Developing a cost-payment coordination model for project cost flow forecasting/Sanaudu ir mokejimo koordinavimo modelio, skirto projektu sanaudu srautu prognozems, kurimas.
Chen, Hong Long ; Chen, Wei Tong ; Wei, Nai-Chieh 等
1. Introduction
Low and unreliably profitability characterize the construction
contracting industry (Garnett, Pickrell 2000; Sorrell 2003). Levy (2009)
and Teerajetgul et al. (2009) further noted that contractors work on
slim profit margins due to fierce competition. While researchers
continually develop methods and approaches for reducing engineering
project costs (e.g., Dainty et al. 2001; Humphreys et al. 2003; Yeo,
Ning 2002), some authors (e.g., Navon 1994, 1995; Kaka 1996; Kenley
1999) have focused on improving profitability of engineering projects by
improving the efficiency of project cash flows. Since net positive
project cash flows reduce the project working capital, smaller working
capital needs indicate better profitability performance, defined as Net
Profit/Net Investment, where Net Investment represents the working
capital committed to the project to generate profits. Consequently,
companies that predict and plan operating cash flows so as to slow cash
outflows or reduce working capital needs will achieve higher ROI.
Among the models and approaches reviewed, the most
information-intensive models for predicting operating cash flows are
those based on the cost-schedule integration (CSI) techniques (e.g.,
Abudayyeh, Rasdorf 1993; Carr 1993; Chen, Chen 2005; Navon 1996).
However, despite using extensive schedule and estimated data information
as inputs to provide highly integrated models for predicting cash flows,
existing CSI approaches still lead to large discrepancies between
payment flows and cost flows. This discrepancy stemmed from the problems
of differential schedules between network and cost activities, lags
between applications for payment and actual disbursement of funds,
payment components for materials and labor (payment split between labor
and materials), and payment frequency, as well as the combined impacts
of payment irregularity (the amount of a progress payment different from
the actual accumulated activity cost, or the disbursement of that
progress payment different from the projected schedule) and uniform
distribution of cost over time (a key assumption of CSI models).
Research thus continues on extensions of CSI models to provide
solution methods for these limitations. First, this study briefly
discusses the background of methods and approaches for operating cash
flows. Next, this study describes the development of the coordination
mechanisms based on CSI models. Finally, this study validates the
coordination mechanisms by two construction projects. Analysis of
pattern matching logic using simulated cost flow data by coordination
mechanisms indicates that while input parameters are based on the actual
cost and schedule of the work performed, the coordination mechanisms are
able to eliminate the difference between cost flows and payment flows.
More broadly, this study provides a methodology and starting point for
further refinement of CSI models to include future sales and overhead
flows.
2. Background
This paper first offers some definitions: cash flows, generated by
operating, investing, and financing activities, are the inflows and
outflows of cash into and out of a business (Needles et al. 1999).
Operating activities are defined as transactions other than investing or
financing activities. Investing activities include purchasing and
selling long-term productive assets and equity and debt investments that
are cash equivalents, as well as making and collecting loans. Financing
activities include issuing equity securities and long-term and
short-term liabilities, paying dividends to stockholders, purchasing
treasury stock, and repaying cash loans. Thus, operating activities that
produce operating cash flows include sales, costs of goods sold or
services rendered, and overhead costs. Operating cash flows are more
important than investing and financial cash flows, as they reflect the
financial health of a business and its value (Barth et al. 2001;
Krishnan, Largay 2000).
Operating cash flows comprise the inflows and outflows of cash.
Inflows consist of sales flows, whereas outflows are composed of payment
flows and overhead flows. Sales flows are income realized on contractual
agreements with clients relating to activity and project completion.
Payment flows are the disbursement of costs of goods sold or services
rendered as a function of time. Overhead flows are the disbursement of
the overhead costs (field and main office) as a function of time. From a
modeling perspective, cost flows are defined as forecasts of payment
flows. Cost flow forecasting has proven to be more difficult to generate
than that of sales flows and overhead flows for reasons of complexity,
as there are typically many activities generating costs, and partial
payments are made to vendors (Chen, Chen 2005). Therefore, this research
focuses on improving the accuracy of cost flow predictions.
Though cash flow management is relatively well researched, those
standard direct and indirect methods used for predicting operating cash
flows that have been extensively addressed in previous studies (e.g.,
Barth et al. 2001; Krishnan, Largay 2000; Lorek, Willinger 1996) are not
relevant in a project-based industry, especially one such as
construction contracting. It is widely believed that in a project-based
industry, a product (project) contributes a relatively large proportion
of the overall level of sales volume that may destabilize these models
(Chen, Chen 2005; Kaka, Lewis 2003). Several methods, principally the
CSI techniques, thus are developed to meet the needs of project-based
industries. These techniques focus on the project contracts rather than
firm income statement and balance sheet, since the contracts determine
both the timing and amount of the cash inflows and outflows.
CSI models forecast operating cash flows by using forecast work
schedules and activities (e.g., Abudayyeh, Rasdorf 1993; Carr 1993;
Chen, Chen 2005; Navon 1995). CSI models therefore produce cost flows
either as a continuous function, or in more refined models, periodic
function summing the costs of scheduled work as a function of time.
While the costs of scheduled work are budgeted costs, CSI models produce
the budgeted cost for work scheduled (BCWS), or the budgeted cost for
work performed (BCWP) after the scheduled work is accomplished. When the
scheduled work is accomplished and the corresponding actual cost is
incurred, CSI models produce the actual cost of work performed (ACWP).
BCWS serves as a time-phased budgetary baseline for the entire project,
representing the standard or plan against which the performance (BCWP)
and the cost (ACWP) of the project are compared. BCWS, BCWP, and ACWP,
which are also called planned value (PV), earned value (EV), and actual
value (AV), respectively, formulate earned value management (EVM)
systems.
While based on different input data, CSI models produce EVM systems
that evaluate a project's technical performance (i.e.,
accomplishment of planned work), schedule performance (i.e.,
behind/ahead of schedule), and cost performance (i.e., under/over
budget), some authors further refine CSI models for use in cost flow
predictions. For example, Abudayyeh and Rasdorf (1993) designed the
basic approaches and computer implementations for cost flow predictions
using CSI techniques. Carr (1993) provided refinements to accounting for
schedule variance in cost flow predictions. Building upon this work,
Navon (1995, 1996) refined the CSI technique to account for time lags
between application for payment and actual disbursement of funds,
providing a model that assumes monthly dates for application of vendor
payment. Building on this level of detail, Fayek (2001) further
discusses fusing CSI techniques with firm accounting systems.
Hwee and Tiogn (2002) developed a sophisticated S-curve profile
model from CSI that is equipped with progressive construction data
feedback mechanisms. Kaka and Lewis (2003) further devised a
company-level (CL) S-curve model that accounts for both known and
unknown individual projects at the time of the forecast. Subsequent work
by Park (2004) developed a project-level cash flow forecasting model
using moving weights of cost categories in a budget over project
duration based on the planned earned value and the cost from a GC's
view on a jobsite. He concluded that the proposed model is more
accurate, flexible, and yet simpler than traditional models from the
validation results of four real projects.
Mavrotas et al. (2005) further modeled cash flows based on a
bottom-up approach starting from the level of a single contract
(project) towards the level of the entire organization, where each
contract's cash flow is approximated and updated with an
appropriate S-curve that is based on a conventional non-linear
regression model.
Recently, Jimenez and Pascual (2008) modeled cash flow components
by incorporating preferences and expectations in the form of specific
projection criteria for each of the components (e.g., sales and debts.),
such as the use of ratios and rates of change. Cheng et al. (2009)
developed a cash flow model from a set of artificial intelligence (AI)
approaches and CSI to predict project cash flow trends. Gorog (2009)
presented a comprehensive model for planning and controlling contractor
cash flows, based on the expansion of EVM to include new performance
measurements and indicators, such as PVWP (Price Value of Work
Performed) and IVWS Invoiced Value of Work Scheduled. More recently,
Cheng and Roy (2011) proposed an evolutionary fuzzy decision model for
cash flow prediction using time-dependent support vector machines and
historical S-curve data by CSI.
However, despite the panoply of approaches to generating project
cash flow forecasts, there still exist several potential limitations.
First, CSI models do not consider important information of payment
conditions, including differential payment lags, components for
materials and labor (payment split between labor and materials), and
payment frequency. Second, CSI models appear not to consider the
problems of differential schedules between network and cost activities.
Third, research on construction has mainly focused on studying how to
improve the integration of cost activities and their corresponding
resources (e.g., Abudayyeh, Rasdorf 1993; Chen 2007; Fayek 2001; Navon
1994). Relatively little research has addressed relationships between
cost and progress payment activities. Thus, little research has provided
methods of alleviating the influences of progress payment irregularity
(the discrepancy between a progress payment and the actual accumulated
activity cost, or the disbursement of that progress payment at a time
different from the projected schedule) and uniform distribution of cost
over time (a key assumption of CSI models) on the creation of cash
flows.
3. Development of the model and the algorithm
The previous section criticized the ability of the CSI techniques.
The primary objective of this study is to develop coordination
mechanisms that are capable of resolving and/or alleviating the problems
of existing CSI models, and hence, enhance the accuracy and reliability
of forecasts of future cost flows produced by CSI models. Development of
the coordination mechanisms are described in several parts, including
rectifying differential schedules between network and cost activities,
extending CSI models to include payment conditions, and alleviating the
combined effect of payment irregularity and uniform distribution of cost
over time.
3.1. Rectification of differential schedules between network and
cost activities
CSI models assume that schedules between network and cost
activities are identical; nonetheless, differential schedules between
them often occur in practice. For instance, two subcontractors follow
each other around fabricating a main structure of a building. The slab
formwork must be installed before the concrete subcontractor can do its
work; the slab formwork acts as a sustainer for concrete weight. Hence,
there is a finish-to-start relationship between the work of the formwork
subcontractor and that of the concrete subcontractor. However, the
general contactor will not approve the cost of the formwork work until
the concrete is placed, which acts as a verifier activity used to
confirm whether or not the quality (or safety) requirements of the
formwork work are achieved. Therefore, not only the relationship between
the activities of slab formwork and concrete is transformed to a
finish-to-finish relationship, but the cost of the formwork activity is
viewed as being incurred on the very last day of the verifier activity.
When differential schedules exist in a project activity, the
activity is defined as a scheduling conflict activity. The rectification
for a scheduling conflict activity is as follows:
[f.sub.SCA]([PCE.sub.ij]) = {Dur, [Dep.sub.v](Dur = 1, [Dep.sub.v]
= [F.sub.V][F.sub.SCA]} , (1)
where: i is project contracting entity (PCE) index, i = 1, ..., N,
where PCE is defined as a subcontractor, supplier, or as the general
contractor itself, and N is the total number of entities; j is activity
index, j = 1, ..., M, where M denotes the total number of activities of
each PCE, for example, [PCE.sub.ij] means the jth activity of the ith
project contracting entity; [f.sub.SCA]([PCE.sub.ij]) is function of
transforming [PCE.sub.ij] while having the scheduling conflict
attribute; Dur is duration of [PCE.sub.ij]; [Dep.sub.V] is dependency of
[PCE.sub.ij] on its verifier activity.
Before applying Eq. (1), a condition must be met: the activity
cannot be partially examined and, thus, the activity cannot be partially
invoiced. If an activity with the scheduling conflict attribute can be
partially examined and billed, that activity needs to be further broken
down until the condition is met.
3.2. Extending CSI models to include payment conditions
Since the cost occurs earlier than the payment of an activity, the
cost flows are ahead of the payment flows of an activity. In practice,
predictions of cost flows are verified by payment flows (the
disbursements of payments as a function of time). Thus, while the effect
of payment conditions on payment flows is significant (Chen, Chen 2005),
there is a need to extend CSI models to include the information of
payment conditions. The information of payment conditions include time
lags between applications for payment and actual disbursement of funds,
components for materials and labor (payment split between labor and
materials), and monthly payment frequency for suppliers and
subcontractors. The following assumptions must be made before extending
CSI models to include payment conditions:
1. The network activity schedule and cost activity schedule are
identical except scheduling conflict activities.
2. A cost loaded activity of a project can only be assigned to a
PCE of that project.
3. The quantity of an activity's progress payment application
is accumulated up to the day before the application date.
The first assumption gives the position of [PCE.sub.ij] relative to
time (dates) of application in the future in the time axis; the second
provides the basis for calculating the cumulative quantity of PCE y in
relation to time (dates) of application in the future in the time axis.
Collectively, these two assumptions generate several possible scenarios
of the relevant pay amount of [PCE.sub.ij]'s kth payment
application, conceptually expressed in Fig. 1. In this Figure, the
relevant pay period of [PCE.sub.ij]'s kth payment application is
the time between [TA.sub.ijlk] and [TA.sub.ijl(k-1)], indicated by the
shaded portion of these scenarios. Scenarios A to L depict the possible
range of [PCE.sub.ij] starting and finishing across multiple times of
applications. These scenarios can be further grouped into four different
types according to the relevant pay period of each scenario. Such
grouping is expressed in Fig. 2 by showing the split among possible
scenarios as a dotted lines perpendicular to the time axis.
More details of the four different types are addressed as follows:
Type 1: [TA.sub.ijlk] [greater than or equal to] [ef.sub.ij]
[greater than or equal to] [TA.sub.ijl(k-V)] [greater than or equal to]
[es.sub.ij].
Under this Type, the pth payment application for activity i of PCEj
is the last payment application. During the pay period, the pth
cumulated activity cost is the multiplication of [ef.sub.ij] -
[TA.sub.ijl(k-1)] + 1 and
[pc.sub.ijl][bq.sub.ij][buc.sub.ij](1-[r.sub.ij])/ ([ef.sub.ij] -
[es.sub.ij] + 1). Type 1 includes scenarios A and B.
Type 2: [TA.sub.ijlk] [greater than or equal to] [ef.sub.ij]
[greater than or equal to] [es.sub.ij] [greater than or equal to]
[TA.sub.ijl(k-1)]
[FIGURE 1 OMITTED]
Under this Type, the pth payment application for activity i of PCEj
is the first and last payment application. During the pay period, the
pth cumulated activity cost is the multiplication of [ef.sub.ij] -
[es.sub.ij] + 1 and [pc.sub.ijl][bq.sub.ij][buc.sub.ij]
(1-[r.sub.ij])/([ef.sub.ij] - [es.sub.ij] + 1). Type 2 includes scenario
C. Type 3: [ef.sub.ij] [greater than or equal to] [TA.sub.ijlk] [greater
than or equal to] [es.sub.ij] [greater than or equal to]
[TA.sub.ijl(k-1)].
Under this Type, the pth payment application for activity i of PCEj
is the first payment application. During the pay period, the pth
cumulated activity cost is the multiplication of TA1jli- esj and
pcjlbq1jbucj(1 - rj)/(efjes1j + 1). Type 3 includes scenarios D, E, and
F.
Type 4: [ef.sub.ij] [greater than or equal to] [TA.sub.ijl(k-1)]
[greater than or equal to] [es.sub.ij] .
Under this Type, the pth payment application for activity i of
[PCE.sub.j] is betweem the first and the last payment application.
During the pay period, the pth cumulated activity cost is the
multiplication of [TA.sub.ijlk] - [TA.sub.ijl(k-1)] and
[pc.sub.ijl][bq.sub.ij][buc.sub.ij](1 - [r.sub.ij])/([ef.sub.ij] -
[es.sub.ij] + 1). Type 4 includes scenarios G to L.
Based on theses scenarios, cost flow forecasting of a project can
be modeled as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2a)
[FIGURE 2 OMITTED]
and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2aa)
where l is component index, l = 1 to 2, where 1 denotes the labor
ratio while 2 represents the material ratio. For example, when
subcontracting the formwork of a project to a third party, the contract
agreement may specify that all progress payments should be split between
labor and materials, where the corresponding labor and materials ratios
are 0.4 and 0.6 of a progress payment; k is payment frequency index, k =
1, ..., P, where P is the total payment frequency of an activity. For
example, if the value of P of a project activity such as laying
foundation rebar is 3, this means that there are 3 progress payments for
the laying foundation rebar activity; [pc.sub.ijl] is ratio of component
l of [PCE.sub.ijis]; [bq.sub.ij] is budgeted quantity of [PCE.sub.ij];
[buc.sub.ij] is budgeted unit cost for [PCE.sub.ij]; [r.sub.ij] is
retainage of [PCE.sub.ij]. Retainage is a portion of a project
contracting entity's earned funds withheld from each progress
payment until the project work is indeed completed under contract;
[T.sub.ijl] is payment time lag for component l of [PCE.sub.ij];
[TA.sub.ijlk] is time (or date) of application for the kth time progress
payment of component l of [PCE.sub.ij]; [ef.sub.ij] is earliest finish
date of [PCE.sub.ij]; [es.sub.ij] is earliest start date of
[PCE.sub.ij]; [N.sub.ijlk] is relevant pay period for the kth time
progress payment of component l of [PCE.sub.ij].
The term, [f.sub.ijlk], used in Eq. (2a) is designed to project the
budgeted cost of the relevant pay period,
[pc.sub.ijl][bq.sub.ij][buc.sub.ij](1 - [r.sub.ij])/([ef.sub.ij] -
[es.sub.ij] + 1) x [N.sub.ijlk], into the time axis in accordance with
lags and the time of application, ([T.sub.ijl] + [TA.sub.ijlk]). The
summation of k of [PCE.sub.ij], where k [member of] (i,...,P}, generates
cost flow prediction at the activity level, and the summation of all
cost-loaded activities of the project produces the project-level cost
flow prediction, expressed as Eq. (2a). However, when [PCE.sub.ij] is a
scheduling conflict activity, future cost flows for this activity is
modified from Eq. (2a) as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2b)
3.3. Combined effect of payment irregularity and uniform
distribution of cost over time
Following the initiation of a project activity, the actual activity
cost simultaneously increases. Due to uncertain variables such as
resource availability, on-site workability, worker skills, field support
for timely responses, and construction management competency that cause
variations in productivity, the actual accumulated cost of an activity
during a period is unlikely to be the same as the predicted cost of the
activity during that period based on assuming a uniform cost
distribution over time. Additionally, because of payment irregularity,
not only might the progress payment differ from the actual accumulated
activity cost, but also the disbursement of the progress payment may
differ from the projected schedule owing to late application for payment
or quantity- and quality-related problems in activity and trade
completion. That is, progress payment is not necessarily equivalent to
the actual accumulated cost on the project construction site, nor is it
necessarily equivalent to its projected schedule.
When [PCE.sub.ij] is initiated and not completed yet, the combined
effect of payment irregularity and uniform distribution of cost over
time on projected future cost flows following each time of payment
application can be conceptually summarized in Fig. 3. The total area of
a scenario bar activity is the budgeted cost of [PCE.sub.ij], while the
shaded black and gray portions of the area are the relevant payment
amount and payment variance of [PCE.sub.ij] for the kth payment
application, respectively. Scenario A' (or A") shows that the
predicted cost of [PCE.sub.ij] for the kth pay period is the same as the
relevant payment amount of that activity for that period, and likewise
scenarios B' (or B") and C' (or C") are less and
more, respectively. Scenario D' (or D") illustrates that the
relevant payment amount of [PCE.sub.ij] for the kth pay period is zero
regardless of whether the cost of that activity is incurred.
To alleviate the combined effect, adjustment for predicted cost
flows following each time of payment application occurs becomes
necessary. When [PCE.sub.ij] is still being constructed following its
kth payment application (i.e., [TA.sub.ijlk] [ef.sub.ij]), the payment
flows of [PCE.sub.ij] can be modeled as follows:
[summation over (ij)][summation over
(lk)][f.sub.ijlk][pc.sub.ijl][DELTA][q.sub.ijk][auc.sub.ij](1 -
[r.sub.ij]), ([T.sub.ijl] + [TA.sub.ijlk])] (3a)
and the adjusted future cost flows of PCE y can be modeled as
follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3b)
[N'.sub.ijl(k+1)] is calculated as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3ba)
where [aq.sub.ij] is accumulated quantity of [PCE.sub.ij];
[auc.sub.ij] is actual unit cost of [PCE.sub.ij]; [DELTA][q.sub.ijk] is
payment quantity for the kth time progress payment of [PCE.sub.ij];
[[summation].sub.ijk] [DELTA][q.sub.ijk] is Accumulated payment quantity
up to the kth time progress payment of [PCE.sub.ij]; [N'.sub.ijlk]
is relevant pay period for the (k+1)th time progress payment of
component l of [PCE.sub.ij].
However, when the activity is completed prior to its relevant time
of payment application ([TA.sub.ijlk][??][ef.sub.ij]), the adjusted
future cost flows of the activity can be modeled as follows:
[summation over (ij)][summation over (lk)][f.sub.ijlk][([aq.sub.ij]
- [[summation].sub.k] [DELTA][q.sub.ijk])[auc.sub.ij][pc.sub.ijl](1 -
[r.sub.ij]), ([T.sub.ijl] + [TA.sub.ijlk])] (3c)
Besides the previous three assumptions, Eq. (3c) assumes that the
amount of deferral payment caused by a payment irregularity is postponed
to the next term of payment application, if the payment irregularity
involves an already completed construction activity.
[FIGURE 3 OMITTED]
3.4. Coordination mechanisms
The reorganization of Eqs (1) to (3 c) forms the coordination
mechanisms capable of projecting payment flows and future operating cost
flows. More specifically, before a project activity starts, i.e., both
[aq.sub.ij] = 0 and [[summation].sub.ijk][DELTA][q.sub.ijk] = 0 are met,
cost flow forecasting of the activity is created with Eqs (2a) and (2aa)
if the activity is not a scheduling conflict activity. However, if the
activity is a scheduling conflict activity, its cost flow forecasting is
generated by Eq. (2b). Together, Eqs (2a), (2aa), and (2b) form the
first part of the mechanisms (4a) and (4aa).
After the activity starts, i.e., [aq.sub.ij] = 0 and
[[summation].sub.ijk][DELTA][q.sub.ijk] = 0 are not met, the payment
flows of the activity is created with Eq. (3a). The adjusted future cost
flow of the activity is created with Eqs (3b) and (3ba) when
[TA.sub.ijlk] < [ef.sub.ij] exists; however, the adjusted future cost
flow is created with Eq. (3c) when [TA.sub.ijlk] > = [ef.sub.ij]
exists. Together, Eqs (3a), (3b), (3ba), and (3c) form the second part
of the mechanisms (4b), (4ba), and (4c).
Collectively, the coordination mechanisms are expressed as follows:
If [aq.sub.ij] = 0 and [[summation].sub.ijk] [DELTA][g.sub.ijk] = 0
are true, then:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4a)
with
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4aa)
otherwise:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4b)
with
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4ba)
or:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4c)
CF denotes cost flow forecasting of a project, ACF denotes adjusted
future cost flows, and PF denotes payment flows. To illustrate how to
compute the value of payment flows and predicted cost flows by using the
coordination mechanisms, this paper provides an algorithm in Fig. 4. In
the algorithm, it first searches all PCEs (N together) and obtains their
relevant cost-loaded activities and the activities' scheduling and
payment term data. The algorithm then reads the accumulated quantity
([aq.sub.ij]) and accumulated payment quantity
([[summation].sub.ijk][DELTA][q.sub.ijk]) of each cost-loaded activity,
creating two scenarios: If aq j=0 and
[[summation].sub.ijk][DELTA][q.sub.ijk] = 0 are true, the algorithm
computes future cost flows using Eqs (4a) and (4aa); otherwise, the
algorithm creates cost flow forecasting and payment flows with two
scenarios. If [PCE.sub.ij] is not completed yet ([TA.sub.ijlk] <
[ef.sub.ij]), Eqs (4b) and (4ba) are used to compute cost flow
forecasting and payment flows; otherwise, Eq. (4c) is used to compute
cost flow forecasting and payment flows.
[FIGURE 4 OMITTED]
4. Model validation
4.1. Projects used for validation
Data to support model validation was gathered on two projects: the
Cambridge project and the Yangkong project. The project names have been
changed at the request of the firms involved. The Cambridge project was
located in central Taiwan and had a total cost of NT105 million (~$3
million). Cambridge is a typical residential project comprising three,
four-story residential buildings constructed of reinforced concrete and
with a total floor area of around 5,400 square meters. Cambridge was
designed completely before the start of construction although customers
buying homes were allowed to specify certain custom particulars, such as
flooring finishes and interior wall coatings. The Yangkong project,
located in south Taiwan, is a NT2.5 billion (~$74 million) refuse
resource recovery plant. The waste-to-energy operating capacity for the
Yangkong project is 900 tons per day, with daily electrical power
generation of approximately 22,000 kilowatts. The Yangkong project was
completed within schedule, and the total project duration was five
years.
The Cambridge and Yangkong projects are representative of the
impact of payment conditions and the combined effect of payment
irregularity and uniform distribution of cost over time on operating
cost flows. For both projects, certain payments to specialist
contractors are split between labor and materials while others are not.
The frequency of payments for suppliers and specialists varies from once
to twice per month; and payment time lags differ between specialist
contractors and suppliers. Payment irregularity in terms of dates and
amounts to both specialist contractors and suppliers is occasionally
incurred. Furthermore, each project is of a standard design and is
administered using a typical general contracting arrangement.
Consequently, both projects can be considered representative of numerous
other projects globally.
To summarize, Table 1 lists the sample subcontractors and suppliers
of the Cambridge and Yangkong projects. The time lags between
application submission and approval for Cambridge and Yangkong projects
are 7 days and 3 days, respectively. Both projects use unit-price
contract. However, the Cambridge project uses unit-price including tax
while the Yangkong project uses unit-price excluding tax. Table 2
illustrates the result of mapping sample activities of the cost loaded
schedule to the PCEs of the projects. Table 3 details sample payment
irregularities in the projects. The two projects involved a total of 77
subcontractors and suppliers generating over 900 data points used for
the analysis; and a total of 45 payment irregularities were incurred.
4.2. Calculation illustrations
For project activity j = 2 (3rd F slab formwork activity) of
project contracting entity i = 2 (the formwork subcontractor) of
Cambridge, denoted as [PCE.sub.22] (shown in Table 2), before it was
initiated, i.e., both [aq.sub.22] = 0 and [[summation].sub.k]
[DELTA][q.sub.22k] = 0 existed, Eqs (4a) and (4aa) were used to compute
future cost flows. Table 1 shows that time of application for payments
of Cambridge's formwork subcontractor ([PCE.sub.2j-]) were 1st and
15th of a month. For [PCE.sub.22] in question, the value of the total
payment frequency index, P, was 1.
The value of P equals (1+PAD), where PAD denotes the number of
payment application dates included in the duration of [PCE.sub.ij]. The
duration of [PCE.sub.22] was between 07/22/09 and 07/26/09 (shown in
Table 2) computed by the critical path method (CPM), however, the
schedule of the activity itself conflicted with that of the pouring 3rd
F reinforced concrete activity, a verifier activity, completed on
07/31/09. Thus, the duration of [PCE.sub.22] needs to be rectified by
Eq. (1) as follows:
[f.sub.SCA]([PCE.sub.22]) = {Dur, [Dep.sub.v]|Dur= 1, [Dep.sub.v] =
[F.sub.v][F.sub.SCA] = 07/13/09}.
Following the rectification, the duration of [PCE.sub.22] was
located on 07/31/09, not containing 1st and 15th of that month; hence, P
was equaled (1+0 = 1).
As also seen in Table 1, payment for the formwork subcontractor
([PCE.sub.2j] (sub)) of the Cambridge project was split between labor
and materials, where the labor is 40% and the materials is 60%, denoted
as [pc.sub.ijl] = [pc.sub.221] = 0.4 and [pc.sub.ijl] = [pc.sub.222] =
0.6, respectively. Payment lags for the corresponding labor and
materials of the subcontractor were 14 and 47 days following each time
of application, denoted as [T.sub.ijl] = [T.sub.221] = 14 and
[T.sub.ijl] = [T.sub.222] = 47, respectively. All additional data for
computation of [PCE.sub.22] could be found in Tables 1, 2, and 3.
Because [PCE.sub.22] had the scheduling conflict attribute, the cost
flow was predicted by the first part of Eq. (4a) as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
As the construction progress to date was before 07/31/09, where the
condition of [aq.sub.22] = 0 and [[summation].sub.k][DELTA][q.sub.22k] =
0 was still met, the future cost flow of [PCE.sub.22] was computed using
Eqs. (4a) and (4aa). When the date was after 07/31/09 and ([TA.sub.ijlk]
= [TA.sub.22l1] = 08/01/09) [??] ([ef.sub.ij] = [ef.sub.22] = 07/31/09)
existed, the condition of [aq.sub.22] = 0 was no longer met, the
adjusted cost flow and payment flows of [PCE.sub.22] were calculated
using Eq. (4c). In addition, the value of P increased by 1, i.e., k
[member of] {1, ...,P} = {1,2}. This phenomenon is according to a key
assumption of the model: the amount of deferral payment resulting from a
payment irregularity is postponed to the next term of payment
application if the payment irregularity involves an activity that is
already completed. Consequently, the adjusted cost flow prediction of
[PCE.sub.22] on 08/01/09 was:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
and payment flows were:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
As shown from the computation examples, the predicted cost flows of
[PCE.sub.22] were (1055609,08/15/09) and (1585584,10/06/09) before
[PCE.sub.22] was initiated. After [PCE.sub.22] was initiated, the
adjusted cost flow predictions of [PCE.sub.22] were (1055609,08/15/09)
and (1583413,10/20/09) that matched the payment flows of [PCE.sub.22].
Because the same logic can be used in computing the rest of the
Cambridge and Yangkong project activities, this study decided not to
present more calculations of the coordination mechanisms. Nonetheless,
to further validate the performance of the coordination mechanisms,
Microsoft Access and Visual Basic were used to program the mechanisms
for simulations.
4.3. Simulation analysis and discussion
Pattern-matching logic compares the history of the payment flows
with projections of expected cost flows (Trochim 1989). Since five
factors needed to be investigated in combination, several scenarios must
be generated. Each factor is either considered or not considered in each
scenario, as follows:
Time lags considered (T) or not considered (NT); frequency (F, NF);
payment components (C, NC); schedule conflicts (SC, NSC); and payment
irregularities (PI, NPI). Some 64 different combinations exist; however,
scenarios considered for the hypothesis test in accordance with the
limitations of CSI modes are (NT, NF, NC, NSC, NPI), (T, F, C, NSC,
NPI), (T, F, C, SC, NPI), and (T, F, C, SC, PI). The hypothesis test is:
When cost and schedule uncertainty do not exist, solutions to the
problems of existing CSI models are capable of eliminating deviations
between the projected cost flows and historical payment flows.
Considering the hypothesis, this study decided to use the actual
cost and schedule rather than the budgeted cost and estimated schedule
of the Yangkong and Cambridge projects for the simulation input data.
This decision eliminated deviations between the projected cost flows and
historical payment flows owing to the cost and schedule variance (or
uncertainty).
Table 4 lists a sample of the cost flow predictions for a specific
combination of variables (T, F, C, SC, NPI) for the Yangkong project.
Similar cost flow predictions were developed for the other three
scenarios (not shown).
Figs 5 to 8 plot the cost flow predictions against the historical
payment flow data. Fig. 5 plots the scenario (NT, NF, NC, NSC, NPI),
Fig. 6 plots (T, F, C, NSC, NPI), Fig. 7 plots (T, F, C, SC, NPI), and
Fig. 8 plots (T, F, C, SC, PI). Figs 5 to 8 show that deviations between
the projected cost flows and historical payment flows are gradually
eliminated. Of the four scenarios, Fig. 5 is with the largest deviation
while Fig. 8 is has the smallest one. In fact, the only one of the four
combinations that matches the pattern of payment flows is the simulated
pattern with the factor combination (T, F, C, SC, PI), shown in Fig. 8.
Pattern-matching was also performed on the Cambridge project. Figs
9, 10, 11 and 12 plot the cost flow predictions against historical
payment data for the scenarios (NT, NF, NC, NSC, NPI), (T, F, C, NSC,
NPI), (T, F, C, SC, NPI), and (T, F, C, SC, PI), respectively. Of all
the scenarios for the Cambridge project, Fig. 9 is with the largest
deviation while Fig. 12 is has the smallest one. Only the pattern of
Fig. 12 (T, F, C, SC, PI) matches the historical pattern of payment
flows, while other patterns progressively eliminate the deviations
between the projected cost flows and historical payment flows.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
For both projects, scenarios (T, F, C, SC, PI), (T, F, C, SC, NPI),
(T, F, C, NSC, NPI), and (NT, NF, NC, NSC, NPI) rank from the first
place to the fourth place, respectively, in terms of effectiveness of
eliminating deviations between the projected cost and historical payment
flows. Consequently, this study accepts the hypothesis and concludes
that solutions the problems of existing CSI models are able to eliminate
deviations between the projected cost flows and historical payment
flows. Furthermore, the combination of (T, F, C, SC, NPI) on the
Cambridge project indicates a larger deviation than the combination of
(T, F, C, SC, NPI) on the Yangkong project. This phenomenon largely
results from the varying size of the two projects. The Cambridge project
is small and a late payment to a single vendor (or late application for
payment) can cause significant deviations from expected payment flows.
The larger Yankong project involves numerous vendors and thus the
effects of late payments on individual vendors are correspondingly
smaller.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
5. Conclusions
This study presents a model of mechanisms for resolving the
limitations of CSI models. These mechanisms include problems in the
logic of the schedule between construction and cost activities, detailed
payment conditions, and the combined effect of payment irregularity and
uniform distribution of cost over time. The developed coordination
mechanisms provide a method of accounting for differential payment lags,
materials and labor components, and payment frequency, as well as
absorbing the combined effect of payment irregularity and uniform
distribution of cost over time.
The model is shown to be effective using a set of case examples.
Analysis of pattern-matching logic using simulated cost flow data
indicates that while the simulation input parameters are based on the
actual cost and schedule for the work performed, the model is capable of
eliminating the deviations between cost flows and historical payment
flows. While substantial efforts remain for obtaining the mechanisms
suitable for industrial use, the growing computerization of schedule and
cost data make the implementation of such mechanisms feasible.
Both researchers and practitioners can directly apply the
mechanisms developed in this study. Accordingly, the specific extensions
of CSI models are a direct benefit to researchers and practitioners,
providing more accurate and reliable means of forecasting cost flow for
projects. More broadly, the research and methods of this study
contribute to a larger discussion of project cash flow models. A more
subtle benefit to practitioners associated with this study is the
reminder that project cash flow forecasts require a multi-disciplinary
effort. Even with sophisticated models and detailed data, project cash
flow predictions are unlikely to be accurate unless they account for
cost and schedule uncertainty. Consequently, assessments of the required
degree of accuracy remain important components for management
decision-making. Furthermore, extending the research in this study to
project sales flow forecasts with project-specific data can provide
management with a complete vision of project cash flow forecasting
techniques.
http://dx.doi.org/ 10.3846/13923730.2011.604540
Acknowledgments
The authors would like to thank Taiwan National Science Council for
financially supporting this research.
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Hong Long Chen (1), Wei Tong Chen (2), Nai-Chieh Wei (3)
(1) Department of Business and Management, National University of
Tainan, Tainan 700, Taiwan
(2) Department of Construction Engineering, National Yunlin
University of Science & Technology, Yunlin 640, Taiwan
(3) Department of Industrial Engineering and Management, I-Shou
University, Kaohsiung 840, Taiwan
E-mails: (1)
[email protected]; (2)
[email protected]
(corresponding author); (3)
[email protected]
Received 01 Sept. 2010; accepted 15 Dec. 2010
Hong Long CHEN. An associate professor in the department of
Business and Management at the National University of Tainan, Taiwan.
Dr. Chen is a member of the Tau Beta Pi Honor Society. He holds a Ph.D.
from the University of Florida. His research interests include project
management, corporate finance, performance management, and supply chain
management.
Wei Tong CHEN. Professor at the Department of Construction
Engineering at the National Yunlin University of Science and Technology,
Taiwan. He is the chief editor of the Value Management Journal published
by the Value Management Association in Taiwan. He is also a member of
the Engineering Management Committee, Chinese Institute of Civil and
Hydraulic Engineering. His research interests include construction
management, value management, performance assessment, and construction
safety management.
Nai-Chieh WEI. An associate professor in the Department of
Industrial Engineering and Management at I-Shou University, Taiwan. He
received his PhD degree in Industrial Engineering from Wayne State
University, Michigan. His current research interest is in manufacturing
systems optimization and design.
Table 1. Sample Subcontractors and Suppliers of the Cambridge and
Yangkong projects
Application Time between Payment
Project Firm Dates of the Application Frequency
Month Submission (Times of
and Approval a month)
Cambridge [PCE.sub.1j] 1st and 15th 7 days Twice
(sub)
[PCE.sub.2j] 1st and 15th 7 days Twice
(sub)
[PCE.sub.3j] 1st 7 days Once
(supplier)
[PCE.sub.4j] 1st and 15th 7 days Twice
(sub)
[PCE.sub.5j] 1st and 15th 7 days Twice
(sub)
[PCE.sub.6j] 1st 7 days Once
(supplier)
Yangkong [PCE.sub.1j] 1st and 15th 3 days Twice
(sub)
[PCE.sub.2j] 1st and 15th 3 days Twice
(sub)
[PCE.sub.3j] 1st and 15th 3 days Twice
(supplier)
[PCE.sub.4j] 1st and 15th 3 days Twice
(sub)
[PCE.sub.5j] 1st 3 days Once
(sub)
[PCE.sub.6j] 1st 3 days Once
(supplier)
Payment Lags Payment Split
Project Firm between Labor between Labor
and Materials and Materials
Cambridge [PCE.sub.1j] 14 days No payment
(sub) split
[PCE.sub.2j] 14 (lab) and 40 (lab) and
(sub) 47 days (mat) 60% (mat)
[PCE.sub.3j] 67 days No payment
(supplier) split
[PCE.sub.4j] 14 days No payment
(sub) split
[PCE.sub.5j] 14 days No payment
(sub) split
[PCE.sub.6j] 67 days No payment
(supplier) split
Yangkong [PCE.sub.1j] 17 (lab) and 50 (lab) and
(sub) 93 days (mat) 50% (mat)
[PCE.sub.2j] 17 (lab) and 30 (lab) and
(sub) 93 days (mat) 70% (mat)
[PCE.sub.3j] 17 (lab) and 70 (lab) and
(supplier) 93 days (mat) 30% (mat)
[PCE.sub.4j] 17 days No payment
(sub) split
[PCE.sub.5j] 93 days No payment
(sub) split
[PCE.sub.6j] 93 days No payment
(supplier) split
Project Firm Contract Type Retainage
Cambridge [PCE.sub.1j] Unit-price contract No
(sub) NT525 [m.sup.3]/unit, retainage
including sales tax
[PCE.sub.2j] Unit-price contract 10%
(sub) NT1,573 [m.sup.2]/unit,
including sales tax
[PCE.sub.3j] Unit-price contract No
(supplier) NT1,105 (3,000psi) retainage
[m.sup.3]/unit
NT1,027 (2,500psi)
[m.sup.3]/unit, including
sales tax
[PCE.sub.4j] Unit-price contract 10%
(sub) NT3,800 t/unit, including
sales tax
[PCE.sub.5j] Unit-price contract 10%
(sub) NT166.4 [m.sup.2]/unit,
including sales tax
[PCE.sub.6j] Unit-price contract No
(supplier) NT9,300 t/unit, including retainage
sales tax
Yangkong [PCE.sub.1j] Unit-price contract 10%
(sub) NT20,342 per pile/unit
(average unit price),
sales tax excluded
[PCE.sub.2j] Unit-price contract 10 %
(sub) NT95 [m.sup.3]unit (average
unit price), sales tax
excluded
[PCE.sub.3j] Unit-price contract 10 %
(supplier) NT300 [m.sup.2]/unit
(average unit price),
sales tax excluded
[PCE.sub.4j] Unit-price contract 15%
(sub) NT3,800 t/unit (average unit
price), including sales
tax
[PCE.sub.5j] Unit-price contract No
(sub) NT9,300 t/unit (average unit retainage
price), sale tax excluded
[PCE.sub.6j] Unit-price contract No
(supplier) 140 kg/[cm.sup.2], NT900 retainage
[m.sup.3]/unit
210 kg/[cm.sup.2], NT1,300
[m.sup.3]/unit,
280 kg/[cm.sup.2],
NT1,570[m.sup.3]/unit
350 kg/[cm.sup.2], NT1,900
[m.sup.3]/unit, sales tax
excluded
Table 2. Mapping Sample Activities of Cost-loaded Schedule to PCEs of
the Cambridge and Yangkong Projects
[PCE.sub.ij] = [PCE.sub.2j] (the formwork subcontractor) of Cambridge
Budget Unit Price,
[buc.sub.ij]
([m.sup.2]/unit)
Act. [PCE.sub.ij] Description
ID
13 [PCE.sub.21] 1st F wall and [buc.sub.21] = 1,573
2nd F formwork
20 [PCE.sub.22] 3rd F slab formwork [buc.sub.22] = 1,573
27 [PCE.sub.23] 4th F slab formwork [buc.sub.23] = 1,573
34 [PCE.sub.24] Roof slab formwork [buc.sub.24] = 1,573
Budget Quantity, Actual Unit
[bq.sub.ij] Cost, [bq.sub.ij]
([m.sup.2]) ([m.sup.2]/unit)
Act.
ID
13 [bq.sub.21] = 1500.0 [auc.sub.21] = 1,573
20 [bq.sub.22] = 1680.0 [auc.sub.22] = 1,573
27 [bq.sub.23] = 1680.0 [auc.sub.23] = 1,573
34 [bq.sub.24] = 860.0 [auc.sub.24] = 1,573
Actual Quantity,
[aq.sub.ij] Earliest Start,
([m.sup.2]) [es.sub.ij]
Act.
ID
13 [aq.sub.21] = 1506.7 [es.sub.21] = 06/23/09
20 [aq.sub.22] = 1677.7 [es.sub.22] = 07/22/09
27 [aq.sub.23] = 1677.7 [es.sub.23] = 08/08/09
34 [aq.sub.24] = 851.0 [es.sub.24] = 09/05/09
Earliest Finish, Duration
[ef.sub.ij] (Days)
Act.
ID
13 [ef.sub.21] = 06/25/09 3
20 [ef.sub.22] = 07/26/09 5
27 [ef.sub.23] = 08/14/09 7
34 [ef.sub.24] = 09/9/09 5
[PCE.sub.ij] = [PCE.sub.4j] (the rebar subcontractor) of Yangkong
Act. [PCE.sub.ij] Description
ID
2 [PCE.sub.41] Foundation rebar
5 [PCE.sub.42] Grade beam rebar
9 [PCE.sub.43] 1st F rebar
12 [PCE.sub.44] 1st F column and wall rebar
15 [PCE.sub.45] 2nd F slab and beam rebar
19 [PCE.sub.46] 2nd F column and wall rebar
22 [PCE.sub.47] 3rd F slab and beam rebar
26 [PCE.sub.48] 3rd F column and wall rebar
36 [PCE.sub.49] Roof slab and beam rebar
Budget Unit Price, Budget Quantity,
[buc.sub.ij] [bq.sub.ij]
Act. (ton/unit) (ton)
ID
2 [buc.sub.41] = 3,800 [bq.sub.41] = 30.00
5 [buc.sub.42] = 3,800 [bq.sub.42] = 26.00
9 [buc.sub.43] = 3,800 [bq.sub.4] = 15.00
12 [buc.sub.44] = 3,800 [bq.sub.44] = 8.00
15 [buc.sub.45] = 3,800 [bq.sub.45] = 50.00
19 [buc.sub.46] = 3,800 [bq.sub.46] = 16.00
22 [buc.sub.47] = 3,800 [bq.sub.47] = 55.00
26 [buc.sub.48] = 3,800 [bq.sub.48] = 13.00
36 [buc.sub.49] = 3,800 [bq.sub.49] = 32.00
Actual Unit Actual Quantity,
Cost, [auc.sub.ij] [aq.sub.ij] (ton)
Act. (ton/unit)
ID
2 [auc.sub.41] = 3,800 [aq.sub.41] = 29.78
5 [auc.sub.42] = 3,800 [aq.sub.42] = 24.70
9 [auc.sub.43] = 3,800 [aq.sub.43] = 15.10
12 [auc.sub.44] = 3,800 [aq.sub.44] = 7.50
15 [auc.sub.45] = 3,800 [aq.sub.45] = 46.77
19 [auc.sub.46] = 3,800 [aq.sub.46] = 17.90
22 [auc.sub.47] = 3,800 [aq.sub.47] = 55.85
26 [auc.sub.48] = 3,800 [aq.sub.48] = 12.95
36 [auc.sub.49] = 3,800 [aq.sub.49] = 32.90
Earliest Start, Earliest Finish, Duration
Act. [es.sub.ij] [ef.sub.ij] (Days)
ID
2 es41 = 05/02/07 [ef.sub.41] = 05/05/07 4
5 es42 = 05/08/07 [ef.sub.42] = 05/10/07 3
9 es43 = 06/03/07 [ef.sub.43] = 06/08/07 6
12 es44 = 06/10/07 [ef.sub.44] = 06/10/07 1
15 es45 = 06/26/07 [ef.sub.45] = 06/26/07 1
19 es46 = 07/07/07 [ef.sub.46] = 07/10/07 4
22 es47 = 07/25/07 [ef.sub.47] = 07/29/07 5
26 es48 = 08/02/07 [ef.sub.48] = 08/06/07 5
36 es49 = 09/10/07 [ef.sub.49] = 09/12/07 3
Table 3. Details of Sample Payment Irregularities
Project [PCE.sub.ij] Description
Cambridge [PCE.sub.22] 3rd F slab formwork
Yangkong [PCE.sub.43] 1st F rebar
[PCE.sub.44] 1st F column and wall rebar
[PCE.sub.48] 3rd F column and wall rebar
Expected Date Actual Date Amount of
Project [PCE.sub.ij] of Payment of Payment Payment
Application Application Irregularity
Cambridge [PCE.sub.22] 08/01/09 08/15/09 2,639,033
Yangkong [PCE.sub.43] 06/15/07 07/01/07 77,292
[PCE.sub.44]
[PCE.sub.48] 08/15/07 09/01/07 44,289
Table 4. Cost Flows of Yangkong Project Created with
(T, F, C, SC, NPI)
Date Cost Flows
(1) (2)
April 17, 2007 0
April 30, 2007 495,000
May 17, 2007 3,074,946
May 30, 2007 3,033,659
June 17, 2007 2,935,119
June 30, 2007 3,304,358
July 17, 2007 3,539,871
July 30, 2007 5,153,393
August 17, 2007 6,247,868
August 30, 2007 7,338,106
September 17, 2007 7,989,253
September 30, 2007 11,445,118
October 17, 2007 10,531,096
October 30, 2007 12,841,651
November 17, 2007 8,318,521
November 30, 2007 11,121,052
December 17, 2007 10,244,278
December 30, 2008 16,973,524
January 17, 2008 11,925,418
January 30, 2008 15,030,393
February 17, 2008 7,974,296
February 28, 2008 13,826,885
March 17, 2008 7,681,574
March 30, 2008 16,547,551
April 17, 2008 7,367,968
April 30, 2008 16,221,932
