Why the buyer paid SGD 80 over the minimum

These are original fictional figures. They demonstrate a decision method; no order was placed or business result observed.

Why pay more than the cheapest valid plan? Here the answer is written into the buyer’s policy: accept a small extra cost to reduce the quantity entrusted to one supplier. The important part is making that judgment visible—and applying it again when the facts change.

The decision before the order

An outreach equipment buyer needs exactly 1,200 identical reusable transport crates by November 6. Awards come in lots of 100. At most two suppliers may be used. Any supplier that gets an award must get at least 200 crates, and the buyer may turn that minimum off explicitly. Each supplier has a capacity by the deadline. Nothing has been ordered. The job is to produce a defensible proposal.

Four suppliers quoted. Sticker price is only part of the cost, so each quote also carries delivered freight per crate and a single fixed shipment charge for any positive award:

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Supplier	Sticker (SGD/crate)	Delivered variable (SGD/crate)	Fixed shipment (SGD)
A	11.20	13.00	450
B	12.40	12.80	120
C	12.90	13.20	90
D	13.80	13.90	50

Supplier A looks cheapest on the sticker. Its freight and shipment charge erase that lead.

The trap on the price sheet

Sort by sticker price and fill capacity, and you get A 600 and B 600. It is feasible and costs SGD 16,050. The true minimum is SGD 15,730, so the sticker-first plan costs SGD 320 more. The first lesson is plain and has nothing to do with risk. Compare delivered totals, not headline prices.

Hard feasibility

A single supplier is only an option if it can cover demand. D can, at SGD 16,730. A, B and C cannot individually meet 1,200, so they are not options, however neat a one-supplier story sounds. Any full-demand comparison has to say which quotes are actually capable.

Within the hard rules, the model considered 9,009 bounded allocation vectors and found 37 feasible plans with exact demand. Everything below comes from that set.

The minimum and its concentration

The global minimum is B 800 and C 400 at SGD 15,730. It is the least expensive feasible plan under these inputs. But two thirds of the order sits with B. If B’s whole award failed and everything else arrived, 800 crates would be missing. That is the buyer’s conditional exposure. The buyer knows neither the probability of such a failure nor any tested substitute route. So the exposure is a quantity to weigh, not a risk estimate.

The frontier: what each step costs

Moving award quantity from B to C lowers the largest award and raises cost:

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Plan	Total (SGD)	Premium over minimum	Largest award
B 800 / C 400	15,730	0	800
B 700 / C 500	15,770	40	700
B 600 / C 600	15,810	80	600

With two suppliers, the largest award cannot fall below 600. So B 600 / C 600 is the end of the frontier. The extra SGD 80 buys a 200-crate reduction in the worst conditional shortfall. It is not an expected-loss saving, because no failure probability is supplied.

Policy versus math

The math says which plans are feasible, what each costs and how the cost and exposure tradeoff runs. It does not say how much concentration is worth reducing.

That is the manager’s rule, stored at inputs/policy.json#/management_rule: accept a total up to SGD 100 above the current feasible minimum, then minimize the largest supplier award within that ceiling. The solver applies the rule and invents nothing. In the original episode the ceiling is SGD 15,830. B 600 / C 600 sits at SGD 15,810, inside it, with the smallest possible largest award. So that is the selected plan.

The SGD 100 is the fictional buyer’s stated policy. This chapter does not claim it is the objectively right price for the reduction. A different allowance may select a different plan. Its value depends on that buyer’s priorities.

The second part: the quote changes

In the second part of the fictional example, a new quote arrives on October21 before any purchase. Supplier B revises its quote. Capacity falls from 800 to 400. The sticker price rises from 12.40 to 13.20. Freight (0.40) and the shipment charge (120) are unchanged, and nothing else moves. The replacement sources are S-E2 and S-B2.

First casualty: the original selection. B 600 / C 600 now asks B for 600 against a capacity of 400, so it is infeasible. Mechanically repricing it gives SGD 16,290, but that number describes nothing the buyer could buy. It stays in the record, marked infeasible, so no one revives it by accident.

Second change: the cheapest supplier set moves. The new entire-pool minimum is C 1,000 and D 200 at SGD 16,120, with exposure 1,000. B is no longer in the cheapest plan at all. There are now 26 feasible plans from 5,005 bounded vectors, and the two-supplier maximum still holds.

Same policy, new answer

The ceiling is now SGD 16,220. Compare the nearby plans:

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Plan	Total (SGD)	Premium	Largest award	Within SGD 100?
C 1,000 / D 200	16,120	0	1,000	Yes (minimum)
B 300 / C 900	16,170	50	900	Yes
B 400 / C 800	16,210	90	800	Yes, selected
A 600 / C 600	16,260	140	600	No, over by 40

B 400 / C 800 is selected. It reduces the largest award by 200 against the changed minimum. The managerial judgment is unchanged: the rule still tolerates a small premium to lower concentration.

A 600 / C 600 is the best fifty-fifty split, but it is SGD 40 outside the allowance. A manager could explicitly raise the allowance to SGD 140 and choose it. The solver must not do that quietly. A budget change is a decision for a person, and the record should show who made it.

Compare the two selected plans. The proposal total moves from SGD 15,810 to SGD 16,210, a difference of SGD 400. B’s award goes from 600 to 400, C’s from 600 to 800, and the largest award from 600 to 800. This is a delta between two proposals. It is not an actual expense, and it says nothing about performance.

What could still make this wrong

The arithmetic can be right while the assumptions fail. The fixture assumes that crates are equivalent, the offered capacity is available by the stated deadline, tax is not a separate nonrecoverable cost, and there are no volume discounts, minimum order quantities, extra shipment fees, mixed currencies or missing charges. A real purchase has to confirm each of these. The fixture states them. It does not supply evidence for them. The numbers here were checked by exhaustive enumeration and by an independent allocation oracle. That checks the arithmetic. No business outcome or fresh outside use has been observed.

Try the decision

Open the interactive supplier example to change the premium allowance and compare the original and revised quotes. The calculator uses local arithmetic. The complete folder includes inputs, editable results, instructions and source locators for your own agent.

Evidence and method

The case is authored from synthetic quote and policy files. The supplied Python solver enumerates bounded allocations; a separately constructed pair-allocation check and boundary tests support the arithmetic. These checks do not establish real supplier availability, performance or the right commercial preference. The working folder preserves the exact assumptions and input versions. The illustration, where shown, is AI-generated editorial art, not a supplier photograph.