall at a pressure of 50 mmHg.

			Longitudinal			Transverse
	Wall	Strain (%)	Strain (%)	Ratio	Strain (%)	Strain (%)	Ratio
		Internal	External	Ext. / Int.	Internal	External	Ext. / Int.
		surface	surface		surface	surface
	H1	3.9	5.8	1.5	3.1	4.4	1.4
	H2	2.5	4.6	1.8	4.1	5.1	1.2
	H3	2.5	10.5	4.1	1.8	4.9	2.7
	H4	4.7	7.4	1.6	2.2	6.1	2.8
	H5	5.3	8.2	1.6	1.6	6.1	3.9
	H6	3.0	3.1	1.0	3.0	3.1	1.0
	Mean	3.7	6.6	1.9	2.6	5.0	2.2
	SD	1.0	2.4	1.0	0.9	1.0	1.0

Acknowledgements

The authors would like to acknowledge David Voirin from CHU Grenoble for his contribution to this study.

Conflict of interest statement

This study was partly funded by Covidien Company. G. Guérin and F. Turquier are employees of Covidien France.


Bernard Ycart
email: bernard.ycart@imag.fr

Rémy Drouilhet

Computing wedge probabilities *

Keywords: Brownian motion, double boundary crossing, theta functions MSC 2010: 60J65

A new formula for the probability that a standard Brownian motion stays between two linear boundaries is proved. A simple algorithm is deduced. Uniform precision estimates are computed. Different implementations have been made available online as R packages.

Introduction

Let W = {W t , t 0} be a standard Brownian motion defined on a filtered probability space (Ω, F, P). The probability that W t remains in the planar region between two linear boundaries -a 1 t -b 1 and a 2 t + b 2 will be referred to as wedge probability, and denoted by k(a 1 , b 1 ; a 2 , b 2 ):

k(a 1 , b 1 ; a 2 , b 2 ) = P[-a 1 t -b 1 W t a 2 t + b 2 , for all t 0] . (1)
It is positive if and only if a 1 , b 1 , a 2 , b 2 are all positive, which will be assumed from now on. Doob [START_REF] Doob | Heuristic approach to the Kolmogorov-Smirnov theorems[END_REF] expressed k(a 1 , b 1 ; a 2 , b 2 ) as the sum of a convergent series. Since then, Doob's formula has been extended or applied by many authors, including [START_REF] Anderson | A modification of the sequential probability ratio test to reduce the sample size[END_REF][START_REF] Durbin | Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test[END_REF][START_REF] Kennedy | Limit theorems for finite dams[END_REF][START_REF] Escriba | A stopped Brownian motion formula with two sloping line boundaries[END_REF][START_REF] Hall | The distribution of Brownian motion on linear crossing boundaries[END_REF][START_REF] Salminen | On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes[END_REF]. One reason for its success is that many boundary crossing problems reduce to computing a wedge probability, through the representation of a certain Gaussian process in terms of W [START_REF] Park | Representations of Gaussian processes by Wiener processes[END_REF][START_REF] Borodin | Handbook of Brownian motion -Facts and formulae[END_REF].

The earliest example is the standard Brownian bridge:

{B t , 0 t < 1} d = (1 -t)W t/(1-t) , 0 t < 1 .
1

From this representation one gets:

P[ sup t∈[0,1] |B t | a] = k(a, a; a, a) , (2)
which is the the distribution function of the test statistic in the Kolmogorov-Smirnov two-sided test, computed by Kolmogorov [START_REF] Kolmogorov | Sulla determinazione empirica di una legge di distribuzione[END_REF]; see [START_REF] Stephens | Introduction to Kolmogorov (1933) On the Empirical Determination of a Distribution[END_REF] for historical aspects. More generally, the probability that a (non necessarily standard) Brownian bridge stays between two linear segments is a wedge probability. This remark makes wedge probabilities a building block for more general boundary crossing problems, through the method of piecewise linear approximations.

The exit probability of a stochastic process from a region of the plane limited by two curves is called Boundary Crossing Probability (BCP). Applications of BCP's can be found in many fields, from non-parametric statistics to biology or finance: see [START_REF] Wang | Crossing probabilities for diffusion processes with piecewise continuous boundaries[END_REF] and references therein. Explicit results are scarse [START_REF] Kahale | Analytic crossing probabilities for certain barriers by Brownian motion[END_REF]. A general approximation method has been proposed by Wang and Potzelberger [START_REF] Wang | Boundary crossing probability for Brownian motion and general boundary[END_REF] for single boundaries and Novikov et al. [START_REF] Novikov | Approximations of boundary crossing probabilities for a Brownian motion[END_REF] for double boundaries; see also [START_REF] Pötzelberger | Boundary crossing probability for Brownian motion[END_REF][START_REF] Borovkov | Explicit bounds for appproximation rates of boundary crossing probabilities for the Wiener process[END_REF][START_REF] Wang | Crossing probabilities for diffusion processes with piecewise continuous boundaries[END_REF]. The idea is to replace the two (nonlinear) boundaries by piecewise linear approximations. Given its two values at the bounds of an interval, the conditional distribution of W is that of a Brownian bridge on that interval. Thus the probability that it stays between two linear segments is a wedge probability. Using the independent increment property of W , the probability that the standard Brownian motion stays between two piecewise linear boundaries is written as a multidimensional Gaussian integral, the integrand being a product of wedge probabilities [START_REF] Novikov | Approximations of boundary crossing probabilities for a Brownian motion[END_REF]Theorem 1]. The integral can be approximated either as a Gauss-Hermite quadrature [START_REF] Genz | Computation of multivariate normal and t probabilities[END_REF] or by a Monte Carlo method [START_REF] Pötzelberger | Improving the Monte Carlo estimation of boundary crossing probabilities by control variables[END_REF]. In both cases, the integrand must be repeatedly evaluated, which implies that many wedge probabilities must be calculated for very different sets of values. The problem is that in Doob's formula, as well as in all other equivalent formulas published since, the speed of convergence of the series depends on the parameters, and may be very slow for small values. This makes the BCP approximation algorithms numerically unstable.

The key to efficient computation of wedge probabilities has long been available: Jacobi's theta functions and their double expression through Poisson's summation formula. Kolmogorov [START_REF] Kolmogorov | Sulla determinazione empirica di una legge di distribuzione[END_REF] had already given two formulas for k(a, a; a, a), and remarked the interest for numerical computation: one converges fast for relatively large values of a, the other for relatively small values. This is routinely used in statistical softwares implementing the Kolmogorov-Smirnov test. The connection of k(a 1 , b 1 ; a 2 , b 2 ) with theta functions has been pointed out by Salminen and Yor [START_REF] Salminen | On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes[END_REF]. However, no alternative to Doob's formula has been deduced so far; this is the main contribution of this paper (Proposition 2.1). The algorithmic consequence is that computing at most three terms of the series either in Doob's formula or in the new alternative suffices to approximate k(a 1 , b 1 ; a 2 , b 2 ) with precision smaller than 10 -16 . Uniform bounds on precision and algorithmic consequences are presented in section 3. Several implementations are compared in section 4. An R package wedge has been made available online [START_REF] Drouilhet | wedge: an R package for computing wedge probabilities[END_REF]. Its companion wedgeParallel permits full use of a multicore structure.

2 Alternative to Doob's formula

Doob [8] (formula (4.3) p. 398) expresses k(a 1 , b 1 ; a 2 , b 2 ) as follows: k(a 1 , b 1 ; a 2 , b 2 ) = 1 - +∞ n=1 e -2An + e -2Bn -e -2Cn -e -2Dn , (3)
with:

A n = n 2 a 2 b 2 + (n -1) 2 a 1 b 1 + n(n -1)(a 2 b 1 + a 1 b 2 ) , B n = (n -1) 2 a 2 b 2 + n 2 a 1 b 1 + n(n -1)(a 2 b 1 + a 1 b 2 ) , C n = n 2 (a 1 b 1 + a 2 b 2 ) + n(n -1)a 2 b 1 + n(n + 1)a 1 b 2 , D n = n 2 (a 1 b 1 + a 2 b 2 ) + n(n + 1)a 2 b 1 + n(n -1)a 1 b 2 .
Here is another expression.

Proposition 2.1 For a 1 , b 1 , a 2 , b 2 > 0, denote: a ± = a 1 ±a 2 2 ; b ± = b 1 ±b 2 2 ; c = a 1 b 1 -a 2 b 2 2 ; d = a 1 b 2 -a 2 b 1 2 .
Then:

k(a 1 , b 1 ; a 2 , b 2 ) = π 2a + b + e d 2 2a + b + +∞ n=1 e - π 2 (2n) 2 8a + b + cos( π(2n)d 2a + b + ) -cos( π(2n)c 2a + b + ) +e - π 2 (2n-1) 2 8a + b + cos( π(2n-1)d 2a + b + ) + cos( π(2n-1)c 2a + b + ) . (4)
Proof: In terms of a ± , b ± , c, d, the expressions of A n , B n , C n , D n are:

A n = (2n -1) 2 a + b + -(2n -1)c + a -b -, B n = (2n -1) 2 a + b + + (2n -1)c + a -b -, C n = (2n) 2 a + b + + 2nd , D n = (2n) 2 a + b + -2nd .
Hence:

k(a 1 , b 1 ; a 2 , b 2 ) = 1 + 2 +∞ n=1 e -2(2n) 2 a + b + cosh(2(2n)d) -e -2a -b -e -2(2n-1) 2 a + b + cosh(2(2n -1)c) .
(5) Not meaning to add anything to the "bewildering variety of notations" for theta functions [1, p. 576], let us denote by θ the following function of two complex variables:

θ(u, v) = +∞ n=-∞ e -2n 2 u cosh(2nv) . (6)
Observe that:

θ(u, v + iπ 2 ) = +∞ n=-∞ (-1) n e -2n 2 u cosh(2nv) . (7)
By Poisson's summation formula (see for instance formula [START_REF] Eddelbuettel | Seamless R and C++ Integration with Rcpp[END_REF] p. 236 of [START_REF] Van Der Pol | Operational calculus based on the twosided Laplace integral[END_REF]), one gets:

θ(u, v) = π 2u e v 2 /(2u) +∞ n=-∞ e -π 2 n 2 /(2u) cos(πnv/u) , (8)
and:

θ(u, v + iπ 2 ) = π 2u e v 2 /(2u) +∞ n=-∞ e -π 2 (n+ 1 2 ) 2 /(2u) cos(π(n + 1 2 )v/u) . (9)
From ( 5), [START_REF] Borodin | Handbook of Brownian motion -Facts and formulae[END_REF], and [START_REF] Borovkov | Explicit bounds for appproximation rates of boundary crossing probabilities for the Wiener process[END_REF]:

k(a 1 , b 1 ; a 2 , b 2 ) = 1 2 θ(a + b + , d) + θ(a + b + , d + iπ 2 ) - e -2a -b - 2 θ(a + b + , c) -θ(a + b + , c + iπ 2 ) .
Combining four evaluations of θ does not quite solve the numerical problem for small values of a + b + . The terms of the four series need further rearrangement. It is obtained observing that:

c 2 -4a -b -a + b + = d 2 .
Hence:

e -2a -b -e c 2 2a + b + = e d 2 2a + b + .
From there, (4) follows.

As remarked by Salminen and Yor [START_REF] Salminen | On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes[END_REF], the symmetry and scaling properties of k can be read on Doob's formula. They also appear on (4):

k(a 1 , b 1 ; a 2 , b 2 ) = k(a 2 , b 2 ; a 1 , b 1 ) = k(b 1 , a 1 ; b 2 , a 2 ) = k( a 1 u , ub 1 ; a 2 u , ub 2 ) .
When slopes or intercepts are equal the expressions are simpler. If a 1 = a 2 = a then a + = a, a -= 0, c = -d = ab -, and:

k(a, b 1 ; a, b 2 ) = 1 + 2 +∞ n=1 (-1) n e -2n 2 ab + cosh(2nab -) = 2π ab + e ab 2 - 2b + +∞ n=1 e - π 2 (2n-1) 2 8ab + cos(π(2n -1) b - 2b + )) .
When both slopes and intercepts are equal one gets: .

The first sum is formula (4.3') of [START_REF] Doob | Heuristic approach to the Kolmogorov-Smirnov theorems[END_REF]. When slopes equal intercepts, the probability for a standard Brownian bridge to stay in a horizontal band is obtained, i.e. formula (4.9) p. 448 of [START_REF] Biane | Probability laws related to he Jacobi theta and Riemann zeta functions, and Brownian excursions[END_REF]. If b 1 = a 1 and b 2 = a 2 , then b ± = a ± , c = 2a + a -, d = 0, and:

k(a 1 , a 1 ; a 2 , a 2 ) = 1 + +∞ n=1 2e -2(n(a 1 +a 2 )) 2 -e -(2n(a 1 +a 2 )-a 1 ) 2 -e -(2n(a 1 +a 2 )-a 2 ) 2 = π 2 1 a + +∞ n=1 e - π 2 (2n) 2 8a 2 + (1 -cos(π(2n) a - a + )) +e - π 2 (2n-1) 2 8a 2 + (1 + cos(π(2n -1) a - a + )) .
Finally, the case where all four parameters are equal is the probability for a standard Brownian bridge to stay in a horizontal band centered at 0, i.e. the distribution function of the test statistic in the Kolmogorov-Smirnov twosided test. The formulas were originally found by Kolmogorov [START_REF] Kolmogorov | Sulla determinazione empirica di una legge di distribuzione[END_REF]; Feller [START_REF] Feller | On the Kolmogorov-Smirnov limit theorems for empirical distributions[END_REF] gave a simpler proof. Both had remarked the double expression coming from theta functions, and its interest for numerical computation.

k(a, a; a, a) = 1 + 2

+∞ n=1 (-1) n e -2n 2 a 2 = √ 2π a +∞ n=1 e -π 2 (2n-1) 2 8a 2
.

Algorithm and precision

Denote by K 1,N and K 2,N the partial sums up to N in formulas ( 3) and ( 4).

K 1,N = 1 - N n=1 e -2An + e -2Bn -e -2Cn -e -2Dn , (10)
K 2,N = π 2a + b + e d 2 2a + b + N n=1 e - π 2 (2n) 2 8a + b + cos( π(2n)d 2a + b + ) -cos( π(2n)c 2a + b + ) +e - π 2 (2n-1) 2 8a + b + cos( π(2n-1)d 2a + b + ) + cos( π(2n-1)c 2a + b + ) . ( 11
R 1,N = K 1,∞ -K 1,N and R 2,N = K 2,∞ -K 2,N . For N > 1: R 1,N 1 4a + b + (N -1) e -8a + b + (N -1) 2 , ( 12
)
R 2,N ( 2 π ) 3/2 √ a + b + N e 2a + b + e -π 2 N 2 2a + b + . ( 13
)
Proof: For both bounds, the following well known inequality is used: for any positive u,

+∞ n=N +1 e -un 2 e -uN 2 2uN . (14)
In R 1,N , all four terms A n , B n , C n , D n are larger than 4(n -1) 2 a + b + . Hence:

R 1,N 4 +∞ n=N +1
e -8(n-1) 2 a + b + , from where [START_REF] Feller | On the Kolmogorov-Smirnov limit theorems for empirical distributions[END_REF] follows by [START_REF] Hall | The distribution of Brownian motion on linear crossing boundaries[END_REF]. For R 2,N , notice first that |d| 2 a + b + , by Schwarz inequality. Hence:

R 2,N 2π a + b + e 2a + b + +∞ n=N +1 e - π 2 (2n) 2 8a + b + + e - π 2 (2n-1) 2 8a + b + = 2π a + b + e 2a + b + +∞ n=2N +1 e -π 2 n 2 8a + b + .
Using again ( 14) leads to [START_REF] Genz | Computation of multivariate normal and t probabilities[END_REF].

As expected, the bound on R 1,N decreases with a + b + , the bound on R 2,N increases. Denote by τ N the value of a + b + such that both bounds are equal, and by ε N their common value.

Computing K 1,N if a + b + τ N and K 2,N else ensures ε N precision at least, whatever a 1 , b 1 , a 2 , b 2 .
The values of τ N and ε N for N = 2, . . . , 8 are given in Table 1. In particular, for N = 3 a precision

N 2 3 4 5 6 7 8 τ N
1.380 1.136 1.030 0.973 0.937 0.912 0.895 ε N 2.9 10 -6 1.8 10 -17 5.1 10 -34 5.6 10 -56 2.3 10 -83 3.5 10 -116 1.9 10 -154 Table 1: Threshold and precision per number of terms computed. ε 3 = 1.8 10 -17 is obtained, which is below current machine double precision. Thus N = 3 was chosen as default value in our implementation. Computing more than two terms is usually not necessary. To illustrate this a Monte Carlo study has been conducted, over 10 6 four-tuples of independent random values drawn in the interval [0,10] with cumulative distribution function (x/10) 1/2 . That choice ensured that wedge probabilities covered the whole range of [0, 1], with higher mass on values close to 0 or 1. For both sums the number of terms to convergence was defined as the first value of N such that the remainder is smaller than ε = 10 -16 . As predicted by Proposition 3.1, in all 10 6 cases either K 1,N or K 2,N reached ε precision with N = 3 terms or less. Actually, in 2.5% of the cases, the result was smaller than ε or larger than 1 -ε: no summation was needed. In 73.8% of the cases N = 1 sufficed to get ε precision, and in 20.6% of the cases N = 2 terms were necessary; only in 0.56% of the cases were N = 3 terms necessary. Experimental results evidenced the need for an alternative to K 1,N . Indeed, in 442 out of the 10 6 cases, the number of terms to convergence of K 1,N was larger than 100, and in 1558 cases it was larger than 50. Figure 1 presents the numbers of terms to convergence as a function of log(a + b + ), for all 10 6 random values, and both K 1,N and K 2,N . As expected, the numbers decrease for K 1,N ; they increase for K 2,N .

Implementation

The calculation of successive terms in K 1,N or K 2,N is easily vectorized. This makes the computation of a vector of wedge probabilities relatively fast in pure R [START_REF] Development | R: A Language and Environment for Statistical Computing[END_REF]. Our objective was to explore gains in computing time, using existing R tools. The most widely used of these tools is Rcpp [START_REF] Eddelbuettel | Seamless R and C++ Integration with Rcpp[END_REF]. It uses (usually faster) compiled C++ code, interfaced with the R environment. Most computers now have a multicore architecture. However by default, both R or Rcpp use only one core. Taking full advantage of a multicore stucture can be done for example through RcppParallel [START_REF] Allaire | RcppParallel: Parallel Programming Tools for 'Rcpp[END_REF].

Numerical experiments have been made using vectors of simulated entries with the same distribution as in section 3: independent entries on [0,10] with cumulative distribution function (x/10) 1/2 . Five implementations were considered: pure R, one-core Rcpp, RcppParallel with 4, 6, and 8 cores. Table 2 reports running times on a MacBookPro Retina 15. The running time for 10 6 values in pure R (0.725 second), can be considered satisfactory. However, the gain in time goes up to twentyfold if an eight-core architecture is used. One of the known limitations of vectorized versions in pure R is memory space: ours cannot deal with vectors larger than 10 For n = 10 8 , calculations exceed memory space in pure R.

An R package wedge has been made available online [START_REF] Drouilhet | wedge: an R package for computing wedge probabilities[END_REF]. In order to address installation issues for users not interested by a parallel version, the companion package wedgeParallel has been left as an option.

  ) The question is: for a given set of parameters a 1 , b 1 , a 2 , b 2 , which of K 1,N and K 2,N should be computed, and which value of N ensures a given precision? Proposition 3.1 bounds remainders. Proposition 3.1 Denote by R 1,N and R 2,N the remainders:

Figure 1 :

 1 Figure 1: Number of terms to convergence as a function of log(a + b + ) for K 1,N and K 2,N , over 10 6 simulated values of a 1 , b 1 ; a 2 , b 2 . The dashed vertical line marks the theoretical threshold for N = 3 i.e. τ 3 = 1.136.

Table 2 :

 2 7 entries. Times in second for calculating wedge probabilities over vectors of size n = 10 6 , 10 7 , 10 8 , in pure R, Rcpp, RcppParallel with 4, 6, 8 threads.

	n	R	Rcpp RcppParallel (4) RcppParallel (6) RcppParallel (8)
	10 6 0.725 0.169	0.05	0.044	0.036
	10 7 5.854 1.785	0.471	0.417	0.353
	10 8	-	17.607	4.725	4.266	3.987


Yacine Bouallouche
email: yacine.bouallouche@ec-nantes.fr

Catherine Da Cunha
email: catherine.da-cunha@ec-nantes.fr

Raphael Chenouard
email: raphael.chenouard@ec-nantes.fr

Alain Bernard
email: alain.bernard@ec-nantes.fr

Extended Administration: Public-Private Management

Keywords: extended administration, public-private partnership, simulation, network performance

In a difficult economic context, the control of public efficiency and the steering of public investment in the private sector are of paramount importance. Here we focus on the evaluation of public-private partnerships efficiency regarding key performance indicators relating to quality of service and financial cost. Computational results on a case study validate the potential of discrete-event simulation for the clothing function in the French army. Initial and final steps are simulated, but also transition steps.

Context

The economic crisis and the budgetary rigor that followed had many consequences. In Europe it drove the States to diminish their expenses and reduce the number of public servants. Yet one of the levers to boost the economic recovery was to inject public money in sectors that would allow the most pay back in terms of innovation, employment, and public value. Both objectives can be obtained when externalizing previous state realized mission to private tiers. In France the public budget that is re-injected in the private economy to maintain public value mission represents 10% of global GDP [START_REF]LIVRE VERT sur la modernisation de la politique de l'Union européenne en matière de marchés publics /GREEN PAPER on the modernisation of EU public procurement policy Towards a more efficient[END_REF]. Furthermore the lever effect is then of 1 to 5 (depending on the sector) [START_REF]Assemblée des communautés de France: Assises de l'investissement : propositions pour un investissement public levier de croissance[END_REF]. The main challenge is then to use this great opportunity to overcome the economic crisis by optimizing the public-private relationships. The resulting network of actors forms a extended administration

The economic recovery plans are not limited to programs of public work (by nature one-time and limited to construction) but also a real sustainable investment of public found in the private economy. The European Commission [START_REF]European commission: Reforming the budget, changing Europe -A public consultation[END_REF] proposed 3 indicators to estimate the added value of expenses:

-Do the expenses have a political nature? -Do tey offer a payback at the European level? -Do they enable to meet their objective (efficiency)?

In France, a major difficulty is that most investments are done by regions or cities [START_REF]Assemblée des communautés de France: Assises de l'investissement : propositions pour un investissement public levier de croissance[END_REF]. National directives have little impact, yet a successful example at the national level could play the role of a good practice to follow. Like the Canadian "Program Review" [START_REF] Bourgon | Program Review, the Government of Canada's Experience Eliminating the Deficit, 1994-1999: A Canadian Case Study[END_REF] and many other programs conducted by OECD countries and inspired by the New Public Management (NPM) [START_REF] Osborne | Reinventing government: How the entrepreneurial spirit is transforming the public sector[END_REF], the French General Revision of Public Policies aims at:

focalizing the State on its sovereign functions, doing better and cheaper, creating and developing intern and extern providers.

Faced with the limits of the NPM, several countries have begun to amend the reforms inspired by NPM. The French General Revision of Public Policies (GRPP) was deleted and replaced by the Modernization of Public Action (MPA). If the spirit of reform changes, the goal remains the same: reduce the operating costs of administrations. In addition, the MPA has do deal with the legacy of the NPM. The previous reforms have caused fragmentation of public value chains, leaving a legacy of multiple public and private organisms engaged in public services [START_REF] Lévesque | Social In novation in Governance and Public Management Systems: Towards a New Paradigm[END_REF]. The production and service networks should combine the strengths of public and private actors to enable the 3 phases of the relationship: shift from public only to private-public partnership (PPP), PPP management but also the destruction of the relationship either to re-integrate the function into the public area or to choose another private provider.

Definitions and Difficulties

This context requires the establishment and management of networks to deliver public services. The resulting network of actors forms a extended administration that can relies on the advance made on the extended enterprise domain. A public network is composed of public organizations autonomous in their management although controlled by the state and/or local authorities. In this network, the management of interactions is difficult because its structure is by definition legally "split". The complexity rises in an extended administration because of the inclusion of private organizations. The inclusion of a private organization in a network is described as public-private partnership. The notion of partnership here covers all forms of openings and close links between the public and private sectors. The PPP is a "lasting partnership between legally separate entities pursuing private and public aims and objectives, which, taken separately, could not be achieved with efficiency and economy in the context of programs, projects or operations of general interest, common good or public service" [START_REF] Mazouz | Public-private partnership: Elements for a project-based management typology[END_REF]. A literature review and discussions with different actors of the public sectors, we identified three categories of problem with public-private networks -The public-private partnership performance evaluation; -The partnership relationship management throughout its life cycle; -The public-private network management as a whole, to ensure that the local performance is not achieved at the expense of overall performance.

Modeling and Managing

The actual interaction between the State and the potential Private partners takes the form of invitation to tender and corresponding responses. The invitations to tender expose the expectations in term of services and also the contractual commitments in terms of creation of public value (e.g. local supply and employment).

The responses present the estimated price and some implementation solutions. Yet as for today there is no tool that enables the quantitative comparison based on objective simulation.

4 Use Case: Clothing in the French Army

Context

In France the clothing function for the civil servants represents a market of 650Meper year, the French army itself stands for 150Meper year [START_REF]Ministère Français de l'Economie et : Guide Gestion de la fonction habillement dans le secteur public-Groupe d'étude des marchés d'habillement et de textile[END_REF]. Table 1 presents some key figures in 2012.

As Is Modeling

Today, the clothing function is operated by public servants see Fig. 2. The procurement is done at a national level, items being furnished by suppliers (often abroad in low cost countries). The replenishment is done on a temporal basis, volumes negotiated for several years based on forecasting.

The storage is done on 6 warehouses, each of them responsible for several defense bases both in France and abroad (in fixed bases and special operations' bases). When a customer (member of the armed force) need an item he/she goes to its defense base supply shop and receive the required item, in the best case immediately and the worst case within days. Local inventories in defenses bases are managed on a base stock policy. This operating policy is quite effective on a customer view, level of service and time of service are evaluated as more than satisfying. Yet the operating costs are important (cf. 4.1). The objective of the French government is to reduce both the employment cost and the inventory cost. For instance, there is more than 2 years of inventory held in the 6 warehouses for some items like socks. In this context a proposition is to create a private public network to operate the clothing service.

To Be Modeling

The proposed scenario is to externalize the purchasing and warehousing function for the non-specialized items (high-tech and strategically items such as deminers' vests will remain in the public management). The private provider will manage the interaction with the items' suppliers and answer the demand from the defense bases, see Fig. 3. The public value generated by the service provider will be guaranteed per contract, with indicators including insertion of disabled employees, employment of target cities inhabitants.

Computational Results

Fig. 4. Simulation results

Using the python SimPy library1 , we modeled and simulated the As-Is scenario (step 0) and the transition shift to the To-Be PPP (progressive shutting down of the 6 public warehouses: step 1 to 6) using discrete event processes. At each transition step, the private provider increases its activity to answer the bases' needs. This modelling aimed at evaluating the impact in terms of service level for the customers (defense civil servants) and eventually re-assess the replenishment policies in the defense bases.

The simulation encompasses the 90 bases and 6 warehouses. The number of items required reaches 2 million for each step, each having a time window of a year.

Figure 4 presents 2 performance indicators: average lead time (curve) and maximal lead time (sticks) for the different steps of the shift. The lead time highlights the quality of service for the army civil servants i.e. the time between the order and the reception of the goods. This time is conditioned not only by the availability of the items but also by the availability of civil servants for the clerical tasks, the packing, the shipping and delivering of the items.

It is interesting to note that if the replenishment policy of the bases remains the same the average lead-time remains acceptable moving form 1.4h to 1.9h. The maximal lead times correspond to a situation when the defense base needs to replenish its stock to answer the civil servant demand. In this case the lead time is multiplied by 4, but this evolution occurs only in steps 5 and 6 when defense bases abroad shift from public to private provider. The increases is maintained, mostly because to the delivery policy of the PPP agreement, the private partner being committed by contract to ship the items within days of demand reception.

Regarding the HR indicators, the shutting down of public warehouses enable the immediate redeployment of public clothing network civil servants and on the long term their non-replacement.

Conclusion

The first results presented here enable us to verify that a simulation of a PPP is possible even with little knowledge of the internal private actor activities. The representation of the contractual obligation only permits to obtain KPI for the public service.

This new tool will enable to evaluate objectively and more quantitatively the response to the public invitation to tender. Further research will aim at including more activities to enlarge the evaluation of the private propositions before engaging in a PPP.

Fig. 1 .

 1 Fig. 1. General government gross debt (Percentage of GDP) [3]

Fig. 2 .

 2 Fig. 2. BPMN diagram for As-Is Modelling

Fig. 3 .

 3 Fig. 3. BPMN diagram for To-Be modelling

Table 1 .

 1 Key figures in 2012[START_REF] Roger | Projet de loi de finances pour 2013 : Défense : préparation et emploi des force[END_REF]

	Headcount of the users	300 000
	Headcount of the public clothing 1 600 people
	network civil servants	1 300 Full time equivalent
	Warehouses	6 in France
	Defense bases (France & abroad) 90
	Value of the stocked items	800 Me

https://simpy.readthedocs.org/en/latest/


Valdir Morales
email: valdir_morales@yahoo.com.br

Oduvaldo Vendrametto
email: oduvaldov@uol.com.br

Samuel Dos Santos

Edivaldo Vanessa Santos Lessa

Antonio Sartor

Samuel Dereste
email: samuel_dereste@yahoo.com.br

Santos

Edivaldo Antonio Sartor
email: edivaldo@tjsp.jus.br

ERP Evaluation in Cloud Computing Environment

Keywords: ERP, Cloud Computing, System, Market

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Upon the Internet arrival, changes began to happen more frequently and with a smaller time interval. Many companies seek new technological tools for decision-making processes with greater efficiency. Within the market alternatives, Cloud Computing emerges as a service available to organizations, in collaboration with organizational strategy.

Systems before located in the organizational environment, according to the company's strategy, can now be relocated to this new cloud service.

As an object of research, ERP is already established in organizations where it provides better process control, monitoring, informing, and enabling top management to have an increased visibility about the results.

Organizations usually keep information systems within their organizational environment, but with this new technology of Cloud Computing, one can envision a greater flexibility and at the same time be less dependent on the enterprise computational environment by decentralizing the workload capacity to the cloud.

Among the ERP objectives are included the integration of automation systems and their vital activities, such as manufacturing, human resources, finance and supply chain management [START_REF] Razmi | Developing a practical framework for ERP readiness assessment using fuzzy analytic network process[END_REF]. The information generated from this process serves to support organizational decision-making processes.

The ERP solution is considered a business application, enabling the interconnection of data, processes and functional areas from an organization, providing a graphical interface so the user can manage such information [START_REF]ERP Implementation Success and Knowledge Capability[END_REF].

The Enterprise Resource Planning (ERP) is seen as a strategic information and a tool to face competitors and to allow corporations to improve productivity [START_REF] Wu | Segmenting and mining the ERP users' perceived benefits using the rough set approach[END_REF]. Organizations implement ERP to gain visibility into business processes in a dynamic environment [START_REF]ERP Implementation Success and Knowledge Capability[END_REF].

The expansion of the Internet and business led to a conceptual change in which the services performed on a desktop computer migrated to the internet providers [START_REF] Cheng | The Impact of Cloud Computing Technology on Legal Infrastructure within Internet-Focusing on the Protection of Information Privacy[END_REF].

The characteristics of cloud computing are: it is sold on demand; the service is managed by the provider; users can determine the amount of service to be taken; and users can log on to the network from any computer in the world [START_REF] Bose | The Roles of Security and Trust: Comparing Cloud Computing and Banking[END_REF].

A comprehensive definition is given by the National Institute of Standards and Technology, that states: "Cloud computing is a model for enabling ubiquitous, convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, servers, storage, applications, and services) that can be rapidly provisioned and released with minimal management effort or service provider interaction" [START_REF] Bose | The Roles of Security and Trust: Comparing Cloud Computing and Banking[END_REF].

Cloud computing is a new way to provide information technology (IT) services for individuals and organizations. Its adoption is driven by availability, flexibility and agility [START_REF] Stieninger | Impacts on the Organizational Adoption of Cloud Computing: A Reconceptualization of Influencing Factors[END_REF].

Cloud computing offers a new computing paradigm that provides IT as a service. Service models (IaaS, PaaS, SaaS) provides a basis for understanding cloud computing and its capabilities [START_REF] Ferreira | Cloud Computing Implementation Level in Portuguese Companies[END_REF].

IaaS -Infrastructure as a Service -the computing environment is provided as requested by the customer, as if it were rented, so the customer does not have to worry about maintenance costs or to upgrade the hardware used on the basis because the cloud environment is being used [START_REF] Ferreira | Cloud Computing Implementation Level in Portuguese Companies[END_REF].

PaaS -Platform as a Service Cloud -the customers' capacity to move to cloud applications, designed and developed by themselves using certain programming language and tools provided by the supplier [START_REF] Ferreira | Cloud Computing Implementation Level in Portuguese Companies[END_REF].

SaaS -Cloud Software as a Service -the consumers have the possibility to use an application that is not installed on their personal computer, just accessing the Internet [START_REF] Ferreira | Cloud Computing Implementation Level in Portuguese Companies[END_REF].

Through this new scenario, there are questions between the use of local form ERP or in the Cloud.

Materials and Methods

Survey Procedure

Global companies conducted an exploratory research with reference to the research firm Gartner data in order to assess the world stage as the use and trends of Cloud Computing.

Gartner Research had a global character with 89 respondents. Respondents were distributed geographically: 33 were from North America, 36 from EMEA (Europe, the Middle East, and Africa), 13 from the APAC (Asia Pacific Region) and five from Latin American countries (two of them did not provide details of their location). There were companies in the service and manufacturing segments.

It is shown Ten Myths of Cloud Computing, data from Gartner [START_REF] Gartner Inc | The Top 10 Cloud Myths[END_REF]. Next, we highlight the local ERP characteristics confronting it with the Cloud environment.

It was also developed a survey applied to about sixteen IT specialists in Brazil aiming to identify the stage of Internet service providers in Brazil, with the following questions: 1-Do you consider that broadband providers meet the SLA (Service Level Agreement) standards? 2-Do you consider that broadband providers meet the connection speed expectations contracted? 3-What are the aspects to be observed for migrating from an ERP site to Cloud Computing?

To obtain feedback on the technical feasibility of a possible change to the Cloud ERP.

3

Results and Discussion

Research Summary

The worldwide market for ERP has a large competition in several segments, the companies market share that sell ERP shows a significant revenue: SAP 24% U$ 26.6 billion, Oracle 12% U$ 3.07 billion, Sage 6% U$ 2.1 billion, Infor 5.8% U$ 1.49 billion, Microsoft 5% U$ 1.28 billion, Other 41.2 [START_REF]Infográfico Mercado de ERP[END_REF].

What makes shows the ERP market as promising and expanding in the most several segments, stimulating employment new technologies.

There is a long way to go by migrating from Local ERP to Cloud ERP and there is a paradigm shift, because not all businesses have full compliance with this emerging concept. Gartner magazine published a report on the 10 Myths of Cloud Computing, and described shows below [START_REF] Gartner Inc | The Top 10 Cloud Myths[END_REF]:

1. Addresses that changing to the Cloud Computing (CC) technology is always related to money. Only 14% of companies choose to work with CC for cost reduction reasons. 2. You will have a Cloud Computing technology and everything will work well. The demands and the strategy for this decision-making should be analyzed. 3. The cloud should be used for everything. Not all the available service will indeed adherence.

4. The CEO decides the cloud strategy. 5. We need to understand if CC is a strategy or just a natural sale. The cloud strategy must be aligned with business objectives in order to meet multiple responses for investment. 6. The cloud is less secure than the local capacity of organizations. It depends on the suppliers to meet security standards. 7. Cloud is not for critical use mission. For certain segments it fits perfectly. 8. Cloud corresponds to Data Center. Which services should be taken to cloud. 9. Migrating to the cloud means automatically obtaining all features of Cloud.

Cloud computing has attributes and unique features, including scalability and elasticity, service based (and selfservice) Internet technologies are used, as it is shared (and uniform) and measured by use. 10. Virtualization = Private Cloud. Virtualization is commonly used enabling technology for cloud computing. However, it is not the only way to implement cloud computing.

Observing the 10 Myths of Cloud Computing presents the fundamental aspects such as relevance of the business, adhering to provide services in the Cloud, the organization's strategic alignment to use the new computing environment in order to contribute to the success of CC.

The benefits of cloud computing for users consists of: providing access to various applications without the need for installation on computers; applications can be accessed anywhere from any computer; avoiding the costs of hardware and software, using only what is necessary [START_REF] Bose | The Roles of Security and Trust: Comparing Cloud Computing and Banking[END_REF]. According to the Gartner research, cost is not always the relevant factor to opt for Cloud Computing.

The Gartner global survey reiterates the scenario about the decision-making to migrate to Cloud Computing [START_REF]Survey Analysis: Adoption of Cloud ERP, 2013 Through[END_REF]. In Fig. 1, a degree of uncertainty among opting for the new technology was identified, with about 30% of the participants choosing to keep the technology of the local ERP in their own organization, while 17% did not know, which shows lack of visibility planning and a timid tendency to make changes in a medium to long term period. The most common disadvantages of cloud computing are related to the users identity and data security, because the shared environment generates a margin of doubt, another critical point that touches the supplier's security model and the loss of physical control of the environment [START_REF] Mezgár | The challenge of networked enterprises for cloud computing interoperability[END_REF].

As Gartner research, there is a percentage between 40 and 100% of failing the changes in manufacturing sector companies, because the use of ERP by departments such as MRP (Material Resource Planning) and PCP (Production Planning Control) require availability in information systems [START_REF]Survey Analysis: Adoption of Cloud ERP, 2013 Through[END_REF]. Although it is already being strongly used in the Communications and Services, Government and Education segments, the best insight for the next three years stands out in the Communication and Service segment.

The choice of not migrating to Cloud Computing in the manufacturing segment may be related to operations involved within the Organization because the ERP operation basically focuses on the following functions: Demand (Demand Forecast), Production (Planning and Control), Displacement (Data Transition, Shift Movement Material, Quality Control, Inventory) [START_REF] Kandananond | A Roadmap to Green Supply Chain System through Enterprise Resource Planning (ERP) Implementation[END_REF].

The Gartner research shows that for companies whose revenue is less than 10 million dollars, plans to implement it during the next 3 years varies around 70% while for companies with revenues exceeding 10 billion there is a more cautious attitude to move to cloud computing [START_REF]Survey Analysis: Adoption of Cloud ERP, 2013 Through[END_REF]. Thus, we can say that for small to medium-sized companies there is a need or strategy to change the paradigm in hardware investment and maintenance. This aspect can bring out that for large corporations, new technology goes through a maturation process but it do not let explicit the risk issue.

Observing the Cloud Computing scenario, it was developed a comparison to the Local ERP in order to establish the different characteristics of computer environments. The following differences are listed below:

1. There is a need to invest in infrastructure such as hardware, software, database and networks in the local environment. 2. Since ERP is in the organization's environment, adjustments can flow more naturally and quickly. 3. Several departments and stakeholders are involved; people have a degree of knowledge because either they have participated in its implantation or they have experienced system change. 4. It depends exclusively Organization's investments in security in the local. 5. On the Local ERP, being critical or not, the services work to meet the company's demands.

The topics cited above make clear the needs of each environment, providing an insight into the use of resources and their strategies. Thus, a survey was applied.

The success of ERP implementation depends on various types of integrations, such as processes, organization, data and applications [START_REF] Wu | Segmenting and mining the ERP users' perceived benefits using the rough set approach[END_REF]. Thus we can say that a synergy between people, processes and technology is necessary to achieve the critical success factor.

The ERP plays a vital role in the organization. Therefore changes such as corrections and improvements need to be planned and verified with greater certainty before entering the production environment, since the investment in hardware and software is highly critical [START_REF] Law | Managing the full ERP life-cycle: Considerations of maintenance and support requirements and IT governance practice as integral elements of the formula for successful ERP adoption[END_REF].

The first question addressed in the survey applied is about the broadband access providers in Brazil that you use (or have used). Do you consider they meet the SLA (Service Level Agreement) standards? The responses obtained were as follows: Totally Agree 6.3%, Agree 6.3%, neither agree nor disagree 12.5% Disagree 62.5% Strongly Disagree 12.5%. Thus, it can be said: observing the availability criteria to keep the service in the air, if a company had total dependence on Internet providers and required some maintenance, it faced major disruptions.

This aspect is of paramount importance and shocking to opt for a location shift to ERP Cloud. The availability criterion in the IT field, should always be assessed and rated to not damage the provision of services with users.

Cloud Computing allows greater flexibility to the user through high-speed Internet, highlighting the use of the remote service and the low commitment of the use of hardware and software [START_REF] Pardeshi | Cloud Computing for Higher Education Institutes: Architecture, Strategy and Recommendations for Effective Adaptation[END_REF]. Based on this, the second question of the applied survey is whether the providers meet the connection speed expectations contracted from the broadband.

The scenario was as follows: 0% totally agree, 18.8% agree, 0% neither agree nor disagree, 68.8% disagree, 12.5% totally disagree. Based on this scenario, the internet speed question highlights that the level of dissatisfaction is latent based on the service offered, showing weaknesses regarding the necessary infrastructure.

The following scenario can be envisioned with Cloud Computing as opinions posed by experts:  Before opting to migrate, it is required to mitigate the risks, identifying criteria to apply a methodology for decision-making. Alternatively, the Analytic Hierarchy Process (AHP) method allows better visibility.  The business must grip on CC in the types of services that will be available; otherwise, it will be more feasible to keep the ERP at the new location.  The hybrid solution (cloud services and some local services) initially shows the most cautious decision enabling to measure what should in fact be made available in the cloud.  In case of a disaster in an organization, the data would be secure in a cloud environment.  The security that was controlled by the organization's computing environment is decentralized to the IT providing company, with a need for trust in the services provided.

The hybrid cloud environment combine cloud services public and private allowing require extra capacity to a cloud public for temporary workload peaks [START_REF] Garrison | The effects of IT capabilities and delivery model on cloud computing success and firm performance for cloud supported processes and operations[END_REF]. The hybrid solution is cautious in decision making and what kind of services can be allocated in Local mode or in the Cloud.

Cloud Computing provides best results in the management of scalable hardware and software resources, optimizing the work, increasing the performance of implementation of computational tools [START_REF] Oliveira | Assessing the determinants of cloud computing adoption: An analysis of the manufacturing and services sectors[END_REF].

Thus, alternative methods were presented in order to channel efforts as a suggestion for improving the selection and applicability of Cloud Computing environment.

Conclusions

The development of this research allowed to reveal that cloud computing is in a maturing stage, not everything that is currently being done in the local environment of an organization is exactly in accordance with the cloud environment. There is a conceptual change in the aspect of using the new technology. The real needs of an organization that leads to cloud computing should be identified in order to achieve an effective decision-making, assessing critically the adhesion of technology for business.

Fig. 1 .

 1 Fig. 1. Decision-making to migrate to Cloud Computing.


Steinar Kristoffersen
email: steinar.kristoffersen@himolde.no

Co-operative Production Planning: Dynamic Documents in Manufacturing

Keywords: Design and manufacturing in a collaborative setting, engineer-toorder (ETO), lean documentation, quality, IT support for industry

This case study describes the manufacturing of advanced, highvalue maritime vessel equipment as an opportunistic, dynamic, knowledgeneedy and collaborative process, in which planning and construction is closely integrated, rather than as a repeatable physical assembly that takes place in phases, for each of which planning is pre-hoc and pre-emptive. We assert that this is one reason that the anachronistic perspective of "documents as documentation", contributes to actors' conflicting views of their project. This paper examines these difficulties, offers a theoretical examination and design implications for next generation industries to consider.

Introduction

Many enterprises in high-income countries are bound to struggle with higher production costs than those of many less-mature, yet ambitious economies. Straight competition on identical terms is impossible. Hence a succession of process re-construction efforts has been launched in high-cost countries [START_REF] Ekstedt | A New Division of Labour: The "projectification" of working and industrial life. Building Anticipation of Restructuring in Europe[END_REF]. Most reformation programs bring together existing schemes, such as lean, mass customization and ETO (engineer-toorder), concurrent engineering and front-end loading [START_REF] King | Robustness Development and Reliability Growth: Value Adding Strategies for New Products and Processes[END_REF][START_REF] Rocha | Mass Customization Enablement Through Lean Design & Set-Based Concurrent Engineering Application[END_REF]. There has been little improvement, however. Traditionally bureaucratic and vertically integrated manufacturing, with centralized planning, scheduling, and control mechanisms are not sufficiently flexible for this type of production and product-mix [START_REF] Shen | Applications of agent-based systems in intelligent manufacturing: An updated review[END_REF]. We find suggestions in the literature that hard problems of process planning and manufacturing control in a dynamic, distributed portfolio may possibly be solved using agent technology [START_REF] Shen | Applications of agent-based systems in intelligent manufacturing: An updated review[END_REF], expert systems [START_REF] Choy | Design of an intelligent supplier relationship management system: a hybrid case based neural network approach[END_REF] or case-based reasoning [START_REF] Choy | Design of an intelligent supplier relationship management system: a hybrid case based neural network approach[END_REF], etc. However, experience shows us that most businesses rely on simple software, such as spread sheets and text editors, email and databases for their manufacturing management support. As a consequence, multiple perspectives on planning, evaluation and the economy of the project arise, which reduces manageability. This paper's objective is to explicate this practice and initiate a road map ahead that may alleviate the situation.

In the domain that pertains to this paper ratio of labor to value-creation has been relatively stable since the seventies [START_REF] Froud | Financialization across the Pacific: Manufacturing cost ratios, supply chains and power[END_REF], which might imply that our industry's "high value-creation knowledge networks" (cf. [START_REF] Camarinha-Matos | Collaborative networks: Value creation in a knowledge society[END_REF]) are less efficient than we believe. This might have to be improved shortly.

2

Research problem

The ability to be flexible and respond favorably to change orders is a distinguishing characteristic of the so-called "engineer-to-order" industries [START_REF] Grabenstetter | Developing due dates in an engineer-to-order engineering environment[END_REF]. However, when extraneous factors such as a fall in the oil price comes into play, it turns out that this edge becomes very blunt, indeed, as customers start demanding that "flexible costs" regardless, are made "off-the-shelf". In the current paradigm, outsourcing to low-cost countries possible has contributed to make this possible as well as profitable [START_REF] Hummels | Transportation costs and international trade in the second era of globalization[END_REF]. However, when the same performance become universally available, customer do not wish to pay a premium for tradition [START_REF] Venkata | What future distribution engineers need to learn[END_REF]. Hence, a next step up and forward is required for European industries to survive in global competition [START_REF] Brettel | How virtualization, decentralization and network building change the manufacturing landscape: An Industry 4.0 Perspective[END_REF].

We believe that poorly understood documentation practices have contributed to reduce innovation of the current situation. Outsourcing as a "division of labor" has often been based on insufficient specifications, incomplete planning or inaccurate estimation techniques [START_REF] Dwivedi | IS/IT project failures: A review of the extant literature for deriving a taxonomy of failure factors, in Grand successes and failures in IT[END_REF], which may be hard to change, essentially, but the situation is exacerbated when documents are presented as objectively describing the state of affairs, whilst in reality they are interacted with as a type of agent [START_REF] Christensen | Documentscape: intertextuality, sequentiality, & autonomy at work[END_REF].

Any detached and extraneous description is bound to be out of synch, inconsistent and erroneous, but this is not a problem unless it is poorly handled [START_REF] Massey | Cloudy forecast: an exploration of the factors underlying shared repository use[END_REF]. Members of an organization purposefully create different documents describing the same phenomena. If conflicts occur, however, the exposition of them in a technical perspective only [START_REF] Sun | Creative conflict resolution in realtime collaborative editing systems[END_REF], is not sufficient. Current digitization of production processes hide the coexistence of multi-perspective documentation and when retrieved, purport that they are equivalent representation of a phenomena. That is, as we shall demonstrate in this paper, when the trouble begins.

This paper proposes to treat documentation as "perspective elements". It may seem like a paradox that it thus thus rejects the objectivity of "documents as labels" in favor of a subjective, constructionist view of "documents in actor-networks", but in the transformation of our industry to a 4.0-type "internet of things", this is, we believe, exactly what is needed. Operationally, as well, we aim to demonstrate that this approach can be modelled using object-oriented techniques [START_REF] Iivari | Object-orientation as structural, functional and behavioural modelling: a comparison of six methods for object-oriented analysis[END_REF].

Research methodology

This study is based on ethnographic and participative research in one company. It is of course always a challenge to generalize from single case studies. However, the rich experience, which have been gained from taking part in more than 10 project meetings, in addition to phone calls/discussions and document exchanges per meeting and finally to contribute with findings, ideas and as a discussion partner in a project, do give a solid grounding for qualitative, theoretical reasoning. This research methodology, admittedly, does look broadly and pragmatically on what constitutes "data" for research purposes [START_REF] Twidale | Quick and dirty: lightweight methods for heavyweight research[END_REF]. It represents, however, a well-known foundation for qualitative research [START_REF] Crabtree | Ethnomethodologically informed ethnography and information system design[END_REF].

Investigation results in A Crane Company (ACC)

The company that we have studied makes small and mid-sized (up to ca. 50 metric tons) cranes and handling systems, which can operate on depths down to 4000 meters. Typically, the cranes are used to place and recover underwater unmanned robots or excavators, that dig tranches, connect cables and pipes, etc., which are necessary infrastructure to support the oil and gas industry offshore.

Early projects in ACC were commonly termed "prototypes" and the current process is seen as one of increasing standardization. From the sales division's point of view, the predictability of the cost situation is crucial. They have to defend the price to the customer as well as the margins internally, towards their role as a profit centre in a group consisting of many engineering-oriented companies in a diverse concern.

The market connections are made locally, although the customers themselves already operate internationally and many have subsidiaries worldwide. Inevitably, as the business grows, so does the network and sales, which are made independently of geography.

There are clearly many rational reasons to outsource industrial production from high-cost countries, which are usually near to the affluent market and its ambition to innovate, to low-cost countries offshore, which cannot market and sell their skills in an integrated and packaged product. Repetitive or at least voluminous, man-hour intensive and burdensome parts of the manufacturing process, will still be decisive parts of large-scale industrial projects. The solution for ACC has been to stop doing manufacturing and and specialize instead on sales, design, engineering, integration and commissioning. Steel work, therefore, is outsourced. Engines and pumps are procured, as is the control system and drives. Electrical systems design, however, is mainly carried out locally.

The following recount explains the procedure of contracting and building an ETO offshore crane, together with its multifarious documentation practices.

The go-ahead decision

After initial contact with a customer and preliminary information exchange concerning the scope of the project, the VP of the offshore division calls a go-ahead board meeting to make the decision about bidding. The ambition has to be commercially sound, which in this context means a solid 15% margin on the total cost of sales. The decision is tricky, since there are many variables, especially connected to the ratio of value created through labour vs. procurement. For many suppliers to the offshore industry, it has been treated as a common fact that outsourced and procured parts of a project typically constitute 80% of the value created. If the parts were standardized or easily available, the decision to build a 1 million GBP crane, if it comprised 800 000 GBP of parts and only 200 000 of management and engineering work at home, to produce a profit of 150 000 would be relatively transparent, albeit hard to achieve. It is, however, neither the case that the first 800 000 are risk-free, nor that the 200 000 in "knowledge work" are fixed, predictable or even particularly "manageable" as we shall show below. We put forward that one of the reasons is the way in which documents are used as documentation, paradoxically a role for which they seem wholly unsuited.

Assertions about a procurement-centric process

The market situation is dynamic, with oil prices governing much of what the customers on the one hand know or think they need and are willing to pay, on the other. One aspect of the current conjunctures is that the pioneering spirit of the oil & gas sector, which has dominated for the past 15 years, have created a steady increase in demand for capacity, i.e., ships, cranes, rigs and therefore engineering work volume connect to the production of steel units and structures. Sales, design and engineering, on the other hand, which we have called knowledge work, is crucial to every project, but this intellectual capacity is rather more "flexibly available" in a way that steel work is not.

First assertion: Affluent economies educate technical engineers and accountants steadily. They take well-paid, salaried jobs mainly, which in the welfare state-models in Europe entail relatively little risk. Therefore, although companies think they struggle to find the best people and certainly would have liked to have to pay them less, they are not strongly limiting factors.

Second assertion: Pertaining somewhat to the nature of intellectual capacity as a non-limiting factor as well, is the inherent ability of knowledge work, especially in the consulting nature that dominates the market in an upward conjuncture, to be available at "super capacity", or in another less euphemistic term, over-booked. This entails that the design team might quite simply not be as available as the project needs them, due to other competing and sometimes conflicting assignments.

Third assertion: As the physical labour and manipulation of materials, which require production facilities and workshops have been "offshored", the threshold of establishing competing businesses is low. Typically, consultants, engineers and sales staff need only a laptop and a mobile phone, before they are can operate. This means that a profitable area of operation will soon be saturated with equally skilled and motivated actors, who put commercial pressure on each other.

Together these observations mean that there is much demand in the "front end" (from customer trough sales and design), whose conceptual products cannot easily be met by simply turning up the intensity of supplies from factories that make physical goods. Engineering is the bridge between design and procurement, and its interface to the factory means that it often ends up being a bottle-neck. When all projects are "urgent" and many offer to take them on, the middle-tier components suppliers, which are ETO, becomes a victim of customers who can always go elsewhere and suppliers who know that the ETO-companies inevitable come back to them, because there is no other easily available alternatives. Thus, when prices are transparent in an international market (everybody can call and get a quote), downwardly static and upwardly mobile, as a consequence there is no profit easily won for the ETO companies in terms of putting a margin on top the goods that they buy.

Fourth assertion: There are a growing number of designers and engineers who due to the specialized and reductionist nature of the distributed manufacturing processes do not have any hands-on experience with production as such. Hence, they depend on their own suppliers for integration and feedback on the designs they have made. Drawings are frequently incomplete or erroneous, at least in the perspective of what may be manufactured in a streamlined fashion.

Fifth assertion: When physical production facilities, such as ship yards, welding stations, rollers and forges are physical limiting production factors, at the same time as optimism is creating a drive to invest in new project (a trend that has turned, just recently, but never influenced this case), investors may want to put money into projects just to get them going, and secure their slot on the production conveyor belt, as it were. During the year or so that an advanced offshore or seismic vessel is under production, thus, it may be modified many times due to change of demand, new ideas or owners and the plans for future contracts, which have still to be negotiated. This is the business opportunity and uniqueness indicator of the ETO as well, and probably the main reason they are even still in business. They can and will change their designs to accommodate new requests and change orders from the customer in a way that larger set-ups abroad have not been able to.

5

The ubiquitous spreadsheet

In all stages, front-end as well as back-end reporting, the company relies on spreadsheets in various formats and designs (numbered below as i)-viii)). The sales people use it to create i) a preliminary parts + work overview, to indicate how much of a margin the project may be able to fetch in terms of profit margins. This is also used to produce an offer to the customer. The go-ahead-decision ii) revises and expands the simple set-up, with the iii) offer made to the customer as a "ceiling" idea of how much the cost of parts plus work and margins should be. This is where the first observable set of opportunistic-dynamic strategies connected to documents (as-such) become manifest. The first document (i)) is created as the technical division feeds in experienced-based numbers of the number of hours and thus the cost, of the engineering, integration and commissioning. The numbers are still uncertain, because the exact organization of activities within each of these functional areas is variable according to which sub supplier is going to be picked. This is not known for certain at this stage. Some suppliers include the work needed to do the FAT (Factory Acceptance Test) and others do not. Some turn out to need a lot of support from the engineering team. With margins like we have indicated, of (in the order of) 100 000 GBP (which corresponds to 1000 hours from a budget of work that typically sums of to 3000 hours), this is a vulnerable situation. Depending on the sub supplier alternatives that exist, therefore, several variants of this "go-ahead" spreadsheet (ii)) are created. During the discussions (and certainly before), variables are adjusted and tuned in order to see if it is at all possible to create viable project. If it is accepted, a bid is made (iii)), and hopefully won.

The accounting budget (another spreadsheet iv, Fig. 1), eventually pasted into or attached with a formal letter) is then made and passed on to cost centre management, in order for them to know what to expect from the project. This is the most formal so far, and it represents the official view of the cost and risk of the project, and finally, the profit it is going to offer to the company.

The project manager, on the other hand, in parallel with this process, has already started looking at specifically which sub suppliers are willing, capable and available to offer the best combination of work capacity, skills, courage and physical location of the company and their facilities. In addition, they usually need to have validated (pre-qualified) working relations with the customer as well. This spreadsheet variant (v)) is worked out in close collaboration with the procurement officer responsible for the project. Next, one spread sheet is created to account for the orders that are placed of parts, with currency risk, volumes and discounts analysed and accounted for (vi)). This spreadsheet, which is an export from the accounting system (part of the company's ERP (Enterprise Resource Planning) system) may have thousands of lines, for which generally a "Pareto-principle" of 20/80 applies: The 20 topmost-% accounts for 80% of the cost. In the same format, but separately, parts confirmed and delivered are accounted for (vii)). Finally, accounting keeps track of the hours worked (viii)).

Digital manufacturing: a concept for dynamic design

Design in most senses is clearly already dynamic. Its processes and outcomes can and will be changed. It is forward moving and creative. Hence it is also open-ended and expansive. "Front-end loading" relies on the assumption that all current and future dimensions can be fully explored and dealt with. Usually, they cannot.

Design captures experiences and evaluates previous drafts. The trouble is that when they are embedded into design, this new design rationale tends to be forgotten [START_REF] Engelbart | Toward high-performance organizations: A strategic role for groupware[END_REF]. Hence, when the next problem of a similar kind is addressed, designers tends to start from the original "template", which is either completely from scratch or an anticipation of needs, which is lacking recent practical experiences that might have been embedded.

Therefore, we suggest challenging the current notion of design, which entails going from idea to product, by "inverse conceptualization", which would be to start from finished, well-known and functional products, which are the re-engineered step-bystep, in a backwards fashion, through all previous versions, releases and assembly steps, in a collaborative and problem-solving process. Clearly this cannot replace "standard design", but may complement it.

Another design-approach might be to start from a library of exceptions, deviations and previous recoveries, to look for enhancements and extensions. Products for reengineering as well as exceptions and experiences might be documented in an advanced, branch-oriented and snapshot-preserving version management system (similar to GitHub) for software.

This way of working dynamically and experience-based with design should aim to move the decoupling point as far along the production timeline as possible. There is no real product designed until it has been built. Similarly, documents should be seen as representations of ambition and a decision-making agenda, rather than snapshots of complete state. Documents are not managed, instead they manage, fit, force and frame processes. Each data element ought then to be versioned and new snapshots made every time one is requested. The planning and control of manufacturing may thus become a data-driven dynamic design science.

Fig. 1 .

 1 Fig. 1. Final sales/profit calculations of ACC for project P

Acknowledgments

The financial support of VRI Møre & Norway is appreciatively acknowledged, as well as the willingness of ACC to explore this set of ideas within a project that first and foremost aimed at reducing the cost of building cranes. We would especially like to thank managers, engineers and administrators in ACC who spent extra time in meetings and dialog with the author and other researches.