International Construction Specialty Conference of the Canadian Society for Civil Engineering (ICSC) (5th : 2015)

Scheduling optimization of linear projects considering spatio-temporal constraints Esfahan, Nazila Roofigari; Razavi, Saiedeh Jun 30, 2015

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
52660-Esfahan_N_et_al_ICSC15_107_Scheduling _Optimization.pdf [ 1.1MB ]
Metadata
JSON: 52660-1.0076314.json
JSON-LD: 52660-1.0076314-ld.json
RDF/XML (Pretty): 52660-1.0076314-rdf.xml
RDF/JSON: 52660-1.0076314-rdf.json
Turtle: 52660-1.0076314-turtle.txt
N-Triples: 52660-1.0076314-rdf-ntriples.txt
Original Record: 52660-1.0076314-source.json
Full Text
52660-1.0076314-fulltext.txt
Citation
52660-1.0076314.ris

Full Text

5th International/11th Construction Specialty Conference 5e International/11e Conférence spécialisée sur la construction    Vancouver, British Columbia June 8 to June 10, 2015 / 8 juin au 10 juin 2015   SCHEDULING OPTIMIZATION OF LINEAR PROJECTS CONSIDERING SPATIO-TEMPORAL CONSTRAINTS Nazila Roofigari Esfahan1,3, Saiedeh Razavi2 1 PhD Candidate, Dept. Of Civil Engineering, McMaster University, 1280, Main West, Hamilton, Canada. 2 Assistant Professor, Dept. Of Civil Engineering, McMaster University, 1280, Main West, Hamilton, Canada 3 roofign@mcmaster.ca Abstract: Overall schedule optimization, considering all temporal, spatial and precedence constraints is a difficult task due to the complexity which is inherent in construction projects. The difficulties associated with modeling all aspects combined become more considerable when optimizing linear type of projects with high activities’ inter-relations. The progress of these projects highly depends on the productivity achieved from their resources which is directly dependent upon the space and time available to these resources. As a result, in order to practically optimize linear schedules, not only their achieved productivities need to be managed well, but also the spatio-temporal flexibilities and constraints are to be integrated into the optimization process.  This paper aims to fill the gap in the current literature by proposing a practical approach for modeling and optimization of linear schedules while taking into account all the project-dependent constraints. For this purpose, the methodology is built on the new concept of Space-Time float for explicit consideration of spatio-temporal constraints of activities. The developed method uses constraint-satisfaction optimization approach to minimize duration of the generated schedules. As such, by having Space-Time floats for different activities’ resources and using such constraints, the schedule is optimized to get the minimum achievable duration for the total project. A numerical example is analyzed to present the proposed and developed method as well as its added benefits. Key words: Schedule optimization; Spatio-temporal constraints; Constraint programming; Linear projects; Space-time float. 1 INTRODUCTION Having accurate and up-to-date information of each activity and its respective resources has a large impact on effective project scheduling and control of linear construction projects (Roofigari Esfahan and Razavi, 2013, Roofigari Esfahan and Razavi, 2012, Andersson et al., 2007, Roofigari Esfahan et al., 2014). This is due to the fact that, in this class of projects, construction crews are often required to repeat the same work in various locations and therefore, move from one location to another. As a result, the spatio-temporal constraints of such movements need to be considered when scheduling each and any of the linear activities.  As such, the schedule developed for these projects should first be enhanced taking into account all the logical precedence constraints of activities as well as spatio-temporal constraints on movement of resources (Hegazy, 2005, Moselhi and Hassanein, 2003, Polat et al., 2009, Yang and Chi-Yi, 2005, Song et al., 2009).  107-1 The current scheduling methods for linear projects do not consider spatio-temporal constraints for movement of activities’ resources and the flexibility in their movement to enhance and improve the schedules. This subsequently causes them to overlook other possible whole range of productivity rates that can be achieved without delaying activities.  The limitations stated can be tackled by the new concept of Space-Time float prisms to generate and optimize schedules of linear projects. The scheduling framework presented here integrates location of construction resources through an innovative modification of Linear Scheduling Method LSM by adding the spatio-temporal constraints to the traditional LSM productivity. Using such constraints, the schedule is then optimized to get the minimum achievable duration for the total project. The optimization phase of the proposed method takes a constraint-satisfaction approach to find the optimum productivity rates for activities that will lead to minimum achievable duration for the project. To achieve this goal, the objective of the optimization process is set as duration minimization, and the decision variables include the start date and productivity rates of linear activities. All the project precedence, and spatio-temporal constraints identified through using Space-Time float prisms are then used to limit the search space into practical solutions. The output of the optimization phase, i.e. the optimum schedule for the project and the optimum productivity rates of activities, are then used to visualize and track the progress of the project schedule.  The remaining of the paper is organized as follows: first, an overview of the current state of scheduling linear projects is presented. Subsequently, the new concept of Space-Time float prisms previously published by the authors (Roofigari Esfahan et al., 2014) is briefly introduced and the modification to traditional linear scheduling method using Space-Time float prisms is then described. In the next step, the optimization framework used to optimize the duration of the generated schedule is presented followed by the details of tracking and control of such schedules. Finally a numerical example is analyzed using the proposed framework to present the method as well as its added benefits. 2 BACKGROUND Due consideration to space and time constraints and requirements should be given when it comes to scheduling linear construction projects. This is because the dynamic resources on sites of linear projects are more likely to interact with each other in a complex spatial-temporal manner. Current  available  network  techniques  and  linear  scheduling  methods  mainly  consider  technological  constraints  and  resource  requirements in  generating schedules  for repetitive and linear works. Such techniques and methods overlook the requirements  of  activities  for  the requisite work  space   for  material  storage  and movement  of manpower  and equipment. The literature on scheduling and planning linear projects is rich. A number of methods including Linear Scheduling Method (LSM), Repetitive Scheduling Method (RSM), and Line of Balance (LOB) are presented in the literature to plan, schedule and control linear projects; e.g.  ((O'Brien, 1975, Stradal and Cacha, 1982, Harmelink, 2001, Harmelink and Rowings, 1998, Harris and Ioannou, 1998, Johnston, 1981, Cosma, 2003).  Much research also has been performed to predict the production rate of linear projects based on simulation, probability, or regression analysis (e.g.(Duffy et al., 2011, Watkins et al., 2009, O'Connor and Huh, 2005, Woldesenbet et al., 2012, Jiang and Wu, 2007, Kuo, 2004).  The methods presented in the literature to optimize schedules of linear project can be divided into four main categories: 1) the methods whose purpose is to minimize resource fluctuation of these projects (e.g. (Georgy, 2008, Mattila and Abraham, 1998, Tang et al., 2014a, Tang et al., 2014b, Shu-Shun and Chang-Jung, 2007);  2) methods that tend to minimize resource idle times (Vanhoucke, 2006, Gonzalez et al., 2013); 3) Methods that optimize project schedule considering minimization of project cost as objective (e.g. (Handa and Barcia, 1986, Senouci and Eldin, 1996, Hegazy and Wassef, 2001, Moselhi and Hassanein, 2003, Ezeldin and Soliman, 2009, Ipsilandis, 2007, Menesi et al., 2013); and 4) the methods which reduce the duration of the linear projects (Russell and Caselton, 1988, Fan and Lin, 2007, Bakry et al., 2013, Bakry et al., 2014, Cho et al., 2013). 107-2 3.1 Scheduling Module: Scheduling Linear Projects using Space-Time Float Prisms The Linear Scheduling Method (LSM) is used to schedule linear projects in this study. For this purpose, the Space-Time float is considered in this study to take into account the movement constraints of the resources in scheduling linear activities. Space-Time float is an envelope for all possible movement patterns that an activity or its associated resources can take considering the time and space constraints of that activity (Roofigari-Esfahan et al., 2014). Movement of resources can be classified as actual and potential. Actual movement is represented by a space-time path, that is, the set of space-time coordinates where a resource entity is actually taken. Potential movement is represented by a Space-Time float prism, which consists of the set of space-time coordinates representing the activity-related constraints. Each spatially dispersed activity has association with spatial anchors, i.e. pre-determined locations at which an activity must take place. Such activities are not only associated with a duration, but also with locations, showing where they start and/or finish. These activities’ start and end locations are assumed as the anchor points of Space-Time float prisms (see Figure 2).  Figure 2: Realization of a) 2D and b) 3D Space-Time Float Prism Traditionally, productivity has been defined as the ratio of input/output, e.g. the ratio of the input of an associated resource (usually, but not necessarily, expressed in person per hours (p-hrs)) to its real output (in creating economic value). To restate this definition for use in the construction industry it can be said that labor productivity is the physical progress achieved per p-hrs(Dozzi & AbouRizk, 1993).  Converting this definition to Space-Time float and path, the slope of the space-time paths in each time interval can be used as an indicator of crew productivity within that interval. Vertical paths accordingly demonstrate idle times in an activity when no productive work is actually executed. The optimum path can also be identified. This is the path for which the slopes of the line at each time interval are equal to the planned productivity for that activity at the corresponding time interval (see Figure 2(a)) In order to draw respective Space-Time float prisms for all possible productivity rates for each activity, prism boundaries are also needed in addition to its anchor points. These boundaries in the construction concept can be considered as maximum and minimum allowable productivity rates for resources. As can be seen in Figure 2(b), the minimum productivity rate can be zero, meaning that the activity can be stopped for some time. This, as known, is consistent with the definition of activity floats in construction scheduling. Subsequently, based on the maximum and minimum acceptable productivity rates for activities, the respective Space-Time float prism is constructed. The prism is an envelope which comprises all the possible productivity rates for an activity at each time interval (see Figure 2(b)).  Further, scheduling the project through the generation of a Space-Time float for each activity also provides a better understanding and realization of Space-Time flexibilities that are available for each activity. Identifying spatial conflicts between activities and their respective resources in construction sites provides a potential to minimize delays caused by such conflicts. Because deviation from planned production rates 107-4 in linear projects’ activities may result in spatial conflicts between their respective resources, the generation of Space-Time Float prisms is important to help detect such conflicts. Through the use of Space-Time float, the schedule can adapt to variable production rates at each time interval and subsequently the system can potentially identify and forecast potential space-time conflicts (i.e. congestion). It should be noted that identification, quantification, and optimization of space-time conflicts are not within the scope of this paper. After scheduling the linear activities and visualizing this initial-non optimum schedule using Space-Time Float prisms, the method proceeds to the next module to optimize the generated schedule. The optimization method presented in this paper aims at generating optimized schedules for linear schedules, taking into account all logical and spatio-temporal constraints of linear activities as described in the next section. 3.2 Schedule Optimization Module using  Constraint-based integer programming The optimization phase of the proposed scheduling and control model is a Constraint Satisfaction -based integer optimization model. This module can automatically establish linear schedules with minimum achievable schedule duration. Optimal or near-optimal schedules can be obtained in a relatively short period of time using Constraint Programming (CP) techniques. It should be noted that Constraint Satisfaction Problems are defined by a set of variables, X1;X2; … ;Xn, and a set of constraints, C1;C2; … ;Cm. Each variable Xi has a non-empty domain Di of possible values. Each constraint Ci involves some subset of the variables and specifies the allowable combinations of values for that subset. A state of the problem is defined by an assignment of values to some or all of the variables. An assignment that does not violate any constraints is called a consistent assignment. A complete assignment is one in which every variable is mentioned, and a solution to a CSP is a complete assignment that satisfies all the constraints.  Constraint programming  is a programming paradigm being used for solving Constraint Satisfaction Problems (CSPs) through using a combination of mathematics, artificial intelligence, and operations research techniques (Chan and Hu 2002; Liu and Wang 2012; Tang et al. 2014b). It has been successfully used to solve complex combinatorial problems in a wide variety of domains. Its Selection of appropriate variables and values through heuristics reduces the required computational effort and improves the search ability (Liu and Wang 2007; Russell and Norvig 2009). Apart from being an effective tool  in solving a variety of problems, CP has particular advantages in solving scheduling problems  (Menesi et al. 2013;Chan and Hu 2002; Heipcke 1999) due to: (1) its efficient solution search mechanism, (2) flexibility to consider a variety of constraint types, and (3) convenience of model formulation. In other words, the highly constrained problems associated with project scheduling can be best modeled and optimized using  CP because of its flexibility in description of constraints as well as its capacity to naturally incorporate constraints into the problem description (Chan and Hu 2002) and in processing complex and special constraints (Tang et al., 2014a). When solving an optimization problem in CP, the objective function in the problem is treated as a constraint and this additional constraint forces the new feasible schedule to have a better objective value than the current schedule. The upper or lower bounds of the constraint are replaced as soon as a better objective function value is found. The propagation mechanism narrows the domains of decision variables to reduce the size of the search space while recording the current best schedule. The search terminates when no more feasible schedule is found and the last feasible schedule is the optimal schedule (Pinedo 2008; Liu and Wang 2008). For the proposed model in this study, the objective and variables were determined in the problem specification stage. In the research reported in this paper, the objective was considered as duration minimization, and the decision variables include the start date and productivity rates of linear activities. To facilitate the use of CP algorithms in scheduling problems, a powerful optimization package, termed ILOG CPLEX Optimization Studio (Beck et al. 2011), was developed incorporating a CP optimizer engine that offers features specially for solving scheduling problems. ILOG CPLEX Optimization Studio was used and the ILOG OPL language was adopted as the model formulation language. 107-5 To optimize the schedule with the objective of minimizing duration for the initial schedule, spatial and temporal availabilities to each activity are considered as constraints applied in the optimization process. To do so, all the productivity rates in the feasible productivity interval for each activity (i.e. within prism boundaries) are translated into integer feasible durations for that activity. The search engine then explore these options and finds the productivity rate for each activity that optimizes the overall project duration.  The following variables, constraints, and objectives were adopted in the construction of the CSP-based model: Constants: SLi   Start location of activity i; ELi   End location of activity i; Pmini   Minimum productivity rate of activity i; Pmaxi   Maximum productivity rate of activity i; Bi,j   Required time buffer between activity i and activity j; D   Project deadline Decision variables: OptProi   Optimum resource production rate of activity i; OptProi ∈ [Pmini, Pmaxi] STi    Start time of activity i; STi ∈ [0 , D] Decision expressions: ETi   End time of activity i; ETi=STi + (ELi-SLi)/ OptProi Constraints: The precedence relationships between activities are considered as the main constraints applied to the optimization model. In this study, all kinds of precedence relations are taken into account, namely: Finish to Start (FT), Start to Finish (SF), Finish to Finish (FF) and Start to Start (SS). The required time buffers between activities are also considered when considering the precedence relationships between succeeding activities.  There are also fixed constraints applied to the model. These fixed constraints are as follows: STi ≥ 0 ETi ≤ D ET(la(last activity)) ≤ D ET(fa(first activity)) = 0 ( or the start time assigned to the project) The output of this Module is the best option of each activity i.e. optimum productivity rates for each activity which will minimize the project duration. These rates along with maximum and minimum productivity rates of each activity are then used to visualize the generated optimum schedule. 4 CASE STUDY The method presented here was applied to a case study previously presented in the literature (Mattila and Abraham, 1998, Tang et al., 2014a). The minimum and maximum productivities are calculated from the minimum and maximum resources available in the original example. In the real-world examples also project management teams are requested to enter general information about the project and respective activities.  The project network consists of 9 activities. The project included widening of a segment of U.S. Route 41, located in northern Michigan. Major activities consist of removal of existing concrete paving, ditch excavation, embankment, sub-base, gravel, and bituminous paving. This highway construction project was used for verifying the scheduling and optimization capabilities of the proposed model. The 107-6 finish date presented in the literature for this example is 38 days. The description of each activity as well as inputs and outputs of the optimization process are included in Table 1.  As it is shown in Table 1, the input data of the optimization process include Activity IDs, their start and end location, successors, and their minimum and maximum achievable productivity rates. It should be noted that these boundaries were calculated using minimum and maximum available resources used. The optimization engine used this information to search for the minimum duration for the project considering all logical and spatio-temporal (productivity) constraints for each activity. As shown in that Table, the project deadline, and project start day are other constraints inputted to the optimization process. If some activities are required to start or finish at a certain day, this information will also be included as constraints. The output of this process includes optimum productivity rate and the duration associated with this productivity rate, as well as start and end times of all the activities, considering precedence relationships. The optimum duration for each activity is also calculated from the optimum productivities attained in the optimization process. It should be noted that in case of non-repetitive activities, the start time is calculated based on the precedence relationships with their predecessors and successors.  Table 1: Input data to the optimization process NbTasks 9  Deadline 38  Input Task Name Task succsId SL EL Pmin Pmax Ditch excavation 1 2,3 0 50 3.3 10 Culvert installation 2  0 50 1 5 Concrete pavement removal 3 4,5 0 50 1.67 5.83 Peat excavation and swamp backfill 4 5 30 50 8 12 Embankment 5 6 0 50 2.5 8.75 Utility work 6 7 30 50 10 15 Sub-base 7 8 0 50 2.56 6.41 Gravel 8 9 0 50 5 12.5 Paving 9  0 50 8.33 20.83 The optimum duration for the project was calculated to be 36 days in the optimization module which is 2 days shorter than the other methods (Mattila and Abraham, 1998, Tang et al., 2014a) (see Table 3). The optimum productivity rates achieved in the optimization process, which creates the duration of 36 days, are listed in Table 2 for all activities.It should be noted that because integer approach has been used, the conversion errors persist to exist, causing some values to be located near the assigned interval. Table 2 also shows the comparison of the activity durations and optimum productivities of the initial schedule with the optimized schedule obtained through the optimization process. Table 3 shows the durations achieved previously for this example versus the results of this study. By considering the whole range of possible productivity rates of each activity, the current method is able to relax some activities, causing less required resources per day. This consequently reduces the potential congestion in the job site while still not passing the project deadline. It should be noted that in relaxing of activities, daily fluctuation of the resource usage is also taken into account. Furthermore, generating schedules with due consideration of the Space-Time floats for each activity instead of only the optimum path helps in better management and control of these projects. This simple example demonstrates the ability of the proposed method to derive alternative plans in order to meet project deadlines. The optimized generated schedule demonstrates that by considering flexibility of movement in addition to all activity constraints, the best duration for the project can be achieved that can be shorter than the estimated duration. Summary and concluding remarks 107-7 This study proposed a scheduling and control system for linear projects. The proposed method aims to address the limitation of the current scheduling and control methods for linear projects by taking into consideration the spatio-temporal as well as logical constraints of linear activities. For this purpose, the new concept of Space-Time float and constraint satisfaction problem approach were incorporated.  As such, by having Space-Time floats for different activities’ resources and using such constraints, the schedule is optimized to get the minimum achievable duration for the total project.  Furthermore, knowing the exact or near exact location of required resources for each activity (or set of activities) and visually integrating such information with the project schedule and space-time constraints, leads not only to an optimized and more practical, updated, and executable schedules, but also to more efficient project control. Consequently, management decisions and corrective actions can be made to prevent/treat the identified issues. Table 2: Output of the optimization Output Start End Duration OptPro 0 12 12 4.17 0 4 4 2.00 3 24 21 2.38 5 7 2 6.00 7 26 19 2.63 26 28 2 10.00 12 32 20 2.50 24 34 10 5.00 30 36 6 8.33 Table 3: Comparison of the results Method Study by Mattila and Abraham (1998) Study by Georgy (2008) Study by Tang et al. (2014) Current study Total duration (days) 38 38 38 36 To demonstrate the use of the proposed method and to illustrate its capabilities, a numerical example was analyzed. This example shows the benefits of considering space-time flexibilities and constraints when optimizing schedules of linear projects. As the results of the numerical example illustrates, the optimized schedule saves 2 days in overall duration of the project. Also, despite other methods whose objective is to minimize the daily fluctuation in resource usage  linear projects, considering number of resources as variable, here the productivity rate are considered which is a more meaningful factor showing progress of activities over time. Furthermore, the spatio-temporal constraints considered in the optimization process not only facilitate the search for the optimum solution by narrowing down the search space but also leads to having more practical schedules this way, the scheduling optimization method presented in this paper provides an efficient tool for scheduling of linear projects. The method can help the manager teams of liner projects to plan their activities in the most efficient way, while also decrease delays to their minimum, and accordingly prevent cost overruns 5 SUMMARY AND CONCLUDING REMARKS This study proposed a scheduling and control system for linear projects. The proposed method aims to address  the  limitation  of  the  current  scheduling  and  control  methods  for  linear  projects  by  taking  into consideration the spatio-temporal as well as logical constraints of linear activities. For this purpose, the new concept of Space-Time float and constraint satisfaction problem approach was used. As such, by 107-8 having  Space-Time  floats for  different  activities’  resources and  using  such  constraints,  the  schedule  is optimized to get the minimum achievable duration for the total project.  Furthermore, knowing the exact or near exact location of required resources for each activity (or set of activities) and visually integrating such information with the project schedule and space-time constraints, leads not only to optimized and more  practical,  updated,  and  executable  schedules,  but  also  to  more  efficient  project  control.  Consequently, management decisions and corrective actions can be made to prevent/treat the identified issues. To demonstrate the use of the proposed method and to illustrate its capabilities, a numerical example has been analyzed.  This example shows the benefits  of considering  space-time  flexibilities  and  constraints when  optimizing  schedules  of  linear  projects. By bringing all the necessary elements of a successful control system, i.e. timely schedule, tacking all the spatio-temporal and  logical  constraints  of  activities  in  the  optimization  phase, the method provides an efficient tool in scheduling and control of linear projects. Such a control system can also decrease delays to their minimum, and accordingly prevent cost overruns. References Andersson, N., Christensen, K.. 2007. Practical Implications Of Location-based Scheduling. CME25:Construction Management and Economics: past, present and future. Taylor and Francis Group. Bakry, I., Moselhi, O. & Zayed, T. Fuzzy Dynamic Programming for Optimized Scheduling of Repetitive Construction Projects. 2013 Piscataway, NJ, USA. IEEE, 1172-6. Bakry, I., Moselhi, O. & Zayed, T. 2014. Optimized acceleration of repetitive construction projects. Automation in Construction, 39, 145-151. Beck, J.C. , Feng, T.K. and Watson, J. 2011. Combining constraint programming and local search for job-shop scheduling, INFORMS J. Comput., 23(1), 1–14, 2011.  Cho, K., Hong, T. & Hyun, C. T. 2013. Space Zoning Concept-based Scheduling Model for Repetitive Construction Process. Journal of Civil Engineering and Management, 19, 409-421. Cosma, C. 2003. Development of a systematic approach for uncertainty assessment in scheduling multiple repetitive construction processes by using fuzzy set theory. PhD, Univ. of Florida, Gainesville, FL. Duffy, G., Oberlender, G. & Seok J.D. 2011. Linear Scheduling Model with Varying Production Rates. Journal of Construction Engineering and Management, 137, 574-582. Ergen, E. & Akinci, B. An overview of approaches for utilizing RFID in construction industry.  1st Annual RFID Eurasia Eurasia Conference, 2007, 5-6 Sept. 2007, 2007 Piscataway, NJ, USA. IEEE, 7-11. Ezeldin, A. & Soliman, A. 2009. Hybrid Time-Cost Optimization of Nonserial Repetitive Construction Projects. Journal of Construction Engineering and Management, 135, 42-55. Fan, S. & Lin, Y. 2007. Time-Cost Trade-Off in Repetitive Projects with Soft Logic. Computing in Civil Engineering (2007). Geogry, M. E. 2008. Evolutionary resource scheduler for linear projects. 17, 573-83. Gonzalez, V., Alarcon, L. F. & Yiu, T. W. 2013. Integrated methodology to design and manage work-in-process buffers in repetitive building projects. 64, 1182-93. Handa, V. & Barcia, R. 1986. Linear Scheduling Using Optimal Control Theory. Journal of Construction Engineering and Management, 112, 387-393. Harmelink, D. & Rowings, J. 1998. Linear Scheduling Model: Development of Controlling Activity Path. Journal of Construction Engineering and Management, 124, 263-268. Harmelink, D. J. 2001. Linear scheduling model: Float characteristics. Journal of Construction Engineering and Management, 127, 255-260. Harris, R. & Ioannou, P. 1998. Scheduling Projects with Repeating Activities. Journal of Construction Engineering and Management, 124, 269-278. Hegazy, T. Computerized system for efficient scheduling of highway construction. 2005. National Research Council, 8-14. Hegazy, T. & Wassef, N. 2001. Cost Optimization in Projects with Repetitive Nonserial Activities. Journal of Construction Engineering and Management, 127, 183-191. Ipsilandis, P. 2007. Multiobjective Linear Programming Model for Scheduling Linear Repetitive Projects. Journal of Construction Engineering and Management, 133, 417-424. Jiang, Y. & Wu, H. 2007. Production Rates of Highway Construction Activities. International Journal of Construction Education and Research, 3, 81-98. 107-9 Johnston, D. W. 1981. LINEAR SCHEDULING METHOD FOR HIGHWAY CONSTRUCTION. Journal of the Construction Division, 107, 247-261. Kuo, Y.-C. 2004. Highway earthwork and pavement production rates for construction time estimation. 3143291 Ph.D., The University of Texas at Austin. Lluch, J. 2009. Visualization of Repetitive Construction Activities in Excel. Computing in Civil Eng. (2009). Lucko, G. 2008. Productivity Scheduling Method Compared to Linear and Repetitive Project Scheduling Methods. Journal of Construction Engineering and Management, 134, 711-720. Lucko, G., SAID, H. M. M. & BOUFERGUENE, A. 2014. Construction spatial modeling and scheduling with three-dimensional singularity functions. Automation in Construction, 43, 132-143. Mattila, K. & Abraham, D. 1998. Resource Leveling of Linear Schedules Using Integer Linear Programming. Journal of Construction Engineering and Management, 124, 232-244. Menesi, W., Golzarpoor, B. & Hegazy, T. 2013. Fast and Near-Optimum Schedule Optimization for Large-Scale Projects. Journal of Construction Engineering and Management, 139, 1117-1124. Moselhi, O. & Hassanein, A. 2003. Optimized scheduling of linear projects. Journal of Construction Engineering and Management, 129, 664-673. O'Brien, J. J. 1975. VPM Scheduling for High-rise Buildings. American Society of Civil Engineers, Journal of the Construction Division, 101, 895-905. O'Connor, J. T. & Huh, Y. 2005. Crew production rates for contract time estimation: Bent footing, column, and cap of highway bridges. Journal of Construction Engineering and Management, 131, 1013-1020. Polat, G., Buyuksaracoglu, Y. & Damci, A. Scheduling asphalt highway construction operations using the combination of line-of-balance and discrete event simulation techniques.  2009 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM 2009), 8-11 Dec. 2009, 2009 Piscataway, NJ, USA. IEEE, 1126-30. Roofigari Esfahan , N., Paez, A. & RazaviS. 2015. Location-Aware Scheduling and Control of Linear Projects: Introducing Space-Time Float Prisms. Journal of Construction Engineering and Management, 141(1), 06014008. Russell, A. & Caselton, W. 1988. Extensions to Linear Scheduling Optimization. Journal of Construction Engineering and Management, 114, 36-52. Senouci, A. & Eldin, N. 1996. Dynamic Programming Approach to Scheduling of Nonserial Linear Project. Journal of Computing in Civil Engineering, 10, 106-114. Shah, R. K. 2014. A new approach for automation of location-based earthwork scheduling in road construction projects. Automation in Construction, 43, 156-169. Shu-ShunL. & Chang-Jung, W. 2007. Optimization model for resource assignment problems of linear construction projects. 16, 460-73. Song, L., Cooper, C. & Lee, S.-H. Real-time simulation for look-ahead scheduling of heavy construction projects.  2009 Construction Research Congress - Building a Sustainable Future, April 5, 2009 - April 7, 2009, 2009 Seattle, WA, United states. American Society of Civil Engineers, 1318-1327. Staub-French, S., Russell, A. & Tran, N. 2008. Linear Scheduling and 4D Visualization. Journal of Computing in Civil Engineering, 22, 192-205. Stradel, O. & Cacha, J. 1982. TIME SPACE SCHEDULING METHOD. Journal of the Construction Division, 108, 445-457. Tang, Y., Liu, R. & Sun, Q. 2014a. Schedule control model for linear projects based on linear scheduling method and constraint programming. Automation in Construction, 37, 22-37. Tang, Y., Liu, R. & Sun, Q. 2014b. Two-Stage Scheduling Model for Resource Leveling of Linear Projects. Journal of Construction Engineering and Management, 0, 04014022. Vanhoucke, M. 2006. Work Continuity Constraints in Project Scheduling. Journal of Construction Engineering and Management, 132, 14-25. Watkins, M., Mukherjee, A., Onder, N. & Mattilla, K. 2009. Using Agent-Based Modeling to Study Construction Labor Productivity as an Emergent Property of Individual and Crew Interactions. Journal of Construction Engineering and Management, 135, 657-667. Woldesenbet, A., Jeong, D. H. S. & Oberlender, G. D. 2012. Daily work reports-based production rate estimation for highway projects. Journal of Construction Engineering and Management, 138, 481-490. Yamin, R. A. 2001. Cumulative effect of productivity rates in linear schedules. PhD, Purdue University. Yang, I. T. & Chi-Yi, C. 2005. Stochastic resource-constrained scheduling for repetitive construction projects with uncertain supply of resources and funding. International Journal of Project Management, 23, 546-53. 107-10 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.52660.1-0076314/manifest

Comment

Related Items