Cost and Scope

Honest Crashing Scope

The final lesson separates a feasible displayed plan from a minimum-cost model claim.

highlighted = computed this step

Displayed is feasible

The B then D plan is feasible and costs 6.

displayed feasible cost=6\text{displayed feasible cost}=6
Cost and scopeThe chart separates the displayed plan cost from the exact minimum-cost comparison.cost and scopedeadline 6activity crash dataactnormalmaxcost/dayA213B422C315D214path lengths after each recomputestateA-B-DA-C-Dcostbaseline8*70crash B7*7*2crash D6*6*6asterisk marks a recomputed critical pathdisplayed plan cost 6exact minimum cost 5final duration 6recompute critical paths after every crash

Exact comparison

Exact enumeration finds a cheaper deadline plan costing 5.

minimum deadline cost=5\text{minimum deadline cost}=5
Cost and scopeThe chart separates the displayed plan cost from the exact minimum-cost comparison.cost and scopedeadline 6activity crash dataactnormalmaxcost/dayA213B422C315D214path lengths after each recomputestateA-B-DA-C-Dcostbaseline8*70crash B7*7*2crash D6*6*6asterisk marks a recomputed critical pathdisplayed plan cost 6exact minimum cost 5final duration 6recompute critical paths after every crash

Minimum plan

That cheaper plan crashes A by 1 day and B by 1 day.

ΔA=1ΔB=1\Delta_A=1\quad \Delta_B=1
Cost and scopeThe chart separates the displayed plan cost from the exact minimum-cost comparison.cost and scopedeadline 6activity crash dataactnormalmaxcost/dayA213B422C315D214path lengths after each recomputestateA-B-DA-C-Dcostbaseline8*70crash B7*7*2crash D6*6*6asterisk marks a recomputed critical pathdisplayed plan cost 6exact minimum cost 5final duration 6recompute critical paths after every crash

Honesty note

The displayed B then D plan is feasible and costs six. Exact enumeration also shows a cheaper deadline plan costing five, so the displayed plan is not claimed to be cost-minimal. This is a tiny deterministic crash plan. Recompute critical paths after every crash; for a minimum-cost deadline plan, solve the exact model instead of assuming the next cheap-looking activity is best.

recompute paths and solve the exact model for cost optimality\text{recompute paths and solve the exact model for cost optimality}
Cost and scopeThe chart separates the displayed plan cost from the exact minimum-cost comparison.cost and scopedeadline 6activity crash dataactnormalmaxcost/dayA213B422C315D214path lengths after each recomputestateA-B-DA-C-Dcostbaseline8*70crash B7*7*2crash D6*6*6asterisk marks a recomputed critical pathdisplayed plan cost 6exact minimum cost 5final duration 6recompute critical paths after every crash