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A Computational Formulation of WBS in Construction Project Management

February 7, 2010 | Author: PM Hut | Filed under: Project Plan Development

A Computational Formulation of WBS in Construction Project Management
By Mohamed Shameer

It has been long acknowledged that the distinctive difficulty in Project management is transient, opening challenges such as follows:

  • Definition of a project and its objectives are one-time. Hence, they tend to be incomplete (causes scope-creep), optimistic (causes cost over-run), non-comprehensive (causes rework) and ineffectively communicated (causes conflict).
  • Processes in a project are short lived; documentation & data-capture are non-routine. Identification and implementation of suitable control system may be longer than process duration.
  • Project organizations are ad-hoc. They are assembled specifically for the project and are hence subject to considerable inertia and perturbation on existing system.

Cyclic control systems in projects by Deming-Shewhart PDCA cycle, Meredith-Meyer Cybernetic Control and Lean Project Management are hence most suited to project management. Cyclic control attempts to plan projects in measureable parts, execute them, measure them and take corrective action at distinct intervals of time. Frequency of the cycle vary among projects (suggested for instance as weekly in WWP of lean management). Such cycles create a short-lived system and closes itself at predetermined intervals.

From a mathematical or computational perspective, most cyclic systems would require definition of works in the WBS from two perspectives – one in terms of actual deliverables and other in terms of resource planning. A deviation between the two measures defines project deviations along with their causes and suggestions regarding remedial measures.

The deliverable of a work is measured by Lebesgue measures such as lengths, areas, volumes, weights and counts, say by a measurement function:
Vb = g (x1, x2, x3,………….. xm)
Where x1, x2, x3,………….. xm are Lebesgue dimensions. For example, construction of a wall would be measured by (length x breadth x height) in cubic meters of volume.

Resource plan of a work package is in turn measured as Value ΔV of a work package in a control period Δt by a cost function
ΔV = f (c,r,t).Δt
Where c is the contribution of different resources to achieve unit quantum of work, r is the cost of resources and f is a function of productivity, cost and time. For example, brickwork for the wall needs say 500 bricks, 62 kg cement, 0.2 cubic meters of sand, 30 litres of water, 0.7 masons and 0.35 helpers for each cubic meter of work. (This is only indicative)

Besides definition of suitable measurement and cost function, management control also requires that:

  • It should be possible to evaluate measurement function in control periods during execution of work and report the extent of work completed at the end of the control period (say a day).
  • It should be possible to vary the output of work by varying the extent of resources employed in the work.

Hence, mathematically, cost function should be such that kΔV = f (kc,r,t).Δt where k is a resource scale. Similarly, measurement function should be such that value of work done upto period i shall be Vi = mi Vb {where mi < 1}.

Works that can be defined in this manner shall be called homogeneous works, because the functions f and g are homogeneous mathematical functions. In other words, homogeneous work functions are scalable in terms of resources and measurable during execution. Earned value theorem uses Unit Value measurement for measurement of homogeneous works.

Homogeneous works are amenable to computational PDCA or other cyclic analysis provided work packages in the WBS are mutually exclusive – that is one work is independent of another in terms of cost, productivity, scale and time. In such cases, computational cyclic analysis can be carried out as follows:

  1. All works are defined as mutually exclusive homogeneous works.
  2. The logical relationship between works is established using Gantt chart and CPM analysis.
  3. Planned value curve can be established as cumulative summation of cost functions on Gantt chart.
  4. At any time during the project, a desired planned value of work is scheduled for a control duration. The resources required for this objective may be calculated and sub-optimised by inverting the cost function to find a suitable scale factor k.
  5. Project managers advise contractors and vendors to supply material, equipment and labour in accordance with the sub-optimized value of k during the control duration.
  6. Earned value shall be measured at generic instances within control duration evaluating the measurement function. The actual resources employed are also reported through material receipts, equipment time cards and muster roll registers.
  7. Deviation between generic earned value and planned value in control period indicates the difference between slope of the cumulative planned and earned value curves. For instance, a deviation on a weekly work plan, may be corrected by a different k value for next week. In effect, the slope of earned value curve is changed at will, to rectify the deviation.

Mohamed Shameer is a civil engineer consultant currently working in Chennai, India. His expertise includes construction management for residential, industrial, commercial, and heavy engineering projects. Mohamed writes a lot about Construction Project Management on his blog, the Indian Civil Engineer.

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