Weighting and the decision matrix

The matrix

The fourth and fifth lines of R-psp-3: weighting stated and justified and every matrix cell has a reason. The tool is the weighted decision matrix: criteria as rows, each with a weight — the weights sum to 1.00 (or 100) — and alternatives as columns; each cell holds a score from 1 to 5 and, in the write-up, a one-line reason; the last row is the weighted total, the sum of score × weight down each column. Smith's cost-benefit table uses High / Medium / Low; that is the sketch stage. The SAF expectation, per every student account this course could find, is the numeric matrix — and the memo rubric's analysis organised by criteria is satisfied by exactly this table plus its reasons.

Worked example — Lakeshore, cell by cell

Weights. Annual cost 0.30 — Priya named cash first and it is the constraint everyone shares. On-time reliability 0.25 — two of three key accounts have threatened to leave; this is the objective under immediate threat. Cash-flow impact 0.15, staff impact 0.15, flexibility 0.15 — real, shared by fewer stakeholders, and none of them the reason the memo was commissioned. Sum: 1.00. Every weight has a reason, and the two largest go to the criteria several stakeholders share.

Scores. Annual cost: A 2 ($38,000 and rising — cheap today, not next year); B 2 ($67,400: the loan payment plus repairs); C 3 ($58,000, maintenance included — the lowest of the three fixes); D 1 ($74,400 of margin lost, the highest annual cost of all). Reliability: A 1 (a nine-year-old press with 14 breakdowns); B 5 and C 5 (a new press either way); D 3 (reliable only as far as the trade printer's schedule allows). Cash-flow: A 5 (no outlay); B 1 ($260,000 of new debt); C 4 (no outlay, a monthly commitment); D 4 (no outlay, margin lost gradually). Staff: A 5, B 5, C 5 (both operators kept); D 1 (two operators redundant). Flexibility: A 3 (nothing committed, nothing fixed); B 2 (a press owned for years, debt for five); C 4 (a term with an exit and an upgrade clause); D 4 (a contract that can be ended).

Totals. A: 0.60 + 0.25 + 0.75 + 0.75 + 0.45 = 2.80. B: 0.60 + 1.25 + 0.15 + 0.75 + 0.30 = 3.05. C: 0.90 + 1.25 + 0.60 + 0.75 + 0.60 = 4.10. D: 0.30 + 0.75 + 0.60 + 0.15 + 0.60 = 2.40. The lease leads by more than a point.

What the total is, and is not

The totals inform the decision; they do not make it. 4.10 is a summary of twenty judgements and five weights, every one of which can be argued with — which is why the reasons are written down and why the next lesson tests whether the answer moves. A matrix presented as proof ("C wins, 4.10 to 3.05") is a lens mistaken for a verdict; a matrix presented as a lens ("C leads on cost among the fixes and ties on reliability, and the lead survives the weightings we tested") is what stage 4 will build on.

Score two rows of the clinic's matrix

Alternatives: paper (status quo) · reminder-only service · full online booking · hybrid. Annual cost: paper 5 (nothing new), reminder 4 (about $60 a month), full 3 (about $150 a month), hybrid 3. Scheduling accuracy: paper 1 (one book, two hands), reminder 1 (the book is unchanged), full 5 (one shared calendar), hybrid 4 (shared calendar for most bookings; phone bookings still keyed in). Two rows, eight cells, eight reasons. The remaining three rows are yours.

Type the skeleton

The snippet is the shape: a header row with the weight beside each criterion, one row per criterion, and the weighted-total row last. Type it until it is automatic; then every matrix you build starts with the weights visible and summing to one.