Project Time Exchange

1. Start with a declared baseline

Activities A–G form a fictional construction example. Each menu starts with the original duration at zero extra cost. The forward pass finds earliest starts and finishes; the backward pass finds latest times and float. Disconnected tasks are allowed and all must finish. Zero-duration tasks can represent milestones. The model has finish-to-start relationships, zero lag and a common project start at week zero.

Every portfolio recomputes the network. A task that was critical can cease to be critical, and parallel paths can become tied. The baseline remains option 0 even if another menu option offers a faster duration at zero cost. These CPM concepts are covered in MIT’s Critical Path Method lecture.

2. Menus are bundles, not independent time savings

An option supplies a duration and incremental cost. For example, B offers 5 weeks at 0, 4 at 70, or 3 at 160. Only one option is selected per activity. Shortening a non-binding path may produce no finish-time gain unless other activities also change. This is the useful part of the original “market for time” metaphor.

Keep a non-crashable floor where a task cannot safely become shorter. A declared floor is enforced; otherwise the supplied options define the available durations. Menus should be justified by method, crew, equipment, quality and delivery evidence. Increasing marginal costs may be plausible, but are not a mathematical requirement of this enumerator.

3. A frontier and two different choices

The frontier contains portfolios for which no other combination has both no greater cost and no later finish, with at least one strict improvement. Equivalent cost/finish portfolios use the first combination in sorted activity-ID and menu order. The full frontier is visible, including points above budget; selection is restricted to affordable points.

The knee is a heuristic bend in the affordable frontier, using distance from the endpoints’ chord after normalising both axes to 0–1. It is independent of cost-unit scaling, not proof of the best trade-off. With fewer than three points it chooses the fastest affordable endpoint; tied interior distances favour lower cost.

The highest net value choice maximises v × (T₀ − T) − C subject to C ≤ B. Equal net values prefer lower cost, then earlier finish. “Welfare” in the old app meant this stated objective, not a measurement of social welfare. The cap constrains declared crash cost, not supplier payments.

4. What the calculation establishes

Within the supplied finite menus and precedence assumptions, exhaustive enumeration considers every combination. It therefore identifies the nondominated time/cost points and the best affordable stated objective. It does not establish that the menus are true, the network complete, or the resulting schedule executable on site.

Duration and cost comparisons use integer millionths to avoid decimal budget errors; net-value ranking uses exact integer products of the declared inputs. Displayed numbers may be rounded. Original option indices, unrounded model values and the full input remain in the exported result.

5. Hidden coupling and risk

Two options may both rely on the same crane, specialist crew, possession window or permit. CPM alone cannot enforce those joint constraints. Add a resource/calendar model or explicitly exclude conflicting combinations before relying on a plan; this version does neither. Earlier finish is not a quality or safety benefit by itself.

Optional risk, notes and evidence descriptions are retained as text, not probabilities or penalties. A scenario or stochastic extension would need duration distributions, correlations, resource rules and an explicit risk objective. A “P80” label cannot be inferred from this deterministic result, and a payment is not a probability or scenario weight.

6. Audit and rebaseline

Export the applied dataset, option IDs, costs, baseline, selected ES/EF/LS/LF/float, frontier, budget and value assumption. Record who supplied the menus, the evidence and version date in notes or your controlled source. Comparing snapshots can explain why the critical set changed.

The output is a candidate schedule change for review. Exporting does not authorise a rebaseline, alter an earned-value system, approve a change or authenticate a record. Agree the scope, resource feasibility and change-control decision before updating maintained plans.

7. Scaling the experiment

The number of portfolios is the product of the menu sizes: 20 activities with three choices already produce 3,486,784,401 combinations. This browser tool rejects cases beyond its stated caps, runs bounded work in chunks and allows cancellation. It does not silently sample or describe an incomplete frontier as exhaustive.

A larger study could use a separately validated mixed-integer or constraint-programming model for discrete choices and longest-path constraints. Resource-limited scheduling requires additional constraints. Searching only near-critical tasks is a heuristic unless a complete argument establishes what may safely be excluded.

8. A bounded pilot and the value assumption

Choose a small network that fits the enumeration cap. Obtain credible menu points from task owners; review floors and hidden shared resources. Vary the budget and your explicit value per week, inspect the selected options and compare the result with the declared baseline. A constant value assumes each week saved is equally valuable over the explored range.

Keep a dated record of chosen options and realised durations/costs. Repeated comparison can test menu credibility and reveal where assumptions failed. It does not by itself identify causal “crash elasticity”, establish supplier honesty, or validate a procurement mechanism. A proposal to start with 20 tasks belongs in a scalable solver study, not this small enumerator.