Compare complete machine assignments instead of choosing the cheapest pair

Define the job and the equipment promise

Google’s assignment model gives each job exactly one resource and each resource at most one job, minimizing total cost. This exercise assigns machines, never people.

Use two fictional machines, A and B, and two complete print-finishing jobs, X and Y. Costs are teaching currency units for the whole job. They are supplied inputs, not vendor quotations or hourly rates. The exercise assumes each listed pairing meets the same agreed output requirements.

Before comparing actual equipment proposals, ask the production owner what acceptance means. A low estimate that excludes required finishing, inspection or consumables would answer a different question. Obtain eligibility from qualified owners; a cost worksheet cannot certify machinery, materials or safe operation. Keep the comparison separate from permission to book equipment.

Compare both complete pairings

SciPy expresses assignment cost as the sum of selected matrix entries. Set A–X = 1, A–Y = 2, B–X = 2 and B–Y = 100. The complete pairings are A–X with B–Y, costing 1 + 100 = 101, and A–Y with B–X, costing 2 + 2 = 4. Choosing the cheapest entry first commits to the former. Its apparent saving of 1 forces an extra 98 on the remaining job, leaving a net disadvantage of 97.

Write the two full recommendations before highlighting a preferred one. A presentation that shows the first attractive quotation on one slide and leaves its consequence in an appendix invites the wrong comparison. Put the same scope statement beside both alternatives and preserve the supplied quotes as teaching inputs.

Ask a reviewer to explain the expensive outcome in words. They should identify the displaced option, not merely repeat that the second total is smaller. That explanation is useful when a sponsor asks why the team declined an individually cheaper quote. It also exposes whether someone has accidentally compared a whole-job cost with an hourly figure.

Separate an expensive solution from no solution

Now prohibit B–X. Only the 101 pairing remains eligible. Next prohibit both B–X and B–Y. B can do neither job; A cannot take both, so no complete assignment exists. Do not encode a prohibition as a large invented price: an expensive pairing and an impossible pairing mean different things.

Keep each restriction as a separately named scenario with its evidence owner. Do not let an unresolved operational concern silently become a permanent exclusion, but do not ignore a confirmed restriction merely because it spoils the low-cost answer. The planner needs to know which factual question would reopen the comparison.

When the exercise has no acceptable recommendation, describe the missing capability. Possible responses for an authorized owner might include a different scope or another verified resource. Do not fill the gap by waiving a production requirement, assigning prohibited work or treating an unconfirmed supplier as available. The absence of a feasible proposal is itself useful information.

Hand over the reason for the choice

Package the unchanged job definitions, supplied prices and eligibility evidence with the recommendation. The owner should be able to tell whether a change arose from a new quotation, a corrected scope or a real restriction. Those explanations have different commercial implications even when they produce the same preferred arrangement.

Check the recommendation against the actual decision being requested. This example says nothing about completion dates, changeover order or shared supervision. If those issues matter, ask a qualified planner for the appropriate extension rather than presenting this exercise as a finished production schedule.

After review, preserve the rejected alternatives and the owner’s reason for proceeding or stopping. Do not claim realized savings from the difference between two fictional totals. A useful result is a decision that can be reconstructed, including the reason an attractive individual quote did not lead to the strongest complete proposal.

Make the reasoning concrete.

A finishing coordinator is asked to justify a proposal that declines the cheapest individual quote.

The coordinator presents the comparison, not a booking or safety decision.

Take the questions into your next brief.

Use these prompts in your own notes. Nothing is submitted from this page.

1. Scope

   What does each complete job require?

2. Price

   Are all supplied figures on the same commercial basis?

3. Consequence

   Which displaced option explains the recommendation?

4. Evidence

   Who confirms each restriction?

5. Handoff

   What operational question remains outside this exercise?

Watch for the wrong conclusion.

• Comparing quotations with different finishing scope.
• Treating an unresolved capability question as permission.
• Claiming fictional cost differences as realized savings.

Sources & scope

The decision reasoning and fictional inputs are original. Method statements and mathematical applications remain attributed, including later restatements. Documentation was read on the stated date; no installed solver version is asserted. Local exhaustive arithmetic was executed, not real operations. No purchasing, staffing, shipment, scheduling or account change is authorized.

• Solving an Assignment Problem →Primary documentation · Supports: Supports the stated model.
• linear_sum_assignment →Primary documentation · Supports: Supports the mathematical formulation.