Lifting Sequence Optimization of Luffing Tower Cranes Considering Motion Paths with Dynamic Programming
Publication: Journal of Construction Engineering and Management
Volume 147, Issue 10
Abstract
The lifting sequence of luffing tower cranes is a key factor in the normal operation of construction projects. Accurate estimation of total lifting time is necessary for lifting sequence optimization. Existing formulations for lifting time estimation have two main deficiencies. One is that the relationship between the hoist motion path of the hook and the luffing motion path of the boom is often neglected. The other is that lifting delays resulting from the horizontal motion path of the boom caused by the relative locations of the crane and the lifting start and end points are rarely taken into account. To address those limitations, this paper proposes a lifting sequence optimization model (LSOM) considering motion paths with dynamic programming. The effectiveness of the proposed model is evaluated by comparing it with three conventional lifting strategies [first in–first serve (FIFS), shortest job first (SJF), and nearest neighbor first (NNF)]. The results show that LSOM achieves a shorter total lifting time and higher crane utilization when compared with FIFS, SJF, and NNF.
Introduction
With continuous urbanization around the world, more construction projects take place in dense urban areas, which limit the space of construction sites (Ibrahim et al. 2018). Construction sites with limited space pose a severe challenge to the layout of tower cranes (Tam et al. 2001; Abdelmegid et al. 2015; Ji and Leite 2018). According to their luffing modes, tower cranes can be mainly classified as T-type and luffing tower cranes (Wu et al. 2020). Compared with the T-type tower crane with a fixed boom, the luffing tower crane is easier to lay out because of its structural characteristics, which are ideal for construction sites with limited space (Li et al. 2012).
Construction sites with limited space typically have higher requirements for space utilization (Al-Hussein et al. 2006; Irizarry and Karan 2012; Marzouk and Abubakr 2016). As one of the main space users, the luffing tower crane plays an important role in space utilization, and thus the lifting sequence is a key factor in normal project operation (Lee et al. 2015; Younes and Marzouk 2018). Total lifting time is one of the most basic elements in evaluating the effectiveness of a lifting sequence. That is, the less the total lifting time in the sequence, the higher the space utilization (Younes and Marzouk 2018; Wu and García de Soto 2020).
Having an accurate estimate of total lifting time is beneficial to lifting sequence optimization. Similar to that of the T-type tower crane, the lifting cycle time of the luffing tower crane mainly depends on its potential no-load lifting from the last demand point to the current supply point, essential loaded lifting from the current supply point to the current demand point, and potential lifting delay to avoid space conflicts with other cranes. However, the lifting details are different due to the separate luffing modes of the two crane types (Zhang et al. 1999; Lee et al. 2015; Younes and Marzouk 2018). Compared with that of the T-type tower crane, luffing tower crane lifting time estimation has received little attention. Therefore, it is necessary to establish a lifting time estimation formulation for the luffing tower crane according to its motion characteristics (Lee et al. 2015; Younes and Marzouk 2018). Specifically, it is necessary to consider the relationship between the hoist motion path of the hook and the luffing motion path of the boom as well as the lifting delay resulting from the horizontal motion path of the boom caused by the relative locations of the crane and the lifting start and end points.
An effective optimization method can enhance lifting sequence optimization. First in–first serve (FIFS), shortest job first (SJF), and nearest neighbor first (NNF) are conventional lifting strategies that decrease total lifting time in some cases, but cannot guarantee optimal total lifting time (Huang and Wong 2018). Lifting sequence optimization is determining the optimal lifting task and crane at each stage in the lifting process. Dynamic programming can realize the global optimum of multistage decision-making which matches the lifting sequence problem (Lazarev and Werner 2009; Bürgy et al. 2020). Although dynamic programming is seldom applied to such optimization problems, it is expected to be effective.
To sum up, this paper proposes a lifting sequence optimization model (LSOM) to minimize total luffing tower crane lifting time. The estimation formulation is explicitly established by taking the crane’s motion characteristics into account, and dynamic programming is used to enhance the optimization solution. The remainder of this paper is structured as follows. In the section “Literature Review,” studies on lifting sequence optimization are reviewed and summarized. In the section “Lifting Sequence Optimization Model,” the LSOM is established. The section “Example,” evaluates LSOM by comparing it with FIFS, SJF, and NNF in a realistic situation. In the section “Discussion,” the significance and limitation of LSOM are discussed. The section “Conclusion,” draws conclusions and discusses future work.
Literature Review
In construction projects, determination of the lifting sequence of tower cranes means sequence planning of lifting tasks and corresponding cranes (Wu and García de Soto 2020). In order to improve lifting efficiency, the lifting sequence is usually optimized using conventional lifting strategies such as FIFS, SJF, and NNF and, in some cases, specific lifting sequence optimization models (Zavichi et al. 2014; Huang and Wong 2018). Common objective metrics are minimum total lifting time, total lifting cost, pending time, and so on; the exact choice depends on the needs of project teams (Monghasemi et al. 2016; Al Hattab et al. 2017).
Lifting time estimation formulation is the basis of lifting sequence optimization (Rodriguez-Ramos and Francis 1983). In the 1970s, the relationship between lifting time, crane location, and lifting start and end point locations was established, providing the opportunity for quantitative evaluation of lifting time (Warszawski 1973). The luffing motion of T-type tower cranes is via trolley motion on the boom track, while that of luffing tower cranes is via boom motion; therefore lifting time estimation formulations for the two are different (Younes and Marzouk 2018). The formulation for T-type cranes mainly considers radial motion time of the trolley and slewing motion time of the boom in the horizontal plane; hook hoist motion time in the vertical plane; and loading and unloading time (Zhang et al. 1996, 1999). According to lifting locations (of T-type tower cranes and lifting start and end points), crane specifications (e.g., trolley radial speed, boom slewing speed, hook hoist speed), motion coordination (radial and slewing motion coordination in the horizontal plane and motion coordination in the horizontal and vertical planes), and lifted object characteristics (e.g., weight, loading and unloading time), lifting time can be estimated (Huang et al. 2011; Lien and Cheng 2014; Wang et al. 2015; Moussavi Nadoushani et al. 2017).
Unlike the formulation for T-type tower cranes in the horizontal plane, that for luffing tower cranes mainly takes into account the duration of boom luffing and slewing motion. Based on the Cartesian coordinate system, a formulation for luffing tower crane motion duration in the horizontal and vertical planes was proposed by Lee et al. (2015). In this formulation, luffing and slewing motion in the horizontal plane and hook hoist motion in the vertical plane were considered consecutive. To estimate the simultaneous motion time for luffing tower cranes, another formulation added the slewing and luffing motion coordination in the horizontal plane and the motion coordination in the horizontal and vertical planes (Younes and Marzouk 2018).
A type of lifting time estimation formulation was created according to the historical data of construction projects, including multiple linear regression, multilayer feed-forward neural network, general regression neural network, and group method of data handling (Leung and Tam 1999; Leung et al. 2001; Tam et al. 2002; Tam and Tong 2003). The factors affecting lifting time can be classified as controllable and uncontrollable. The controllable factors are manipulated by planning, such as crane specifications and supply point locations; the uncontrollable factors include demand point locations and lifted object weights (Leung et al. 2001). The factors affecting loaded and no-load lifting time are partly different. For loaded lifting time, factors such as lifting height, lifted object areas, and supply point locations have a greater impact (Tam et al. 2002). For no-load lifting time, factors such as lifting height and motion coordination have a more significant impact (Tam et al. 2002). Therefore, formulations for loaded and no-load lifting time estimation were created separately (Leung and Tam 1999; Leung et al. 2001; Tam et al. 2002; Tam and Tong 2003).
Compared with the multiple linear regression model and the multilayer feed-forward neural network, the general regression neural network shows good prediction of loaded and no-load lifting time. However, it cannot describe the relationship between input and output variables (Leung et al. 2001; Tam et al. 2002). The performance of the group method of data handling is slightly lower than that of the general regression neural network, but still achieves significant and acceptable prediction; meanwhile, it can reveal the relationship between input and output variables in the form of a complicated set of mathematical expressions (Tam et al. 2002).
Consideration of lifting delay to avoid space conflicts among tower cranes cannot be neglected in lifting time estimation (Hwang 2012; Wu et al. 2020). Four main criteria are proposed to identify these conflicts. The first criterion regards the location of a crane and those of its lifting start and end points as three points of a triangle. If two triangles intersect, space conflict occurs and increases as the number of intersection among six sides of two triangles increases (Zhang et al. 1999). The second criterion regards crane coverage as a circle. If two circles intersect, space conflict occurs and increases as the intersection area increases (Shapira and Simcha 2009; Irizarry and Karan 2012). The third criterion considers hook position. If two crane hooks are within the intersection area, space conflict is likely (Al Hattab et al. 2018). The fourth criterion further formalizes the previous criteria according to category, height, and motion path. Space conflict occurs in the following situations: (1) the trolley motion path of a taller T-type tower crane intersects with the boom motion path of a shorter T-type tower crane; (2) the boom slewing motion path of a luffing tower crane intersects with that of another luffing tower crane irrespective of the height ranking between them; (3) the trolley motion path of the taller T-type tower crane intersects with the boom slewing motion path of the shorter luffing tower crane; and (4) the boom slewing path of a taller luffing tower crane intersects with the boom motion path of a shorter T-type tower crane (Wu et al. 2020).
In earlier studies, the possibility of space conflicts was incorporated into tower crane planning as the objective index or constraint (Zhang et al. 1999; Irizarry and Karan 2012). Later studies began to focus on quantitative evaluation of the lifting delay caused by potential space conflicts among tower cranes (Al Hattab et al. 2018; Younes and Marzouk 2018; Wu et al. 2020).
Due to the luffing mode of luffing tower cranes, the luffing motion of the boom is associated with the hoist motion of the hook. Therefore, the hoist motion distance of the hook depends not only on the height difference between the lifting start and end points but also on the boom vertical motion distance. However, the relationship between the hook hoist motion path and the boom luffing motion path is often neglected, which leads to overestimation or underestimation of the hoist motion time of the hook. The lifting delay of luffing tower cranes is related to the relative locations of the cranes and the lifting start and end points, and the boom horizontal motion path caused by different relative locations can result in various lifting delays. However, such factors are rarely considered, making delay time estimation inaccurate. In this paper, the lifting time estimation formulation for luffing tower cranes presented here is aimed at solving these two problems.
Optimization methods include mathematical programming and metaheuristic algorithms (Wu and García de Soto 2020). In mathematical programming, the lifting sequence is formulated as an integer programming problem to minimize total lifting time (Zavichi et al. 2014; Huang and Wong 2018). In metaheuristic algorithms, harmony search and tabu search are used to search the optimal lifting sequence in terms of the least deviation of pending time and minimum total lifting time, respectively (Monghasemi et al. 2016; Al Hattab et al. 2017; Wu and García de Soto 2020).
As a branch of mathematical programming, dynamic programming was developed by Bellman (1957). Dynamic programming transforms the multistage decision-making problem into a series of single-stage decision-making subproblems according to its characteristics, and then solves the subproblems one by one to reach the optimal decision-making sequence of the whole problem (Lazarev and Werner 2009; de Matos et al. 2015). It solves each subproblem only once, and if there is a common subproblem, the stored state is used directly without repeated decision making (Lazarev and Werner 2009; de Matos et al. 2015; Grevtsov et al. 2017). Dynamic programming has been widely applied in various sectors with significant results (Konak et al. 2011; Grevtsov et al. 2017; Bürgy et al. 2020). Since it is seldom applied to lifting sequence optimization for luffing tower cranes, this paper addresses how to integrate such optimization problems with dynamic programming to extend its application.
Lifting Sequence Optimization Model
In this section, LSOM is elaborated. The model comprises two parts: (1) lifting time estimation considering motion paths and (2) integration of lifting time estimation and dynamic programming.
Loaded Lifting Time
Loaded lifting is essential in a lifting task. Fig. 1 shows loaded lifting in the horizontal and vertical planes; (), (), (), and () are the locations of crane , lifting start point (current supply point), lifting end point (current demand point), and transformed lifting start point (current transformed supply point) in lifting task , respectively.
CO.1943-7862.0002129/asset/d2e7e4f3-8c32-4641-a67b-429343bdfeed/assets/images/large/figure1.jpg)
Loaded lifting time () depends on loading time (), loaded motion time (), and unloading time (), as expressed in Eq. (1)
(1)
Loaded motion time () is determined by horizontal motion time (), vertical motion time (), and motion coordination in the horizontal and vertical planes () between 0 and 1, as expressed in Eq. (2); being equal to 0 or 1 means simultaneous or consecutive motion and typically defaults to 1 (Zhang et al. 1999)
(2)
Horizontal motion time () is determined by boom slewing motion time (), boom luffing motion time (), and slewing and luffing motion coordination in the horizontal plane () between 0 and 1, as expressed in Eq. (3); being equal to 0 or 1 means simultaneous or consecutive motion and typically defaults to 0.25 (Zhang et al. 1999)
(3)
Boom slewing motion time () is determined by the slewing angle of the boom from lifting start point to lifting end point () and by boom slewing speed (), as expressed in Eq. (4). Slewing angle () is calculated using Eqs. (5)–(8)
(4)
(5)
(6)
(7)
(8)
Boom luffing motion time () is determined by the luffing angle from the transformed lifting start point to lifting end point () and by luffing speed (), as expressed in Eq. (9). Luffing angle () is calculated using Eqs. (10)–(13)
(9)
(10)
(11)
(12)
(13)
Vertical motion time () is determined by hoist motion distance of the hook from lifting start point to lifting end point () and by hoist speed of the hook (), as expressed in Eq. (14). Hoist motion distance of the hook () is determined by the height difference between lifting end point () and lifting start point () and by boom vertical motion distance from the transformed lifting start point to lifting end point (). Boom vertical motion distance () is calculated using Eq. (15)
(14)
(15)
If the horizontal distance between crane and lifting start point [] is equal to the horizontal distance between crane and lifting end point [], as shown in Fig. 2, hoist motion distance of the hook () is calculated using Eq. (16)
(16)
CO.1943-7862.0002129/asset/7a9b7f2c-55c3-4e5d-9620-a3229b1d4bcb/assets/images/large/figure2.jpg)
If the horizontal distance between crane and lifting start point [] is greater than the horizontal distance between crane and lifting end point [], it is classified as one of three situations. In the first situation, the height of lifting end point () is less than or equal to that of lifting start point (), and the hoist motion distance of the hook () is calculated using the first fraction of Eq. (17), as shown in Figs. 3(a and b). In the second situation, the height of lifting end point () is greater than that of lifting start point (), and this height difference is less than or equal to the boom vertical motion distance from transformed lifting start point to lifting end point (); the hoist motion distance of the hook () is calculated using the second fraction of Eq. (17), as shown in Figs. 3(a and c). In the third situation, the height of lifting end point () is greater than that of lifting start (), and this difference is greater than the boom vertical motion distance from transformed lifting start point to lifting end point (); the hoist motion distance of the hook () is calculated using the third fraction of Eq. (17), as shown in Figs. 3(a and d)
(17)
CO.1943-7862.0002129/asset/98af2b88-1d99-4d8b-a9b1-a51524b8bb5b/assets/images/large/figure3.jpg)
If the horizontal distance between crane and lifting start point ] is less than the horizontal distance between crane and lifting end point [], it is also classified as one of three situations. In the first situation, the height of lifting start point () is less than or equal to that of the lifting end point (), and the hoist motion distance of the hook () is calculated using the first fraction of Eq. (18), as shown in Figs. 4(a and b). In the second situation, the height of lifting start point () is greater than that of lifting end point () and this height difference is less than or equal to the boom vertical motion distance from transformed lifting start point to lifting end point (); the hoist motion distance of the hook () is calculated using the second fraction of Eq. (18), as shown in Figs. 4(a and c). In the third situation, the height of lifting start point () is greater than that of lifting end point () and this height difference is greater than the boom vertical motion distance from transformed lifting start point to lifting end point (); the hoist motion distance of the hook () is calculated using the third fraction of Eq. (18), as shown in Figs. 4(a and d)
(18)
CO.1943-7862.0002129/asset/0da046d6-1b6d-4cac-a99b-3aa5a1105367/assets/images/large/figure4.jpg)
No-Load Lifting Time
No-load lifting in a lifting task depends on the current lifting number of crane () and the locations of lifting start point (; last demand point) and lifting end point (; current supply point) in lifting task . This is classified as one of three situations.
Situation 1
In Situation 1, the current lifting number of crane () is 0, so crane starts moving from the current supply point. Lifting task does not have a no-load lifting process, and no-load lifting time () is equal to 0, as expressed in the first fraction of Eq. (19).
Situation 2
In Situation 2, the current lifting number of crane () is not 0, and the locations of lifting start point () and lifting end point () are the same. Therefore, crane starts moving from the current supply point, lifting task does not have a no-load lifting process, and no-load lifting time () is equal to 0, as expressed in the second fraction of Eq. (19).
Situation 3
In Situation 3, the current lifting number of crane () is not 0, and the locations of lifting start point () and lifting end point () are not the same. Therefore, crane starts moving from the last demand point, and lifting task has a no-load lifting process. Estimation of no-load lifting time () is the same as that of loaded lifting time () except for loading time () and unloading time (). It only needs to replace the current supply point and the current demand point with the last demand point and the current supply point, respectively, as expressed in the third fraction of Eq. (19)
(19)
Lifting Delay Time
Lifting delay in a lifting task depends on the location of crane (), lifting start point (), and lifting end point () in current lifting task and relative to the location of crane (), lifting start point (), and lifting end point () in previous lifting task . This is represented by one of the following four situations.
Situation 1
In Situation 1, none of the three stages of crane ()—boom at lifting start point (), the motion path, and lifting end point ()—intersects with the boom of crane (), and lifting task does not have a lifting delay. There is only one case in this situation (Case 1 in Fig. 5):
•
Case 1: the boom of crane () at lifting start point (), the motion path, and lifting end point () do not intersect with the boom of () at lifting start point (), the motion path, or lifting end point ().
CO.1943-7862.0002129/asset/2804e9ce-c2cb-442b-8c04-f4cae9be6ad0/assets/images/large/figure5.jpg)
Situation 2
In Situation 2, the only stage of crane ()—the boom at lifting start point ()—intersects with the boom of crane (), and lifting task has a lifting delay. There are six cases in this situation (Cases 2–7 in Fig. 5):
•
Case 2: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting start point () and does not intersect with the boom of () at the motion path or lifting end point ().
•
Case 3: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting start point () and the motion path, and does not intersect with the boom of crane () at lifting end point ().
•
Case 4: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting start point (), the motion path, and lifting end point ().
•
Case 5: the boom of crane () at lifting start point () intersects with the boom of crane () at the motion path and does not intersect with the boom of crane () at lifting start point () or lifting end point ().
•
Case 6: the boom of crane () at lifting start point () intersects with the boom of crane () at the motion path and lifting end point () and does not intersect with the boom of crane () at lifting start point ().
•
Case 7: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting end point () and does not intersect with the boom of crane () at lifting start point () or the motion path.
Situation 3
In Situation 3, at least two stages of crane (), including the boom at lifting start point (), intersect with the boom of crane (), and lifting task has a lifting delay. There are six cases in this situation (Cases 8–13 in Fig. 5):
•
Case 8: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting start point () and does not intersect with the boom of crane () at the motion path or lifting end point (); the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at lifting start point (); neither of them intersects with the boom of crane () at the motion path or lifting end point ().
•
Case 9: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting start point () and does not intersect with the boom of crane () at the motion path or lifting end point (); the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at the motion path; neither of them intersects with the boom of crane () at lifting end point ().
•
Case 10: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting start point () and does not intersect with the boom of crane () at the motion path or lifting end point (); the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at lifting end point ().
•
Case 11: the boom of crane () at lifting start point () intersects with the boom of crane () at the motion path and does not intersect with the boom of crane () at lifting end point (); the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at lifting start point () and/or the motion path; neither of them intersects with the boom of crane () at lifting end point ().
•
Case 12: the boom of crane () at lifting start point () intersects with the boom of crane () at the motion path and does not intersect with the boom of crane () at lifting end point (); the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at lifting end point ().
•
Case 13: the boom of crane () at lifting start point () intersects with the boom of crane () at lifting end point (); the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at lifting start point (), the motion path, and/or lifting end point (),
Situation 4
In Situation 4, at least one stage of crane (), excluding the boom at lifting start point (), intersects with the boom of crane (), and lifting task has a lifting delay. There are three cases in this situation (Cases 14–16 in Fig. 5):
•
Case 14: the boom of crane () at the motion path and/or lifting end point () intersects with the boom of crane () at lifting start point (); neither of them intersects with the boom of () at the motion path or lifting end point ().
•
Case 15: the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at the motion path; neither of them intersects with the boom of crane () at lifting end point ().
•
Case 16: the boom of crane () at the motion path and/or lifting end point () intersect(s) with the boom of crane () at lifting end point ().
According to the distinction between loaded and no-load lifting of current lifting task and previous lifting task , estimation of lifting delay time () in the 16 cases is divided into four situations, as shown in Fig. 6, which assumes that the two lifting tasks start at the same time and that is completed before .
CO.1943-7862.0002129/asset/b82f1069-00c2-4ffd-9dc9-169d1bc491c8/assets/images/large/figure6.jpg)
In Situation 1, lifting tasks and are both in no-load lifting, and the estimation of lifting delay time () is divided into two fractions.
•
In Case 1, 2, 5, 6, 7, 8, or 14, crane () starts moving once crane () starts moving; lifting delay time () is 0, as expressed in the first fraction of Eq. (20).
•
In Case 3, 4, 9, 10, 11, 12, 13, 15, or 16, crane () starts moving once crane () ends moving; lifting delay time () is the difference between the end time of no-load lifting in lifting task () and the start time of no-load lifting in lifting task (), as expressed in the second fraction of Eq. (20)
(20)
In Situation 2, lifting tasks and are in no-load and loaded-lifting, respectively, and the estimation of lifting delay time () is divided into four fractions:
•
In Case 1, 5, 6, or 7, crane () starts moving once crane () starts loading; lifting delay time () is 0, as expressed in the first fraction of Eq. (21).
•
In Case 2, 8, or 14, crane () starts moving once crane () starts moving; lifting delay time () is the difference between the start time of the loaded motion stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task (), as expressed in the second fraction of Eq. (21).
•
In Case 3, 9, 11, or 15, crane () starts moving once crane () ends moving; lifting delay time () is the difference between the end time of the loaded motion stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task (), as expressed in the third fraction of Eq. (21).
•
In Case 4, 10, 12, 13, or 16, crane () starts moving once crane () ends unloading; lifting delay time () is the difference between the end time of the unloading stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task (), as expressed in the fourth fraction of Eq. (21)
(21)
In Situation 3, lifting tasks and are in loaded and no-load lifting, respectively, and the estimation of lifting delay time () is divided into three fractions:
•
In Case 1, 2, 8, or 14, crane () starts loading once crane () starts moving; lifting delay time () is 0, as expressed in the first fraction of Eq. (22).
•
In Case 3, 4, 5, 6, 7, 11, 12, or 13, crane () starts loading once crane () ends moving; lifting delay time () is the difference between the end time of no-load lifting in lifting task () and the start time of no-load lifting in lifting task (), as expressed in the second fraction of Eq. (22).
•
In Case 9, 10, 15, or 16, crane () starts loading once crane () starts moving and waits to start moving until () ends moving; lifting delay time () is 0 if the end time of the loading stage of loaded lifting in lifting task () is not earlier than the end time of no-load lifting in lifting task (); otherwise, lifting delay time () is the difference between the end time of no-load lifting in lifting task () and the end time of the loading stage of loaded lifting in lifting task (), as expressed in the third fraction of Eq. (22)
(22)
In Situation 4, lifting tasks and are both in loaded lifting, and the estimation of lifting delay time () is divided into ten fractions:
•
In Case 1, crane () starts loading once crane () starts loading. Lifting delay time () is 0, as expressed in the first fraction of Eq. (23).
•
In Case 2 or 8, crane () starts loading once crane () starts moving. Lifting delay time () is the difference between the start time of the loaded motion stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in the lifting task (), as expressed in the second fraction of Eq. (23).
•
In Case 3, 5, or 11, crane () starts loading once crane () ends moving. Lifting delay time () is the difference between the end time of the loaded motion stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task (), as expressed in the third fraction of Eq. (23).
•
In Case 4, 6, 7, or 13, crane () starts loading once crane () ends unloading. Lifting delay time () is the difference between the end time of the unloading stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task (), as expressed in the fourth fraction of Eq. (23).
•
In Case 9, crane () starts loading once crane () starts moving and waits to start moving until crane () ends moving. Lifting delay time () is the difference between the start time of the loaded motion stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task () if the end time of the loading stage of loaded lifting in lifting task () is not earlier than the end time of the loaded motion stage of loaded lifting in lifting task (); otherwise, lifting delay time () is their difference plus the difference between the end time of the loaded motion stage of loaded lifting in lifting task () and the end time of the loading stage of loaded lifting in lifting task (), as expressed in the fifth fraction of Eq. (23).
•
In Case 10, crane () starts loading once crane () starts moving and waits to start moving until crane () ends unloading. Lifting delay time () is the difference between the start time of the loaded motion stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task () if the end time of the loading stage of loaded lifting in lifting task () is not earlier than the end time of the unloading stage of loaded lifting in lifting task (); otherwise, lifting delay time () is their difference plus the difference between the end time of the unloading stage of loaded lifting in lifting task () and the end time of the loading stage of loaded lifting in lifting task (), as expressed in the sixth fraction of Eq. (23).
•
In Case 12, crane () starts loading once crane () ends moving and waits to start moving until crane () ends unloading. Lifting delay time () is the difference between the end time of the loaded motion stage of loaded lifting in lifting task () and the start time of the loading stage of loaded lifting in lifting task () if the end time of the loading stage of loaded lifting in lifting task () is not earlier than the end time of the unloading stage of loaded lifting in lifting task (); otherwise, lifting delay time () is their difference plus the difference between the end time of the unloading stage of loaded lifting in lifting task () and the end time of the loading stage of loaded lifting in lifting task (), as expressed in the seventh fraction of Eq. (23).
•
In Case 14, crane () starts loading once crane () starts loading and waits to start moving until crane () starts moving. Lifting delay time () is 0 if the end time of the loading stage of loaded lifting in lifting task () is not earlier than the start time of the loaded motion stage of loaded lifting in lifting task (); otherwise, lifting delay time () is the difference between the start time of the loaded motion stage of loaded lifting in lifting task () and the end time of the loading stage of loaded lifting in lifting task (), as expressed in the eighth fraction of Eq. (23).
•
In Case 15, crane () starts loading once crane () starts loading and waits to start moving until crane () ends moving. Lifting delay time () is 0 if the end time of the loading stage of loaded lifting in lifting task () is not earlier than the end time of the loaded motion stage of loaded lifting in lifting task (); otherwise, lifting delay time () is the difference between the end time of the loaded motion stage of loaded lifting in lifting task () and the end time of the loading stage of loaded lifting in lifting task (), as expressed in the ninth fraction of Eq. (23).
•
In Case 16, crane () starts loading once crane () starts loading and waits to start moving until crane () ends unloading. Lifting delay time () is 0 if the end time of the loading stage of loaded lifting in lifting task () is not earlier than the end time of the unloading stage of loaded lifting in lifting task (); otherwise, lifting delay time () is the difference between the end time of the unloading stage of loaded lifting in lifting task () and the end time of the loading stage of loaded lifting in lifting task (), as expressed in the tenth fraction of Eq. (23)
(23)
Dynamic Programming
The lifting process can be divided into interrelated stages according to the lifting sequence, and a lifting task and a crane should be determined at each stage to minimize total lifting time. In this way, lifting sequence optimization is formulated into dynamic programming.
The decision-making process for lifting tasks and cranes at different stages is shown in Fig. 7, where , , and refer to stage , lifting task , and crane , respectively. The state variables represent lifting state information such as lifting tasks performed before or after a given stage. For example, is lifting state information after Stage 1 and before Stage 2. The decision variables represent the performed lifting task and the performing crane at a given stage. For example, decision indicates Task 2 performed by Crane 3 at Stage 1. The effect variables (i.e., stage index functions)——represent current total lifting time at a given stage when a previous state and a decision are determined. For example, indicates current total lifting time at Stage 1 if lifting state information before Stage 1 is given and Task 2 is performed by Crane 3 at Stage 1
(24)
(25)
(26)
CO.1943-7862.0002129/asset/85e80a5a-f370-421e-b811-38a6e188cb41/assets/images/large/figure7.jpg)
The state transfer function is expressed in Eq. (24). State after stage is determined according to state before stage and the decision at stage . The relationship between the process index function and the stage index functions is expressed in Eq. (25), where process index in Stages is the maximum of the stage index functions —that is, the maximum current total lifting time at all stages. The optimal process index function is expressed in Eq. (26), and the optimal process index in Stages is the minimum of existing process indexes —that is, the minimum total lifting time in existing solutions.
Fig. 8 shows the dynamic programming pseudocode for lifting sequence optimization. The input is the set of lifting tasks and the set of cranes . The output is the minimum total lifting time and its corresponding lifting sequence. Dynamic programming adopts the bottom-up recursive method in Stages , and the state after a stage depends on its previous state. The set of tasks and the set of cranes form a two-level nested loop from outside to inside. If Stage exceeds the last stage of the lifting process, this loop is skipped and the next loop starts directly; else, the following three conditions are evaluated successively.
•
If the number of existing states is greater than or equal to the current stage value, remove the last state until it is one less than the current stage value.
•
If the criteria for avoiding infeasible solutions are satisfied, determine state according to Eq. (24); else, skip this loop and start the next loop. The three criteria to be satisfied are as follows: (1) the current lifting task has not yet been performed; (2) the locations of supply and demand points as well as the weight in the current task are covered by the capacity of the performing crane; and (3) the masts of other cranes are not covered by the motion range of the performing crane.
CO.1943-7862.0002129/asset/9063c679-a61e-461e-92cd-abbe766a90c5/assets/images/large/figure8.jpg)
Example
To evaluate the effectiveness of LSOM, an example with 12 lifting tasks and two luffing tower cranes in a 75-story building project with a total height of 348.5 m was tested. The example is a typical arrangement in construction projects, involving lifting tasks with different weights and locations as well as potential space conflicts between luffing tower cranes. FIFS, SJF, and NNF are compared with LSOM in this example, and lifting tasks are performed according to number, loaded lifting time, and no-load lifting time, respectively.
The structure is based on a concrete-filled steel tube frame with a reinforced concrete core tube and outrigger trusses. The installation of Cranes and is by external climbing. There are seven supply points and nine demand points. Supply points , , and , and demand point are on the ground; Demand points , , , and are on the 23rd floor of the outer frame; common supply/demand points (), (), (), and () are on the 29th floor of the core tube, as shown in Fig. 9. The coordinates of the cranes and supply and demand points are summarized in Table 1.
CO.1943-7862.0002129/asset/a749619c-dbb6-44f7-a9fb-b38ae06b02e2/assets/images/large/figure9.jpg)
| Name | Coordinate () | Coordinate () | Coordinate () |
|---|---|---|---|
| 14.050 | 0.000 | — | |
| — | |||
| 32.650 | 19.600 | ||
| 40.350 | |||
| () | 4.775 | 8.200 | 124.750 |
| () | 8.200 | 124.750 | |
| () | 4.775 | 124.750 | |
| () | 124.750 | ||
| 13.330 | 17.650 | 98.650 | |
| 17.650 | 98.650 | ||
| 13.330 | 98.650 | ||
| 98.650 | |||
Lifting weights and supply and demand points are provided in Table 2. The lifting weight of Tasks 1–4 is 11 tons, and the supply and demand points are on the ground floor and the 29th floor of the core tube, respectively. The lifting weight of Tasks 5–8 is 15 t, and the supply and demand points are on the ground floor and the 23rd floor of the outer frame, respectively. The lifting weight of Tasks 9–12 is 12 t, and the supply and demand points are on the 29th floor of the core tube and the ground floor, respectively.
| Task | Weight (t) | Supply point | Demand point |
|---|---|---|---|
| 1 | 11 | ||
| 2 | 11 | ||
| 3 | 11 | ||
| 4 | 11 | ||
| 5 | 15 | ||
| 6 | 15 | ||
| 7 | 15 | ||
| 8 | 15 | ||
| 9 | 12 | ||
| 10 | 12 | ||
| 11 | 12 | ||
| 12 | 12 |
Crane specifications are listed in Table 3; they consist of boom length, maximum working radius, minimum working radius, maximum lifting capacity, whole-range luffing time, boom slewing speed, and hook hoist speed. These are 55.0 m, 52.5 m, 4.4 m, 50.0 t, 1.5 min, 0.8 rpm, and , respectively.
| Boom length (m) | Maximum working radius (m) | Minimum working radius (m) | Maximum lifting capacity (t) | Whole-range luffing time (min) | Slewing speed of boom (rpm) | Hoist speed of hook () |
|---|---|---|---|---|---|---|
| 55.0 | 52.5 | 4.4 | 50.0 | 1.5 | 0.8 | 75 |
All tests are done in Visual Studio version 2015 with C# on a laptop with a Windows 7 64-bit operating system, Intel(R) Corei7-6700HQ CPU @ 2.60GHz, and 16 GB of RAM. The FIFS, SJF, and NNF computation time is less than 1 min, and that of LSOM about 1 h.
Lifting sequences for FIFS, SJF, NNF, and LSOM are provided in Table 4. In FIFS, the sequence is Tasks 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Tasks 1, 2, 3, 4, 5, and 6 are performed by Crane successively; Tasks 7, 8, 9, 10, 11, and 12 are performed by Crane successively; total lifting time is 154.27 min. In SJF, the lifting task sequence is 1, 2, 4, 3, 11, 12, 9, 10, 8, 6, 5, and 7; Tasks 1, 2, 4, 3, 6, and 5 are performed by Crane successively; Tasks 11, 12, 9, 10, 8, and 7 are performed by Crane successively; total lifting time is 126.83 min. In NNF, the lifting sequence is 12, 7, 10, 8, 11, 9, 5, 1, 2, 3, 6, and 4; Tasks 5, 1, 2, 3, 6, and 4 are performed by Crane successively; Tasks 12, 7, 10, 8, 11, and 9 are performed by Crane successively; total lifting time is 166.61 min. In LSOM, the lifting task sequence is 3, 9, 1, 8, 2, 4, 5, 12, 7, 6, 10, and 11; Tasks 3, 1, 2, 4, 5, and 6 are performed by Crane successively; Tasks 9, 8, 12, 7, 10, and 11 are performed by Crane successively; the total lifting time is 89.22 min.
| Sequence | FIFS | SJF | NNF | LSOM | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Task | Crane | Schedule (min) | Task | Crane | Schedule (min) | Task | Crane | Schedule (min) | Task | Crane | Schedule (min) | |||||||||
| Start | End | Duration | Start | End | Duration | Start | End | Duration | Start | End | Duration | |||||||||
| 1 | 1 | 1 | 0.00 | 6.03 | 6.03 | 1 | 1 | 0.00 | 6.03 | 6.03 | 12 | 2 | 0.00 | 8.10 | 8.10 | 3 | 1 | 0.00 | 6.29 | 6.29 |
| 2 | 2 | 1 | 6.03 | 14.10 | 8.07 | 2 | 1 | 6.03 | 14.10 | 8.07 | 7 | 2 | 8.10 | 35.03 | 26.93 | 9 | 2 | 0.00 | 8.14 | 8.14 |
| 3 | 3 | 1 | 14.10 | 22.43 | 8.33 | 4 | 1 | 14.10 | 22.36 | 8.26 | 10 | 2 | 35.03 | 43.76 | 8.73 | 1 | 1 | 6.29 | 14.60 | 8.31 |
| 4 | 4 | 1 | 22.43 | 30.93 | 8.50 | 3 | 1 | 22.36 | 30.85 | 8.49 | 8 | 2 | 43.76 | 70.59 | 26.83 | 8 | 2 | 8.14 | 34.97 | 26.83 |
| 5 | 5 | 1 | 30.93 | 59.78 | 28.85 | 11 | 2 | 22.36 | 38.83 | 16.47 | 11 | 2 | 70.59 | 79.18 | 8.59 | 2 | 1 | 14.60 | 22.67 | 8.07 |
| 6 | 6 | 1 | 59.78 | 88.06 | 28.28 | 12 | 2 | 38.83 | 49.03 | 10.20 | 9 | 2 | 79.18 | 89.46 | 10.28 | 4 | 1 | 22.67 | 30.93 | 8.26 |
| 7 | 7 | 2 | 59.78 | 86.47 | 26.69 | 9 | 2 | 49.03 | 59.31 | 10.28 | 5 | 1 | 79.18 | 105.82 | 26.64 | 5 | 1 | 30.93 | 59.78 | 28.85 |
| 8 | 8 | 2 | 86.47 | 114.75 | 28.28 | 10 | 2 | 59.31 | 69.75 | 10.44 | 1 | 1 | 105.82 | 113.38 | 7.56 | 12 | 2 | 34.97 | 43.60 | 8.63 |
| 9 | 9 | 2 | 114.75 | 123.68 | 8.93 | 8 | 2 | 69.75 | 96.58 | 26.83 | 2 | 1 | 113.38 | 121.46 | 8.08 | 7 | 2 | 43.60 | 70.53 | 26.93 |
| 10 | 10 | 2 | 123.68 | 134.12 | 10.44 | 6 | 1 | 69.75 | 98.55 | 28.80 | 3 | 1 | 121.46 | 129.79 | 8.33 | 6 | 1 | 59.78 | 88.06 | 28.28 |
| 11 | 11 | 2 | 134.12 | 144.07 | 9.95 | 5 | 1 | 98.55 | 126.83 | 28.28 | 6 | 1 | 129.79 | 158.59 | 28.80 | 10 | 2 | 70.53 | 79.26 | 8.73 |
| 12 | 12 | 2 | 144.07 | 154.27 | 10.20 | 7 | 2 | 98.55 | 126.83 | 28.28 | 4 | 1 | 158.59 | 166.61 | 8.02 | 11 | 2 | 79.26 | 89.22 | 9.96 |
Compared with FIFS, SJF, and NNF, LSOM decreases total lifting time by 65.05, 37.61, and 77.39 min, respectively, which corresponds to respective decrease rates of 42.17%, 29.65%, and 46.45%.
Crane utilization in FIFS, SJF, NNF, and LSOM is listed in Table 5. It signifies the ratio of each crane’s lifting time, excluding delay time, to total lifting time and indicates that the greater the crane utilization, the greater the crane’s space utilization. In FIFS, utilization of Cranes 1 and 2 is 57.09% and 61.25%, respectively. In SJF, utilization of Cranes 1 and 2 is 69.33% and 74.12%, respectively. In NNF, utilization of Cranes 1 and 2 is 52.47% and 53.70%, respectively. In LSOM, utilization of Cranes 1 and 2 is 98.71% and 100.00%, respectively. Compared with FIFS, SJF, and NNF, LSOM increases utilization of Cranes 1 and 2 by 41.62%, 38.75%, 29.38%, 25.88%, 46.24%, and 46.30%, respectively, which corresponds to increase rates of 72.90%, 63.27%, 42.38%, 34.92%, 88.13%, and 86.22%.
| Crane | Utilization (%) | |||
|---|---|---|---|---|
| FIFS | SJF | NNF | LSOM | |
| 1 | 57.09 | 69.33 | 52.47 | 98.71 |
| 2 | 61.25 | 74.12 | 53.70 | 100.00 |
Discussion
The proposed LSOM with dynamic programming based on motion characteristics of luffing tower cranes has demonstrated its effectiveness in an example of 12 lifting tasks and two cranes. The example involves only lifting sequence optimization, which is the research boundary of this study. LSOM can be integrated in planning, such as layout optimization, as well.
The luffing mode of luffing tower cranes makes the hoist motion of the hook dependent on the luffing motion of the boom, and the hoist motion distance of the hook depends not only on the height difference between the lifting start and end points but also on the vertical motion distance of the boom. In construction projects, lifting task start and end points typically differ in horizontal distance and height. This is particularly evident in large-scale and high-rise construction projects, enhancing the impact of the hoist motion of the hook on total lifting time. Thus, the connection between hoist motion distance and boom luffing motion has been taken into account in the proposed formulation.
Estimation of hoist motion distance of the hook is classified in two ways: one way is based on the respective horizontal distance between the crane and the lifting start point and between the crane and the lifting end point; the other way is based on the height difference between the lifting start and end points and the boom vertical motion distance. This classification can estimate the hoist motion distance of the hook more effectively and reduces the risk of overestimating and underestimating the actual situation.
For construction sites with limited space, lifting delay caused by avoiding space conflicts among luffing tower cranes is common and often has a great impact on total lifting time. The horizontal motion path of the boom created by the relative locations of the crane and the lifting start and end points can result in delays, so it is essential to evaluate the impact of delays accurately. In the proposed formulation, the boom’s horizontal motion path is divided into three stages: lifting start point, motion path, and lifting end point. The intersection of these stages determines the relative locations of two lifting tasks, which have been classified as four situations consisting of 16 cases. According to the distinction between loaded and no-load lifting, the specific lifting delays for 16 cases have been detailed and quantified to refine estimation of lifting delay time and make them more reliable.
In construction projects with loose time, conventional lifting strategies such as FIFS, SJF, and NNF provide adequate lifting-sequence solutions. However, in projects with limited time, these strategies are not guaranteed. Therefore, dynamic programming has been used here to achieve the global optimum of multistage decision-making in lifting sequence optimization. By analyzing the lifting sequence characteristics of luffing tower cranes, the lifting process is divided into stages according to lifting sequence, and a lifting task and a crane are determined at each stage in terms of minimum total lifting time.
The example results have shown that LSOM is significantly better than FIFS, SJF, and NNF in reducing total lifting time and improving crane utilization. Although its computation takes more time when compared with the other strategies in the example, this problem can be effectively solved using compiled languages, such as C++, and parallel computing. The pros and cons of each strategy could be weighed to select the most suitable one when specific total lifting time, crane utilization, and computation time are required.
The proposed formulation for loaded and no-load lifting time is based on ideal environmental conditions. In practice, bad weather and complex site characteristics may result in increased lifting difficulty and longer lifting time. The method of multiplying lifting time by numerical parameters to account for impact factors may be useful. The determination of impact factors, although beyond the scope of this study, can be made according to data from similar construction projects.
The proposed formulation for lifting delay time is presented in the basic form of two lifting tasks. In practice, however, no matter how many lifting tasks there are, a space conflict always results from the intersection of two luffing tower cranes. Thus, when there are multiple potential space conflicts among more than two lifting tasks, the situation can be dealt with according to the basic form of two lifting tasks. However, when a lifting task faces more than one space conflict, estimation of lifting delay time becomes more complex, and extensions need to be investigated.
Conclusion
Considering the importance of the lifting sequence of luffing tower cranes in construction projects, a lifting sequence optimization model based on motion paths has been proposed to minimize total lifting time. The model consists of loaded lifting time, no-load lifting time, and lifting delay time, integrating these parameters into dynamic programming. Specifically, it (1) quantitatively evaluates the influence of the boom’s luffing motion on the hoist motion distance of the hook; (2) refines the solution to various lifting delays resulting from the boom’s horizontal motion path based on different relative locations of the crane and the lifting start and end points; and (3) integrates the lifting sequence optimization problem and dynamic programming. The effectiveness of LSOM is evaluated by comparing it with FIFS, SJF, and NNF. Total lifting time using LSOM decreases by 65.05, 37.61, and 77.39 min, respectively, which corresponds to decrease rates of 42.17%, 29.65%, and 46.45%. Utilization of Cranes 1 and 2 in the example increases by 41.62%, 38.75%, 29.38%, 25.88%, 46.24%, and 46.30%, respectively, which corresponds to increase rates of 72.90%, 63.27%, 42.38%, 34.92%, 88.13%, and 86.22%. The results show that LSOM effectively decreases total lifting time and increases crane utilization.
In some cases, lifting tasks have fixed lifting sequences or special time limits, which affects the motion path of luffing tower cranes, so corresponding constraints should be added to lifting sequence optimization. For example, the shoring system needs to be lifted before the structural steel is lifted, and concrete needs to be lifted within a specific period of time. The proposed model has to be adjusted when considering such conditions. This issue will be addressed in future work.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Abdelmegid, M. A., K. M. Shawki, and H. Abdel-Khalek. 2015. “GA optimization model for solving tower crane location problem in construction sites.” Alexandria Eng. J. 54 (3): 519–526. https://doi.org/10.1016/j.aej.2015.05.011.
Al Hattab, M., E. Zankoul, and F. R. Hamzeh. 2017. “Near-real-time optimization of overlapping tower crane operations: A model case study.” J. Comput. Civ. Eng. 31 (4): 05017001. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000666.
Al Hattab, M., M. Zankoul, M. Barakat, and F. Hamzeh. 2018. “Crane overlap and operational flexibility: Balancing utilization, duration, and safety.” Constr. Innovation 18 (1): 43–63. https://doi.org/10.1108/CI-11-2016-0062.
Al-Hussein, M., M. A. Niaz, H. Yu, and H. Kim. 2006. “Integrating 3D visualization simulation for tower crane operations on construction sites.” Autom. Constr. 15 (5): 554–562. https://doi.org/10.1016/j.autcon.2005.07.007.
Bellman, R. 1957. Dynamic programming. Princeton, NJ: Princeton University Press.
Bürgy, R., A. Hertz, and P. Baptiste. 2020. “An exact dynamic programming algorithm for the precedence-constrained class sequencing problem.” Comput. Oper. Res. 124 (Dec): 105063. https://doi.org/10.1016/j.cor.2020.105063.
de Matos, V. L., A. B. Philpott, and E. C. Finardi. 2015. “Improving the performance of stochastic dual dynamic programming.” J. Comput. Appl. Math. 290 (Dec): 196–208. https://doi.org/10.1016/j.cam.2015.04.048.
Grevtsov, N. M., S. A. Kumakshev, and A. M. Shmatkov. 2017. “Optimization of the flight trajectory of a non-manoeuvrable aircraft to minimize fuel consumption by the dynamic programming method.” J. Appl. Math. Mech. 81 (5): 368–374. https://doi.org/10.1016/j.jappmathmech.2018.03.004.
Huang, C., and C. K. Wong. 2018. “Optimization of crane setup location and servicing schedule for urgent material requests with non-homogeneous and non-fixed material supply.” Autom. Constr. 89 (May): 183–198. https://doi.org/10.1016/j.autcon.2018.01.015.
Huang, C., C. K. Wong, and C. M. Tam. 2011. “Optimization of tower crane and material supply locations in a high-rise building site by mixed-integer linear programming.” Autom. Constr. 20 (5): 571–580. https://doi.org/10.1016/j.autcon.2010.11.023.
Hwang, S. 2012. “Ultra-wide band technology experiments for real-time prevention of tower crane collisions.” Autom. Constr. 22 (Mar): 545–553. https://doi.org/10.1016/j.autcon.2011.11.015.
Ibrahim, A., O. El-Anwar, and M. Marzouk. 2018. “Socioeconomic impact assessment of highly dense-urban construction projects.” Autom. Constr. 92 (Aug): 230–241. https://doi.org/10.1016/j.autcon.2018.04.001.
Irizarry, J., and E. P. Karan. 2012. “Optimizing location of tower cranes on construction sites through GIS and BIM integration.” J. Inf. Technol. Constr. 17 (23): 351–366.
Ji, Y., and F. Leite. 2018. “Automated tower crane planning: Leveraging 4-dimensional BIM rule-based checking.” Autom. Constr. 93 (Sep): 78–90. https://doi.org/10.1016/j.autcon.2018.05.003.
Konak, A., M. R. Bartolacci, and B. Gavish. 2011. “A dynamic programming approach for batch sizing in a multi-stage production process with random yields.” Appl. Math. Comput. 218 (4): 1399–1406. https://doi.org/10.1016/j.amc.2011.06.022.
Lazarev, A. A., and F. Werner. 2009. “A graphical realization of the dynamic programming method for solving NP-hard combinatorial problems.” Comput. Math. Appl. 58 (4): 619–631. https://doi.org/10.1016/j.camwa.2009.06.008.
Lee, D., H. Lim, H. Cho, and K.-I. Kang. 2015. “Optimization of luffing-tower crane location in tall building construction.” KICEM J. Constr. Eng. Project Manage. 5 (4): 7–11. https://doi.org/10.6106/JCEPM.2015.5.4.007.
Leung, A. W. T., and C. M. Tam. 1999. “Prediction of hoisting time for tower cranes for public housing construction in Hong Kong.” Constr. Manage. Econ. 17 (3): 305–314. https://doi.org/10.1080/014461999371510.
Leung, A. W. T., C. M. Tam, and D. K. Liu. 2001. “Comparative study of artificial neural networks and multiple regression analysis for predicting hoisting times of tower cranes.” Build. Environ. 36 (4): 457–467. https://doi.org/10.1016/S0360-1323(00)00029-9.
Li, B., B. Cai, H. Liu, F. Wang, and J. Zhang. 2012. “Research on anti-backward-tipping device of luffing jib tower crane.” In Vol. 229–231 of Proc., Applied Mechanics and Materials, 521–525. Bäch, Switzerland: Trans Tech Publications. https://doi.org/10.4028/www.scientific.net/AMM.229-231.521.
Lien, L.-C., and M.-Y. Cheng. 2014. “Particle bee algorithm for tower crane layout with material quantity supply and demand optimization.” Autom. Constr. 45 (Sep): 25–32. https://doi.org/10.1016/j.autcon.2014.05.002.
Marzouk, M., and A. Abubakr. 2016. “Decision support for tower crane selection with building information models and genetic algorithms.” Autom. Constr. 61 (Jan): 1–15. https://doi.org/10.1016/j.autcon.2015.09.008.
Monghasemi, S., M. R. Nikoo, and J. Adamowski. 2016. “Sequential ordering of crane service requests considering the pending times of the requests: An approach based on game theory and optimization techniques.” Autom. Constr. 70 (Oct): 62–76. https://doi.org/10.1016/j.autcon.2016.06.006.
Moussavi Nadoushani, Z. S., A. W. A. Hammad, and A. Akbarnezhad. 2017. “Location optimization of tower crane and allocation of material supply points in a construction site considering operating and rental costs.” J. Constr. Eng. Manage. 143 (1): 04016089. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001215.
Rodriguez-Ramos, W. E., and R. L. Francis. 1983. “Single crane location optimization.” J. Constr. Eng. Manage. 109 (4): 387–397. https://doi.org/10.1061/(ASCE)0733-9364(1983)109:4(387).
Shapira, A., and M. Simcha. 2009. “Measurement and risk scales of crane-related safety factors on construction sites.” J. Constr. Eng. Manage. 135 (10): 979–989. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000066.
Tam, C. M., A. W. T. Leung, and D. K. Liu. 2002. “Nonlinear models for predicting hoisting times of tower cranes.” J. Comput. Civ. Eng. 16 (1): 76–81. https://doi.org/10.1061/(ASCE)0887-3801(2002)16:1(76).
Tam, C. M., and K. L. T. Tong. 2003. “GA-ANN model for optimizing the locations of tower crane and supply points for high-rise public housing construction.” Constr. Manage. Econ. 21 (3): 257–266. https://doi.org/10.1080/0144619032000049665.
Tam, C. M., K. L. T. Tong, and W. K. W. Chan. 2001. “Genetic algorithm for optimizing supply locations around tower crane.” J. Constr. Eng. Manage. 127 (4): 315–321. https://doi.org/10.1061/(ASCE)0733-9364(2001)127:4(315).
Wang, J., X. Zhang, W. Shou, X. Wang, B. Xu, M. J. Kim, and P. Wu. 2015. “A BIM-based approach for automated tower crane layout planning.” Autom. Constr. 59 (Nov): 168–178. https://doi.org/10.1016/j.autcon.2015.05.006.
Warszawski, A. 1973. “Analysis of transportation methods in construction.” J. Constr. Div. 99 (1): 191–202. https://doi.org/10.1061/JCCEAZ.0000373.
Wu, K., and B. García de Soto. 2020. “Spatiotemporal modeling of lifting task scheduling for tower cranes with a tabu search and 4D simulation.” Front. Built Environ. 6: 79. https://doi.org/10.3389/fbuil.2020.00079.
Wu, K., B. García de Soto, and F. Zhang. 2020. “Spatio-temporal planning for tower cranes in construction projects with simulated annealing.” Autom. Constr. 111 (Mar): 103060. https://doi.org/10.1016/j.autcon.2019.103060.
Younes, A., and M. Marzouk. 2018. “Tower cranes layout planning using agent-based simulation considering activity conflicts.” Autom. Constr. 93 (Sep): 348–360. https://doi.org/10.1016/j.autcon.2018.05.030.
Zavichi, A., K. Madani, P. Xanthopoulos, and A. A. Oloufa. 2014. “Enhanced crane operations in construction using service request optimization.” Autom. Constr. 47 (Nov): 69–77. https://doi.org/10.1016/j.autcon.2014.07.011.
Zhang, P., F. C. Harris, and P. O. Olomolaiye. 1996. “A computer-based model for optimizing the location of a single tower crane.” Build. Res. Inf. 24 (2): 113–123. https://doi.org/10.1080/09613219608727511.
Zhang, P., F. C. Harris, P. O. Olomolaiye, and G. D. Holt. 1999. “Location optimization for a group of tower cranes.” J. Constr. Eng. Manage. 125 (2): 115–122. https://doi.org/10.1061/(ASCE)0733-9364(1999)125:2(115).
Information & Authors
Information
Published In
Journal of Construction Engineering and Management
Volume 147 • Issue 10 • October 2021
Copyright
This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.
History
Received: Dec 9, 2020
Accepted: Apr 6, 2021
Published online: Aug 4, 2021
Published in print: Oct 1, 2021
Discussion open until: Jan 4, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Mun On Wong, Zhiqian Zhang, Wei Pan, Multiuser Virtual Reality-Enabled Collaborative Heavy Lift Planning in Construction, Journal of Construction Engineering and Management, 10.1061/JCEMD4.COENG-14102, 150, 4, (2024).