Cost impact of float loss on a project with adjustable activity durations

Abstract

Although delays to non-critical activities within the float do not always affect the overall completion time of a project, they commonly cause disputes over the impact cost and apportionment resulting from the complexity of resource utilization in construction projects. Therefore, considerable attention has been focused on providing an effective and reliable method for analysing the effects of float loss. Several recent studies have proposed various methods; however, most of these methods are based on the assumption of a fixed duration for each activity or activity-based cost simulation. Few studies have considered the trade-off between time and costs and the integration of project resources. Using genetic algorithms, this study introduces a critical path method (CPM)-modified resource-integrated optimization model and successfully quantifies the impact of float loss on the total cost of the project. The results provide objective quantification for accurately evaluating the impact of within-float delays and facilitate the analysis of the impact of delay claims on cost and apportionment in construction projects.

Keywords:

• optimization
• resource integration
• time-cost trade-off
• genetic algorithms

Notation

The following symbols are used in this paper:

AC= total activity cost of a project

a_j= a positive constant for each resource j

DC=direct cost

d_i= duration of activity i

dn_i= the normal duration of activity i

dp_i= the duration of activity i in the baseline schedule

E_ijt= the efficiency of resource j of activity i on Day t

EF_i= earliest finish time of activity i

EF_k= earliest finish time of activity k that precedes activity i

ES_i= earliest start time of activity i

ES_k= earliest start time of activity k that succeeds activity i

ET_i= end time of activity i

ET_k= end time of activity k that precedes activity i

F= fitness value, the minimal ratio of TC over TC₀

FF_i= free float of activity i

FL_i= float consumption of activity i

HC= total resource handling cost of a project

IC= total indirect cost of a project

IDC= total idle cost of a project

IDQ_jt= quantity of idle resource j on Day t

IT= impact time

K_j= the ratio of mobilization/demobilization unit cost over the resource unit cost for resource j

LF_i= latest finish time of activity i

LS_i= latest start time of activity i

LS_k=latest start time of activity k that succeeds activity i

MC=sum of total resource mobilization cost and demobilization cost

MC_d= resource demobilization cost

MC_m=resource mobilization cost

P_g=parent population in generation g

PS_i=immediate predecessor of activity i

Q_ijt=the quantity of resource j used for activity i on Day t

Q_ij(t−1)=the quantity of resource j used for activity i on Day (t−1)

Qn_ij= the quantity of resource j used for activity i at the normal duration

q_ijt= the daily quantity of resource j used for activity i with 100% efficiency at the duration d_i on Day t

S_i= shifting days of activity i

SS_i= immediate successor of activity i

ST_i= start time of activity i

STP_i= start time of activity i at the baseline schedule

s= solution in GA module (s=1 to S)

T= total project duration

TC= total cost of the project

TC_p= total cost of the project for the baseline schedule

TC₀= total cost of the project calculated with normal activity durations based on the early-start schedule

TF_i=total float of activity i

U_d=the daily cost rate for the indirect cost in $/day

U_j= unit cost of resource j

Notation

The following symbols are used in this paper:

AC= total activity cost of a project

a_j= a positive constant for each resource j

DC=direct cost

d_i= duration of activity i

dn_i= the normal duration of activity i

dp_i= the duration of activity i in the baseline schedule

E_ijt= the efficiency of resource j of activity i on Day t

EF_i= earliest finish time of activity i

EF_k= earliest finish time of activity k that precedes activity i

ES_i= earliest start time of activity i

ES_k= earliest start time of activity k that succeeds activity i

ET_i= end time of activity i

ET_k= end time of activity k that precedes activity i

F= fitness value, the minimal ratio of TC over TC₀

FF_i= free float of activity i

FL_i= float consumption of activity i

HC= total resource handling cost of a project

IC= total indirect cost of a project

IDC= total idle cost of a project

IDQ_jt= quantity of idle resource j on Day t

IT= impact time

K_j= the ratio of mobilization/demobilization unit cost over the resource unit cost for resource j

LF_i= latest finish time of activity i

LS_i= latest start time of activity i

LS_k=latest start time of activity k that succeeds activity i

MC=sum of total resource mobilization cost and demobilization cost

MC_d= resource demobilization cost

MC_m=resource mobilization cost

P_g=parent population in generation g

PS_i=immediate predecessor of activity i

Q_ijt=the quantity of resource j used for activity i on Day t

Q_ij(t−1)=the quantity of resource j used for activity i on Day (t−1)

Qn_ij= the quantity of resource j used for activity i at the normal duration

q_ijt= the daily quantity of resource j used for activity i with 100% efficiency at the duration d_i on Day t

S_i= shifting days of activity i

SS_i= immediate successor of activity i

ST_i= start time of activity i

STP_i= start time of activity i at the baseline schedule

s= solution in GA module (s=1 to S)

T= total project duration

TC= total cost of the project

TC_p= total cost of the project for the baseline schedule

TC₀= total cost of the project calculated with normal activity durations based on the early-start schedule

TF_i=total float of activity i

U_d=the daily cost rate for the indirect cost in $/day

U_j= unit cost of resource j

Acknowledgements

This research was supported financially by the National Science Council in Taiwan.