Williams Rl

Garvey Day

Mj

Stappler

Dr Rachel L Williams

Injectability of silicone oil-based tamponade agents

Keywords: Tamponade agents, silicone oil, viscosity, retinal detachment

Background/aims: High viscosity silicone oils are used as tamponade agents to increase the resistance to emulsification, however this makes the oils more difficult to inject. Increasing the extensional viscosity is one way to reduce emulsification. This study aimed to evaluate how silicone oils with increased extensional viscosity behave in terms of their ease of injection. Methods: The shear viscosity and the length of time taken to inject 9mls of Siluron 1000™, Siluron 2000™, Siluron 5000™, SiliconMate™, a 56/44 w/w blend of Siluron 1000™/ Siluron 5000™ (Blend A) and a 90/10 w/w blend of Siluron 1000™/ PDMS M w 423k Da (Blend B) were examined. Results: The shear viscosity of Siluron 1000™, Siluron 2000™ and Siluron 5000™ were within the expected ranges. The shear viscosity of Blend A was 2283 mPa.s, Blend B was 4710 mPa.s and SiliconMate™ was 995.3 mPa.s. Siluron 1000™ and SiliconMate™ had the shortest injection times as expected due to their lower shear viscosities. Comparison of Siluron 2000™ and Blend A demonstrated that Siluron 2000™ was easier to inject. Similarly, Blend B was easier to inject than Siluron 5000™. Conclusion: Silicone oil blends containing small percentages of a high molecular weight additive are easier to inject than single grade oils of the equivalent shear viscosity.

Introduction

Silicone oils (PDMS) are well established long term intraocular tamponade agents particularly in the treatment of complex retinal detachments [1,2]. Early improvements in the production of medicalgrade silicone oils aimed at removing PDMS molecules with short chain lengths since the latter were thought to be one of the causes of postoperative ocular inflammation. Another reason for silicone oil-associated adverse reactions such as inflammation, glaucoma and even the development of proliferative vitreoretinopathy (PVR) has been the propensity of silicone oils to emulsify. Small droplets are formed due to shear forces acting at the interface between oil and water during eye movements. These satellite droplets may either coalesce back into the bulk oil or, if surfactant are available can become stable within the aqueous surrounding the bulk oil. These droplets remain in the patient's eye for life even when the bulk oil has been removed. Such considerations have led to the manufacture of silicone oils with even higher (shear) viscosities as in-vitro experiments indicate that such increased viscosity reduces emulsification [START_REF] Caramoy | In vitro emulsification assessment of new silicone oils[END_REF]. The silicone oils currently on the market generally have a shear viscosity of either 1000 or 5000 mPa.s. The former type is easier to inject into the eye but is also believed to be more prone to emulsification, while the higher viscosity oil is perceived to be less prone to emulsification but is also more difficult to inject. Such advances in the field of silicone oils now have to adapt to parallel advances in the field of microsurgical instrumentation. Since their inception [START_REF] De Juan | Refinements in microinstrumentation for vitreous surgery[END_REF], there has been a recognised trend towards small gauge surgery [START_REF] Williams | 25-, 23-, or 20-gauge instrumentation for vitreous surgery?[END_REF]. Complex procedures have now become accessible to such minimally invasive surgical techniques, including the injection of viscous silicone oil through the small gauge needles [START_REF] Riemann | Outcomes of transconjunctival sutureless 25-gauge vitrectomy with silicone oil infusion[END_REF]. Furthermore, once injected, high viscosity silicone oils can prove equally difficult to remove from the eye [START_REF] Rizzo | A new heavy silicone oil (HWS 46-3000) used as a prolonged internal tamponade agent in complicated vitreoretinal surgery: a pilot study[END_REF].

There is, therefore, an accepted need for a product that is significantly easier to inject than 5000 mPa.s oil (ideally approaching 1000 mPa.s oil in this respect) whilst at the same time possessing comparable resistance to emulsification. It has previously been shown that addition of a small (5-10% w/w) amount of a very high molecular weight PDMS polymer to 1000 mPa.s oil gives a composition with a greatly increased high strain rate extensional viscosity and consequently an enhanced resistance to emulsification (comparable to 5000 mPa.s oil) [START_REF] Williams | Increasing the extensional viscosity of silicone oil reduces the tendency for emulsification[END_REF]. At the same time, the shear viscosity of such compositions remains lower than 5000 mPa.s thereby rendering them easier to inject than the latter. One such composition comprising 5% w/w 423,000 molecular weight PDMS polymer in 1000 mPa.s oil, having a shear viscosity of ca. 2000 mPa.s, has recently been introduced as a tamponade in Europe under the brand name Siluron 2000™.

In this study, the rate of injection of Siluron 2000™ using an Accurus Viscous Fluid Injection system (with both 20 and 23 Gauge cannula) was compared to that of 1000 and 5000 mPa.s oils along with the recently launched tamponade SiliconMate™ (Howard Instruments). The latter was included as it claims a similar shear viscosity to Siluron 2000™. Further, a particular aim of the study was to determine whether the high molecular weight PDMS polymer had any effect on injection rate over and above simply giving a particular composition shear rate. Siluron 2000™ was therefore also compared to a control blend of 1000 and 5000 mPa.s oils having a similar shear viscosity. Similarly, a composition comprising 10.0% w/w PDMS polymer having a shear viscosity close to that of 5000 mPa.s oil was examined.

Materials and methods

Siluron 1000™ mPa.s (MW 37 kDa) and Siluron 5000 ™mPa.s (MW 65 kDa) were donated by Fluoron GmbH (Ulm, Germany). Poly(dimethylsiloxane) (PDMS) with a molecular weight of 423 kDa and a cited shear viscosity of 2,500,000 mPa.s (PS050) was purchased from Fluorochem Ltd. (Glossop, UK).

Blends of 56/44 w/w Siluron 1000™ and Siluron 5000 ™ (Blend A), 90/10 w/w Siluron 1000™ and PDMS 423 kDa (Blend B) and 95/5 w/w Siluron 1000™ and PDMS 423 kDa (Siluron 2000™) were prepared. The Siluron 1000™ / high MW silicone additive blends were prepared as follows. The oil was added to a polystyrene container (Bibby Sterilin) followed by the additive. The mixture was stirred on a roller mixer (model SRT2, Stuart Scientific) for 72 hours and then more vigorously mixed for 24 hours using an overhead stirrer. Blend A was prepared following the roller mixing step only.

All mixing was performed at ambient temperature. A sample of SiliconMate™ 2000cS (Lot 200708 072013/ Howard Instruments Inc) was received from Fluoron GmbH.

Rotational (Shear) Rheometry:

For all samples, shear viscosities were measured at 25°C using a TA Instruments Advanced Rheometer AR500, using a cone and plate geometry (2°, 40 mm) at shear rates 10, 25 and 100 s -1

. In all cases, the average value of the viscosity measured at each of these three shear rates is quoted.

Injection tests:

In order to simulate real-life surgical situations the following setup was used: The Accurus Viscous Fluid Injection system (Alcon, USA) was used in conjunction with the original viscous fluid injection pack. The programme "viscous fluid injection" was chosen and the injection pressure was set to 80psi, the maximum for this type of machine. These also represent the injection settings in routine vitreoretinal surgery when silicone oils are being infused. The standard 20-gauge metal cannula provided as standard with every silicone oil injection pack was used. This is approximately 7.5 mm in length from the plastic hub to the tip of the cannula. The 23 gauge metal cannula was cut to be of the same length as the 20 gauge cannula so that the different lumen size was the only variable factor. Furthermore the same needles were used for all experiments in order to rule out further potential confounding factors. All injection tests were performed in triplicates and fresh oils were used for each run to avoid aeration effects. When the oil to be infused was changed, the cannulae were flushed with several ml of the new silicone oil to minimise cross-contamination. No detergents were used throughout the injection experiments to clean any piece of equipment. The time for each increment of 1 ml of the various silicone oils to be injected were measured using a stopwatch. The injection times for a total of 9 ml for each silicone oil were measured, again mimicking a real-life situation such as the volume of the eye.

Statistical analysis

One-way ANOVA analysis was performed using a Dunnett's T3 post-hoc test for small sample size pairwise comparisons on the injection times for 9 mls of each sample. Comparisons were made within the group of data for each needle size.

Results

Shear viscosity measurements

The shear viscosity measurements of the Siluron 1000™ and Siluron 5000 ™ were within the range expected at 1114 mPa.s and 4975 mPa.s respectively (Table 1). Siluron 2000™ was prepared in a standard ratio of Siluron 1000™ plus 5% of a high molecular weight additive and fitted into the expected range of shear viscosity at 2155 mPa.s. Blend A was made for comparison with Siluron 2000™ to match the shear viscosity without using the high molecular weight additive. The resultant shear viscosity was measured to be 2283 mPa.s. Blend B was made from Siluron 1000™ plus 10% of the high molecular weight additive and its resultant shear viscosity was measured to be 4710 mPa.s.

The shear viscosity of SiliconMate™ was measured to be 995. [START_REF] Caramoy | In vitro emulsification assessment of new silicone oils[END_REF] 3) attached to the Accurus Viscous Fluid Injection system it was not possible to inject the Siluron 5000™. An attempt was made to inject the Blend B and it was demonstrated that this could be achieved with a total time to inject 9 mls in the order of 23 minutes.

Multiple runs of this blend have not been run as it was considered that 23 minutes was too long to be clinically relevant. Comparison of the total injection time of Siluron 2000™ and the shear viscosity-matched Blend A demonstrated that the Siluron 2000™ with the high molecular weight additive was significantly easier to inject than the simple mixture of Siluron 1000™ and Siluron 5000™. The total times taken to inject 9 mls were approximately 11 and 17 minutes respectively.

Shorter times for injection of 9mls of Siluron 1000™ and SiliconMate™ were measured as expected due to their lower shear viscosity. Statistical analysis demonstrated that the injection times for 9mls of each fluid was significantly different from all others at the p<0.05 level. These data are presented graphically in Figure 2.

gauge

Discussion

The behaviour of silicone oil tamponade agents in terms of their emulsification resistance and ease of injection will be influenced by their viscosity. Siluron 2000™ was designed to address the emulsification of silicone oil tamponades by increasing the extensional viscosity of the material while keeping the shear viscosity lower than Siluron 5000™ so that it is easier to inject than Siluron 5000™.

Blend B is an experimental oil that takes advantage of the same rheological property of an increase in extensional viscosity. By adding a greater percentage of the high molecular weight additive it has the potential to increase the resistance to emulsification even further than Siluron 2000™ but has an increased shear viscosity and therefore is not expected to be any easier to inject than Siluron 5000™.

In general the shear viscosity of the oils will control their ease of injection, however, this study has shown that both Siluron 2000™ and Blend B were significantly easier to inject than their equivalent single phase oils Blend A and Siluron 5000™, respectively. This fact has also been reported by clinicians using Siluron 2000™ during surgery. Siluron 2000™ and Blend B were both produced by taking Siluron 1000™ and adding 5% and 10% respectively of a high molecular weight PDMS polymer. The polymer is fully soluble throughout the Siluron 1000™ and increases the shear viscosity of the latter by enhancing the interpenetration of the molecular coils within the bulk oil and giving an increased resistance to shear flow. Although not observed from classical rheological analysis via cone and plate rheometry it would appear that when these composite oils are subjected to the pressure of the injection and the high shear rates in the narrow bore of the cannulae, less resistance to flow is experienced. This phenomenon is termed 'shear thinning' in the field of polymer science and is caused by the high molecular weight chains becoming elongated and aligned to the flow direction. In contrast the 56/44 w/w mixture of Siluron 1000™ and Siluron 5000™ did not behave in a similar way due to the comparable sizes of the molecular chains in the two components.

The SiliconMate™ silicone oil, although claiming to have a viscosity of 2000cS, was measured to have a viscosity of 995.3 mPa.s. This shear viscosity was also reflected in its injection behaviour where the injection times were very similar to those of Siluron 1000™. Owing to these data this oil would be expected to behave in a similar manner to Siluron 1000™ in terms of its emulsification resistance.

Conclusion

These data suggest that Siluron 2000™ and Blend B have a significant advantage for clinical practice in terms of their ease of injection as well as their expected emulsification resistance related to their increased extensional viscosity.

References:

1

Table 2

 2 mPa.s although it was labelled as 2000cS.

	Silicone oil	Batch/manufacturer	Viscosity at 25°C
			/mPa.s
	Siluron 1000™	Lot SIL1 121009/Fluoron GmbH	1114
	Blend A (56/44 Siluron 1000™/	Lots SIL1 121009 + SIL5 230609/ Fluoron	2283
	Siluron 5000 ™ w/w blend)	GmbH
	Siluron 2000™ (90/5 Siluron 1000™	Tech grade SO1000/Fluoron GmbH;	2155
	/SO423k MW additive)	Additive/ Fluorochem Ltd.
	Siluron 5000™	Lot SIL5 230609/ Fluoron GmbH	4975
	Blend B (90/10 Siluron 1000™	Lot SIL5 230609/ Fluoron GmbH	4710
	/SO423k MW additive)	Additive/ Fluorochem Ltd.
	SiliconMate™ (2000 cs)	Lot 200708 072013/ Howard Instruments	995.3

between Blend A and Siluron 2000™, both of which had very similar shear viscosities, it was demonstrated that the addition of the high molecular weight additive resulted in a reduction in the injection time for 9 mls (103 s to 71 s). The time taken to inject Siluron 1000™ was lower again as expected due to the lower shear viscosity. Similarly the time taken to inject the SiliconMate™ reflected the measured shear viscosity. Statistical analysis demonstrated that the injection times for 9mls of each fluid was significantly different from all others at the p<0.05 level. These data are presented graphically is Figure

1

. Injection time in s, presented as the mean ± SD of three measurements using the Accurus Viscous Fluid Injection system attached to a 20 gauge needle Using a 23 gauge needle (Table

Table 3

 3 Injection time in s, presented as the mean ± SD of three measurements using the Accurus Viscous Fluid Injection system attached to a 23 gauge needle.

	Siluron 1000™	Blend A	Siluron 2000™	SiliconMate™

  . McCuen BW II, de Juan E Jr, Machemer R. Silicone oil in vitreoretinal surgery. Part 1. Surgical techniques. Retina 1985;5:189-197. 2. McCuen BW II, de Juan E Jr, Landers MB III, et al. Silicone oil in vitreoretinal surgery. Part 2.

Results and complications.

Retina 1985;5:198-205.

Acknowledgements: The authors are grateful to Fluoron GmbH for providing materials for this study to Drs R English and T Dobbie, Glyndwr University, for their invaluable rheological advice and to Dr V Kearns for her assistance with the statistical analysis.

Figure captions

Figure 1 Injection rates of the silicone oil tamponade agents using the Accurus Viscous Fluid Injection system attached to a 20 gauge cannula Figure 2 Injection rates of the silicone oil tamponade agents using the Accurus Viscous Fluid Injection system attached to a 23 gauge cannula "The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non-exclusive for government employees) on a worldwide basis to the BMJ Group and co-owners or contracting owning societies (where published by the BMJ Group on their behalf), and its Licensees to permit this article (if accepted) to be published in British Journal of Ophthalmology and any other BMJ Group products and to exploit all subsidiary rights, as set out in our licence."

Competing interests: Authors RLW, MD and MJG are inventors on a patent related to the development of silicone oils with high molecular additives and the University of Liverpool have a licence agreement for this technology which includes royalties for the inventors. The other authors have no competing interests in this work.


Andreas Heerwig

Cyril Louis

Jaques Thybaut

Dr Michael Ruck
email: michael.ruck@chemie.tu-dresden.de

Dr C L J Thybaut

Dipl.-Chem A Heerwig

Extended Occupational and Positional Disorder in Pavonite Homologous Copper Bismuth Chalcogenide

Keywords: Bismuth, Copper, One-dimensional ionic conductors, Pavonite, Thermoelectrics Bismuth, Copper, One-dimensional ionic conductors, Pavonite, Thermoelectrics Copper Bismuth Chalcogenide Halogenides

 °. Black needles of the selenide iodides Cu 1.57 Bi 4.69 Se 7.64 I 0.36 and Cu 2.31 Bi 5 Se 8.31 I 0.69 were obtained by chemical vapor transport of CuI and Bi 2 Se 3 . They also crystallize in space group type C2/m with a = 1373.9(4) pm, b = 417.4(1) pm, c = 1464.6(4) pm, β = 115.57(2) °, and a = 1369.1(3) pm, b = 416.6(1) pm, c = 1526.4(3) pm, β = 99.81(3) °, respectively. All four compounds belong to pavonite homologous series. Their structures are built up of two alternating types of layered modules parallel (001), denoted A and B. Composition and shape of module A are almost the same in all structures. They consist of paired rods 1 ∞ [BiQ 3/3 X 2/2 Z 2/2 ] (Z = Q/X; X = Br, I) running along [010] and copper(I) cations that are distributed over various voids between the rods. Modules of type B are composed of [MZ 6 ] octahedra (M = Bi/Cu), which are arranged in NaCl-type fragments of thickness N = 1, 3 or 4. The Joint Probability Density Function (JPDF) reveals a continuous pathway for copper ion transport along [010] in the case of the sulfide bromide. The pseudo-potential for hopping of copper ions was calculated as 47 meV only. The electrical and thermal conductivities as well as the Seebeck coefficient were determined to evaluate the thermoelectric properties.

Introduction

Potentially good thermoelectric materials should have a sufficiently high electrical conductivity σ, a poor thermal conductivity κ, and a large Seebeck coefficient S. These parameters are combined in the dimensionless figure of merit ZT = S 2 • σ • T / κ [1]. Within the phonon-glass electron-crystal model [2], small band gap semiconductors with only partial structural order are favored. Metallic characteristics are not desired, because high electronic conductivity is usually accompanied by high thermal conductivity [1]. Chalcogenides of heavy atoms like mercury, lead, or bismuth are wellknown basic thermoelectrics, which can be improved further by chemical modification or nanostructuring [1]. An example for the first approach is K 2 Bi 8 Se 13 , where the degree of mixed occupancies for Bi/K-positions strongly influences the thermoelectric parameters [3]. Parallel occupational disorder of cations as well as anions was found in silver bismuth chalcogenide halogenides, a wide class of compounds with tunable compositions, structures, and band gaps [4][5][6][7][8][9][10][11]. In the corresponding quaternary systems that are based on copper instead of silver an additional feature appears: positional disorder or even mobility of cations [12]. This unique combination of structural characteristics raises expectations for potentially good performance in thermoelectric energy conversion. Here we report on the syntheses, crystal structures and properties of four copper bismuth chalcogenide halogenides with a common structural principle: Cu 1. 5

Experimental Part

Syntheses

The starting materials for the syntheses of the chalcogenide bromides (I) and (II) were BiBr 3 (Alfa Aesar, 99.9 %; sublimated twice), CuBr (Fluka, > 98.0 %; purified according to [13]), Bi 2 S 3 (Alfa Aesar, 99.9 %) or Bi 2 Se 3 , which had been synthesized from Bi (Riedel de Haën, chemically pure; treated with H 2 at 520 K) and Se (Fluka, 99.99 %). In an argon filled glove box (M. Braun,

c(O 2 ) ≤ 1 ppm, c(H 2 O) ≤ 1
ppm), silica ampoules (150 mm in length, 15 mm inner diameter) were loaded with about 1 g of approximately stoichiometric mixtures. In a tubular furnace, the evacuated (p ≈ 0.1 Pa) and sealed ampoules were heated to 770 K, cooled to 620 K with ∆T / t = 1 K/h, and tempered at 620 K for one week before quenching in water. The products consisted of needleshaped black platelets with shiny surfaces. The compounds are inert to water and alcoholic solvents, but decompose in inorganic acids.

The selenide iodides were obtained in a similar procedure, starting from CuI (Riedel de Haen, > 99 %) and Bi 2 Se 3 in the molar ratio 1 : 1 in case of (III) and 3 : 2 in case of (IV). The mixtures were heated to 670 K for five days, before they were placed in a temperature gradient from 670 K to 620 K. After one week, black and shiny needles had grown at the cooler end.

Thermal Analyses

Powdered samples of (I) and (II) (m ≈ 30 mg) sealed in evacuated (p ≈ 0.1 Pa) silica microampoules were analyzed using a DTA-DSC device (Labsys DSC 12, Setaram). With a rate of ∆T / t = 5 K/min the samples were heated to 770 K and subsequently cooled to ambient temperature. The residua of the thermal analysis were characterized by X-ray powder diffraction.

Thermoelectric measurements

Powdered and pressed samples of (I) and (II) with the dimensions l = 35 mm, w = 15 mm and h = 10 mm were analyzed for electrical and thermal conductivity as well as Seebeck coefficient in the temperature range between 2.9 K and 305 K with a step width of about 6 K using a Quantum Design PPMS with thermal transport option.

Crystallographic Structure Determinations

Powder diffractograms were measured with a Stadi-P diffractometer (Stoe) equipped with a position sensitive detector using Cu-Kα 1 radiation. Single-crystals of all four compounds were examined using Buerger precession method (Zr-filtered Mo radiation, imaging plate technique). The collection of reflection intensities was carried out with a single-crystal diffractometer using monochromatized Mo-Kα-radiation (IPDS I or II, Stoe; CAD 4, Enraf-Nonius) at 293(2) K (Table 1). The optically determined crystal descriptions were optimized using symmetry equivalent reflections [START_REF]Crystal Optimisation for Numerical Absorption Correction Program[END_REF] in case of IPDS data and ψ-scans in case of CAD 4 data. After the numerical absorption corrections [START_REF]Data Reduction Program, Version 1.01[END_REF], the structure solutions and refinements succeeded using direct methods and subsequent difference Fourier syntheses [16]. Due to the very similar X-ray scattering factors, the assignment of Se and Br atoms to the anion positions in (II) is based on bond-length bondstrength considerations [17]. For all Cu1x atoms on partially occupied sites only one (isotropic) displacement parameter was refined. The same holds for spatially separated mixed occupied positions Z = Se/I in (III) and (IV). Anisotropic displacement parameters were determined for the other positions. In the case of mixed occupied sites M = Bi/Cu or Z = Q/Br the same atomic parameters were applied. In order to assure charge balance, the sum of occupancies of the Cu sites and the occupancy ratios of the mixed sites were constrained. Maxima of the residual electron density are close to heavy atom positions and seem to be artifacts of the structural disorder. Atomic parameters are listed in Tables 2 to 4. Selected interatomic distances can be found in Tables 5 and6.

Further data, in the form of CIFs, have been deposited with the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany (E-mail address: crysdata@fizkarlsruhe.de), as supplementary material no. CSD-421681 (I), CSD-421682 (II), CSD-421683 (III), and CSD-421684 (IV). Graphical representations of the crystal structures were developed with Diamond [START_REF] Brandenburg | Diamond 3.2d, Crystal and Molecular Structure Visualization[END_REF].

In the case of the bromides, the Cu1 disorder can be described with only one anharmonically refined copper position [19]: (I) Cu1 in ½, 0.18(2), 0 and a fourth order tensor; (II) Cu1 in ½, 0.10(2), 0 and a third order tensor. For (III) two positions are necessary: one in ½, 0.09(1), 0 with a third order tensor, and the other in 0.5460(9) ½, 0.072(1) with a second order tensor (harmonically refined). In the case of (IV), the same refinement strategy resulted in the positions ½, 0.09(1), 0 and 0.528(1), ½, 0.0660 (9). All four anharmonic refinements do not show large negative residual electron densities and can be regarded as adequate descriptions of the disorder [19]. Since the Joint Probability Density Function (JPDF) of (I) reveals a continuous pathway, one particle potentials and their errors were determined [19,20]. The program VESTA was used for visualizing the JPDF [21]. Z 2

ρ calc × cm 3 /

Results and Discussion

Black, flat needles of the two copper bismuth chalcogenide bromides Cu In all probability, the formation of the copper bismuth selenide iodides Cu tempering CuI and Bi 2 Se 3 at 670 K. In the temperature gradient from 670 K to 620 K that is applied subsequently, an auto-transport [22] via the gas phase takes place. The dominant gas phase species should be BiI (g) , Se 2(g) , and Cu 3 I 3(g) [23]. The fact that Bi 2 Se 3 is more easily transported than CuI is reflected in the composition of the quaternary compounds: The deposited Cu All four compounds crystallize in the monoclinic space group type C2/m (for lattice parameters cf. Table 1). They can be categorized as members of pavonite homologous series, similar to those found in the Ag/Bi/Q/X systems (X = Cl, Br) [4][5][6]. The bromides (I) and (II) are isostructural with members of the solid solution series Ag 2x Bi 4-2x S 6-4x Br 4x [4]. The Bi III atoms are coordinated by three Q, two Br, and two mixed occupied Z = Q/Br atom positions (Figure 1). The mono-capped belong to the series Ag 4x Bi 6-4x Q 10-8x X 8x-2 [5] and Ag 5x Bi 7-5x Q 12-10x X 10x-3 [6]. For the Ag compounds the general sum formula

[
[BiQX] 2 [Ag x Bi 1-x Q 2-2x X 2x-1 ] N+1
with N ≥ 0 and 1/2 ≤ x ≤ 1 had been found [6]. Individual compounds are characterized by their parameters N and x in the symbol (N, x) P. When the particular chalcogen and halogen are listed in a subscript, for example (2, 0.67) P S,Cl , this code properly defines a composition.

In the underlying Cu compounds, however, the Cu content in module A is an additional parameter, since the occupancy of the atoms around the octahedral void between the rods can exceed unity -in the case of (I) Σk(Cu1) = 1.13, (III) Σk(Cu1) = 1.26, and (IV) Σk(Cu1) = 1.31or fall below unity -in the case of (II) Σk(Cu1) = 0.94 -by the displacement of the Cu atoms into tetrahedral or trigonal voids. The charge is compensated by the atomic ratios on the mixed cation positions M as well as on the anion positions Z. Thus, a general formula would be very complex and should not be set up on the basis of a few representatives.

) ( pdf ln ) ( 0 x kT V x V - =
, the potential barriers were derived from the anharmonic refinement [19,20]. The calculated potentials are very small, about 47 meV only (Figure 4), yet the effective potential could be substantially higher [19].

In the case of the chemically related compound Ag 10 Te 4 Br 3 , which was identified as an excellent cation conductor, potentials of 450 meV were calculated with the same method [START_REF] Lange | 42Br2.58 (I)[END_REF]. In (II), (III), and (IV) the Cu1 atoms are more localized than in the sulfide bromide (I), and the JPDF do not show continuous pathways through the crystals.

Concluding Remark

Although at least the two bromides presented here do not seem to be suitable thermoelectrics, the class of compounds is promising, since the tunable composition and structures of the pavonite homologous series offers numerous chemical variables for optimizing the thermoelectric properties.

Their chemical and thermal stability should allow application in the low and medium temperature regime up to 600 K.

  b = 410.28(5) pm c = 937.2(2) pm β = 90.33(2) ° V = 505.7(2) × 10 6 pm 3 a = 1353.9(3) pm b = 417.54(5) pm c = 960.4(2) pm β = 91.13(2) ° V = 542.8(2) × 10 6 pm 3 a = 1373.9(4) pm b = 417.4(1) pm c = 1464.6(4) pm β = 115.57(2) ° V = 758.2(4) × 10 6 pm 3 a = 1369.1(3) pm b = 416.6(1) pm c = 1526.4(3) pm β = 99.81(3) ° V = 857.9(3) × 10 6 pm 3

3 ,

 3 Bi 2 Q 3 (Q = S, Se) and CuBr. According to X-ray powder diffraction, the yield of the syntheses exceeds 90 %. The melting points of the compounds are 708(5) K (I) and 724(5) K (II).(I) and (II) belong to the pseudo-ternary systems CuBr/BiBr 3 /Bi 2 Q 3 , i.e. they are substantially richer in Bi and halogen compared to the iodides (III) and (IV), which belong to the system CuI/Cu 2 Se/Bi 2 Se 3 .

  BiQ 3 Br 2 Z 2 ] prisms share faces and edges to form paired rods 1 ∞ [BiQ 3/3 Br 2/2 Z 2/2 ] along [010]. While in the corresponding Ag compounds the octahedral voids between the rods are mixed occupied with Bi/Ag, here Cu I atoms are distributed over numerous octahedral, tetrahedral, and trigonal voids. Between these layers parallel to (001), which are denoted as A modules, mixed occupied octahedrally coordinated cation positions M = Bi/Cu form the B modules. The [MBr 4 Z 2 ] octahedra share trans edges along [010].Since the various pavonite homologous series mainly differ in the thickness of module B, the number N of octahedra stacked perpendicular to (001) is a characteristic[6]. At constant N, the coupled modification of the Bi/Cu and the Q/Br ratios yields to a continuous series of isostructural compounds. In the case of the bromides (I) and (II), N equals 1. The two selenide iodides are members of pavonite homologous series with N = 3 (III) and N = 4 (IV), i.e. the NaCl-type modules B consist of three or four layers of octahedrally coordinated M cations (Figure2). The modules A differ only in details from those found in (I) and (II). Corresponding Ag compounds

Figure 2 .

 2 Figure 2. Crystal structure of N = 3 pavonite homologue Cu 1.57 Bi 4.69 Se 7.64 I 0.36 (III).

Figure 3 .

 3 Figure 3. Cu1 distribution (split atoms) in the sulfide bromide (I) and the respective JPDF isosurface at an electron density of η = 0.08 e/(10 6 pm 3 ).

Figure 4 .

 4 Figure 4. Left: JPDF based on an anharmonically (fourth order tensor) refined Cu1 atom in ½, 0.18,

I),

  Bi 2.64 S 3.42 Br 2.58 (Cu 1.57 Bi 2.37 Se 2.68 Br 3.32 (II), Cu 1.57 Bi 4.69 Se 7.64 I 0.36 (III), and Cu 2.31 Bi 5 Se 8.31 I 0.69 (

IV).

Page 6 of 21 Wiley-VCH ZAACTable 1 .

 1 Crystallographic data and details of the structure refinements. Composition Cu 1.49(6) Bi 2.646(1) S 3.42(2) Br 2.58(2) Cu 1.57(5) Bi 2.370(1) Se 2.68(2) Br 3.32(2) Cu 1.57(2) Bi 4.690(1) Se 7.640(8) I 0.360(8) Cu 2.31(3) Bi 5.00(1) Se 8.31(1) I 0.69(1)

	Compound no. (I)	(II)	(III)	(IV)
	T / K		293(2)
	Crystal system		monoclinic
	Space group		C2/m (no.

Table 2 .

 2 Wyckoff positions, coordinates, occupancy factors (k) und displacement parameters of the atoms in the sulfide bromide (I) (upper lines) and the selenide bromide (II) (lower lines). U eq is defined as one third of the trace of the orthogonalized tensor U ij . M = kBi + (1-k)Cu; Z = kQ + (1k)Br with Q = S, Se.

	g 6.33	6.56	7.57	7.49
	Crystal size / mm 3	0.01 × 0.17 × 0.01	0.01 × 0.11 × 0.01	0.32 × 0.07 × 0.03	0.25 × 0.12 × 0.07
	Measuring	imaging plate diffractometer	imaging plate diffractometer	four-circle diffractometer CAD 4 (Enraf-Nonius)
	device	IPDS-II (Stoe)	IPDS-I (Stoe)
	Radiation		Mo-Kα, λ = 71.073 pm
	Measuring	2θ ≤ 60.0 º	2θ ≤ 51.6 º	2θ ≤ 69.9 º	2θ ≤ 80.6 º
	range	-18 ≤ h ≤ 18	-16 ≤ h ≤ 16	-22 ≤ h ≤ 22	-24 ≤ h ≤ 24
		-5 ≤ k ≤ 5	-4 ≤ k ≤ 4	-6 ≤ k ≤ 6	-7 ≤ k ≤ 7
		-13 ≤ l ≤ 13	-11 ≤ l ≤ 11	-23 ≤ l ≤ 23	-27 ≤ l ≤ 27
	Absorption	numerical; crystal description optimized using sets of	numerical; crystal description optimized using 8 and 17 ψ-
	correction	symmetry equivalent reflections		scans
	µ(Mo-Kα) ×	59.8	62.5	75.4	72.7
	mm
	Transmission	0.06 to 0.70	0.57 to 0.69	0.01 to 0.11	0.01 to 0.07
	factors
	Measured	3532	2897	6658	10048
	reflections
	Unique	845	580	1852	2930
	reflections
	R int	0.046	0.077	0.046	0.074
	R σ	0.032	0.050	0.033	0.052
	Refinement		least squares method; full matrix; based on F 2
	Extinction	23(3) × 10 -4	11(1) × 10 -4	12.8(2) × 10 -4	-
	parameter
	Parameters;	49; 1	39; 1	59; 1	68; 1
	restrictions
	∆ρ × 10 6 pm 3 /e +1.9 to -1.6	+2.6 to -3.0	+3.9 to -3.8	+3.9 to -3.6
	R 1 (all F o )	0.041	0.074	0.055	0.107
	R 1 (F o >4σ(F o )) wR 2 (all F o 2 )	0.038 0.102	0.049 0.060	0.033 0.039	0.040 0.041

Table 3 .

 3 Wyckoff positions, coordinates, occupancy factors (k) und equivalent isotropic displacement parameters of atoms in the selenide iodide (III). U eq is defined as one third of the trace of the orthogonalized tensor U ij . M = kBi + (1-k)Cu.

	Atom	Position	x	y	z	k	U eq , U iso
	Bi1	4i	0.28391(3)	0	0.13995(3) 1	385(1)
	M2	4i	0.65457(2)	0	0.35888(3) 1	256.1(8)
	M3	2c	0	0	½	0.6901(9)	195(1)
	Cu1a	2b	½	0	0	0.105(5)	351(8)
	Cu1b	4i	0.4679(4)	0	0.0336(5) 0.192(3)	U iso (Cu1a)
	Cu1c	4g	½	0.174(1) 0	0.253(3)	U iso (Cu1a)
	Cu1d	4i	0.5454(6)	½	0.0711(7) 0.133(2)	U iso (Cu1a)
	Se1	4i	0.87591(5)	0	0.05070(6) 1	179(1)
	Se2	4i	0.99761(7)	0	0.30225(9) 0.885(2)	222(2)
	Se3	4i	0.6450(1)	0	0.15965(9) 0.935(2)	178(2)
	Se4	4i	0.33267(5)	0	0.42410(6) 1	176(1)
	I2	4i	0.9900(4)	0	0.3388(4) 0.115(2)	U eq (Se2)
	I3	4i	0.645(1)	0	0.179(1)	0.065(2)	U eq (Se3)

Table 4 .

 4 Wyckoff

	Atom	Position	x	y	z	k	U eq , U iso
	Bi1	4i	0.24321(3)	0	0.12284(2) 1	450(1)
	M2	4i	0.54909(3)	0	0.31293(2) 0.748(2)	277(1)
	M3	4i	0.84829(3)	0	0.43633(3) 0.751(2)	285(1)
	Cu1a	2b	½	0	0	0.137(6)	400(9)
	Cu1b	4i	0.4533(5)	0	0.0318(4) 0.193(3)	U iso (Cu1a)
	Cu1c	4g	½	0.176(1) 0	0.256(3)	U iso (Cu1a)
	Cu1d	4i	0.5290(6)	½	0.0662(5) 0.138(3)	U iso (Cu1a)
	Se1	4i	0.86189(5)	0	0.04452(4) 1	195(1)
	Se2	4i	0.90490(9)	0	0.26944(9) 0.852(3)	211(2)
	Se3	4i	0.59690(6)	0	0.14157(8) 0.928(2)	218(2)
	Se4	4i	0.20550(7)	0	0.37167(7) 0.8722(8)	242(2)
	Se5	2d	½	0	½	1	205(2)
	I2	4i	0.8889(3)	0	0.2958(3) 0.148(3)	U eq (Se2)
	I3	4i	0.5990(6)	0	0.1757(6) 0.072(2)	U eq (Se3)
	I4	4i	0.1937(3)	0	0.4136(3) 0.1278(1)	U eq (Se4)

positions, coordinates, occupancy factors (k) und equivalent isotropic displacement parameters of atoms in the selenide iodide (IV). U eq is defined as one third of the trace of the orthogonalized tensor U ij . M = kBi + (1-k)Cu.

Table 5 .

 5 Selected

	x+1/2, y-1/2, z;

interatomic distances (/ pm) for the chalcogenide bromides (I) and (II). M = Bi/Cu; Q = S, Se; Z = Q/Br. Symmetry operators: (i): x, y, z; (ii): 1-x, -y, -z; (iii):

Table 6 .

 6 Selected interatomic distances (/ pm) for the selenide iodides (III) and (IV). M = Bi/Cu; Z

	= Se/I. Symmetry operators: (i): x, y, z; (ii): 1-x, -y, -z; (iii): x-1/2, y-1/2, z; (iv): x-1/2, y+1/2, z;
	(v): x+3/2, -y-1/2, -z; (vi): 3/2-x, 1/2-y, -z; (vii): x, y+1, z; (viii): x+1/2, y-1/2, z; (ix): x+1/2, y+1/2,
	z; (x): 1-x, -y, 1-z; (xi): x-1, y, z; (xii): 1/2-x, -y-1/2, 1-z; (xiii): 1/2-x, 1/2-y, 1-z.
		(III)	(IV)
	Bi1-Se1 ii	270.8(1) 271.0(1)
	Se3 iii, iv	292.5(1) 293.75(8)
	Se1 iii, iv	301.52(8) 301.17(8)
	I3 iii, iv	305(1) 307.1(6)
	Se2 iii, iv	355.0(1) 354.4(1)
	I2 iii, iv	370.7(4) 367.3(3)
	M2-I3	258(1) 231.1(9)
	Se2 iii, iv	285.48(8) 286.89(9)
	Se3	286.6(1) 280.2(1)
	I2 iii, iv	299.6(3) 300.4(3)
	Se4 viii, ix	303.93(8) 301.23(9)
	Se4 x	310.9(1)	-
	Se5	-304.29(7)
	I4 viii, ix	-309.6(3)
	M3-I2 x, xi	230.8(6)	-
	Se2 x, xi	288.4(2)	-
	Se4 iii, iv, xii, xiii 294.46(8)	-
	I2	-230.6(5)
	I4 x	-245.5(5)
	Se2	-278.6(2)
	Se4 viii, ix	-291.16(9)
	I4 viii, ix	-294.7(3)
	Se5 viii, ix	-298.49(6)
	Se4 x	-314.1(1)
	Cu1a-Se3 i, ii	232.8(2) 233.5(1)
	I3 i, ii	252(2) 279.1(9)
	Se1 iii, iv, v, vi 298.46(7) 296.88(7)
	Cu1b-Se3	233.5(6) 235.7(6)
	I3	244(2)	270(1)
	Se1 iii, iv	250.8(3) 245.5(3)
	Se3 ii	257.6(7) 261.8(6)
	I3 ii	282(2)	312(1)
	Cu1c-Se3 i, ii	243.9(2) 244.7(2)
	Se1 iv, vi	253.0(3) 251.0(3)
	I3 i, ii	262(2) 288.5(9)
	Cu1d-Se1 iv	221.6(8) 225.6(8)
	Se1 vi	245.5(8) 243.8(8)
	Se3 i, vii	252.6(5) 248.2(4)
	I3 i, vii	262(1) 273.9(8)

  1.49(6) Bi 2.646(1) S 3.42(2) Br 2.58(2) (I) and Cu 1.57(5) Bi 2.370(1) Se 2.68(2) Br 3.32(2) (II) were crystallized from approximately stoichiometric melts of BiBr

  1.57(2) Bi 4.690(1) Se 7.640(8) I 0.360(8) (III) and Cu 2.31(3) Bi 5.00(1) Se 8.31(1) I 0.69(1) (IV) proceeds during

  1.57 Bi 4.69 Se 7.64 I 0.36 (III) = 0.153 CuI • 0.258 Cu 2 Se • Bi 2 Se 3 has a Cu content of 67 % compared to the source, which is based on an equimolar mixture of CuI and Bi 2 Se 3 . The CuI richer mixture (CuI : Bi 2 Se 3 = 3 : 2) yields Cu 2.31 Bi 5 Se 8.31 I 0.69 (IV) = 0.276 CuI • 0.324 Cu 2 Se • Bi 2 Se 3 , i.e. an iodine-richer compound with 62 % of the Cu content of the source.

	Figure 1. Crystal structures of N = 1 pavonite homologue Cu 1.5 Bi 2.64 S 3.42 Br 2.58 (I). Ellipsoids cover
	95 % probability density, as in all following figures.

Wiley-VCH

Acknowledgement

We thank Mrs. Gudrun Kadner and Mrs. Jutta Krug for their support in synthesis, and Dr. Peer Schmidt for valuable discussions on the chemical transport reactions. Dr. Walter Schnelle and Mr.

Ralf Koban (Max Planck Institute for Chemical Physics of Solids, Dresden) are gratefully acknowledged for the measurement of the thermoelectric parameters.

Wiley-VCH ZAAC


Kwabena Agyapong

K Agyapong-Kodua

R H Weston
email: r.h.weston@lboro.ac.uk

Systems approach to modelling cost and value dynamics in Manufacturing Enterprises

Keywords: Manufacturing Enterprise (ME), cost and value dynamics, Causal Loop Modelling (CLM), Simulation Modelling (SM)

come

Systems approach to modelling cost and value dynamics in Manufacturing Enterprises

Introduction

Conventional means of generating and developing Manufacturing Enterprises (MEs) involves bringing people together and providing them with structure and technology for doing work [START_REF] Davis | Organization Design[END_REF]. In most MEs various inputs flow through networks of resourced activities to enable outputs of various forms to be achieved [START_REF] Agyapong-Kodua | Process cost modelling in Manufacturing Enterprises[END_REF]. This means that proper organization of resource elements and business processes in support of enterprise requirements and deliverability is necessary for the survival of the ME. It is therefore required that business processes and their associated resource elements are designed and organized such that value is added to inputs (raw materials) along well defined process threads to obtain outputs (finished products) meeting customer requirements. In the process of deriving this objective, cost is incurred through the distributed use of resources and materials. Best industrial practices recommend that competitive business processes should have less cost consumption and high value generation [START_REF] Agyapong-Kodua | Multi-product cost and value stream modelling in support of Business Process Analysis[END_REF]. Also it is necessary that values so attained are translated into equivalent monetary 'regard' in the form of prices customers are willing to pay. How this can be achieved efficiently will help MEs to develop internal structures and manufacturing policies which reflect customer's perspective of value.

Typically, lots of factors influence the cost of production in MEs. The recent challenges of globalization; varying customer requirements; the drive towards mass customisation; changes in machine and computer technologies, environmental and social constraints have compounded and complicated the issue of timely product and process costing. As would be expected, these external factors impact on the internal operations of MEs and it is necessary to re-organize the internal structures and processes to annex the impact of their effects. The reason is that most MEs are composed of complex process networks which are inter related in a way that changes made to one process thread induce dynamics in the ME by having causal and temporal effects on other process threads .

These dynamics play key roles in 'cost consumption' and 'value generation'. Cost and value are key performance indicators for any ME operating in a dynamic market environment. This is due to their ability to ensure competitiveness of the enterprise. It is therefore useful to adopt methods capable of modelling aspects of dynamics that impact on cost and values. When this is achieved scientifically, measures can be taken to improve value generation along process segments.

Literature has shown that in broad terms, current best modelling techniques with potential to define, measure and utilize aspects of value and cost information in manufacturing processes can be classified into:

1. Process Mapping techniques (PMs) [START_REF] Bicheno | The Lean Toolbox[END_REF][START_REF] Womack | Lean thinking -Banish Waste and Create Wealth in Your Corporation[END_REF] 2. Enterprise Modelling (EM) techniques [START_REF] Vernadat | Enterprise modelling and integration; Principles and Applications[END_REF]CEN/ISO 19440). [START_REF] Humphreys | Project and Cost Engineers Handbook[END_REF][START_REF] Akintoye | A survey of current cost estimating practices in the UK[END_REF] 4. System Dynamics (SD) Modelling techniques [START_REF] Forrester | Industrial Dynamics[END_REF] [START_REF] Carrie | Enterprise integration -Constructs for modelling[END_REF][START_REF] Kosanke | Process oriented presentation of modelling methodologies[END_REF] PMs (for example: value stream mapping, process activity mapping, overall lead time mapping and product variety funnel) are not suitable for capturing aspects of complexities and dynamics in MEs [START_REF] Scholz-Reiter | Modelling and control of production systems based on nonlinear dynamics theory[END_REF][START_REF] Agyapong-Kodua | Multi-product cost and value stream modelling in support of Business Process Analysis[END_REF]. This is because most of the PM tools were designed for mapping processes of linear orientation and do not reflect real-time dynamic instances of MEs. It has also been reported that PM tools do not possess the ability to reflect causal impacts of activities on processes [START_REF] Agyapong-Kodua | Process cost modelling in Manufacturing Enterprises[END_REF]). Enterprise Modelling (EM) tools (for example: CIMOSA, ARIS, PERA) relative to PM tools offer additional modelling concepts that enable the capture of semantically rich models of various aspects of enterprises (Weston 1999;[START_REF] Vernadat | UEML: towards a unified enterprise modelling language[END_REF][START_REF] Ajaefobi | Human Systems Modelling in support of Enhanced Process Realisation[END_REF]). The models provide a multi perspective view of enterprises and thus is more suitable for analysing complex aspects of businesses. In theory enterprise modelling approaches facilitate the design and development of better processes and systems, and can improve the timeliness and cost effectiveness of change projects in MEs, but full and industry wide benefit in practice is yet to be realised [START_REF] Bernus | Enterprise integration-engineering tools for designing enterprises[END_REF][START_REF] Vernadat | Enterprise modelling and integration; Principles and Applications[END_REF][START_REF] Agyapong-Kodua | Multi-product cost and value stream modelling in support of Business Process Analysis[END_REF]. EM tools generate models which are static and demand appropriate transformation mechanisms into 'real-time' dynamic simulation models.

Cost Modelling techniques

Business Process Simulation Modelling techniques (SMs) generate useful dynamic representations of discrete processes in MEs. They are therefore suitable for 'what-if' analysis of business processes and supports virtual process design technologies. However, SMs do not suitably model 'cause and effect' structures of processes and are therefore not suitable for detailed 'process dynamics and complexities' modelling. Cost modelling techniques on the other hand provide a framework for estimating cost based on mathematical algorithms derived from observations and analysis of historic data.

They can provide support to any of the modelling techniques explained above in estimating process or product cost. Literature however shows that SD techniques offer a unique approach towards the modelling of complexities and dynamics in systems [START_REF] Richardson | Reflections for the future of system dynamics[END_REF][START_REF] Wolstenholme | Qualitative verses quantitative modelling: the evolving balance[END_REF][START_REF] Sterman | Business Dynamics: Systems thinking and modeling for a complex world[END_REF]. SD models are able to capture factors or elements which induce dynamics in many social, health, political and economic systems [START_REF] Burns | A component strategy for the formulation of system dynamics models[END_REF]. Later attempts have been made to use these techniques in support of the design of manufacturing systems [START_REF] Ajaefobi | Human Systems Modelling in support of Enhanced Process Realisation[END_REF][START_REF] Chatha | Multi-process modelling approach to complex organisation design[END_REF]. Little successes have been reported though and this may be due to the inability of these techniques to critically model processes at the elementary level. In essence, they are useful tools for capturing and analysing factors which impact on processes and their executing agents.

To further support the application of SD techniques in manufacturing environments, the authors have illustrated how SD techniques can be deployed to model aspects of dynamic instances related to cost and value creation in a make-to-order manufacturing enterprise. Causal Loop [START_REF] Forrester | World dynamics[END_REF][START_REF] Sterman | Modelling managerial behaviour: misconceptions of feedback in a dynamic decision making experiment[END_REF][START_REF] Burns | Simplified translation of CLDs into SFDs[END_REF]) and iThink/Stella (ISEE 2007) modelling techniques were considered very useful in this application. They were coherently used to model aspects of dynamics in MEs which impact on cost and values. The output resulted in generic (or semi-generic) models which are capable of providing support in the analyses of the impact of dynamics on cost and values.

Dynamics in Manufacturing Enterprises

The domain of 'dynamics' is traditionally associated with machines and control systems [START_REF] Forrester | Industrial Dynamics[END_REF]. However literature shows that in general terms, the problems often faced by most manufacturing enterprises can be rooted to the phenomenon of complexity which stems from the complexities involved in current markets [START_REF] Wiendahl | Simulation based analysis of complex production systems with methods of nonlinear dynamics[END_REF]. The structural and dynamic complexity of the markets can be found in the structure and processes of the enterprise too . Hence the complexity of the products have their counterparts in the complexity of the manufacturing systems. For most MEs the dynamics of complexities can be enormous. Partly because MEs are highly organic (people-centred) and achieve their goals only through the integration of people, machines and technology. As a result of the interaction between these functional elements, changes related to any of the elements trigger effects on other elements which are causally related to other elements hence producing 'chains of reactions' in MEs. It is therefore required that decisions associated with processes and their related resources be made properly so that they can best be coordinated to achieve optimal results.

To achieve this, most MEs in their life time would have to realise networks of processes comprising the following process types (Weston 1999): (1) processes that realise products and services for customers and values for stakeholders; (2) processes that ensure that product and service realisation is well managed, such that it remains aligned to established business and manufacturing policies, and strategic goals of the ME, and 3) processes that structure and enable ongoing change as the ME systematically renews and reconfigures itself, developing and implementing new strategies, policies and processes in response to external change. The realisation of these sets of processes are often inhibited by the external factors described in the previous section. In addition, internal issues like machine breakdowns, resource unavailability, shortage of material, operational delays and improper product and resource routings, among other disturbances, also affect MEs. The net effect of the impact of these external and internal factors result in the dynamics or complexities which are imposed on the ME.

Impact of ME dynamics on cost and value generation

The management of the impact of dynamics on cost and value generation is of prime importance if any business is to survive in a competitive and complex market environment. This is so because cost and values are part of the key performance indicators needed in the determination of efficiency and profitability of every business. This is the reason why this paper has focussed on modelling aspects of manufacturing dynamics which impact on cost and values.

Cost is considered to be related to the total cost of resources, materials and their associated support systems which span across the entire supply chain. On the other hand, product value in real economic sense is dependent on market forces. Essentially it is the worth or price that customers are prepared to pay. Most critically, it is dependent on how customers assume the value of the product relative to its ability to solve their needs taking into consideration the product's competitiveness in terms of prices of substitute products (Agyapong-Kodua 2009). It is viewed that cost and values can conveniently be defined in the form of a network of distributed factors from business process models. In effect if a change necessitates the utilization of more resources without an appropriate increase in value then it means that the business will have to cope with running at higher cost of production. On the other hand, if higher values can be attained without necessarily increasing the cost then the business will become competitive on price and may win larger market shares. Latter sections have identified how dynamic models of cost and values can help solve the problems of dynamics and complexities associated with cost reduction and value creation. This involves modelling the set of particular or generic factors which impact on resources, processes, and materials. Resolving cost and value dynamics from this perspective helps eliminates distortions associated with conventional cost allocation methods [START_REF] Johnson | Relevance Lost -The Rise and Fall of Management Accounting[END_REF]. In this approach, instead of allocating cost and assuming values, a description is made of the factors which induce dynamics along process segments such that changes in these factors can be visualised. This gives instantaneous reflection of the impact of changes on the production system.

Review of system dynamics modelling tools

The overwhelming dynamics in MEs require that techniques which enable effective scientific reasoning about complexities and causes of dynamics in MEs be deployed.

Modelling and controlling complexities with conventional methods is becoming more difficult [START_REF] Goldhar | Plan for economies of scope[END_REF] especially with advancing technologies and varying customer requirements.

Generally to aid the analysis of complexities and hence manage dynamics of manufacturing enterprises, modelling plays a key role. Modelling is often used to derive an electronic replication of real life systems so that analysis can be conducted on the system without having to interfere with the operation of the real life systems [START_REF] Carrie | Enterprise integration -Constructs for modelling[END_REF]. Several literature have enumerated the benefits of modelling in manufacturing systems [START_REF] Askin | Modelling and analysis of manufacturing systems[END_REF][START_REF] Vernadat | Enterprise modelling and integration; Principles and Applications[END_REF]Rolstadås 2000;[START_REF] Rahimifard | The enhanced use of enterprise and simulation modelling techniques to support factory changeability[END_REF]. It is behind this background that system dynamics modelling techniques are used to illustrate how dynamics and systems complexities can be fairly modelled to aid decision making and experimentation in MEs. Some scientific methods which have won popularity in terms of their wide usage in modelling dynamics and complexities in systems include Fuzzy Logics (FLs) [START_REF] Batur | Automated rule based model generation for uncertain complex dynamic systems[END_REF][START_REF] Wang | Analysis and design of fuzzy systems[END_REF][START_REF] Yester | Design and automatic tuning of fuzzy logic control for an active suspension system[END_REF], Neural Networks (NNs) [START_REF] Minsky | An Introduction to Computational Geometry[END_REF][START_REF] Gardner | Optimal storage properties of neural network models[END_REF][START_REF] Spooner | Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques[END_REF], Bayesian Networks (BNs) [START_REF] Pearl | Bayesian Networks: A Model of Self-Activated Memory for Evidential Reasoning[END_REF], Petri Nets (PNs) [START_REF] Peterson | Petri net theory and the modelling of systems[END_REF][START_REF] Zhou | Modeling, simulation and control of flexible manufacturing systems-A Petri Net Approach[END_REF], Causal Loops (CLs) [START_REF] Forrester | Industrial Dynamics[END_REF][START_REF] Burns | A component strategy for the formulation of system dynamics models[END_REF] and Stock and Flow models [START_REF] Randers | Elements of the system dynamics method[END_REF][START_REF] Sterman | Business Dynamics: Systems thinking and modeling for a complex world[END_REF][START_REF] Binder | Developing system dynamics models from causal loop diagrams[END_REF]. Table 1 shows the relative strengths of these complex system modelling tools.

The strong mathematical base of system dynamics modelling tools discourage lots of manufacturing experts from deploying them [START_REF] Agyapong-Kodua | Multi-product cost and value stream modelling in support of Business Process Analysis[END_REF]. This is particularly so in the case of BNs, FL, NNs and PN technologies.

The CL technique however does not involve complex mathematical expressions and it is good in illustrating, qualitatively, the cause and effects evident in a system. Also reported is that the CL modelling technique could be used together with process modelling techniques to capture and analyse the causal impact of activities on various business performance indicators. Thus CLs lend support for complex manufacturing systems design. Also factors which influence value generation and cost can be captured and expressed on process-based models for effective economic analysis of manufacturing processes.

For simplicity and first stage qualitative analysis, CLs are considered to be most suitable. However CL models cannot be simulated in their natural state and needs to be enhanced to equivalent simulation models before in-depth process and business analysis can be performed. Generating simulation models can help save cost, generate best results, promote enterprise integration, improve value generation and support the derivation of methods for improving processes in MEs. (ISEE 2007). More so causal relationships can best be described in iThink since it is basically an extension of CLs (Agyapong-Kodua 2009).

Insert Table 1

In general terms iThink is good at depicting overall business behaviour [START_REF] Sterman | Business Dynamics: Systems thinking and modeling for a complex world[END_REF].

Causal loop (CL) and related stock and flow (SF) modelling approach

CLs and SFs evolved from research in control engineering and non-linear dynamics theories [START_REF] Forrester | Industrial Dynamics[END_REF][START_REF] Coyle | The technical elements of the system dynamics approach[END_REF]. Literature shows that CL and SFs have been successfully applied in public policy making and implementation [START_REF] Morecort | Modelling for learning[END_REF][START_REF] Richardson | Modelling for management[END_REF]); product development and project management [START_REF] Ford | Dynamic modelling of product development processes[END_REF]; depicting the dynamics of infectious diseases like HIV [START_REF] Mosekilde | Topics in nonlinear dynamics: applications to Physics, Biology and Economic systems[END_REF][START_REF] Sterman | Business Dynamics: Systems thinking and modeling for a complex world[END_REF]; transportation policy and traffic congestion analysis [START_REF] Meadows | Dynamics of growth in a finite world[END_REF][START_REF] Sterman | Business Dynamics: Systems thinking and modeling for a complex world[END_REF]; supply chain management [START_REF] Akkermans | Developing a logistics strategy through participative business modelling[END_REF] and also as an integrated simulation tool [START_REF] Wolstenholme | Qualitative verses quantitative modelling: the evolving balance[END_REF][START_REF] Homer | Maps and models in system dynamics: a response to Coyle[END_REF][START_REF] Chatha | An approach to modelling dependencies linking engineering processes[END_REF]. Arguably, the best known application of system dynamics is the world model of Forrester and Meadows [START_REF] Forrester | World dynamics[END_REF][START_REF] Meadows | The limits to growth[END_REF], although it has extensively been criticized by Burke as gross underestimation of corrective mechanisms in the world demographic economic system [START_REF] Burke | [END_REF]. Many examples of the application of CLs and SFs appear in publications by Sterman [START_REF] Sterman | Business Dynamics: Systems thinking and modeling for a complex world[END_REF], Forrester [START_REF] Forrester | Information sources for modelling the national economy[END_REF][START_REF] Forrester | Policies, decisions and information sources for modelling[END_REF]), Burns [START_REF] Burns | A component strategy for the formulation of system dynamics models[END_REF], Wolstenholme [START_REF] Wolstenholme | System Enquiry-A system dynamics approach[END_REF][START_REF] Wolstenholme | Qualitative verses quantitative modelling: the evolving balance[END_REF], Richardson [START_REF] Richardson | Reflections for the future of system dynamics[END_REF]) and Meadows [START_REF] Meadows | Dynamics of growth in a finite world[END_REF][START_REF] Meadows | The electronic oracle: computer models and social decisions[END_REF].

CL modelling has long been used in standard system dynamics practice for purposes connected to simulation modelling [START_REF] Binder | Developing system dynamics models from causal loop diagrams[END_REF]). Basically, it contains variables, and arrows which show the causal relationships between the variables. Increasingly, they are now being used to depict the basic causal mechanisms hypothesized to underlie reference mode of behaviour over time, that is for articulation of a dynamic hypothesis of the systems as endogenous consequences of the feed back structure [START_REF] Randers | Elements of the system dynamics method[END_REF][START_REF] Richardson | Reflections for the future of system dynamics[END_REF]. CLs are known to be useful for:

• depicting relationships between cause and possible effects [START_REF] Homer | Maps and models in system dynamics: a response to Coyle[END_REF][START_REF] Binder | Developing system dynamics models from causal loop diagrams[END_REF] • creating dynamic models of businesses for alternative policy verification [START_REF] Wolstenholme | Qualitative verses quantitative modelling: the evolving balance[END_REF][START_REF] Homer | Maps and models in system dynamics: a response to Coyle[END_REF] • capturing mental models of individuals and teams during start of projects and also during project dissemination [START_REF] Ford | Dynamic modelling of product development processes[END_REF] • demonstrating the transformation from static modelling to dynamic modelling [START_REF] Chatha | An approach to modelling dependencies linking engineering processes[END_REF][START_REF] Weston | Unified Modelling of Complex Systems -to facilitate ongoing organisation design and change Loughborough University[END_REF].

Causal loop modelling starts with a variable followed by an arrow which shows the causal links with the effect associated with the variable. Each causal link is denoted by a positive or negative polarity to represent how the variables change in respect to the other. A loop is called positive, regenerating or reinforcing if it has no negative polarized links or if the sum of the negative links is even. Otherwise it is a negative or balancing loop.

In most (if not all) MEs and public policy analysis, it is necessary to quantify the effect of actions before they are taken because of the cost implications they often possess. But as would be observed in the case study applications, the causal loop modelling technique is suitable for qualitative analysis and decision making related to cause and effects. To help quantify alternative business policies, quantifiable 'stock and flow' models are often deployed by researchers in the area of systems thinking. In this paper, an enhanced form of 'stock and flow' model in the form of iThink simulation model is presented.

Proponents of causal loop models laude their accessibility to no-experts and claim that simulation models in the form of 'stock and flows' are useful only for people who understand them [START_REF] Ford | Dynamic modelling of product development processes[END_REF]. Although this may be true, Weston (Weston 1999) noted that 'when the end goal of a modelling exercise is to quantify benefits that can arise from manageable decisions then there arise a need to create models that replicate process behaviours in the context of their use'. They further explained that verified models can be used to predict better ways of optimizing the performance of organizations. In effect the application of dynamic simulation models in manufacturing enterprises can help solve problems of parameter optimization; design of control policies; system operation checking; performance evaluation; system dimensioning and the test of design alternatives [START_REF] Vernadat | Enterprise modelling and integration; Principles and Applications[END_REF].

System dynamics model of case company

Description of case study company

The case study is about a 'make-to-order' furniture company located in the East Midlands of the United Kingdom. The company operates with about fifty regular employees and uses basic furniture manufacturing equipment like sanders, grinders, polishes, benches, saws, planers, etc. Figure 1 shows an overview of the operations of the company. Orders received are grouped and transformed into 'production runs'.

These runs are based on the capacity of the fleet of transport vehicles owned by the company and logistical criteria related to the geographical location of customer stockists.

Insert figure 1

Figure 1: overview of operations in the case study company These runs are converted to a 'so called' picking list which lists the furniture items that need to be manufactured and dispatched to the assembly section. The assembly shop supervisor then issues a mini-order to the machine shop on parts which need to be machined. The machine shop however usually envisages demands at the assembly shop (based on experience) and therefore produces stockpiles of parts which are loaded on racks located in the assembly shop. Parts assembled are transferred to the spray shop.

Finishing operations are performed on these sub-assembled parts as they are released from the spray shop, before final delivery. The total production lead time is approximately 4 weeks. This lead time changed significantly to eight weeks when there was an unexpected increase in customer demand. This was partially due to the company's inability to increase their 'effective' manufacturing capacity to match the customer demands.

Development of causal loop models of case study company

To generate a well informed system dynamics model, it was necessary to review documentation related to operations, production and sale of the products. Most importantly, data related to cost and value generation were reviewed whilst typical operational processes were observed by the authors at the shop floor of the case company. The various shops were required to work with various mixes of products at varying times and quantities to meet the customer requirements. Thus resources were shared and distributed in patterns which in reality caused backlogs at some work centres. This necessitated the need for capturing the shop floor operations and creating models to help improve performance. With the interest of investigating the effect of changes on cost and value, an initial semi-generic causal loop model was created to help provide useful insight about the changes and factors which impact on cost and value.

Fundamentally, for the case company to remain competitive, it must produce products which cost less, with enhanced values and more flexible to changes in production and market conditions. With this background and from a general perspective, it was noted that the rate of delivery of finished goods to customers was partly dependent on the production rate achieved. However the required delivery rate was dependent on the market demand and customer requirements which in a way was expressed in the form of customer orders recieved by the company. Also the production rate achieved was dependent on a number of factors which included the production capacity, ordering rate and the rate of raw material supply. These factors have been illustrated in the open causal loop model shown in figure 2 Insert figure 2 In considering the production rate required, it was observed that factors such as units of work required per item input, product lead time based on customer ordering requirement, estimated work rate of resource elements, expected material supply or availability and internal company manufacturing policies, among others, were necessary. On the other hand, the actual production rate the company achieved was dependent on actual competence and availability of resources and raw materials, ordering requirements, storage and delivery implications. In reality efforts are always made to minimize the difference between the two production rates. The factors described above and other factors which impact on the production rates have been described in figures 3(a) and 3(b). Figure 3(a) shows the initial model which was captured to help understand the factors influencing the production system. Although the final measures were in 'rates', the variables were not captured in time-dependent frames hence the term 'rate' was not used to define them initially.

Insert figure 3(a)

Figure 3

(a): An initial causal loop model describing the impact of production activities

In a more refined or structured model (figure 3b) the various time dependent factors were modelled in their lowest form.

Insert figure 3(b)

Figure 3b: Initial structured causal loop model It was also observed that the production rate achieved impacted positively on the rate of value generation and hence the rate of profit realisation by the company. The cost consumption rate was also influenced by the cost per unit of resource utilization and the sum of all other businesses and material costs.

These two initial models were presented to the Production Manager of the case company to verify if they best represent the factors which normally affect their operations. The feedback obtained from the Manager indicated that the factors and links described in the models were correct. The Manager confirmed that, in general terms, the initial causal loop models enhanced his understanding about how factors were interrelated and therefore the need for an integrated solution approach. After the initial models were verified, a decision was taken to create specific causal loop models which illustrate the reinforcing and balancing loops that existed in the company's operations. As a result, the Sales Manager was interviewed to establish how sale orders were generated. Previous work orders were also studied to establish how many sale orders were produced in time. This was to help establish the impact of increased sale orders on current production capacity. Through the interaction with the Sales Manager, it became evident that the major source of boosting their sales was through sales team promotions and advertisement. Historically, increase in number of sales promotions and adverts, increased the number of orders the company received.

This was demonstrated in the number of emails and faxes as well as telephone orders the company received. Although obvious, the Production Manager confirmed that the increase in sale orders increased the work load on the production system. The work load was in the form of orders to be processed, production runs to be generated and the organization of resources to meet the new order requirements. One of the facets of the work load is described in the loop as having a positive influence on the resource utilization. These resources were in the form of machines, humans and technology required to meet the customer needs. The effect of human resource utilization has been depicted in the main regenerative loop, R1. In the case company, increase in resource utilization coherently increased the labour force required. This reflected in the form of the number of casual or agency staff the company had to employ to meet their required capacity.

Insert figure 4 Figure 4: Balancing loops showing effect of increase in customer orders

The major strategy adopted by the company in seasons of high work loads is to hire workers which tend to temporarily increase their labour force. Historically, the increase in their labour force increase the total number of finished goods. This promoted the timely supply of goods to the customers since delivery schedules were closely tied to completion of the production schedules. This timely supply of finished goods was necessary for customers to maintain their trust in the company. It was however observed from the company data that as demand increased, the lead time changed from four weeks to eight weeks. The subsequent balancing loops, B1 and B2, shown in figure 4 have depicted why there were such delays. From B1 it is clear that the increase in customer orders necessitate an increase in raw materials. This relationship is critical because the case company operated a low stocking policy which allowed only minimal stock of parts to be kept Since the company does not produce its own raw materials, it had to rely on their external suppliers in the mainland United Kingdom and the Scandinavia for supply of raw materials. Hence delays in supplies destabilised production. This delay had direct effect on production lead time and was one of the major causes of the long lead times experienced.

By studying B2, it is evident that customer orders are transformed into mini orders to the assembly and machine shops. The mini orders which go to the machine shop are to alert the machine shop operators of parts which would be required for assembly. Most often the machine shop operators anticipate stock requirement, based on experience, and machine parts to stock. This was based on existing general demand forecast. The unexpected increase therefore increased the number of operations in the machine shop as well as the net utilization of the machine shop. Apparently the total orders were greater than what the capacity of the machine shop could cater hence production backlog was created. The reason was that since the operations of the machine shop was machine-intensive, the increase in work force did not necessarily impact on the timely production of parts. The backlog created had a consequential delay on assembly operations. For instance the assembly of some tables had to be suspended for six days until table tops were machined at the machine shop. A delay in assembly operations affected the total number of finished products and hence the net orders received over the time period.

Other positive and negative loops describing the impact of their activities on cost is shown in figure 5. As can be observed from the loops shown in figure 5, B3 shows that the increase in labour force impact positively on labour cost. Labour cost is an essential and incremental aspect of production cost, therefore the increase in labour cost cause an increase in the cost of production. Without the association of the appropriate level of value creation in favour of customer demand, the increase in production cost has a negative impact on profit margin as well as the total revenue to generated.

As a business strategy, part of revenue generated is invested in sales promotional activities, which has proven to increase customer awareness and hence company's competitiveness.

Insert figure 5

Figure 5: Loops describing impact of activities on cost R2 shows that with increasing competitiveness, large market shares are obtain hence providing a strong customer base capable of generating high profit margins.

Other positive loops of interest are shown as R3, R4 and R5. They illustrate the impact of increase in resource utilization on training and tool cost. In R3, it was observed that increase in resource utilization caused the company to employ more temporary workers who were trained to take up available jobs. Some cost were incurred in the form of training materials, training personnel and resource utilization time. Another prime regenerating loop demonstrating how the cost of tooling was increased in the long term is shown by R4 and R5. R4 demonstrates that as the number of staff increased there was corresponding increase in the number of tools required for the job. Tools in this sense refers to bench working tools like chisel, hammer, drills, polishers, etc which are often contained in a tool box. The purchase of these tools increased the total cost of tools acquired by the company. Also R5 shows that the increase in the number of workers increased the rate of tool usage which resulted in a high rate of tool wear, thereby increasing the total tool cost.

Figure 6 shows the overall influence diagram representing a collection of the causal loop models already explained in preceding pages. This was good to illustrate the feed backs associated with decisions and operations in the company. Discussing these outcomes with Managers of the Company, they expressed satisfaction in the level of learning the models gave them about their own operations. Most importantly, they understood that causal impact of one activity on the other. Without providing quantitative evident of the extent causal variable influenced each other, the Managers confirmed that the models themselves were adequate to qualitatively explain the influential factors on cost and values hence suggesting which 'levers could be pulled to enact required behavioural pattern of cost and values'. This was necessary since it depicted the consequential effect of actions and activities on the shop floor. Not withstanding the causal loop models could not capture the stock and flow structure of the company for quantification purposes. This is required because 'stock and flow models' put structures around causal loop models to avoid misunderstanding and misinterpretation [START_REF] Sterman | Business Dynamics: Systems thinking and modeling for a complex world[END_REF].

Insert figure 6

The conversion of structured causal loop models into 'stock and flow' models require further understanding of the variables in the model and their associated links. The first step in the conversion process is to identify the stocks in the model. Stocks are identified by studying the CL models to observe which of the factors possess a sense of accumulation. This is confirmed by noting the links which flow into those variables.

Insert figure 7

Figure 7: Elements of stock and flow models A snapshot of the iThink system dynamics simulation model derived from figures 3a, 3b and 6, taking into consideration the definition for stocks, flows and converters given above is shown in figure 8. With the adoption of the software, there was no need of going through the rigorous mathematical transformations proposed by some literature.

Insert figure 8

Figure 8: Portion of iThink system dynamics model

Simulation results and analysis

To help validate the model, initial data was inputted into the model and the results were compared with observed trends of performance in the company. Factors such as actual production rate, product value, profit generated, material supply volume, customer orders, labour cost and material cost were critical variables which were verified by the Production Manager to confirm that the model best described their production system.

The logic behind the connectors were also verified and identified to best represent the process states. The existing orders received from customers were mapped against the total cost consumed during the production process and the value generated as well as the profit attained. The graph shown in figure 9 shows a typical model output given a set of constant orders to be processed by the company. This graph was generated through the simulation software based on a set of well defined mathematical relationships between the parameters. Details of the graph has been given in Table 2, which is also an option provided by the software. From the graph and table (figure 9 and Table 2) shown, it can be deduced that for a fixed order of 20, the profit , which is a representation of the difference between the total cost and value generated was marginal. This was within the region of £3238 and £4238. the difference was as a result of the difference in the product types which the customers ordered.

Insert Table 2 Table 2: sample simulation results

That is to say the company made more profit on some product classes than others. The simulation model therefore assisted in informing the company about their capital intensive products as well as their primary profit generating products. Although this was knowledge which existed in the finance department, the modelling results helped validated this assertion and also it became a relevant issue for the production department also. It was realised from the graph that after an initial stage, the product value kept increasing whilst the cost and orders remained approximately constant. The cost was approximately constant because after the initial capital intensive investment, the average cost spread over each month was marginal. Also since the number of human resource and machines remained the same the only variable was the material cost which also did not change significantly based on the order types received. Hence for a company operating within a relatively stable market conditions, values can be enhanced without necessarily increasing the cost. This knowledge was satisfying to the Managers of the company. Thus in reality the ability of a company to annex the effect of market instabilities contributes greatly to their value generation.

According to the Managers of the company, these initial results depicted their current business situation and hence was confident that the model was useful for conducting further experiments which could support decision making in the company. Hence series of experiments were conducted on the model to inform Management of the company about the implication of some business decisions. These experiments were constrained within the perimeters of the interest of the research so that well focussed results could be obtained. A key experiment was conducted for the sustainability of the company in varying customer order conditions. Figure 10 gives a snap shot of the graph representing the effect of customer order increase on the company. It can be deduced from the graph that as the customer orders increased there was increase in both the cost and value generated. The product value exceeded the cost, implying that the company was making profit until the fourth order when the cost exceeded the value generated.

Thus after the fourth order, the company can not produce profitable products meeting customer specifications. proved worthwhile and the system yielded higher values at less cost, rendering the company competitive and more profitable. A snap shot of the results is displayed in the graph shown in figure 11. The graph shows that the initial introduction of the new equipment will not generate enough profit with low customer orders. That was to be expected as the existing capacity was suitable to satisfy low orders. The benefit was clear only at high customer orders. It also denotes that at low ordering capacities equipment may be idle. The decision to invest therefore lies on the company's desire for expansion or ability to win more customer orders.

Insert figure 10

Insert figure 11

Observations about system dynamics modelling of cost and value dynamics

Throughout the research it was observed that the process of capturing elements impacting complexities and dynamics on cost and value generation demanded adequate data collection and thorough understanding of the processes being modelled. The close collaboration of the authors and the staff of the case company was necessary for the successful data collection, validation and analysis. In the case of the company under investigation, various causal loop models describing the operations and change enactors in the company were created. Specific portions of the causal loop were transformed into iThink simulation models for further analysis in terms of a) replicating and understanding historic enterprise behaviour and responses; b) predicting future enterprise behaviours and impact on performance indicators and c) experimenting alternative decisions before implementation to save cost and errors.

In carrying out this research the following observations were made:

1. The causal loop modelling technique was helpful in predicting the possible effects of potential change parameters in the company. Manufacturing elements which impacted on cost could fairly be modelled and controlled. The operation of the company was better understood in the process of modelling with the causal loop technique. The method was not very rigorous but fairly simple to understand. This is the reason why it can easily be misunderstood and interpreted wrongly. It was also observed that identifying key variables was not simple. It demanded thorough understanding of the business processes. A clear limitation of the causal loop modelling technique observed was that each of the loops could be further modelled in detail. The challenge involved is that the end model becomes complex and difficult to understand. As a result, the idea behind creating the model could be lost. The ability to determine the point to end 'decomposition' of variables becomes a key issue to the modeller. Extended literature on process decomposition can be found in [START_REF] Vernadat | Enterprise modelling and integration; Principles and Applications[END_REF][START_REF] Chatha | Combined Enterprise & Simulation Modelling in support of Process Engineering[END_REF][START_REF] Agyapong-Kodua | Multi-product cost and value stream modelling in support of Business Process Analysis[END_REF]. Another observation was that until the as some variables and links could have multiple meanings. That is why for each of the models created attempt was given by the authors to provide explanation in words to outline the meanings of the cause, effects and links involved in the model. Although links and possible effects of causes were observed it was not possible to know the extend of the change which was happening in the company. This gave way to the utilization of the iThink software to capture the extend of the change.

2. The transformation of the causal loop models to iThink software was not straight forward. It demanded further understanding of the relationship between the variables. The relationship had to be expressed mathematically to suitably demonstrate how changes in the variables will impact on the ME. Although literature had attempted to explain the transformation process, it is not simple and easy to apply to manufacturing set ups. The key issue is to be able to extract stocks, flows, convertors and other elements of the software from the causal loop model. It demanded reformatting the causal loop model into what was termed 'structured causal loop models' before the transformation was possible.

The structured causal loop models were helpful but contained some assumptions until they were utilized in the iThink software. As could be observed from the paper, the two modelling techniques were used supportively to derive the results presented. It is therefore required and essential to begin the iThink simulation model from the causal loop modelling technique since it provides a strong foundation for analysis. Also they contain minimal formal notation symbols as compared to the iThink modelling tool. However the price for this abstraction is the lack for its exactness. MEs by this approach has the enhanced benefit of capturing all or at least some of the factors creating dynamics in the company. When this is achieved companies are not surprised by changes and are able to predict likely consequences of events before they happen. Hence for most MEs operating in dynamic markets it is beneficial to deploy these techniques.

5. Although the authors believe that further research is needed to investigate the interplay between causal loop and iThink modelling techniques, they have observed that the causal loop modelling technique provides a suitable backbone model which usefully encode set of needed factors which can be used to facilitate the design and building of simulation models based on system dynamics principles.

To summarize, the system dynamics modelling techniques in the form of causal loop and iThink simulation models were able to capture dynamic properties impacting on cost and values for a case ME. Experiments that test the validity of models before their use were performed. The models became were used to support decision making regarding cost and value generation. The causal loop model was a suitable foundation for building the simulation model in iThink and illustrating the dynamic changes that are possible in the ME. Despite the rich knowledge provided by the causal loop models, they were not parametric and hence could not be used for quantitative analysis. They were thus supported by the iThink software to completely achieve the aims of the research.

Conclusions

Aspects of dynamics impacting on cost and value in a case ME was modelled using CL and iThink modelling techniques. Through the application of these techniques: 1) key industrial dynamics were captured and their causal impact on cost and value generation identified;

2) a new approach to cost and value modelling was demonstrated. The unique advantage in this approach is that cost and values are not assumed but derived from 'causal variables';

3) an alternative understanding of value generation is presented. This is not based on internal practices but external market conditions. Internal practices influence cost and they should be controlled to match values generated. 4) problems inherent in production systems were made clear. This is because the modelling of CLs introduces cross departmental issues and therefore promote 'process integration'. 5) benefits associated with qualitative and quantitative methods were achieved. This is because CLs provided qualitative support whilst iThink gave quantitative benefits.

In addition to the above, following this modelling approach enabled interaction between key system parameters to be observed. Alternative investment plan by the company was assessed through the system dynamics model. This paper expands the manufacturing enterprise and system dynamics concept to include cost and values. Improvement in terms of cost and values made in the direction of purchasing a second equipment resulted in significant reduction in backlogs and customer lead times thereby improving company performance. The models supported the company in measuring their state of performance under increasing customer orders. Also it emphasized the need to increase sales operations to increase customer orders since below a certain ordering quantity the company will be running at a lost. It holds that it is possible to deploy system dynamics modelling techniques in a manufacturing environment to assess the effect of various dynamics on the enterprise.

Figure 2 :

 2 Figure 2: open causal loop illustrating factors affecting production rate achieved

Figure 6 :

 6 Figure 6: Influence loop 1 of case study company

Further

  verifications can be made by identifying the units of measure. Once stocks are identified, all other factors are either flows or converters. The difference is depicted through the nature of the outgoing dependencies. The only means a stock could change is through the influence of a flow. Hence a measure of the flow is the unit of the stock per unit time. Besides stocks and flows, other variables influence systems. These are termed converters. Converters hold values for constants, defines external inputs to the model, calculates algebraic relationships, and serves as the repository for graphical functions. They are linked to the model through connectors. A description of these modelling elements is shown in figure 7. Input converters are defined as all factors by nothing (no other factors) whilst output converters are factors which do not affect anything.

  Figure 9: sample iThink system dynamics results

Figure 10 :

 10 Figure 10: Graph showing the effect of increase in orders

Figure 11 :

 11 Figure 11: Graph showing the effect of introduction of new equipment

  explained by the modeller it is quite difficult to comprehend

3.

  It was observed that many factors impacted on cost and value generation. Hence the generation of a generic cost and value model will required the collection of lots of data and experiments. The system dynamics tool served as a strong modelling technique to capture most of the salient factors in the company. To the expert in modelling, it was an excellent way of illustrating the factors which could be controlled and monitored to reduce cost and improve value. An alternative way was to provide similar models for each section in the company . In the top level models presented it is possible to experiment with controlled variables and examine their influence on cost and value. This is necessary for the MEs profitability and competitiveness 4. Suitable experiments could be conducted to analyse optimal performance in terms of cost and values generated by the company. The critical ordering point was established and the alternative deployment of an extra machine was experimented. It is therefore possible to generate from these system dynamics models, the outcome of possible decisions before implementation. Decisions result in actions and actions generate cost as well as values. How these are matched effectively will show how profitable the company will be. Modelling

  This provides an excellent way of scientifically assessing the impact of decisions especially on key performance indicators including cost and value.In an ongoing research work by the authors, various Enterprise Modelling (EMs) tools are being investigated to identify the possibility of integrating the strengths of EMs with SD tools especially for providing a structure around SD models and limiting the possibility of modelling several unrelated factors.

Figure 4 :

 4 Figure 1: overview of operations in the case study company

Figure 8 :

 8 Figure 8: Portion of iThink system dynamics model

Table 1 : Review of system dynamics modelling tools

 1

	Many commercial simulation software exist but the iThink continous simulation tool
	best support CL models
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

Modelling tools Analysis of multiproduct flows and product dynamics Identification and capturing of aspects of complexities and dynamics in MEs Reflection of causal impacts of activities on financial indicators

					Ability to measure	Availability of suitable
					process cost	constructs for value and
					without	cost modelling
					distortions
	a. Causal Loops (CL)	Causal loop models are not product	The identification of	CL models can be made to depict the causal	There are no	There are no established
	(Forrester 1961;	specific. They represent the causal	aspects of complexities	impacts of activities on financial and	measurable	constructs in CL
	Sterman 2000; Burns	effects of activities. Specific	and dynamics can be	economic indicators in MEs. This depiction	parameters in CL	modelling. They basically
	2001; Burns and	product -based causal loop models	model through CL	is however qualitative and cannot accurately	modelling	represent cause and
	Ulgen 2002)	can however be generated.	modelling technique	be quantified in the CL technique.		effects interlinked by
						arrows and sign polarities.
	c. Petri Net (PN)	PNs can accommodate levels of	PNs are suitable for	PNs are able to analyse qualitative causal	Because of the	There are no well
	(Peterson 1981; Zhou	product complexities but will	capturing aspects of	effects of activities of dynamic systems	mathematical	established constructs for
	and Venkatesh 1999)	require a formalized approach for	system dynamics. Process		support in PNs,	cost and value modelling
		doing so	models can be extracted		they can be useful
			from CIMOSA or IDEF3		in measuring costs
			models
	d. Bayesian networks	BNs is a statistical modelling tool	BNs are capable of	Causal relations can be captured and	Efficient	There are no existing
	(BNs) (Pearl 2000)	and could help classify products but	representing aspects of	represented as conditional dependences and	algorithms exist	constructs for cost and
		not model products with their	dynamics and	used for onward analysis	which can be	value modelling
		process. It is not a process	complexities in MEs in		designed to
		modelling tool	the form of variables and		identify process
			their probabilistic		costs without
			independencies		distortions
	e.

Fuzzy logic (FL) (Batur, Srinivasan et al. 1991) (Wang 1992)

  FL feeds on the fuzzy set theory to support reasoning but it does not explicitly model processes.

	Complexities can be	Causal relations could be depicted but	Process cost can be	No value and cost
	expressed but in a	limited to variables and not processes	estimated with FL	constructs exist
	statistical manner
	f

. Neural networks (NNs) (Minsky and Papert 1969; Gardner and Derrida 1988; Spooner, Maggiore et al. 2002)

	Factors influencing multiproduct	The application of NNs in	It is capable of reflecting causal impacts	NNs possess the	No constructs really exist
	flow can be developed and	real life is suitable for	through the expression of algorithms	ability to measure
	modelled through the application of	modelling complexities		process cost
	NNs but not as a process. For	especially the complexity		through the
	example, NNs can be used to group	of data and not ME design		formulation of
	products into their respective			algorithms
	classes based on a mathematical or
	relational algorithms. it cannot
	match graphically products to their
	processes

Table 1 : Review of system dynamics modelling tools

 1

	total cost consumed			customer
	(£)	product value (£)	profit generated (£)	orders
	17511.4	20750	3238.64	20
	17511.4	20750	3238.64	20
	17511.4	21000	3488.64	20
	17511.4	21250	3738.64	20
	17511.4	21500	3988.64	20
	17511.4	21750	4238.64	20
	F o r
	P
	e
	e r
		R
		e
		v i e
		w
			O n l
			y

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