# Optimization of Vertical Formwork Layout Plans Using Mixed Integer Linear Programming

- 2.9k Downloads
- 2 Citations

## Abstract

A formwork is a structure used to contain poured concrete and to mold it to the required dimensions. Different formwork systems provide a wide range of concrete construction solutions that can be chosen to suit the needs of a particular structure. The selection of panels and the design of the formwork layout for concrete structures, especially if the panels are to be reused many times to form different work zones, are one of the most complex tasks in formwork construction. It influences the quality of work, construction time, site safety and cost. The formwork costs account for a significant part of the total costs for concrete works. The problem of the selection and layout of reusable panel forms is solved mainly based on the intuitive judgment of experienced engineers in collaboration with the form system supplier. This study proposes a mixed integer linear programming modeling approach to support the formwork planning process. The problem consists in determining the number and sizes of the panels according to the geometry of the concrete elements to minimize the rental cost of wall shuttering in a building divided into work zones that are to be completed in sequence, reusing the chosen panels. The model can be solved using typical software dedicated to mixed integer linear programs. A simple example is used to illustrate the efficiency of the proposed approach, where the formwork rental cost is 7.31 % lower than the rental costs of panels and corners optimized without consideration of the reuse in consecutive zones.

## Keywords

Reinforced concrete works Formwork planning Cost minimization Mixed integer linear programming## 1 Introduction

The efficiency of the formwork erection process is one of the most important factors in determining the success of a construction project in terms of speed, quality cost and safety of work. Thus, the choice of formwork has a great effect on the entire construction process as well as the following individual processes.

Formwork costs account for 40–60 % of the cost of the concrete frame and for approximately 10 % of the total building cost [1]. As an object of interest for practitioners, detailed cost breakdowns for a variety of fabricated wall and floor formworks that include labor and materials related with formwork erection and component concreting can be found in numerous handbooks, such as the Formwork User’s Manual [2].

To use the formwork in a cost-efficient way and to assure the continuous work of the teams, the stories of a building under construction are commonly divided into work zones. The construction processes are also divided into simpler sets of operations to be entrusted to specialized crews. In this way, work may proceed in different zones in parallel, ensuring the crews work continuity while the concrete in other zones is reaching the required strength before formwork striking. The size and shape of the work zones are crucial for smooth workflow and economy of formwork usage. To permit maximum reuse of a formwork set in consecutive work zones, the zones should be of similar size, shape and work amount [3]. However, the configuration of walls in particular zones usually varies, and determining the composition of a “universal” set that can be used for all of them and, at the same time, remains cost-effective is not a simple task. If too many formwork elements are ordered, some will lay idle in storage areas. If too few elements are ordered, then the rotation of these elements increases and the possibility of damage grows; the quality and speed of the works might also suffer. Therefore, the formwork process should be well planned before construction begins [3], with the selection of a system allowing for the site-specific conditions and available equipment (e.g., the size and weight of the formwork elements need to be selected to meet the crane parameters, or vice versa) [1, 4].

The formwork plan should be preceded by an economic analysis (system selection) and contain assumptions on the organization of works, including division into work zones and the sequence of their processing.

Even experienced practitioners find it very difficult to select an appropriate formwork system. The economic efficiency, repeatability of work and the shape of the structure represent the main selection criteria [5]. Proverbs et al. [6], based on a literature review and interviews with practitioners from the UK, France and Germany, identified nine predominant formwork selection factors. The authors ranked them in terms of importance for each international group of contractors and found that relative costs, specification (quality) of concrete and degree of repetition were the principal formwork selection criteria. Elazouni et al. [7] divided the factors for selecting the formwork system based on quantitative (cost and construction time) and qualitative (expected familiarity, flexibility, quality and safety) factors.

The philosophy of decision making in every field of economics relates to assessing and selecting the most preferable solution, implementing it and then gaining the greatest profit [8]. Maximization of profit, in the case of formwork design, can be achieved by the reduction of rental or erection costs (or formwork labor) [9, 10, 11]. A number of effective decision-making methods that allow for multiple criteria have appeared in the last decade [12, 13, 14, 15, 16].

## 2 Formwork Selection Problem

The problem of selecting optimal formwork systems has been extensively studied in the literature [17, 18, 19, 20]. A number of studies have proposed the application of neural network theory or expert systems [19, 21, 22, 23]. To assist the contractor with the formwork selection problem, Shin et al. [24] presented a decision-support model using AdaBoost to select a formwork system suitable for the construction site conditions. In their later works, Shin et al. [25] proposed a formwork method selection model based on boosted decision trees intended for tall building problems. Shawki et al. [26] presented a model for determining the minimum weight for a heavy and high reinforced concrete slab formwork system taking account of the design, bearing and stability constraints. The genetic algorithm was built using MatLAB to solve the formwork problems.

While the formwork layout is as important as formwork selection in improving productivity, there have been few studies on formwork layout [27]. Selection of the formwork element types and quantity according to the shape of the structure to be built is often offered as a service by formwork providers, who use dedicated computer systems, such as ELPOS by PERI GmbH or Tipos 7.0 by Doka GmbH.

However, the criteria and methods of element selection used by these systems are not disclosed to their clients; they are most probably related with their business objectives and logistical constraints (availability at local logistic centers). For many contractors, formwork layout planning involves manual work and is done ad hoc according to the experience of the foremen and other site workers; this is a potential source of many errors [27].

These reasons determine the basis for the current interest in formwork optimization problems. Lee et al. [27], having analyzed the literature on the subject and interviewed formwork experts, listed the most important factors affecting formwork layouts, and proposed an algorithm for automated formwork layout planning that allowed for these factors. The authors stated that that the major factors in layout planning were: cost, constructability, safety, quality, and characteristics of the building and the site. They also described the sub-factors that determine the formwork layout.

Lee et al. [27] used BIM (Building Information Modeling) to provide more precise information about the shape, dimensions, and the structure of the buildings than can be found on the existing 2D-based drawings. The system can improve productivity (reduction of workload and work time) and economic efficiency (reduction of formwork types and rational form dimension selection). Once the size of the forms is selected and the forms laid out, it can be decided whether or not a weight should be given to the number of reuses in view of the cost and the size of the forms in terms of constructability. Nevertheless, the exact procedure used for formwork optimization was not presented.

Kannan and Santhi [28] proposed using the BIM technique to rationalize the formwork layout, incorporating the actual site characteristics and imparting the parametric change during construction. Their paper also provides the background concepts and techniques required to adopt the BIM as a simplified and intriguing tool to carry out the 4D Schedule and 5D Cost of the concrete formwork systems. The application of the BIM model to evaluate more formwork alternatives and consider design changes to increase efficiency and productivity was also presented by Meadati et al. [29].

An optimal formwork system to minimize project specific operation costs can be obtained by the use of a formwork selection model based on a modified CYCLONE method [30].

The formwork pairing problem in terms of scheduling wall erection operations and formwork allocation was studied by Benoist [31]. The author aimed to create formwork chains that could be moved from one wall to another without disassembling them in order to save labor costs and crane moves. The main criterion of formwork element allocation may also be minimizing the formwork stock [32]. Biruk and Jaskowski [9] presented a wall formwork layout optimization model for only one work zone. Biruk [33] developed the model for formwork set optimization without considering the possibility of changing the corner forming options.

## 3 Problem Definition and Mathematical Formulation

The formwork systems available on the market allow the user to obtain the same technically correct effect by means of a number of formwork element configurations, using several available types of corner and adjustment elements as well as sizes and configurations of the main wall panels. This makes formwork layout planning easier. If cost-efficient solutions are required, many possibilities of set composition should be evaluated, although this is a time-consuming process without any guarantee of finding the optimal solution. Therefore, it is advisable to describe formwork optimization as a mathematical programming problem, and to solve it using commonly used software (e.g., LINGO, AIMMS, CPLEX, MATLAB and Optimization Toolbox, etc.), or to develop a solving procedure and implement it using dedicated decision-support software.

The aim of the formwork layout planning is to assign the required panels to form the walls of each work zone and corner elements to form the junctions. The following assumptions were made to model the decision problem and the succeeding constraints were identified that limit the set of feasible solutions.

*L*-type (connecting two walls),

*T*-type (three walls) and

*X*-type (four walls). It was assumed that all walls meet at right angles. The decision on which option to select for a particular corner

*r*was modeled by means of the following binary variables:

*w*is selected to form corner

*r*in work zone

*k*, and the value of 0 in other cases. Only one option can be selected for each corner and only one variable for chosen variant can take the value 1, so the sum of these variables for all variants must be equal to 1. Therefore, the variables have to fulfill the following conditions:

These sets will be reused to form corners on consecutive work zones—so their number should be calculated as the maximum number of sets used in each work zone. The inequalities (4)–(6), written in a linear form, allow the determination of a sufficient number of corner sets, minimized in the objective function of the linear program.

*lw*

_{ jk }> 0. Therefore

*M*is a sufficiently large number.

In these cases, constraint (9) is fulfilled for any positive value of *lw* _{ jk }. If any adjustment element is redundant, the respective variables *lw* _{ jk } and *u* _{ jk } take the value 0.

*i*-type formwork panels (

*i*= 1, 2,…,

*n*) used to form walls in zone

*k*(

*k*= 1, 2,…,

*m*) cannot be greater than the number of these panels rented for the project, which should be calculated to minimize the rental cost. Thus, the following relationship among these variables must hold true:

*i*-type elements for work zone

*k*can be calculated on the basis of the following equation:

*δ*

_{ ik }is the number of additional

*i*-type elements needed to form the corners in zone

*k*.

The number of panels (and adjustment elements) is doubled because of the necessity to form both sides of the walls. Only corner elements are used individually.

Symbols and notations

\(m\) | Number of work zones |

\(S_{k}\) | Set of walls in the work zone |

\(S_{k}^{*}\) | Set of walls in the work zone |

\(A_{k}\) | Set of |

\(B_{k}\) | Set of |

\(C_{k}\) | Set of |

\(W_{A}\) | Set of options for |

\(W_{B}\) | Set of options for |

\(W_{C}\) | Set of options for |

\(l_{jk}\) | Length of wall |

\(n\) | Number of formwork panel types |

\(s_{i}\) | Width of a wall formwork panel, |

\(c_{i}\) | Cost of hiring an |

\(cs\) | Fixed cost of providing an adjustment element, (EUR) |

\(cw\) | Unit cost of making an adjustment element, (€/m) |

\(e_{w}\) | Cost of hiring accessories accompanying |

\(f_{w}\) | Cost of hiring accessories accompanying |

\(g_{w}\) | Cost of hiring accessories accompanying |

int | Set of integer numbers |

| A sufficiently large number |

\(x_{ijk}\) | Number of |

\(x_{ik}\) | Number of |

\(x_{i}\) | Number of |

\(lw_{jk}\) | Width of an adjustment element in the formwork of wall |

\(y_{rwk}\) | Binary variable that models the decision of selecting option |

\(z_{rwk}\) | Binary variable that models the decision of selecting option |

\(v_{rwk}\) | Binary variable that models the decision of selecting option |

\(y_{w}\) | Number of corner sets (each set comprises corner elements without panels and accessories for one corner) in the corner option: \(w \in W_{A}\) |

\(z_{w}\) | Number of corner sets in the corner option: \(w \in W_{B}\) |

\(v_{w}\) | Number of corner sets in the corner option: \(w \in W_{C}\) |

\(d_{jk}\) | Length of wall |

\(u_{jk}\) | Binary variable (\(u_{jk} \in \left\{ {0,\;1} \right\}\)), defined for walls in work zone |

\(\delta_{ik}\) | Number of additional |

## 4 Example

The formwork system used in the example had panels of the following widths *s* _{1} = 0.30 m, *s* _{2} = 0.40 m, *s* _{3} = 0.45 m, *s* _{4} = 0.50 m, *s* _{5} = 0.75 m, *s* _{6} = 0.90 m, and *s* _{7} = 0.90 m (basic flat panels). Costs of hiring particular panels for a construction period (1 month) were, respectively, 15.50, 17.00, 17.75, 18.50, 22.50, 24.50, and 25.50 €. Fixed cost of preparing adjustment elements was assumed to be 50.00 €—high enough to avoid time-consuming carpentry works.

*d*

_{ jk }for combinations of corners that end the wall segments.

Formulas for calculating adjusted length of walls *d* _{ jk }

Corner type | ||||
---|---|---|---|---|

| | | | No corner |

| \(\begin{aligned} d_{jk} &= l_{jk} - 0.30y_{s1k} \hfill \\ &\quad - 0.25y_{s2k} - 0.30y_{t1k} \hfill \\ &\quad - 0.25y_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30y_{s1k} \hfill \\ &\quad- 0.25y_{s2k} - 0.25z_{t1k} \hfill \\ &\quad- 0.30z_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30y_{s1k} \hfill \\ &\quad- 0.25y_{s2k} - 0.30\nu_{t1k} \hfill \\ &\quad- 0.25\nu_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30y_{s1k} \hfill \\ &\quad- 0.25y_{s2k} \hfill \\ \end{aligned}\) |

| \(\begin{aligned} d_{jk} &= l_{jk} - 0.25z_{s1k} \hfill \\ &\quad- 0.30z_{s2k} - 0.30y_{t1k} \hfill \\ &\quad- 0.25y_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.25z_{s1k} \hfill \\ &\quad- 0.30z_{s2k} - 0.25z_{t1k} \hfill \\ &\quad- 0.30z_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.25z_{s1k} \hfill \\ &\quad- 0.30z_{s2k} - 0.30\nu_{t1k} \hfill \\ &\quad- 0.25\nu_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.25z_{s1k} \hfill \\ &\quad- 0.30z_{s2k} \hfill \\ \end{aligned}\) |

| \(\begin{aligned} d_{jk} &= l_{jk} - 0.30\nu_{s1k} \hfill \\ &\quad- 0.25\nu_{s2k} - 0.30y_{t1k} \hfill \\ &\quad- 0.25y_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30\nu_{s1k} \hfill \\ &\quad- 0.25\nu_{s2k} - 0.25z_{t1k} \hfill \\ &\quad- 0.30z_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30\nu_{s1k} \hfill \\ &\quad- 0.25\nu_{s2k} - 0.30\nu_{t1k} \hfill \\ &\quad- 0.25\nu_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30\nu_{s1k} \hfill \\ &\quad- 0.25\nu_{s2k} \hfill \\ \end{aligned}\) |

No corner | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30y_{t1k} \hfill \\ &\quad- 0.25y_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.25z_{t1k} \hfill \\ &\quad- 0.30z_{t2k} \hfill \\ \end{aligned}\) | \(\begin{aligned} d_{jk} &= l_{jk} - 0.30\nu_{t1k} \hfill \\ &\quad- 0.25\nu_{t2k} \hfill \\ \end{aligned}\) | |

Solution for the example

Variable | Symbol | Solution with minimal rental cost for two work zones | Solution with minimal rental cost for zone A | Solution with minimal rental cost for zone B |
---|---|---|---|---|

| | | | |

Number of wall panels, 0.30 m wide | | 0 | 0 | 0 |

Number of wall panels, 0.40 m wide | | 0 | 4 | 2 |

Number of wall panels, 0.45 m wide | | 0 | 0 | 0 |

Number of wall panels, 0.50 m wide | | 5 | 3 | 4 |

Number of wall panels, 0.75 m wide | | 9 | 7 | 2 |

Number of wall panels, 0.90 m wide | | 36 | 36 | 40 |

Number of universal wall panels, 0.90 m wide | | 1 | 1 | 0 |

Total width of wooden adjustment elements | \(\sum\limits_{{j \in S_{k} }} {\sum\limits_{k = 1}^{m} {lw_{jk} } }\) | 0 | 0 | 0 |

Number of 0.30 × 0.30 m aluminum corner elements | | 0/0/0 | 0/0/0 | 0/0/0 |

Number of 0.25 × 0.25 m steel corner elements | | 1/1/1 | 1/1/0 | 0/0/1 |

Total rental cost of the set (EUR) | 1305.25 | 1231.75 | 1192.50 |

It is worth considering that zone B walls can be formed more cheaply than the walls in zone A, despite the fact that the total lengths of the walls in both zones are similar. However, it would not be economical to form walls in this way when the work zones are cast subsequently and the panels can be reused. It would be necessary to rent greater numbers of panels and elements of each type (maximum number from columns 4 and 5 for each row in Table 3) to form the walls in zone A and then zone B. The rental cost for this solution is 1408.25 €, so 103 € more than for a formwork set optimized for both zones. While optimizing the formwork plans, it is important to bear in mind the assumptions on formwork reuse in consecutive zones.

The solution was obtained using a mixed linear program solver, for which the limits of variables and constraint numbers in the solved problem depend significantly on the purchased license type, as is the case with other programs. However, if the floor layout was more complex, and the number of constraints and variables greater as in the example, it would be advisable to develop metaheuristic, e.g., genetic or evolutionary algorithms, tabu search, simulated annealing, etc. that could provide solutions within a reasonable period of time. Despite its basic advantage of reducing the computational effort, this approach also has certain disadvantages. Metaheuristics facilitate only the determination of suboptimal solutions, which are relatively good rather than optimal. Effective methods are still being developed to take the constraints into account during the generation of feasible solutions and their recombination using specific operators. The quality of the solution obtained by most metaheuristic methods depends on the algorithm parameters and options, such as coding scheme, population size, mutation probability, and type of crossover. Metaheuristics only determine the problem solving scheme, while the development of an algorithm to solve certain class problems requires IT skills.

Developing efficient metaheuristics suitable for the analyzed problem is area for future research by the authors.

## 5 Conclusions

The development of formwork systems parallels that of the growth in concrete construction throughout the past few decades. Different formwork systems allow a wide range of concrete construction solutions that can be chosen to suit the needs of a particular structure.

The erection of cast-in-place concrete structures, though having a long tradition, remains a challenge for the builder, not only in terms of technical expertise regarding the material but also the ability to select suitable formwork solutions from those present in the market. As price is most often the main criterion of a contractor’s bid assessment, contractors struggle to reduce costs and improve their chances of winning the contract.

Taking into account the high share of formwork costs in the general execution costs of concrete works and cast-in-place structures, the issue of optimization of vertical formwork layout plans to reduce formwork rental cost, as analyzed in this paper, is of high practical significance. The market has a shortage of tools facilitating formwork selection optimization, while the majority of existing software supporting formwork layout plans are developed at the systems suppliers’ request, which in the contractors’ opinion do not provide optimum solutions minimizing their costs.

The paper takes into account the possibility of reusing panels for consecutive work zones, which so far has been omitted by research and software developers. The results obtained in the example have confirmed that optimization of selection panels to form walls for all work zones demonstrates a high cost reduction potential. The relative amount of the savings obtained is close to the profit rate assumed in cost estimations.

The suggested model, written using mathematical symbols, takes into account the specific requirements (criteria, limits) of the issue in question. It provides a specific scheme that may facilitate modeling of given practical problems by introducing/determining real parameter values.

The model of the wall formwork set configuration problem proposed by the authors, being linear and of integer and binary variables, can be solved using widely available solvers. However, it is recommended that it is developed into an independent computer application—a formwork layout planning decision-support system.

## Notes

### Acknowledgments

This work was financially supported by Ministry of Science and Higher Education within the statutory research program, S/63/2015.

## References

- 1.Hanna AS (2005) Concrete formwork systems. Marcel Dekker Inc, New YorkGoogle Scholar
- 2.Harsco, Formwork User’s Manual. Tables, Work scheduling, Concrete Engineering, Site safety, Harsco Infrastructure (2010)Google Scholar
- 3.American Concrete Institute Committee 347 (2014) Guide to Formwork for Concrete (ACI 347R–14). American Concrete Institute, Farmington Hills, MIGoogle Scholar
- 4.Peurifoy RL, Schexnayder CJ, Shapira A (2006) Construction planning, equipment, and methods. McGraw-Hill International Edition, New YorkGoogle Scholar
- 5.Kapp MJ, Girmscheid G (2006) Empirical study reveals deficits in the choice of formwork. In: Pietroforte R, De Angelis E, Polverino F (eds) Construction in the XXI century: local and global challenges. Proceedings of the Joint 2006 CIB W065/W055/W086 international symposium. Edizione Scientifiche Italiane, Napoli, pp 172–173Google Scholar
- 6.Proverbs DG, Holt GD, Olomolaiye PO (1999) Factors in formwork selection: a comparative investigation. Build Res Inf 27(2):109–119CrossRefGoogle Scholar
- 7.Elazouni AM, Ali AE, Abdel-Razek RH (2005) Estimating the acceptability of new formwork systems using neural networks. J Const Eng Manag 131(1):33–41CrossRefGoogle Scholar
- 8.Zavadskas EK, Turskis Z (2011) Multiple criteria decision making (MCDM) methods in economics: an overview. Technol Econ Dev Econ 17(2):397–427CrossRefGoogle Scholar
- 9.Biruk S, Jaskowski P (2013) Economic criteria for the selection of wall formwork (in Polish). Civil Eng Archit 12(1):7–14Google Scholar
- 10.Jarkas AM (2010) The impacts of buildability factors on formwork labor productivity of columns. J Civil Eng Manag 16(4):471–483CrossRefGoogle Scholar
- 11.Dikmen SU, Sonmez M (2011) An artificial neural networks model for the estimation of formwork labor. J Civil Eng Manag 17(3):340–347CrossRefGoogle Scholar
- 12.Balezentis A, Balezentis T, Misiunas A (2012) An integrated assessment of Lithuanian economic sectors based on financial ratios and fuzzy MCDM methods. Technol Econ Dev Econ 18(1):34–53CrossRefGoogle Scholar
- 13.Kaplinski O, Peldschus F (2011) The problems of quantitative evaluation of socio-economic systems development: review. Inz Ekon Eng Econ 22(4):345–355Google Scholar
- 14.Liou JJH (2013) New concepts and trends of MCDM for tomorrow—in honor of professor Gwo-Hshiung Tzeng on the occasion of his 70th birthday. Technol Econ Dev Econ 19(2):367–375CrossRefGoogle Scholar
- 15.Podvezko V (2011) The comparative analysis of MCDA methods SAW and COPRAS. Inz Ekon Eng Econ 22(2):134–146Google Scholar
- 16.Stanujkic D, Magdalinovic N, Jovanovic R, Stojanovic S (2012) An objective multi-criteria approach to optimization using the Moora method and interval grey numbers. Technol Econ Dev Econ 18(2):331–363CrossRefzbMATHGoogle Scholar
- 17.Hanna AS, Sanvido VE (1990) Interactive vertical formwork selection system. Concr Int 12(4):26–32Google Scholar
- 18.Hanna AS, Sanvido VE (1991) Interactive horizontal formwork selection system. Concr Int 13(8):50–56Google Scholar
- 19.Kamarthi SV, Sanvido VE, Kumara SRT (1992) Neuroform—neural network system for vertical formwork selection. J Comput Civil Eng 6(2):178–199CrossRefGoogle Scholar
- 20.Abd-Elrazek ME (1999) Formwork selection systems in building construction. J Eng Appl Sci 46(4):629–644Google Scholar
- 21.Elbeltagi E, Hosny OA, Elhakeem A, Abd-Elrazek ME, Abdullah A (2011) Selection of slab formwork system using fuzzy logic. Constr Manag Econ 29:659–670CrossRefGoogle Scholar
- 22.Shin Y (2011) Formwork system selection model for tall building construction using the Adaboost algorithm. J Korea Inst Build Constr 11(5):523–529CrossRefGoogle Scholar
- 23.Tam CM, Tong TKL, Lau TCT, Chan KK (2005) Selection of vertical formwork system by probabilistic neural networks models. Constr Manag Econ 23:245–254CrossRefGoogle Scholar
- 24.Shin Y, Kim DW, Yang SW, Cho HH, Kang KI (2008) Decision support model using the AdaBoost algorithm to select formwork systems in high-rise building construction. In: Proceedings of the 25th international symposium on automation and robotics in construction, Vilnius. Gediminas Technical University Publishing House “Technika”, Vilnius, Lithuania, pp 644–649Google Scholar
- 25.Shin Y, Kim T, Cho H, Kang K-I (2012) A formwork method selection model based on boosted decision trees in tall building construction. Autom Constr 23:47–54CrossRefGoogle Scholar
- 26.Shawki KM, Emam MA, El-B Osman (2012) Design and construction of multitier shoring towers. J Eng Sci Assiut Univ 40(3):689–700Google Scholar
- 27.Lee C, Ham S, Lee G (2009) The development of automatic module for formwork layout using the BIM. In: Proceedings of the international conference on construction engineering and management/project management (ICCEM/ICCPM 2009), Jeju, Korea 1266–1271Google Scholar
- 28.Kannan MR, Santhi MH (2013) Automated construction layout and simulation of concrete formwork systems using building information modeling. In: Proceedings of the 4th international conference of Euro Asia civil engineering forum on innovations in civil engineering for society and the environment, National University of Singapore, Singapore, C7–C12Google Scholar
- 29.Meadati P, Irizarry J, Aknoukh A (2011) BIM and concrete formwork repository. In: Proceedings 47th ASC annual international conference, associated schools of construction, Omaha, USGoogle Scholar
- 30.Kersting M, Girmscheid G (2011) Process-oriented analysis of the interactions among formwork related teams with a modified Cyclone. In: Proceedings of the 6th international structural engineering and construction conference (ISEC-6) model modern methods and advances in structural engineering and construction, Zürich, Switzerland, 167–173Google Scholar
- 31.Benoist T (2007) Towards optimal formwork pairing on construction sites. RAIRO Oper Res 41(4):381–398MathSciNetCrossRefzbMATHGoogle Scholar
- 32.Benoist T, Jeanjean A, Molin P (2009) Minimum formwork stock problem on residential buildings construction sites. 4OR–A Q J Oper Res 7:275–288MathSciNetCrossRefzbMATHGoogle Scholar
- 33.Biruk S (2013) Minimizing wall formwork cost in residential building construction. Int J Arts Sci 6(3):355–362Google Scholar

## Copyright information

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.