# An Algorithm for Modelling the Impact of the Judicial Conflict-Resolution Process on Construction Investment

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Example and Problem Formulation

^{2}) and multiplying it by its market value in 2007 taken from [31], which is mentioned to be from 1.39 to 2.17 TEUR, and for simplicity we assume that it is 1.5 TEUR per square metre. Thus, the estimation of the price the building was sold for gives 8998.2 TEUR. The building costs data is taken from [32] and is equal to 5508.6 TEUR. We note that we do not expect to estimate the needed data precisely—we consider this example for tests and demonstration purposes only, as our goal is to provide the algorithm for those who have access to this type of data directly. The building price and its distribution in time is important in order to estimate the amount of possible losses in the case when the investor loses the judicial process and fails to complete the project. Unfortunately, we do not have the exact data of the project’s cost distribution in time. However, we have the information on costs of the project that were paid before the judicial process was started—these costs were equal to 236.04 TEUR [33]. We use this number as project costs during the first phase of a project, which lasted for 613 days. The rest of $5508.573-236.04032$ we distribute as follows. We assume that the project costs in TEUR per day are higher at the beginning of the building process by 50% compared to the last phase of the building process due to additional costs of expensive machinery (cranes, etc.). The calculated data is used to compute average daily costs for different time intervals.

## 3. The Data Structure and the Algorithms

- 2—unsuccessful scenario end node,
- 1—investor decision node,
- 0—other nodes.

- The node is fictive, that is, it must be added to the list of nodes to describe the additional edge (since in a graph there is more than one edge pointing to the same node).
- The node has no children—it is reserved to describe the parameters of an edge forming a cycle.
- After cycles are converted to the extended tree, such nodes must be deleted if they are leaves of the tree; the probabilities must be recalculated with the same proportions but without cycle nodes.

Algorithm 1: Data structure |

struct { |

int type; //node type |

float p; //the probability for this node to be selected by parent |

float price; //the price of event |

float time; //the time before event starts |

node* parent; //the pointer to parent node |

vector< node* > children; //the list of children |

node* cycle; //the pointer to the ancestor that forms a cycle |

float priceTotal; //accumulated price |

float timeTotal; //accumulated time |

float value; //node expected profit value |

} node; |

- Recursively make copies of the subgraph from nodes the process is returning to (i.e., looking for the pointer $cycle$), extend the tree by adding additional nodes. For this purpose we define a function $Expand$ in Algorithm 2.
**Algorithm 2:**Cyclic expansion algorithm**Function**$Expand\left(node\right)$**if**$node.cycle!$ = NULL**then****if**$depth<{depth}_{max}$**then**$newNode=CopyOfSubtree(node.cycle)$ $newNode.p=1$ $newNode.parent=node$ $node.children.add\left(newNode\right)$ $depth=depth+1$ $Expand\left(newNode\right)$ $depth=depth-1$ **else**// deletes unneeded fictive node and recalculates the probabilities // of parent’s children nodes leaving the same proportions smartDelete(node) **end****else****for**each node t in $node.children$**do**Expand(t) **end****end****end** - Calculate total times (field $timeTotal$) and costs (field $priceTotal$) up to the moment when events are finished—this is implemented in the function $CalcPars$ in Algorithm 3.
- Evaluate end-node scenarios (calculate field $value$) and select optimal strategy—function $CalcValues$ in Algorithm 4.
- Create profit (field $value$) distribution by calculating different scenario probabilities. A simple implementation is provided in Algorithm 5.
**Algorithm 3:**Costs parameters calculation algorithm**Function**$CalcPars\left(node\right)$**if**$node.parent$ = NULL**then**$node.timeTotal=node.time$ $node.priceTotal=node.price$ **else**$node.timeTotal=node.time+node.parent.timeTotal$ $node.priceTotal=node.price+node.parent.priceTotal$ **end****for**each node t in $node.children$**do**$CalcPars\left(t\right)$ **end****end****Algorithm 4:**Scenario profit evaluation and strategy selection algorithm**Function**CalcValues($node$)**for**each node t in $node.children$**do**CalcValues(t) **end****if**$node.children=NULL$**then**Estimate($node$) **else****if**$node.type=1$**then****for**each node t in $node.children$**do**$t.p=0$ **end**$best=t\phantom{\rule{0.166667em}{0ex}}\mathrm{that}\mathrm{optimise}\phantom{\rule{0.166667em}{0ex}}\underset{t\in node.children}{max}t.value$ $best.p=1$ **end**$n=node.children.size$ $node.value={\displaystyle \sum _{i=1}^{n}}node.children\left[i\right].p\xb7node.children\left[i\right].value$ **end****end****Algorithm 5:**Probabilities calculation algorithm with distribution extraction**Function**CalcProbs($node$, $distribution$)**if**$node.parent$ = NULL**then**$node.probTotal=1$ **else**$node.probTotal=node.p*node.parent.probTotal$ **end****if**$node.children.size\left(\right)>0$**then****for**each node t in $node.children$**do**CalcProbs(t) **end****else**$distribution.add(node.value,node.probTotal)$ **end****end**

Algorithm 6: Subtree-copying algorithm |

Function CopyOfSubtree($node$) |

$newNode\left(node\right)$// copies the node |

$newNode.children.clear\left(\right)$ |

if $node.cycle\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}$ NULL then |

for each node t in $node.children$ do |

$newNode.children.add$($CopyOfSubtree\left(t\right)$) |

end |

for each node t in $newNode.children$ do |

$t.parent=$($newNode$) |

end |

end |

return $newNode$ |

end |

Algorithm 7: Estimator |

Function Estimate($node$) |

if $node.type=2$ then |

$node.value=-\left(node.priceTotal+\underset{0}{\overset{node.timeTotal}{\int}}F\left(t\right)\phantom{\rule{0.166667em}{0ex}}dt\right)$ |

else |

$node.value=P-\left(node.priceTotal+\underset{0}{\overset{{t}_{max}}{\int}}F\left(t\right)\phantom{\rule{0.166667em}{0ex}}dt\right)$ |

end |

end |

## 4. Computational Experiment

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

- Davidov, S.; Pantoš, M. Stochastic assessment of investment efficiency in a power system. Energy
**2017**, 119, 1047–1056. [Google Scholar] [CrossRef] - Li, C. Empirical Study on the Impact Factors of the Investment Efficiency of Urbanization Construction in Guizhou Province, China. DEStech Trans. Econ. Manag.
**2016**. [Google Scholar] [CrossRef] - Focacci, A. Managing project investments irreversibility by accounting relations. Int. J. Proj. Manag.
**2017**, 35, 955–963. [Google Scholar] [CrossRef] - Shariatmadari, M.; Nahavandi, N.; Zegordi, S.H.; Sobhiyah, M.H. Integrated resource management for simultaneous project selection and scheduling. Comput. Ind. Eng.
**2017**, 109, 39–47. [Google Scholar] [CrossRef] - Marugán, A.P.; Márquez, F.P.G.; Lev, B. Optimal decision-making via binary decision diagrams for investments under a risky environment. Int. J. Prod. Res.
**2017**, 55, 5271–5286. [Google Scholar] [CrossRef] - Zavadskas, E.K.; Turskis, Z.; Antucheviciene, J. Selecting a contractor by using a novel method for multiple attribute analysis: Weighted Aggregated Sum Product Assessment with grey values (WASPAS-G). Stud. Inform. Control
**2015**, 24, 141–150. [Google Scholar] [CrossRef] - Trinkūnienė, E.; Podvezko, V.; Zavadskas, E.K.; Jokšienė, I.; Vinogradova, I.; Trinkūnas, V. Evaluation of quality assurance in contractor contracts by multi-attribute decision-making methods. Econ. Res. Ekon. Istraž.
**2017**, 30, 1152–1180. [Google Scholar] [CrossRef] - Lazauskas, M.; Kutut, V.; Zavadskas, E.K. Multicriteria assessment of unfinished construction projects. Gradevinar
**2015**, 67, 319–328. [Google Scholar] - Suh, S.; Suh, W.; Kim, J.I. Risk analysis model for regional railroad investment. Eng. Comput.
**2017**, 34, 164–173. [Google Scholar] [CrossRef] - Xu, J.; Zhao, S. Noncooperative Game-Based Equilibrium Strategy to Address the Conflict between a Construction Company and Selected Suppliers. J. Constr. Eng. Manag.
**2017**, 143, 04017051. [Google Scholar] [CrossRef] - Bellman, R. A Markovian Decision Process. Indiana Univ. Math. J.
**1957**, 6, 679–684. [Google Scholar] [CrossRef] - Richey, M. The evolution of Markov chain Monte Carlo methods. Am. Math. Mon.
**2010**, 117, 383–413. [Google Scholar] [CrossRef] - Šostak, O.R.; Vakrinienė, S. Mathematical modelling of dispute proceedings between investors and third parties on allegedly violated third-party rights. J. Civ. Eng. Manag.
**2011**, 17, 126–136. [Google Scholar] [CrossRef] - Šostak, O.R. Planning Development of Construction by Taking Into Account Interests of the Third Parties (Doctoral Dissertation, in Lithuanian). Ph.D. Thesis, Vilnius Gediminas Technical University, Vilnius, Lithuania, 2011. [Google Scholar]
- Celik, T.; Kamali, S.; Arayici, Y. Social cost in construction projects. Environ. Impact Assess. Rev.
**2017**, 64, 77–86. [Google Scholar] [CrossRef] - Mitkus, S.; Šostak, O.R. Modelling the process for defence of third party rights infringed while implementing construction investment projects. Technol. Econ. Dev. Econ.
**2008**, 14, 208–223. [Google Scholar] [CrossRef] - Mitkus, S.; Šostak, O.R. Preservation of healthy and harmonious residential and work environment during urban development. Int. J. Strateg. Prop. Manag.
**2009**, 13, 339–357. [Google Scholar] [CrossRef] - Šostak, O.R.; Makutėnienė, D. Timely determining and preventing conflict situations between investors and third parties: Some observations from Lithuania. Int. J. Strateg. Prop. Manag.
**2013**, 17, 390–404. [Google Scholar] [CrossRef] - Šostak, O.R.; Makutėnienė, D. Modelling a dispute hearing between an investor and the public concerned in administrative courts of the republic of Lithuania. Technol. Econ. Dev. Econ.
**2013**, 19, 489–509. [Google Scholar] [CrossRef] - Zhou, W.Z.; Peng, Y.; Bao, H.J. Regular pattern of judicial decision on land acquisition and resettlement: An investigation on Zhejiang’s 901 administrative litigation cases. Habitat Int.
**2017**, 63, 79–88. [Google Scholar] [CrossRef] - Manasse, P.; Savona, R.; Vezzoli, M. Danger Zones for Banking Crises in Emerging Markets. Int. J. Financ. Econ.
**2016**, 21, 360–381. [Google Scholar] - Stević, Ž.; Pamućar, D.; Vasiljević, M.; Stojić, G.; Korica, S. Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company. Symmetry
**2017**, 9, 279. [Google Scholar] [CrossRef] - Santos, S.F.; Fitiwi, D.Z.; Bizuayehu, A.W.; Shafie-Khah, M.; Asensio, M.; Contreras, J.; Cabrita, C.M.P.; Catalão, J.P.S. Impacts of Operational Variability and Uncertainty on Distributed Generation Investment Planning: A Comprehensive Sensitivity Analysis. IEEE Trans. Sustain. Energy
**2017**, 8, 855–869. [Google Scholar] [CrossRef] - Eisenhardt, K.M. Agency theory: An assessment and review. Acad. Manag. Rev.
**1989**, 14, 57–74. [Google Scholar] - Mitroff, I.I. Stakeholders of the Organizational Mind; Jossey-Bass: San Francisco, CA, USA, 1983. [Google Scholar]
- Gras-Gil, E.; Manzano, M.P.; Fernandez, J.H. Investigating the relationship between corporate social responsibility and earnings management: Evidence from Spain. Brq-Bus. Res. Q.
**2016**, 19, 289–299. [Google Scholar] [CrossRef] - Martinez-Ferrero, J.; Gallego-Alvarez, I.; Garcia-Sanchez, I.M. A Bidirectional Analysis of Earnings Management and Corporate Social Responsibility: The Moderating Effect of Stakeholder and Investor Protection. Aust. Account. Rev.
**2015**, 25, 359–371. [Google Scholar] [CrossRef] - Schwarzmüller, T.; Brosi, P.; Stelkens, V.; Spörrle, M.; Welpe, I.M. Investors’ reactions to companies’ stakeholder management: the crucial role of assumed costs and perceived sustainability. Bus. Res.
**2017**, 10, 79–96. [Google Scholar] [CrossRef] - GooGle. Object Location on GooGle Maps. 2017. Available online: https://www.google.lt/maps/place/%C5%A0e%C5%A1kin%C4%97s+g.+45C,+Vilnius+07158/@54.7184175,25.2479231,17z/data=!4m5!3m4!1s0x46dd915d44d79665:0x5a00399e0ea3ff3b!8m2!3d54.7184175!4d25.2501118?hl=en (accessed on 11 January 2018).
- Lithuanian State Enterprise Centre of Registers. On the Data About the Real Estate; Document Number (7.2./1147)s-1689; Lithuania, 2007. Available online: http://techmat.vgtu.lt/~ab/docs/EnterpriseRegisters.pdf (accessed on 11 January 2018). (In Lithuanian).
- Www.inreal.lt. Real Estate Market Overview for 2007 Year. 2008. Available online: http://www.inreal.lt/media/editor/inreal/rinkos-apzvalgos/2007_metine_apzvalga.pdf (accessed on 11 January 2018). (In Lithuanian).
- Vilnius County Head Administration. The Copy of the Act of Building Usage Suitability. Document Number (100)11.55-134. Lithuania, 2007. Available online: http://techmat.vgtu.lt/~ab/docs/HeadAdministrationDoc.pdf (accessed on 11 January 2018). (In Lithuanian).
- 690th Dwelling House Construction Association, (Lithuania, Company Code 125112766). Reference Number 20: About Funds Used for Object Financing. 2005. Available online: http://techmat.vgtu.lt/~ab/docs/Bendrija.jpg (accessed on 11 January 2018). (In Lithuanian).
- Weng, S.S.; Yang, M.H.; Koo, T.L.; Hsiao, P.I. Modeling the prediction of business intelligence system effectiveness. SpringerPlus
**2016**, 5, 737. [Google Scholar] [CrossRef] [PubMed] - Bellman, R.E.; Dreyfus, S.E. Applied Dynamic Programming; Princeton University Press: Princeton, NJ, USA, 2015. [Google Scholar]

**Figure 1.**The graph for the considered example. ${C}_{8}^{a}$ copies the node ${C}_{1}$ and all nodes following from it.

**Figure 4.**The impact of the Algorithm 2 on graph. (

**a**) The graph without cycles, $m=0$, $\overline{n}=n=83$; (

**b**) the graph with $m=2$ ($\overline{n}=443$).

**Table 1.**The description of the conflict participants’ behaviour, and the losses due to the judicial process. Costs are presented in TEUR (thousands euros); $I,S,C$ denotes the Investor, the Society and the Court, respectively. R denotes the Result nodes (the ends of scenarios).

Edge | Actions (Decisions) Description | t (Days) | p | Losses (TEUR) |
---|---|---|---|---|

$({I}_{0},{I}_{1})$ | Project begins | 0 | ${x}_{0,1}$ | 0 |

$({I}_{1},{S}_{2})$ | I informs S (according to law) | 180 | ${x}_{1,1}$ | 0 |

$({I}_{1},{S}_{1})$ | I informs S (violates the law) | 630 | ${x}_{1,2}$ | 0 |

$({S}_{2},{R}_{1})$ | S does not submit its suggestions | 30 | 0.8 | 0 |

$({S}_{2},{I}_{2})$ | S submits its suggestions | 14 | 0.2 | 0 |

$({I}_{2},{R}_{2})$ | I accepts suggestions | 14 | ${x}_{2,1}$ | 1000 |

$({I}_{2},{S}_{3})$ | I rejects suggestions | 14 | ${x}_{2,2}$ | 0 |

$({S}_{3},{I}_{3})$ | S applies to an advanced hearing institution | 7 | 0.7 | 0 |

$({S}_{3},{R}_{3})$ | S does not apply to an advanced hearing institution | 30 | 0.3 | 0 |

$({I}_{3},{R}_{4})$ | I makes a peace treaty with S | 14 | ${x}_{3,1}$ | 150 |

$({I}_{3},{C}_{1})$ | I does not make a peace treaty with S | 21 | ${x}_{3,2}$ | 10 |

$({C}_{1},{S}_{4})$ | I loses | 30 | 0.4 | 0 |

$({C}_{1},{I}_{7})$ | I wins | 30 | 0.6 | 0 |

$({S}_{1},{C}_{8})$ | S applies to an advanced hearing institution | 28 | 0.1 | 0 |

$({S}_{1},{R}_{25})$ | S does not apply to an advanced hearing institution | 30 | 0.9 | 0 |

$({S}_{4},{R}_{5})$ | S does not apply to a court of first instance | 14 | 0.25 | $-10$ |

$({S}_{4},{I}_{4})$ | S applies to a court of first instance | 7 | 0.75 | 0 |

$({I}_{4},{C}_{2})$ | I does not make a peace treaty with S | 7 | ${x}_{4,2}$ | 20 |

$({I}_{4},{R}_{6})$ | I makes a peace treaty with S | 7 | ${x}_{4,1}$ | 100 |

$({C}_{2},{S}_{5})$ | I wins | 90 | 0.5 | 0 |

$({C}_{2},{I}_{6})$ | I loses | 90 | 0.5 | 0 |

$({S}_{5},{R}_{7})$ | S does not apply to a court of appeal | 14 | 0.15 | $-30$ |

$({S}_{5},{I}_{5})$ | S applies to a court of appeal | 7 | 0.85 | 0 |

$({I}_{5},{C}_{3})$ | I does not make a peace treaty with S | 7 | ${x}_{5,2}$ | 10 |

$({I}_{5},{R}_{8})$ | I makes peace treaty with S | 7 | ${x}_{5,1}$ | 100 |

$({C}_{3},{R}_{9})$ | I wins | 120 | 0.35 | $-40$ |

$({C}_{3},{R}_{11})$ | I loses | 120 | 0.35 | 0 |

$({C}_{3},{C}_{2})$ | C returns a lawsuit to a court of first instance | 120 | 0.3 | 0 |

$({I}_{6},{R}_{13})$ | I does not apply to a court of appeal | 14 | ${x}_{6,1}$ | 0 |

$({I}_{6},{C}_{4})$ | I applies to a court of appeal | 14 | ${x}_{6,2}$ | 10 |

$({I}_{6},{R}_{12})$ | I makes a peace treaty with S | 14 | ${x}_{6,3}$ | 200 |

$({C}_{4},{R}_{14})$ | I loses | 120 | 0.35 | 0 |

$({C}_{4},{C}_{2})$ | C returns a lawsuit to a court of first instance | 120 | 0.3 | 0 |

$({I}_{7},{R}_{16})$ | I does not apply to a court of appeal | 14 | ${x}_{7,1}$ | 0 |

$({I}_{7},{C}_{5})$ | I applies to a court of first instance | 14 | ${x}_{7,2}$ | 20 |

$({I}_{7},{R}_{15})$ | I makes a peace treaty with S | 14 | ${x}_{7,3}$ | 150 |

$({C}_{5},{S}_{6})$ | I wins | 90 | 0.5 | 0 |

$({C}_{5},{I}_{9})$ | I loses | 90 | 0.5 | 0 |

$({S}_{6},{R}_{17})$ | S does not apply to a court of appeal | 14 | 0.15 | $-30$ |

$({S}_{6},{I}_{8})$ | S applies to a court of appeal | 7 | 0.85 | 0 |

$({I}_{8},{C}_{7})$ | I does not make a peace treaty with S | 7 | ${x}_{8,2}$ | 10 |

$({I}_{8},{R}_{18})$ | I makes a peace treaty with S | 7 | ${x}_{8,1}$ | 100 |

$({C}_{7},{R}_{20})$ | I wins | 120 | 0.35 | $-40$ |

$({C}_{7},{R}_{19})$ | I loses | 120 | 0.35 | 0 |

$({C}_{7},{C}_{5})$ | C returns a lawsuit to a court of first instance | 120 | 0.3 | 0 |

$({I}_{9},{R}_{22})$ | I does not apply to a court of appeal | 14 | ${x}_{9,1}$ | 0 |

$({I}_{9},{C}_{6})$ | I applies to a court of appeal | 14 | ${x}_{9,2}$ | 10 |

$({I}_{9},{R}_{21})$ | I makes a peace treaty with S | 14 | ${x}_{9,3}$ | 200 |

$({C}_{6},{R}_{24})$ | I wins | 120 | 0.35 | $-40$ |

$({C}_{6},{R}_{23})$ | I loses | 120 | 0.35 | 0 |

$({C}_{6},{C}_{5})$ | C returns a lawsuit to a court of first instance | 120 | 0.3 | 0 |

$({C}_{4},{R}_{10})$ | I wins | 120 | 0.35 | $-40$ |

End Nodes | Description | Success |
---|---|---|

${R}_{1},{R}_{3},{R}_{25}$ | successful completion of the judicial conflict | yes |

${R}_{2}$ | project solution is changed, costs are increased | yes |

${R}_{4},{R}_{6},{R}_{8},{R}_{12},{R}_{15},{R}_{18},{R}_{21}$ | peace treaty is signed | yes |

${R}_{5},{R}_{7},{R}_{9},{R}_{10},{R}_{17},{R}_{20},{R}_{24}$ | investor wins the judicial conflict | yes |

${R}_{11},{R}_{13},{R}_{14},{R}_{16},{R}_{19},{R}_{22},{R}_{23}$ | project failure | no |

The Phase | Begin Date | End Date | Duration (Days) | Average Daily Costs (TEUR/Day) |
---|---|---|---|---|

1 | 1 October 2003 | 5 June 2005 | 613 | 0.3851 |

2 | 6 June 2005 | 4 September 2005 | 90 | 12.9018 |

3 | 5 September 2005 | 27 December 2006 | 478 | 8.6012 |

4 | 28 December 2006 | 28 April 2008 | 487 | 0 |

X | −4831.46 | −2794.58 | −417.96 | 3329.63 | 3389.63 | 3439.63 | 3489.63 |

P(X) | 0.0000305 | 0.0000770 | 0.0002775 | 0.06 | 0.00227966 | 0.00593781 | 0.931398 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bugajev, A.; Šostak, O.R.
An Algorithm for Modelling the Impact of the Judicial Conflict-Resolution Process on Construction Investment. *Sustainability* **2018**, *10*, 182.
https://doi.org/10.3390/su10010182

**AMA Style**

Bugajev A, Šostak OR.
An Algorithm for Modelling the Impact of the Judicial Conflict-Resolution Process on Construction Investment. *Sustainability*. 2018; 10(1):182.
https://doi.org/10.3390/su10010182

**Chicago/Turabian Style**

Bugajev, Andrej, and Olga R. Šostak.
2018. "An Algorithm for Modelling the Impact of the Judicial Conflict-Resolution Process on Construction Investment" *Sustainability* 10, no. 1: 182.
https://doi.org/10.3390/su10010182