MGSC Project Process Management

Abstract

Many scientists have worked on the mathematical definition of the S-curve, including mathematicians, statisticians, economists and engineers. The cash flow or S-curve defines costs and revenues in a planned way using a cumulative curve that simulates the existence of the project. There is always a deviation in various process activities and the consequences are financial, which puts the project stakeholders in a difficult position as it usually involves large investments. Therefore, the case of financial flow forecasting is determined by the modification of the Gaussian S-curve (MGSC) through scientific project management, which is very useful for all participants in the production process. The MGSC solves the problem of defining the initial state of the project in terms of the duration and cost interval of the project. However, there is the problem that the duration end and the project costs increase or decrease differently during the realisation of the project, which is defined by different process activities. Simplified assumptions within the process activities and the risk method complement the differentiated development of the process and create a dynamic simulation of the project, that is daily project management. This enables timely regulation of the execution system, that is the management of process projects.

1. Introduction

The rapid development of project management (PM) has been made possible by the rapid development of business process management (BMP) technology. New CAD and SMART technologies and methods within integrated information systems (IIS) contribute to the daily monitoring [1] of business and project management systems. The key processes in these new methods are the planning and regulation of the project system, that is the planning process group and the monitoring and control process group. Standardisation technology, however, does not follow the third and fourth industrial revolutions; hence Professor Rex’s phrase, “If you know technology, you know how to programme”, has been proven true in practice. It was programming that enabled the development of the method of dynamic structural programming (DSP), which, together with operational research as a tool for optimal project management, transforms the static project of building organisation (POB) [2] into a dynamic POB, that is dynamic project management processes (PPM). The implementation of an appropriate enterprise resource planning (ERP) system [3] is a key investment that usually ties up enormous resources and can have a significant impact on the future competitiveness and operation of the company. In today’s practice, the last planning system (LPS), followed by location based management (LBM) and 4D modelling in space with a time component, then planning on work cycles [4] (PCW) and the traditional approach based on critical vay metoda (CPM) in Microsoft Project (MSP), Primavera or SuperProject. Any project realisation is mainly production. It is a function of technology, organisation, management and information and communication technology (ICT). The technology uses differential equations, while the other components run behind the mathematical modelling of these processes. Therefore, software models and simulations, such as BIM and Digital Twins, appear today as tools that aim to complement the missing decision-making processes. This results in the need for vector [5] or parametric [6] modelling and the transformation of static POB and project management documents (PDM) into dynamic scientific documents. The sustainability of BIM requires the modelling of n-dimensional dimensions of nD buildings as components of dynamic structural programming (DSP) or application programming interface (API). Thus, for the process engineer, the focus is on the sustainability of the traditional criteria of structural integrity, constructability and cost. However, today’s ITC digital technology also provides for the automation of the work for which the GPS technology was developed, which converts manual records into automatically collected data in the field and sends it automatically to the central data processing in the company’s IIS system. However, the key to solving the problem lies not only in automating existing administration, but also in standardising production standards (construction, mechanical and electrical) and cost items. Thus was born the DSP [7] dual COD method, which generates the iterative differential of cyclical production processes. Here, mathematical and cybernetic methods are used to transform organisational structures into differential organisational structures as the main components of the artificial intelligent (AI) system. Thus, API and DSP applications are useful links to launch add-ons and external programmes to extend and optimise BIM. Moreover, with robotisation, technology has risen in the organisation, so it is necessary to build dynamic standard models with vector planning [8] and improve them by optimising production processes [9]. Thus, model standardisation of business processes eliminates problems and seeks to optimise the economic and organisational elements in the business system defined by the financial cash flow curve. This process of bringing organisational solutions closer to technological achievements in order to eliminate their gap leads to the creation of the financial MGSC as a simulation element of the production model of modern cyber-physical systems (CPS) [10]. The goal of MGSC automation is softwareisation, that is model standardisation of production processes using mathematical and statistical methods to replace routine and hazardous operations with robots and reduce financial risks to an optimum for investment. The contribution of the management of the MGSC method lies in the adaptation, refinement and solution of problems in processes and methods in project management. Thus, in the first place, the transformation of a static process into a dynamic financial process with a curve linked to resource costs leads to a vector simulation MGSC that allows a technological record of the work or process that largely guarantees the quality of the work, that is integrated information quality management [11]. The objectives of managing the MGSC method are to promote a different way of recording the process as a basis for standardising mobile management to achieve management standards according to the methodology of project management (MP) [12]. Then the creation of a new vector S-curve as the basis for mobile management of management project process groups, especially in the group of planning the implementation and monitoring and controlling or regulating the cybersecurity system [13]. This, in turn, leads to a competitive price and the desired product quality, with the possibility of simulating management. A team manager who has daily dynamic data in smart technology becomes a manager of daily monitoring [14] of the total budget (EAC) and estimating the variance of the total duration of the project (BAC).

2. Vectoral organisation and technology on production process

The postmodern organisation begins with the introduction of information technology and defines the organisation systematically and procedurally with input resources (R) and output system products (S) (Figure 1).

Figure 1.

Systemic-processual [15].

Such a process organisation creates business resource planning (ERP) through the Information Business System of the American company SAP and the Japanese JIT and TQM systems.

The systemic approach is defined by the general theory of the system and strives for all resources of the system to be a function of the dynamics of the environment and feedback or control. All this is based on information moving from the classical vertical hierarchical flow to the horizontal process flow of communication. Thus, the theory of dependency on input resources for the system emerges. Then, business reengineering management (BMR) moves towards thought management of enterprises by creating a creative team leader instead of a command and control leader. MP [16] is done through three, four and five management functions with continuous decision-making that is constantly loaded with risk, as an uncertain event or condition that may occur in the future and disrupt a project goal, temporally, financially or qualitatively, reducing it to a tolerable risk. For the implementation of the project, it is important to prepare the work with the creation of a dynamic POB (Figure 2) [17] or PDM.

Figure 2.

Static and dynamic POB.

It can be seen that static standards and calculations dominate production management and the bid design is very inaccurate both financially and qualitatively as a product. However, with dynamic, vector or parametric modelling of the standard and calculation, this problem is greatly reduced. Therefore, vectorial and parametric models of standards are created, which are used to create digital twin systems for graphical and analytical representation of production.

2.1 Vectoral organisation on production

Every business system consists of 4 functions, and within the management or administrative function, the most important sub-function is the planning of the production process and the regulation of the production processes, which are in the function of technology, organisation, management and ITC system with the daily management of the production or business system. Nevertheless, planning in construction is at a low level due to outdated standards. Therefore, the introduction of dynamic or parametric vector standards is recommended to increase the accuracy of planning and thus the cost of projects. As a result of relational databases, a vector organisational structure [18] of the company is created, which is introduced into the matrix organisational structure with a third axis, namely resource variables, which is stored in the database with histograms and allows access to data up to the resource level (Figure 3).

Figure 3.

IIS construction company with cyclo-space vector structure.

By elaborating the vector structure of the business system down to the level of the construction tender process, through the tender and site and situation documentation, to the level of operations (1 collection of tenders, 2 technological parameters, 3 planning parameters, 4 costing and others), that is working with the same human resources, a process elaboration of the management of Figure 4 is created in five levels, that is processes. Thus, the POB becomes a PDM that goes through five levels, that is a group of processes that are roughly systematised in both systems.

Figure 4.

Vectorial project-process-operation-resource-oriented structure reduced to the level of the function-process-surface.

2.2 Vectoral norm on technology production

In the same way, the 4D model of the norm, or the vector norm, was developed from the static norm. The materials and basic resources in Table 1 are a function of the constructive and geometrical characteristics of the building project using the described technology.

Constructive elements	Geometric charact.	cm	cm^2	I	W	M max	fm	R
	b	h	F	cm^4	cm^3	kNm	kNm^2	kN
Bed	10	12		1440	240	2.4	10,000	7.2
DOKA H20	8	20		3850	385	5	13,000	11
Tubular scaffolding	5		498	12.4	5.14	0.108	21,000	10.33

Table 1.

Construction characteristics carpentry technology GK Međimurje 30 years ago.

Material consumption is defined by connecting the designer’s equations with the effects of resources reduced to the dimensions of the design documentation of GK Međimurje formwork technology defined by the equations in the monogram with units of measurement in cm, m, kN. Labour costs By creating standards according to workers’ occupations, the discrete data of labour standards are shortened and the model is obtained by defining the functional relationship of resource and time standards in relation to the dimension of construction or labour. By analysing and systematising the old standards, the three-dimensional variables of construction, technology and organisation can be used to define the vector standard hypothesis [19] Eq. (1).

$$\mathit{VN}=f\left(\mathit{kd},\mathit{ko},k,r\right)={\mathit{kd}}_i{\mathit{ko}}_{i}f\left(k,r\right)$$E1

Normative time can be represented as a resource effect in a three-dimensional formula. The variables are elements of project construction (Xc) and technology (Yr) defined by the categorised variable of this organisation (Zo) (Figure 5).

Figure 5.

Idea for the creation of a norm vector in the building industry.

Thus, using different technologies as examples, tables were created on the function of the construction element of the execution (k) and the dimensions of this execution element (kd) and on the resource (r), that is the execution technology, and on the organisation with the definition of the basic type of the construction element (ko) as an organisational unit (Figure 6).

Figure 6.

Performance and vector norm for the concreting of buildings.

3. Cash flow of the project

The definition of the S-curve has been achieved by integrating management software, that is using ODBC databases or newer XML internet technology with the software MS Project. The system allows monitoring of resource efficiency by activity and on a daily basis through the presented data model (Figure 7).

Figure 7.

Report on project monitoring and cash flow.

Alternating monitoring of normative and financial indicators has been made possible, which allows increasing, that is streamlining, the resource control of projects previously monitored on a periodic financial basis to define the estimate of the deviation of the EAC and the estimate of the deviation of the project BAC from the planned cash curve, for which we do not have a functional link but an assessment (Figure 8).

Figure 8.

Cash flow [20].

3.1 Planning the project process with MSP

An overview of the S-curves in MSP shows that distribution and cumulative curves are defined with attempts to define equations, but the nearest exponential curve does not satisfy the given S-curve (Figure 9).

Figure 9.

Two specific projects using the S-curve report of the MSP software.

Both examples are different and show the monthly distribution of finances with a circular or approximately modified Erling density distribution similar to the future normative charts. Thus, MSP defines the cumulative quadratic and exponential curve of finances by a general linear, polynomial, quadratic or exponential equation Eq. (2).

$$y=a{x}^2+\mathrm{bx}+\mathrm{c};\mathrm{y}=\mathrm{a}{e}^{\mathit{bx}}$$E2

Based on the detailed presentation of the reconstruction project of the Zagreb Maribor motorway bridge over the Sava in Zaprešić, the part over the railway and the Sava river, a static and dynamic presentation of the project was staged using the IIS system with the MS project presentation of the given project. It is obvious that the given IIS system has a problem with static normalisation. For example, some elements of the offer have no norm, so they are covered with an unanalysed resource and never defined exactly, and we want to define the resources in the project exactly. For a given project, we create a static ABC curve with the direct costs of the project, and we get a summary of the non-indirect costs with the profit that defines the rest of the finances of the project. Thus, the total investment of 26.4 million gives 17.4 million direct costs DT and other indirect costs IT with profit P Eq. (3).

$$\mathit{UP}=\mathit{DT}+\mathit{IT}+P$$E3

ABC Curve direct resource costs are defined in the order of the minimum (Figure 10, Table 2).

Figure 10.

ABC curve direct resource costs.

Bid construction resource	111,743-5R name	MU	Q	Max price	Costs	%	ABC	%
CA_CS_243	Robot	h	3291	2000	6,583,968	38	6,583,968	38
CM_299	Asphalt	T	4198	443	1,861,477	11	8,445,445	48
88,881	Indefinite	HRK	1,550,739	1	1,551,739	9	9,997,185	58
CM_300	Asphalt	T	4198	345	1,451,458	8	11,448,643	65
10	Worker	h	22,354	57	1,281,511	9	12,730,154	73
CM_nafta	Oil	l	166,892	7	1,168,247	7	13,898,402	80
650	Machinist	h	6623	80	529,907	3	14,425,310	81

Table 2.

ABC Curve direct resource costs.

It is noticeable that the leading payback is pumping robots, asphalt, labourers, oil, machinists and concrete, which account for up to 80% of the price. Therefore, these resources should be influenced. To maintain a dynamic state of resources in the project, the labour and machinery resources are used to define the duration of the project. Thus, the labour is about 3 million and the machine is about 8 million kn, which gives the S-curve without material and other (Figure 11).

Figure 11.

Concrete project with the S-curve report of the MSP software of a bridge over the Sava and part of the railway line.

The S curve is incomplete because the transfer of resources has not been completed in full except for time, without which there is no Gantt chart. But for an MSP, moving the activities and transparency of the Gantt chart is a real routine. The direct costs of resources are visible in the histogram and are made up of labour R, material M and machines S Eq. (4).

$$T=R+M+S$$E4

The equation Eq. (5) for the resource in the production time is a linear function of the product of the direction coefficient of the direction (a) or y’ and the production time t.

$$R=M=S=\mathit{at}=y^{\prime }\mathrm{t}$$E5

By reading from the Gantt chart or histogram, the resource R is located in the third dimension of the production budget; therefore, the equation takes the form of a sum Eq. (6).

$$R_j=\sum _{i=1}^n{a}_r{t}_{\mathit{ri}}$$E6

3.2 Planning the project process with MGSC carve

More recently, probabilistic forecasts of project performance and the use of stochastic S-curves with a stochastic S-curve generation software package and a simulation approach have defined the dispersion variance of finances and time of the MGSC project as a function of the density distribution of cost and time. Expected monetary value (EMV) or S-charts are widely used today and are complemented by functional MGSC [21, 22] Eq. (7), (Figure 12).

Figure 12.

MGSC project Zagreb-Zaprešić within –n to n and 5 months.

$$\mathit{\text{skvGr}}\left(x,T\right)=\mathit{\lambda kv}·{\int }_0^x\frac{1}{\left(a·T+b\right)·\sqrt{2·\pi }}·e^{\frac{-{\left(x-\mu \right)}^2}{\mathit{kv}·\left(a·T+b\right)}}\mathit{dx}$$E7

The levelling and fitting of the curves, that is the modification of the Gaussian curve, refers to the introduction of a constant kv parameter in the value of 10,000 units. The value of the investment in the reconstruction of the Zagreb-Zaprešić Bridge, which can be seen on the MSP fall stream, is HRK 2,640,000,000. In the software budget, the cost axis is in thousands, so T = 26,400 × 10³. The number of months working on the project is n = 5, which defines the variable x, and the expectation of μ from the variable x is x/2. The constant variable kv is 10,000, and λkv is taken 100 times larger than the standard value and is 65,000, while the coefficient b of the standard value is 4 × 10⁻³ and has a slightly increased value of 3,81 × 10⁻⁸.

Considering that the S-curve has half monthly rates for the investment distributed within 2.4–2.7 million time-tenths, that is every half month, this is the financial differential, that is the density of the distribution of the financial plan situations in the project time (Figure 13).

Figure 13.

Simulation of the density distribution of financial plan situations with MGSC for the Zagreb-Zaprešić project.

4. Organisational differentiation in MGSC with the method DSP for production companies

The model standardisation of the cost description of items, that is the common harmonisation of the item descriptions in the offer, that is the standards, creates a unique code to define the construction product with the method DSP, that is the code DSP Eq. (8). The method DSP creates a structural organisational differential by levels with the possibility of elaboration at the movement level.

$$\mathit{DSP}\mathit{COD}:=\left[f_n\left(\left[A\left|R\left|D\right|\right|\right]\right)=f_{n+1}\left(\left[\begin{array}{c}A\end{array}\left|R\left|D\right|\right|\right]\right)\right]$$E8

Goods as a function of the variables A-activities, R-resources and D-dimensions of design and resource performance. In this way, product datasets are formed by levels and distribution of complex processes to procedures, and construction production datasets are modelled by combinatorics and connected by standardisation of the model. By converting the code DSP into the structural code of the MGSC curve, an organisational or financial differential is created by a three-dimensional structural model defined in the i, j, k structure S_ijk Eq. (9), and by replacing the structure S with the MGSC curve, the MGSC DSP COD Eq. 10 based on iterative numerical methods [23] (Eqs. 9–11), which generates the future state of structure n + 1 using the existing state of structure n and the differential Δn + 1 shift of the function or structure.

$$\mathit{DSP}\mathit{COD}:=\left[f_n\left(\left[S_{\mathit{ijk}}\right]\right)=f_{n+1}\left(\left[S_{\mathit{ijk}}\right]\right)\right]$$E9

$$x_{n+1}=f\left(x_n\right)$$E10

$$\begin{array}{l}\mathit{\text{MGSc}}\mathit{DSP}\mathit{COD}:=\\ \left[f_{n+1}\left(\left[\mathit{\text{skvGr}}{\left(x,T\right)}_{\mathit{ijk}}\right]\right)=f_n\left(\left[\mathit{\text{skvGr}}{\left(x,T\right)}_{\mathit{ijk}}\right]\right)\right]+∆f_{n+1}\left(\left[\mathit{\text{skvGr}}{\left(x,T\right)}_{\mathit{ijk}}\right]\right)\end{array}$$E11

In implementation, the main problem is to define the change in the EAC, BAC S-curve caused by various risks or changes in labour intensity, that is resource use. This is solved by numerical iteration, that is by induction and iteration of the cost estimating equations Tproc using the planned normative costs Tp and their derivation. The derivative of the MGSC valuation curve is thus the value of the difference between EAC, BAC and the value of the valuation cost (Tproc) and schedule (Tplan) functions, that is the normative cost T (Eqs. 12–14) of the standard MGSC curve plus the differential cost T.

$$T_{x+1}=T_x+∆T_{x+1}$$E12

$$T^{\prime }=\frac{\mathit{\Delta T}}{\mathit{\Delta x}}=\frac{\mathit{\Delta T}}{\mathit{\Delta t}}=y^{\prime }$$E13

$$T_{x+1}=\mathit{\text{skvGr}}\left(x,T\right)=\mathit{\lambda kv}·{\int }_0^x\frac{1}{\left(a·T+b\right)·\sqrt{2·\pi }}·e^{\frac{-{\left(x-\mu \right)}^2}{\mathit{kv}·\left(a·T+b\right)}}\mathit{dx}+T^{\prime }\mathit{\Delta x}$$E14

At intervals of dozens of S-curves creating intervals of half a month within the 5 months of the project. This is how we define the increment ΔT. By numerically deriving the given curve skvGr(x,T) or Tp, the derivative of the function is created by tens parts of the function and approximated by Newton’s tangent method [24], with the possibility of using steps of the degree of rotation or the intensity of resource consumption. The derivative function MGSC of the planned curve is defined with the Gaussian method of the sum of least squares.

$$x=\left[\begin{array}{c}1\\ 2\\ 3\\ 4\\ 5\\ 6\\ 7\\ 8\\ 9\\ 10\end{array}\right]y=\left[\begin{array}{c}4868\\ 5076\\ 5236\\ 5348\\ 5404\\ 5404\\ 5348\\ 5236\\ 5076\\ 4868\end{array}\right]b=\left[\begin{array}{c}b1\\ b2\\ b3\end{array}\right]b1=\sum _{x=1}^{n}x,b2=\sum _{x=1}^n\mathit{xy},b3=\sum _{x=1}^n{x}^{2}y$$E15

$$\left[\begin{array}{ccc}n& \sum _{x=1}^{n}x& \sum _{x=1}^n{x}^2\\ \sum _{x=1}^{n}x& \sum _{x=1}^n{x}^2& \sum _{x=1}^n{x}^3\\ \sum _{x=1}^n{x}^2& \sum _{x=1}^n{x}^3& \sum _{x=1}^n{x}^4\end{array}\right]\times \left[\begin{array}{c}{X}_1\\ X_2\\ X_3\end{array}\right]=\left[\begin{array}{c}b1\\ b2\\ b3\end{array}\right]$$E16

$$X=b{A}^{-1},X=\left[\begin{array}{c}4597\\ 294.66\\ -26.78\end{array}\right],a_i=X_i$$E17

$$y^{\prime }=\frac{\mathit{\Delta T}}{\mathit{\Delta t}}=a_1+a_{2}x+a_3{x}^2$$E18

$$y^{\prime }=\mathit{\text{skvGrplus}}=f_x=4597+294.66x-26.78x^2$$E19

And by including it in MGSC, the future cash flow curve is defined Eq. (20) (Figure 14).

Figure 14.

MGSC project Zagreb-Zaprešić within 5,5 and –n to n months - adding half month.

$$\mathit{\text{skvGr}}\left(x,T\right)=\mathit{\lambda kv}·{\int }_0^x\begin{array}{c}\frac{1}{\left(a·T+b\right)·\sqrt{2·\pi }}·e^{\frac{-{\left(x-\mu \right)}^2}{\mathit{kv}·\left(a·T+b\right)}}\mathit{dx}+\left(4597+294.66x-26.78x^2\right)\mathit{dx}\\ \end{array}$$E20

In the formula of the derivative curve, increasing Δt or dx, for example by half a month or 1 dx, increases the derivative of function 4597, from which ΔT is calculated, and thus MGSC is set at new intervals and with new values. So, for the given assumption of the extension of the project duration, the planned cost of the project ΔT increases by HRK 2.3 million, which increases the budget to HRK 28.3 million. How to assume the extension or reduction of the project can be realised by the step of differentiating the function or creating the intensity of resource use T´ = f (degree of rotation intensity of resource use). If we assume that ΔT is equal to the sum of the costs of all resource structures S_ijk, that is R_jEq. 21, then Δt can also be calculated from this data.

$$S_{\mathit{ijk}}=R_j=\sum _{i=1}^{\mathit{nr}}{a}_r{i}_r{t}_{\mathit{ri}}$$E21

In this way, we cover the planned normative money curve in all areas. In this way, the same is mapped equivalently to the valuation curve, which we define based on risk.

5. Risk simulations with MGSC for production operations

Process business activities are highly susceptible to risks, and manufacturers are interested in business risks, which can be internal or external. Risks can be defined qualitatively and quantitatively, so such management is also defined. The analysis and control of risks, that is the identification and evaluation of risks through the regulation of the project, go through a cyclical process.

5.1 Risk management in processes

Japanese and American process control in corporate production processes has developed standards for product quality management, creating a general framework of standards for risk management published by various organisations in the world (ISO, IEC, etc.). In this way, the risk management process according to the standard ISO /IEC 31000 [25] was created, which covers all operations from the identification to the acceptance of risks with analysis and evaluation, as well as the assessment and management of risks through risk monitoring and consultation.

5.2 Quantitative risk analysis MGSK

To quantify the risk (Eg) of MGSK, mathematical, statistical and simulation modelling methods are used to simulate the financial situation of the project as it progresses. Based on previous research, trying to add the risk parameter (λr) to the investment level of 10% on the normative planned MGSC is highly probable, i.e. optimal for managing the investment, and the real cost curve with an estimate takes the form Eq. (22).

$$\mathit{\text{skvGr}}\left(x,T\right)=\mathit{\lambda r}·\mathit{\lambda kv}·{\int }_0^x\frac{1}{\left(a·T+b\right)·\sqrt{2·\pi }}·e^{\frac{-{\left(x-\mu \right)}^2}{\mathit{kv}·\left(a·T+b\right)}}\mathit{dx}+\left(a1+a2x-a3x^2\right)\mathit{dx}$$E22

Risk structuring by activities of the project plan in terms of the probability of occurrence of deviations from the planned cost variables of the project is done by the method of simple evaluation of site management. By dividing the MGSC of a given project into term tenths, the probability of the deviation or risk occurring in a given segment is obtained Eq. (23).

$$\mathit{\text{skvGr}}\left(x,T\right)=\mathit{\lambda r}·\mathit{\lambda kv}·{\int }_0^{x+\mathit{\Delta t}}\frac{1}{\left(a·\mathit{Tp}+b\right)·\sqrt{2·\pi }}·e^{\frac{-{\left(x-\mu \right)}^2}{\mathit{kv}·\left(a·\mathit{Tp}+b\right)}}\mathit{dx}+\left(4597+294.66x-26.78x^2\right)\mathit{dx}$$E23

Increasing the price of a given project by λr = 1.1 of the risk parameter added to the default parameter of the MGSC λkv leads to an increase of the estimated cost by about 2.6 million on the planning curve, which from the cost derivation defines the extension of the project duration by half a month. By assuming the addition of these cost increases to the planned S-curve, the possibility of extending the project by half a month is defined, bringing the budget of the estimation curve to 31 million (Table 3).

ris	25,932	sum10	T′		2593	28,525.2
	ΔT	Δt	ΔT/Δt	Arctan(T′)	λR	ΔTr
1	2434	0.5	4868	1.570591	1.1	2677.4
2	2538	0.5	5076	1.570599	1.1	2791.8
3	2618	0.5	5236	1.570605	1.1	2879.8
4	2674	0.5	5348	1.570609	1.1	2941.4
5	2702	0.5	5404	1.570611	1.1	2972.2
6	2702	0.5	5404	1.570611	1.1	2972.2
7	2674	0.5	5348	1.570609	1.1	2941,4
8	2618	0.5	5236	1.570605	1.1	2879.8
9	2538	0.5	5076	1.570599	1.1	2791.8
10	2434	0.5	4868	1.570591	1.1	2677.4
11	2313	0.5	4597	1.570579	1.1	2544.3
	28,245	sum11				31,069.5

Table 3.

Planned and estimated (risk) iterations of the MGSC curve.

It is interesting to note that in practice estimators process bids and their manager usually reduces the estimate by 10% in order to be competitive.

6. Automation and AI systems for process production (DSP, MGSC and CPM) MSP

Planning with the DSP code is achieved by using a combinatorial eq. [26] to define all paths in product manufacturing. Thus, the DSP code is a universal equation that can be used for all equations, including CPM equations or DSPiP modelling. By simulating the MSP model with a Gantt chart and an S-curve over the key resources given by the ABC curve, it comes down to defining the working time of the resources with costs (Eqs. 24–26) using the direction coefficient (a) of the linear direction of the representation of the resource costs plus the product with the intensity of the commitment of the resources (i) or the double direction coefficient.

$$\mathrm{\Delta t}\left(R_j\right)=\mathrm{\Delta T}\left(R_j\right)/T^{´}$$E24

$${\mathrm{\Delta t}}_i\left(R_j\right)=\mathrm{\Delta T}\left(\sum _{i=1}^{\mathit{nr}}{a}_{\mathit{ri}}{i}_{\mathit{ri}}{t}_{\mathit{ri}}\right)/{T_i}^{´}$$E25

$$\mathit{\text{skvGr}}\left(x,T\right)=\mathit{\lambda kv}·{\int }_0^x\frac{1}{\left(a·T+b\right)·\sqrt{2·\pi }}·e^{\frac{-{\left(x-\mu \right)}^2}{\mathit{kv}·\left(a·T+b\right)}}\mathit{dx}+{\mathrm{\Delta T}}_i\left(R_j\right)$$E26

In the planned example itself, the curve ABC narrows the normative resource risk involved in about 80% of the project, and this is the Conject robot with a hydraulic pump involved in half of the project with almost 40% of this cost. By observing the given resource and reading the histogram of hydrodemolition activities, we simulate the method CPM, by increasing the resource. It can be seen that hydrodemolition takes 4 activities and 30 working days. If we double the labour intensity by introducing a second shift, the duration decreases proportionally, (Figure 15), but we maintain the cost in relation to the total labour. But now the whole structure of MGSC DSP changes and the curve takes a different shape, however, the time does not decrease proportionally in the CPM method.

Figure 15.

Gantt chart of the revised Zaprešić project - introduction of a new work shift for the Conjet robot resource with hydraulic pump.

Instead of half a month, the reduction is 8 days, which is half a semester unit less in our MGSC system. So the budget in the normative project is slightly reduced compared to the budget of the original S-curve plan, and there is a greater density, that is an increase in monthly situations and a loss in risk costs. Another estimation method is possible by creating steps according to mathematical iteration methods (Eqs. 27–30) with the variables BAC and EAC.

$$T_{x+1}=T_x+∆T_{x+1}$$E27

$$T^{\prime }=\frac{\mathit{\Delta T}}{\mathit{\Delta x}}=\frac{\mathit{\Delta T}}{\mathit{\Delta t}}=\frac{\mathit{EAC}-\left(T_{\mathit{\text{proc}}}-T_p\right)}{\mathit{BAC}}$$E28

$${\mathit{T}}_{\mathit{x}+\mathbf{1}}={\mathit{T}}_{\mathit{x}}+\left(\mathit{EAC}-{\left({\mathit{T}}_{\mathit{\text{proc}}}-{\mathit{T}}_{\mathit{p}}\right)}_{\mathit{x}+\mathbf{1}}\right)$$E29

$${\mathit{T}}_{\mathit{x}+\mathbf{1}}-{\mathit{T}}_{\mathit{x}}+{\left({\mathit{T}}_{\mathit{\text{proc}}}-{\mathit{T}}_{\mathit{p}}\right)}_{\mathit{x}+\mathbf{1}}=\mathit{EAC}$$E30

By introducing the MGSC equation into the iteration series of the S-curve, the EAC query Figure 16 was solved.

Figure 16.

Cash flow curve with risk in all states (x_estimat = 5.5, x_plan = 5).

While simulating an increase in the BAC valuation curve with risk without extending the life of the project BAC costs the company about HRK 2.6 million, if BAC is extended by half a month, it is about HRK 5 million, which is a big warning from the EAC for management.

7. Conclusions

Mathematical modelling of the organisation is catching up with technology, and with the advent of computer and software support, the desire to define a dynamic POB or PDM is being realised. This is achieved through model standardisation with vector and parametric normalisation of production processes, and mathematical and statistical methods are used to approach precision and reduce risk or increase sustainability of projects. In order to define the precision of finances in production processes, a new attitude in defining the model is needed, without rewriting old technologies into software technologies, in addition to the technological support provided by ITC. Moreover, every production wants to be improved, that is to achieve more indicators of the economic principles of efficiency, economy and productivity. Thus, in the process industry, the direct cost method is developed and the cash flow curve is presented in the project presentation of the budget. By creating a cash flow curve by defining the planned MGSC based on the case study method and an estimate based on some data from practice, that is from the data of the Međimurje Graditeljstvo company, an overall model of the cash flow curve is created without realisation. Thus, defining the general equation of the S-curve in multidimensional space, the entire series of S-curves is obtained as the supremum and infimum of the S-curve data set in a project. This creates a probability domain using statistical curves so that better risk management in the project is possible, that is production management is also possible with an assumed modified Gaussian S-curve, which opens a new research area for BAC and EAC dimensions in the project. It is recommended that further research be conducted based on implementation and planning projects to determine the risk coefficient or λr as realistically as possible and to seek a creative team leader in corporate security who has the skills of an IT manager [27] who has a new tool for defining risks in a corporate project. The iterative structural DSP method enables further linkage of product surveillance with the ITC system and leads to fragmentation, that is automation and robotisation of large infrastructural investments in a circular sustainable economy in the economic sense with an increase in the principles of economy, productivity and profitability. In the humanistic sense, AI systems free workers from dangerous and difficult work and open up DSP and cost-effective constant modelling and simulation of model standardisation. This, in turn, strives for the sustainability of the business model with AI [28] and cyberphysical processes (CPS), that is a system for initiating new discoveries in defining the development of standards of technology and organisation in MP. This connection with the sequence numbers on RMGSC creates a simulation of the development of the project according to possible risk scenarios in relation to the cost variable, which is similar to the Joint Resources Allocation Panel method that CPS uses for the time variable. The team also addresses the organisational differential, which has been introduced into engineering since the seventeenth century with the invention of mathematical differential models through iteration equations, and in the mid-twentieth century, operational research emerged, especially dynamic programming, which is also based on mathematical induction, that is the definition of iteration equations favourable to computers. However, in order to round off the cycle for simulation or automatic modelling of the S-curve, the equations need to be refined, especially in the case of the 4D model, where the resource ABC is considered as the third dimension in the function of s t and T, with the possibility of daily project management with differentiation of the intensity of the resources in the project, especially with the method DSP or DSP code similar to XML code. The management team becomes dynamic, a digital twin system is created and in the organisation, we simulate the reality of the projects through the model standardisation recommended by the DSP method.

Conflict of interest

The authors declare no conflict of interest.

Notes/thanks/other declarations

Thanks for IntechOpen.