Structural Engineering

Construction Materials & Management

Concrete ingredients, PERT/CPM network analysis and inventory (EOQ) — the materials and project-planning scorers in GATE CE.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Construction management plans time, cost and resources. A CPM network finds the critical path — the longest chain of activities with zero float that fixes the project duration. PERT treats activity times as uncertain, using a weighted expected time

t_{e} = \frac{t _{o} + 4 t _{m} + t _{p}}{6}

. Inventory is optimised by the Economic Order Quantity that balances ordering and holding costs.

The Core Formula Matrix

PERT expected time:

t_{e} = \frac{t _{o} + 4 t _{m} + t _{p}}{6}

PERT variance:

σ^{2} = (\frac{t _{p} - t _{o}}{6})^{2}

Total float:

T F = L F - E F = L S - E S

(zero on the critical path)

Economic Order Quantity:

E O Q = \frac{2 D S}{H}

The ‘IIT Traps’

⚠
Critical path = longest path, not shortest. It has zero total float and governs project duration.
⚠
PERT uses a weighted mean ( $4 t_{m}$ ), not a simple average of the three times.
⚠
**EOQ uses annual demand $D$ and per-unit holding cost $H$ ** — mixing monthly and annual figures is the usual error.

📚 Standard references

Project Planning and Control with PERT and CPM — B.C. Punmia & K.K. Khandelwal
Construction Engineering and Management — S. Seetharaman

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

Annual demand

D = 10000

units, ordering cost

S = ₹ 50

, holding cost

H = ₹ 4

/unit/yr. The EOQ is _____ units.

Q2MEDIUM2 Marks · NAT

For an activity

t_{o} = 4

t_{m} = 6

t_{p} = 14

days, the PERT expected time is _____ days.

Q3HARD2 Marks · MCQ

On a CPM network, the critical path is the path with: