Method for Base Estimation of Construction Time for Linear Projects in Front-end Project Phases

Ivana Burcar Dunovic; Kristijan Robert Prebanic; Pavao Durrigl

doi:10.2478/otmcj-2018-0026

Figures & Tables

Simplified outline of the construction plan based on condensed work packages.Source: Nkado (1992).

Example of controlling activity path (CAP) in time–location diagram.Source: Mattila and Park (2003).

Graphical representation of the equation of total project time in LSM for continuous full-span activities.Source: Radujkovic (2012).

Representative pipeline project from the analyzed sewer system.Source: project technical documentation

Task links and the three possible variations between two activities.

Leading activities and their related variables of another pipeline project from the same sewer system

	Leading activities	ΔQ	U_p	Δl	α, β (tan⁻¹)	t_a (days)	Task link	k	y
1	Pulverizing and grinding of existing roadway asphalt or concrete curtain	4500	292.08	2113	0.0073	16	F-F	1	8
2	Mechanical excavation	5653.52	669.76	2113	0.0040	9	F-F	1	7
3	Manual excavation	1413.38	669.76	2113	0.0010	3	F-F	0	2
4	Replacement of low foundation material	559.98	878.40	2113	0.0003	1	S-S	1	1
5	Trimming, leveling, and grading the landfill base	1610	2927.9	2113	0.0003	1	S-S	1	1
6	Spreading filter pedestrian finishing base	209	878.40	2113	0.0001	1	S-S	1	1
7	Installation of manholes	133	2.00	2113	0.0197	42	S-S	0	0
8	Lowering pipe into trench	2113.6	36.40	2113	0.0275	59	F-F	1	58
9	Spreading rounded gravel above the pipes	1071.1296	878.40	2113	0.0006	2	S-S	1	1
10	Backfill	2480	1152.9	2113	0.0010	3	F-F	1	2
11	Embankment-road compacting	2080	1112.6	2113	0.0009	2	S-S	1	1
12	Base pavement-base course layer	5195	1145.4	2113	0.0021	5	S-S	1	1
13	Surface pavement-binder and wearing course	5195	1145.4	2113	0.0021	5

					Total time: 88 days

Linear continuous activities of the analyzed pipeline project and their related variables

	Leading activities	First three variables determined from technical documentation

		ΔQ	U_p	Δl	α, β (tan⁻¹)	t_n (days)	Task link	k	y
1	Pulverizing and grinding of existing roadway asphalt or concrete curtain	2662.807	292.08	920	0.009909	10	F-F	1	6
2	Mechanical excavation	2949.962	669.76	920	0.004787	5	F-F	1	4
3	Manual excavation	737.49	669.76	920	0.001199	2	F-F	0	1
4	Replacement of low foundation material	474.896	878.40	920	0.000588	1	S-S	1	1
5	Trimming, leveling, and grading of the landfill base	1637.047	2927.9	920	0.000608	1	F-F	1	1
6	Spreading filter pedestrian finishing base	248.39	878.40	920	0.00030	1	S-S	1	1
7	Installation of manholes	47	2.00	920	0.012771	24	S-S	0	0
8	Lowering of pipe into trench	849.38	36.40	920	0.025358	24	F-F	1	23
9	Spreading rounded gravel above the pipes	1273.79	878.40	920	0.001576	2	S-S	1	1
10	Backfill	2815.45	1152.9	920	0.002654	3	F-F	1	3
11	Embankment-road compacting	941.31	1112.6	920	0.000920	1	S-S	1	1
12	Base pavement-base course layer	2344.797	1145.4	920	0.002225	3	S-S	1	1
13	Surface pavement-binder and wearing course	2344.797	1145.4	920	0.002225	3

							Total time		46d

The equations for calculation of time buffer and duration of two adjacent activities

Situation 1. α = βProduction rate: tasks A1 and A2 are equal. Recommended task link: Start–Start (S–S) Total duration: T = k + t(A₂) Time buffer: y = k	Situation 2. α < βProduction rate: task A1 is faster than task A2.Recommended task link:Start–Start (S–S)Total duration: T = k + t(A₂)Time buffer: y = k
Situation 3. α > βProduction rate: task A2 is faster than task A1.Recommended task link: Finish–Finish (F–F)Total duration: T = k + t(A₁) - t(A₂) + t(A₂)Time buffer: y = k + Δt = k + t(A₁) - t(A₂)

Comparison of the new LSM-based method for time estimation with the two existing methods

Integrated CPM–LOB model (Ammar, 2013)	PSM (Lucko, 2007, 2008)	LSM-based method for early time estimation
1) LOB calculationsThis step consists of (at least) four (sub)steps. First is to draw a unit network (of repetitive activities for single work unit); second is to estimate the crew size for each activity; third is to establish a target rate of output (this (sub)step can be further divided into smaller steps); fourth is to derive the LOB diagram.	1) Initial equationsThe execution of PSM starts with describing all activities in the Macaulay bracket notation (e.g., singularity functions). However, no links are considered for the initial equations (one equation for each activity).	1) Activity listBased on available technical documentation, devise the list of linear activities of the projects, along with their parameters of work quantity and work group productivity (average). Work quantity is spread through work units using linear interpolation to make every activity continuous. Their sequence must be established unambiguously.
2) Calculating activity durationOverlapping activities are generalized to represent repetitive activities. For this generalization to be possible, the duration is assumed constant in all units of a repetitive activity.	2) Buffer equationsIn the second step, the singularity functions for buffers are set up (one equation for each buffer).	2) Calculating activity durations and slopesCalculate durations and unit production rates (e.g., slopes) for every linear continuous activity.
3) Specifying logical relationships using overlapping activities (buffer time)To specify relationships, the actual progress rate of each activity is compared with that of its successors. Three scenarios can be encountered: diverging, converging, and parallel activities. Based on the scenario, the buffer time is placed on the first or the last unit.	3) Initial stackingIn the third step, the initial activity and buffer equations are stacked up in the order of precedence with the set of singularity functions (one equation for each activity).	3) Using the newly developed algorithm for determination of buffers between activitiesPair of activities can converge, can diverge, or be parallel depending on the relation of production rates of two adjacent activities. Depending on this relation, the equation for every buffer y is determined, and calculation of the buffer is performed.
4) Time scheduling1. Forward pass – the early timings (belong to the first and last units only) are determined for each activity. 2. Backward pass – the late timings (belong to the first and last units only) are determined for each activity.	4) Minimum differencesIn the fourth step, the differences between neighboring predecessor buffer equations and successor equations are taken and the minima of these difference equations are determined across all positive values of x (one equation for each activity–buffer link).	4) Using the newly developed algorithm for calculation of project durationBased on the determined buffer times, the project duration is calculated as the sum of the buffers and the duration of the last activity.
5) Criticality analysis	5) DifferentiationDifferences are differentiated using equations to confirm the nature of the vertices (set of equations)
	6) Final consolidationIn the sixth step, the vertex distances between a neighboring predecessor buffer equation and successor equation are compared to identify the overall minimum distance (set of equations).
	7) Criticality analysisThe equivalent of a critical path from CPM is calculated (set of equations).

Time–cost performance for civil engineering projects in the expanded Hong Kong sample

Project type	K	B	R	Total projects
Total civil works	250.5	0.206	0.79	148
Roadworks	251.2	0.225	0.87	57
Other civil works	262.5	0.185	0.69	91

Method for Base Estimation of Construction Time for Linear Projects in Front-end Project Phases

Figures & Tables

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Leading activities and their related variables of another pipeline project from the same sewer system

Linear continuous activities of the analyzed pipeline project and their related variables

The equations for calculation of time buffer and duration of two adjacent activities

Comparison of the new LSM-based method for time estimation with the two existing methods

Time–cost performance for civil engineering projects in the expanded Hong Kong sample

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