Keywords

Introduction

Tackling the issue of greenhouse gas (GHG) emissions in urban developments is of paramount importance nowadays, especially with governments and regulating authorities focusing more on the need to establish a sustainable environment within their cities. Urban regions are responsible for up to 80% of the total GHG emissions (United Nations Environment Programme 2010) with this figure expected to increase as the urbanisation rate continues to rise. The construction sector constitutes a large portion of the carbon emissions produced within urban environments. Current studies suggest that around 45–60% of total GHG emissions in urban regions are caused by construction activities (Orabi et al. 2012). Within construction industry, which encompasses areas such as road and infrastructure construction, the building sector is the largest contributor to GHG emissions (Intergovernmental Panel on Climate Change (IPCC) 2007). As such it seems reasonable to address the rising rates of emissions in urban environments through reduction of the embodied carbon of building construction activities.

In order to quantify environmental impacts of products or services, life cycle assessment (LCA) is deployed in the existing literature. In construction, it is commonly adopted for establishing the environmental impacts of buildings, with focus primarily on the maintenance and operational phase of buildings (Brocklesby and Davison 2000; Hong et al. 2012; Bilec et al. 2006; Park and Hong 2011). However, carbon emitted during the construction process has not received much attention, in comparison to the maintenance or operational phases (Monahan and Powell 2011; Pomponi and Moncaster 2017), due to its relatively smaller impact on overall carbon emission. Yet, as stated by IPCC, an encompassing strategy that aims to minimise embodied carbon in construction should also consider the GHG emissions from the construction phase (Metz et al. 2007). Additionally, when considering the short duration of the construction phase, relative to the operation and maintenance phases, the resulting carbon emitted, when conducting an analysis that cancels the effects of phase duration, reveals the critical nature of the construction stage on total carbon emissions (Hong et al. 2013). This has prompted many regulations to specify the need for extensive measures that address carbon emissions in buildings, which requires consideration of the construction phase (Core Writing Team et al. 2007; Greenhouse Gas Inventory and Research Center of Korea (GGIRCK) 2011).

One means of reducing GHG emissions in construction is through addressing the associated embodied carbon, defined as the total carbon emitted during the life cycle of the building process, excluding its operation phase. Mitigation measures recommended by the IPCC include the use of low-carbon buildings, which can be achieved through proper planning that is carried out at the onset of projects. Though methods have been extensively implemented for assessing and addressing the emissions at the operational phase of buildings, the same cannot be said for embodied carbon, as this is not commonly considered in the design and planning phases of buildings (Monahan and Powell 2011).

This chapter proposes to tackle the issue of embodied carbon emissions in building projects, through addressing the transportation cycle in building construction operations. The literature highlights that transportation activities account for almost 16.5% of the overall embodied emissions in building construction (Rodríguez Serrano and Porras Álvarez 2016). Other works have suggested that within the TC350 standards defining the cradle to grave impact of buildings, the transportation stage, which considers transport from factory gate to site, accounts for around 9% of the total embodied energy in residential dwellings (Moncaster and Symons 2013). This figure however does not account for transport that occurs during construction stage.

Two well-known problems with applications within construction are modelled and solved here to optimise their performance, hence leading to reductions in transport-related carbon emissions. The first problem is a site layout planning problem (SLPP) (Hammad et al. 2015, 2016; Zouein et al. 2002), where the location of tower cranes on construction sites is optimised, so that carbon emissions resulting from their operations are minimised. The selection of locations can considerably impact transport needs between facilities on construction sites and hence emissions. Factors including the transportation distance and mode of transportation, which are known to influence total embodied carbon (Akbarnezhad and Xiao 2017), are related to the location decisions taken within the presented models. The SLPP presented in this chapter is modelled combining principles from the facility location problem (FLP) and the facility layout problem (FLAP). In FLAP, the focus is on finding a layout for the facilities within a constrained area during the different phases of the project such that a certain objective function is minimised/maximised, while in the FLP, the focus is placed on locating facilities in a relatively larger area. In particular, two relevant FLP formulations, adapted to the context of the SLPP, are contrasted, namely, a set covering location model (Eiselt and Marianov 2009), where full coverage by the tower crane to all material demand points on a construction site is achieved, and the maximal coverage model (Karasakal and Karasakal 2004), where coverage to the demand points is maximised. In the set covering model, given a set of elements called U and a collection of finite sets labelled, S, the aim is to find the smallest subcollection of S whose union equals U. On the other hand, in the maximal coverage problem, it is not necessary to fully cover each element in U; the aim is to choose at most k sets to cover as many elements in U as possible. Figure 14.1 highlights the difference between FLAP and FLP.

Fig. 14.1
figure 1

Major difference between FLAP and FLP

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The second problem type, the container loading problem (CLP) , deals with off-site transportation activities. This is particularly relevant to the transportation activities involved with moving material from manufacturers to suppliers and also from suppliers to construction sites.

Although the problems presented in this chapter have been widely adopted in supply chain management, their use in construction for the purpose of minimising embodied carbon during construction activities has not been explored. Hence the optimisation framework proposed in this work is a novel contribution to the reduction of embodied carbon in construction through solving the tower crane location and the container loading problem.

The rest of the chapter is organised as follows. In the next section, a brief literature review of the problems from which SLPP is adopted, namely, FLAP and FLP, is given. In addition, a review on CLP is presented. Next, models are presented to locate the tower crane and associated material supply facilities in such a way that carbon emissions resulting from the crane’s operation are minimised. Following that, a CLP model is described where the number of truck trips required to be performed is minimised, hence leading to a reduction in carbon emitted due to truck transport activities. Case examples are presented to highlight the applicability of the models. Lastly, concluding remarks are highlighted.

Literature Review

Facility Layout Problem

The FLAP is applicable where departments with known dimensions, examples of which are workshops and plants/machines, are to be located within a known area, such that the travel cost/material handling between the various departments is minimised (Heragu and Kusiak 1991; Kulturel-Konak and Konak 2013). Within FLAP, a facility is defined as an entity which facilitates the performance of a task (Drira et al. 2007). The solution to the FLAP is a block layout displaying the dimensions along with the relative positions of the departments within a given area (Chen et al. 2015). In engineering construction and management, an adaptation of the FLAP, called the SLPP, involves finding an appropriate physical arrangement for a given number of temporary facilities operating during the construction process, to the available planar region of the construction site (Andayesh and Sadeghpour 2013; Hammad et al. 2016; Khalafallah and El-Rayes 2011; Li and Love 2000; Zouein et al. 2002).

Facility Location Problem

The FLP, which involves locating single/multiple facilities in a wide planar region, forms a vital facet for many strategic planning applications (Drezner and Hamacher 2004). Applications of FLP in the literature include locating public facilities, such as fire stations, hospitals and emergency response units (Badri et al. 1998; Balcik and Beamon 2008; Batta et al. 2014; Hahn and Krarup 2001; Li et al. 2011), as well as private facilities, such as warehouses and manufacturing firms (Revelle et al. 1970; Klose and Drexl 2005; Thanh et al. 2008), to maximise delivery efficiency of services to customers. FLP can either be solved as an uncapacitated FLP, where each facility to be located is assumed to be able to supply all demand points (Ghosh 2003; Kratica et al. 2014; Verter 2011), or as a capacitated problem, where a limit is placed on the demand that can be supplied by each positioned facility (Boyaci et al. 2013; Fischetti et al. 2016).

Categorising the FLP is based on the type of model that is formulated to solve the problem. Two major problem types, adopted in the literature, include the set covering location problem and maximum covering location problem (Farahani et al. 2012). In the set covering problem (Eiselt and Marianov 2009; Gunawardane 1982; Rajagopalan et al. 2008; ReVelle et al. 1976), the aim is to satisfy all demand leading to a specified level of coverage, through minimising the average cost of locating the facilities. For maximal coverage problems, the aim is to maximise the demand coverage (Church and Velle 1974; Church et al. 1996; Hochbaum and Pathria 1998; Karasakal and Karasakal 2004; Murawski and Church 2009).

Container Loading Problem

Packing problems have been widely studied since the early 1960s. During this period, many variants have been developed, including knapsack loading (Gehring et al. 1990), bin-packing (Martello et al. 2000) and strip packing (Bischoff et al. 1995) problems. In this chapter, the focus is on the container loading problem, which involves a given set of items that need to be placed within a container of a specified size, so that the space of the container is fully utilised (Eley 2002). Two constraints need to be satisfied, namely, ensuring that the items are fully loaded within the container and that none of the items overlap with one another. The problem has numerous practical applications in the industry; this is due to its impact on transportation and shipping costs (Huang et al. 2016; Nowakowski 2016). In particular, an optimised packing pattern within the container will reduce the number of containers required to load the items and hence will also reduce the total number of trips that need to be conducted to transport the items to their destination. Given that transport activities contribute heavily to the embodied carbon in construction (British Standards Institution 2011; Moncaster and Symons 2013), addressing the CLP leads to an efficient utilisation of total number of trucks required to transport construction materials and hence the reduction of embodied carbon that is a result of such transport activities. Many of the inefficiencies in material transportation in construction are caused by incorrect loading operations of materials. This is specifically true whenever forklifts are deployed to load trucks from the top, as commonly occurs in construction (Nowakowski 2016). This in turn leads to the ill use of space in transport truck and trailers which entails extended transportation activities and hence an increase in the resulting carbon emissions released as a result.

Framework

In this chapter, an optimisation framework is presented to address the overall embodied carbon in construction transport activities. This is depicted in Fig. 14.2. As can be seen, two major optimisation problems are addressed, namely, a SLPP, which is solved to minimise the total carbon emissions resulting from the tower crane operations on site, and a CLP, which is solved such that the number of trips required to transport materials to the construction site is reduced, hence reducing carbon emissions due to material transportation to the construction site.

Fig. 14.2
figure 2

Framework for reducing embodied carbon through optimising transport activities in construction

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The framework is based on having a building information model (BIM) as the primary source of data regarding the building elements making up the construction project. From BIM, a preliminary site layout plan can be deduced, which is used to obtain information regarding demand point locations, possible supply points associated with the demand points and potential locations of cranes on site. All of this information is then directed to the optimisation module , where a site layout planning problem is solved. At the same time a production plan can be devised, which incorporates the various materials and element compositions that will be required to be delivered to the construction site during the various stages of construction. It is through the component production plan that data, regarding the dimensions of the material components to be delivered to the construction site, can be obtained. A CLP is then solved, which reduces the total number of trips required to be conducted between the material suppliers and construction site. Both optimisation problems are designed to minimise the total carbon emissions, aiming to provide significant reductions in embodied carbon of construction building materials.

Site Layout Planning Models

In the industry, the location of tower cranes is achieved through trial and error, with reference to loading charts. Practitioners rely mostly on experience to align the location of tower canes with the topology of the construction site (Zhang et al. 1999). Therefore, qualitative references are lacking for project engineers to rely on when making tower crane location decisions. In literature, the tower crane location problem is typically formulated as a SLPP, where studies focus on optimising the location of the tower cranes through minimising the crane operating cost (Zhang et al. 1996, 1999). Some studies have also focused on the assignment of a priori placed supply points to known demand regions as part of the tower crane location process (Huang et al. 2011; Lien and Cheng 2014; Nadoushani et al. 2016; Tam and Tong 2003). Yet to the authors’ best knowledge, no attempt has been made to integrate modelling formulations from FLP to locate tower cranes on a construction site, for the sake of minimising embodied carbon emissions associated with crane operations.

In this section, two models are proposed to solve the SLPP, with a focus on minimising carbon emissions resulting from crane operation. The first model, labelled as the set covering tower crane location (SCTL) model, aims to minimise the total carbon emission associated with the tower crane operations while ensuring that all demand points on the construction site are serviced. The second model, labelled as the maximum covering tower crane location (MCTL) model , maximises the total number of demand points that are serviced given a restrained total number of tower cranes that can be installed on site. Both models address the issue of carbon emission reduction in a different way. Model SCTL tries to minimise emissions directly without sacrificing the servicing of all demand points. Model MCTL influences carbon emissions through limiting the number of tower cranes that can operate during the project while maximising the total demand points that are serviced by the located tower cranes. The optimisation models presented in this section are assumed to be applicable to medium/large construction sites, where significant savings in carbon can be realised through optimising the transport activities involved. Given that in large construction sites it is very common to see multiple tower cranes in operation, the proposed models are also applicable to such cases.

The representation of nodes making up the tower cranes, supply points and demand regions in both models is depicted in Fig. 14.3. Formulations for both models are presented next.

Fig. 14.3
figure 3

Crane model representation, with the dashed circles highlighting the operating radius of the tower cranes, in accordance with their relevant loading charts

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SCTL

Since carbon emissions associated with tower cranes on a construction site are impacted by both the number of operating tower cranes during the construction phase and the operating duration of the tower crane, an important parameter making up the objective function defined for Model SCTL is the crane’s operating time parameter, \( {T}_{\mathrm{ij}}^k \). This is determined by the crane’s tangential and radial trolley travel time, \( {T}_{\mathrm{ijk}}^{\omega } \) and \( {T}_{\mathrm{ijk}}^r \), respectively, and the horizontal and vertical hook travel time, \( {T}_{\mathrm{ijk}}^h \) and \( {T}_{\mathrm{ijk}}^v \), respectively. The following equations, commonly adopted in the literature (Zhang et al. 1996), Eqs. 14.1, 14.2, 14.3, 14.4, 14.5, 14.6, 14.7, and 14.8, are used to derive the operation timing parameter of the tower crane:

$$ {\rho}_{\mathrm{ak}}=\sqrt{{\left({\mathrm{xc}}_a-{\mathrm{xc}}_k\right)}^2+{\left({\mathrm{yc}}_a-{\mathrm{yc}}_k\right)}^2}\kern0.6em \forall a\in I\cup J,\forall k\in K $$
(14.1)
$$ {l}_{\mathrm{ij}}=\sqrt{{\left({\mathrm{xc}}_i-{\mathrm{xc}}_j\right)}^2+{\left({\mathrm{yc}}_i-{\mathrm{yc}}_j\right)}^2}\kern0.6em \forall i\in I,\forall j\in J $$
(14.2)
$$ {T}_{\mathrm{ijk}}^r=\frac{\left|{\rho}_{\mathrm{ik}}-{\rho}_{\mathrm{jk}}\right|}{V_r}\kern0.6em \forall i\in I,\forall j\in J,\forall k\in K $$
(14.3)
$$ {\eta}_{\mathrm{ij}\mathrm{k}}=\frac{{l_{\mathrm{ij}}}^2-{\rho_{\mathrm{ik}}}^2-{\rho_{\mathrm{jk}}}^2}{2{\rho}_{\mathrm{ik}}{\rho}_{\mathrm{jk}}}\kern0.6em \forall i\in I,\forall j\in J,\forall k\in K $$
(14.4)
$$ {T}_{\mathrm{ijk}}^{\omega }=\frac{1}{V_{\omega }}{\cos}^{-1}\left({\eta}_{\mathrm{ijk}}\right),\kern0.5em {\displaystyle \begin{array}{c}\forall i\in I,\forall j\in J,\forall k\in K,\\ {}0\le \theta ={\cos}^{-1}\left({\eta}_{\mathrm{ijk}}\right)\le \pi \end{array}} $$
(14.5)
$$ {T}_{\mathrm{ijk}}^h=\max \left\{{T}_{\mathrm{ijk}}^r,{T}_{\mathrm{ijk}}^{\omega}\right\}+\alpha \min \left\{{T}_{\mathrm{ijk}}^r,{T}_{\mathrm{ijk}}^{\omega}\right\}\kern0.6em \forall i\in I,\forall j\in J,\forall k\in K $$
(14.6)
$$ {T}_{\mathrm{ij}}^v=\frac{\left|{\mathrm{zc}}_i-{\mathrm{zc}}_j\right|}{V_v}\kern0.6em \forall i\in I,\forall j\in J $$
(14.7)
$$ {T}_{\mathrm{ij}\mathrm{k}}={\gamma}_k\left(\max \left\{{T}_{\mathrm{ij}\mathrm{k}}^h,{T}_{\mathrm{ij}}^v\right\}+\beta \min \left\{{T}_{\mathrm{ij}\mathrm{k}}^h,{T}_{\mathrm{ij}}^v\right\}\right)\kern0.36em \forall i\in I,\forall j\in J,\forall k\in K $$
(14.8)

Let I, J and K denote the sets of demand points, potential supply points’ locations and potential tower cranes’ locations, respectively. Notation for Eqs. 14.1, 14.2, 14.3, 14.4, 14.5, 14.6, 14.7, and 14.8 is highlighted in Fig. 14.3. Parameters α, β and γ k define the degree of coordination of hook movement in tangential and radial direction, in vertical and horizontal planes, and the degree of difficulty in hook movement control for a crane located at k, respectively. For further explanation of Eqs. 14.1, 14.2, 14.3, 14.4, 14.5, 14.6, 14.7, and 14.8, the reader is referred to Zhang et al. (1996) (Fig. 14.4).

Fig. 14.4
figure 4

Notation adopted for crane location models

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The sets J i and K j are defined as: J i  = {j ∈ J : D ji < ρ} for i ∈ I, and K j  = {k ∈ K : D jk < ρ} for j ∈ J, respectively. The parameter ρ acts as an upper limit imposed on the distance D SW between two nodes s and w in the network representation. This ensures that the supply points chosen, j, are positioned at a servicing distance away from the demand point, i, and crane point k. The carbon emissions per hour resulting from a single tower crane operation are denoted by E. An arbitrary large value is given as M. The binary variable, δ k , is defined to equal 1 if a tower crane is positioned at location k, and zero otherwise, while the binary variable, x ij, takes the value 1 if supply node j is assigned to a demand point i, and zero otherwise. An auxiliary binary variable, namely, ϕ j , is adopted. For the SCTL the formulation is then given as:

$$ \min \kern0.6em E\sum \limits_{i\in I}\sum \limits_{j\in J}\sum \limits_{k\in K}{T}_{\mathrm{ij}}^k{\delta}_k{x}_{\mathrm{ij}} $$
(14.9)

subject to

$$ \sum \limits_{j\in {J}_i}{x}_{\mathrm{ij}}\ge 1\kern0.6em \forall i\in I $$
(14.10)
$$ \sum \limits_{i\in I}{x}_{\mathrm{ij}}\le {\phi}_jM\kern0.6em \forall j\in J $$
(14.11)
$$ \sum \limits_{k\in {K}_j}{\delta}_k\ge {\phi}_j\kern0.6em \forall j\in J $$
(14.12)
$$ {x}_{\mathrm{ij}},{\phi}_j,{\delta}_k\in \left\{0,1\right\}\kern0.6em \forall i\in I,\forall j\in J,\forall k\in K $$
(14.13)

The objective function in SCTL, Eq. 14.9, is formulated as a quadratic function, which minimises the overall carbon emissions resulting from the operations of tower cranes on the construction site, which achieve full level of coverage to all demand points. Equation 14.10 requires that each demand point is serviced by at least one supply point that is close enough to permit the tower crane’s jib to reach it. Equations 14.11 and 14.12 are defined to control the auxiliary variable ϕ j , which linearises the condition that a supply point is assigned to one or more demand points and permits a link between the supply points assignment variables, and x ij and the variable for locating a tower crane δ k . This ensures that the supply point is positioned within operating distance of the tower crane. Equation 14.13 establishes the domain of the model variables.

MCTL

The second model, defined for solving the tower crane location problem, maximises the coverage of a maximum number of tower cranes that can be set up on the construction site. Through restraining the maximum number of tower cranes that can operate on the construction site, a limit is placed on the total carbon emissions that result from tower crane operations.

The MCTL model is presented as:

$$ \max \kern0.6em \sum \limits_{i\in I}{Q}_i{Z}_i $$
(14.14)

subject to

$$ \sum \limits_{j\in J}{\psi}_j\le \mathrm{PS} $$
(14.15)
$$ \sum \limits_{k\in K}{\delta}_k\le \mathrm{PT} $$
(14.16)
$$ \sum \limits_{i\in {I}_j}{x}_{\mathrm{ij}}\le \overline{M}{\psi}_j\kern0.6em \forall j\in J $$
(14.17)
$$ \sum \limits_{i\in {I}_j}{x}_{\mathrm{ij}}\ge {\psi}_j\kern0.6em \forall j\in J $$
(14.18)
$$ {Z}_i\le \sum \limits_{k\in K}{\delta}_k\kern0.6em \forall i\in I $$
(14.19)
$$ {Z}_i\le \sum \limits_{j\in {J}_i}{x}_{\mathrm{ij}}\kern0.6em \forall i\in I $$
(14.20)
$$ \sum \limits_{j\in {J}_i}{x}_{\mathrm{ij}}\le 1\kern0.6em \forall i\in I $$
(14.21)
$${x_{{\rm{ij}}}},{Z_i},{\delta _k},{\psi _j} \in \left\{ {0{\rm{,}}1} \right\}\;\;\forall i \in I,\forall j \in J,\forall k \in K $$
(14.22)

Where the set I j is defined as I j  = {i ∈ I : D ij < ρ}. Parameters PS and PT define the maximum number of supply points and tower cranes to be assigned, while parameter \( \overline{M} \) denotes an arbitrary large value. The binary variable Ψj equals 1 if a supply point is activated at node j, while the binary variable Zi equals 1 if demand node is covered and 0 otherwise. The rest of the notation is described for Model SCTL.

The objective function, Eq. 14.14, maximises the number of demand points covered. Equations 14.15 and 14.16 state that the maximum number of supply points and tower cranes is to be less than the specified limits, PS and PT, respectively. Equations 14.17 and 14.18 link variables x ij and Ψj. The coverage variable is activated only if a supply point is assigned to a demand point and a tower crane is placed in close proximity to the demand point; this is specified through Eqs. 14.19 and 14.20. Equation 14.21 requires that each demand point be associated with a maximum of 1 supply point, to avoid over allocation to the demand points. Finally, the domain of the variables is given by Eq. 14.22.

For the MCTL model , the following equation is used to assess the carbon emissions per unit material resulting from the site plan adopted, Eq. 14.23:

$$ E\sum \limits_{i\in I}\sum \limits_{j\in J}\sum \limits_{k\in K}{T}_{\mathrm{ij}\kern0.2em i}^k{\overline{\delta}}_k{\overline{x}}_{\mathrm{ij}} $$
(14.23)

Where \( {\overline{\delta}}_k \) and \( {\overline{x}}_{\mathrm{ij}} \) are now both parameters whose values are obtained after solving the model. This then enables contrasting both SCTL and MCTL to find which results in the site layout with the least embodied carbon emissions.

Container Loading Problem Model

The second aspect contained within the highlighted framework of Fig. 14.2 addresses the embodied carbon resulting from transportation activities of the construction industry, through optimising the layout of materials within the shipping container used to transport materials to and from the construction site, in such a manner that container space utilisation is maximised. This ensures that the total trips to be performed is minimised. As a result, the model to be presented next solves a container loading problem, where materials are assumed to be represented as a convex polyhedron bounded by six quadrilateral faces, Fig. 14.5. All material types are assumed to be bounded by such polyhedron in the proposed model.

Fig. 14.5
figure 5

Steel reinforcement , enclosed within a cuboid for the CLP

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Let V c denote the volume of item c, and let (x n , y n , z n ) be the bottom left corner coordinate of item c. Define l cs and r cs to equal 1 if item S is positioned to the left and right of item C, respectively. Also, define a cs and blcs to equal 1 if item S is placed above and below item C, respectively. Finally, define f cs and bhcs to equal 1 if item S is placed in front of and behind item C, respectively. The notation for the CLP presented is given in Fig. 14.6.

Fig. 14.6
figure 6

Notation used in CLP model

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To solve the CLP, the following model is presented, namely, CL:

$$ \max \kern0.48em \sum \limits_{c\in C}{w}_c{d}_c{h}_c{\zeta}_z $$
(14.24)

Subject to

$$ {l}_{\mathrm{cs}}+{r}_{\mathrm{cs}}+{a}_{\mathrm{cs}}+{\mathrm{bl}}_{\mathrm{cs}}+{f}_{\mathrm{cs}}+{\mathrm{bh}}_{\mathrm{cs}}={\zeta}_s+{\zeta}_c-1\kern0.6em \forall s,c\in C:c<s $$
(14.25)
$$ {x}_c-{x}_s\ge {w}_s{l}_{\mathrm{cs}}-W\left(1-{l}_{\mathrm{cs}}\right)\kern0.6em \forall s,c\in C:c<s $$
(14.26)
$$ {x}_s-{x}_c\ge {w}_c{r}_{\mathrm{cs}}-W\left(1-{r}_{\mathrm{cs}}\right)\kern0.6em \forall s,c\in C:c<s $$
(14.27)
$$ {z}_c-{z}_s\ge {h}_s{\mathrm{bl}}_{\mathrm{cs}}-H\left(1-{\mathrm{bl}}_{\mathrm{cs}}\right)\kern0.6em \forall s,c\in C:c<s $$
(14.28)
$$ {z}_s-{z}_c\ge {h}_c{a}_{\mathrm{cs}}-H\left(1-{a}_{\mathrm{cs}}\right)\kern0.6em \forall s,c\in C:c<s $$
(14.29)
$$ {y}_c-{y}_s\ge {d}_s{f}_{\mathrm{cs}}-D\left(1-{f}_{\mathrm{cs}}\right)\kern0.6em \forall s,c\in C:c<s $$
(14.30)
$$ {y}_s-{y}_c\ge {d}_c{\mathrm{bh}}_{\mathrm{cs}}-D\left(1-{\mathrm{bh}}_{\mathrm{cs}}\right)\kern0.6em \forall s,c\in C:c<s $$
(14.31)
$$ {x}_c,{y}_c,{z}_c\ge 0\kern0.6em \forall c\in C $$
(14.32)
$$ {r}_{\mathrm{cs}},{l}_{\mathrm{cs}},{a}_{\mathrm{cs}},{\mathrm{bl}}_{\mathrm{cs}},{f}_{\mathrm{cs}},{\mathrm{bh}}_{\mathrm{cs}}\in \left\{0,1\right\}\kern0.6em \forall s,c\in C:c<s $$
(14.33)

The objective function, Eq. 14.24, maximises the total volume utilised within the loaded container. Equation 14.25 requires one condition to hold, in order to ensure that the loaded items do not overlap within the container. These conditions are determined by Eqs. 14.26, 14.27, 14.28, 14.29, 14.30, and 14.31. In particular, Eqs. 14.26 and 14.27 state that item S is to the left or to the right of item C, respectively. Equations 14.28 and 14.29 state that item S is either below or above item C, respectively. Equations 14.30 and 14.31 state that item S is in front of or behind item C, respectively. Equations 14.32 and 14.33 define the domain of the variables within Model CL.

Once optimised solutions are obtained, to calculate the total embodied carbon, the following equation is used, as given in (Hong et al. 2013) Eq. 14.34:

$$ \sum \limits_{c\in C}\mathrm{TD}\cdot f\cdot {Q}_c $$
(14.34)

where TD is the total travel distance, f is the carbon emission factor of truck/trailer, and Q is the weight of material loaded into the truck/trailer, in tonnes.

Case Studies

In this section, the proposed models will be tested on two practical cases, obtained from a building contractor in Sydney, Australia. In particular, Case 1 involves a site layout planning problem for a medium-sized project, where tower cranes and material supply storage are desired to be located, while Case 2 represents a container loading problem for the same project that requires stocks to be delivered to the site to satisfy project requirements. The models proposed are implemented in AMPL (Fourer et al. 1993) and solved using CPLEX 12.6.0 (IBM Knowledge Center 2016). In all cases the units for embodied carbon is reported in kilogrammes carbon dioxide equivalent, kgCO2e.

Case 1

In the first case study, the contractor needs to determine an appropriate site layout where supply points and tower cranes need to be located to service a set of predefined points. Both location models proposed above, SCTL and MCTL, are assessed for their relative impact on total carbon emissions resulting from the tower crane operations. The construction site has dimensions of 300 m by 200 m and is displayed in Fig. 14.7. A total of four tower crane locations are identified beforehand, along with four suitable supply point locations. The demand points correspond to areas within the constructed building where material is required. The site layout is analysed for a single phase of the construction process, namely, Phase 2 of the project, involving the erection of the first and second floors of the steel building. The coordinates of predefined locations for the tower crane, supply points and existing demand regions are given in Table 14.1.

Fig. 14.7
figure 7

Construction site layout for Case 1

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Table 14.1 Coordinates for site layout of Case 1
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The time needed for the tower crane operations per unit of material transfer in both models is calculated using Eqs. 14.1, 14.2, 14.3, 14.4, 14.5, 14.6, 14.7, and 14.8. The results obtained from both models are contrasted with the decision-making of a site planning engineer, whose solution is based solely on experience.

Table 14.2 displays the optimised results for Models SCTL and MCTL. A 32-ton electric tower crane is assumed for this example with an associated emission rate of 465 g/kWh (Hasan et al. 2013). Average tower crane load and total hours use are derived from Aurecon Australasia (2016). As can be noticed, the total embodied carbon of the site layout, measured as the carbon emissions released from tower crane operations per unit of material transported, produced by Model SCTL is 86 % less than that resulting from Model MCTL (2.83 kgCO2e/unit material vs 21 kgCO2e/unit material). This result is explained by the number of tower cranes deployed by both models, where for Model SCTL, only a single crane is utilised, whereas Model MCLP specifies the installation of four tower cranes. In both models, two supply points are placed, namely, at Nodes 10 and 11. The allocation of demand regions to these supply points is a bit different in both models, since in Model SCLP, demand regions 5, 6, 7 and 8 are assigned to supply point 10, while demand region 8 is assigned to supply point 11. The allocation is almost the same in Model MCLP, with demand region 8 this time assigned to supply region 11. Compared with the results of an experienced engineer, Models SCLP and MCLP produce a layout that is associated with 87% and 5% lower embodied carbon.

Table 14.2 Optimised results for the site layout
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For the full duration of Phase 2 of the project, a total of 734 units of material is required to be transported between the supply points and demand points. Considering the distribution of materials for this phase of the project, the bar chart of Fig. 14.8 is produced. Again, a significant saving in total carbon emissions is noticed in Model SCLT, in comparison to Model MCTL (2001 kgCO2e vs 16,785 kgCO2e). It is noted that the total carbon emissions associated with the project considered were measured at around 155,310 kgCO2e.

Fig. 14.8
figure 8

Bar chart, showing total transport-related embodied carbon of site layout resulting due to tower crane operations, during Phase 2 of the project

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Case 2

The problem in many construction transport activities is due to the inefficient use of available capacity for transporting materials. In this case study, a 15-tonne truck, with dimensions 7 × 2.5 × 2.5 m and a total capacity of 43 m3, is to be loaded with seven items whose dimensions are given in Table 14.3. The materials are to be transported to the construction site, located at a distance of 30 km away from the material manufacturer. An emission rate of 0.065 kgCO2e/ton.km by the truck, as deduced from emission databases, like MOVES (US EPA 2016), is assumed.

Table 14.3 Dimensions of items to be transported to construction site
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The results of the model are then contrasted with the container layout decided on by the experienced engineer. The loading layout produced by the optimised model uses 65% of the truck, as opposed to only 40% when the expert opinion is sought. For the overall duration of the project, a total of 5530 kgCO2e will be emitted from material transportation, if an expert opinion is sought, compared to 4095 kgCO2e if the CL model is utilised. A 26% reduction in total embodied carbon is achieved in the material transportation mode if the proposed optimisation model is used, which equates to 1435 kgCO2e in of carbon emissions. This number is around 9% of the total embodied carbon of the project considered. The use of the proposed CL model therefore achieves a significant reduction in embodied carbon associated with the building.

Conclusion

In this chapter, optimisation models were presented to address the embodied carbon resulting from transportation activities in the construction sector. In particular, the focus was on tower crane operations, through optimising the site layout plan and material transportation efficiency. The results indicated that considerable reduction in the transport-related embodied carbon of buildings can be achieved through optimising these operations.

For the site layout plans, two models were introduced, namely, SCLP, where a set covering problem is solved to minimise the total carbon emissions resulting from the movement of a tower crane between supply and demand points, and MCLP, where coverage of all demand points by a set of tower crane is maximised. When compared with a solution offered by an experienced engineer, both SCLP and MCLP produced a site layout with 46% and 21% less carbon emissions, respectively. In particular, comparisons between both of these models revealed that SCLP was able to save up to 86% of total carbon emissions from tower cranes.

In terms of addressing material transportation to construction sites, Model CL was introduced. The aim was to maximise the utilisation space of the truck used to transport materials to the construction site, hence minimising the total number of trips conducted and the total carbon emissions produced during the material hauling trip. Again, considerable improvements were noticed when utilising the model as opposed to solely relying on the expertise of an experienced practitioner, with a total carbon emission saving of 26%.

Model CL only accounts for space use within the container. The model can be expanded to encompass other factors such as the weight of materials and their impact on the resulting carbon emissions.

The models presented in this chapter can be used by decision-makers to reduce transport-related embodied carbon in construction. Future work will consider the overall transport activities that comprise a typical life cycle of a project, including various other equipment elements.