Check changeover cost before batching preparation work

Grouping similar preparation work can reduce a modeled switching cost while leaving the work itself unchanged. Make that mechanism visible before describing a batch as quicker. A transition ledger helps distinguish an order-dependent overhead calculation from a claim about real productivity.

Specify service and switching separately

Use three fictional jobs. A and C have type X; B has type Y. Every job needs two service turns on one preparation station. Switching between different types takes three additional turns, while switching between the same type takes zero. Initial setup takes zero in this exercise.

All jobs are ready at turn zero. There are no deadlines, prerequisites, interruptions, or quality differences. These invented conditions isolate one question: how does the sequence alter transition overhead? An actual preparation plan needs evidence for its costs and constraints before this model could inform a proposed change.

Trace the alternating order

Consider A, B, C. A uses two service turns. Moving from X to Y adds three, then B uses two. Moving from Y back to X adds another three, then C uses two.

The service total is six and the transition total is six, giving twelve occupied turns. Record both transitions by their neighboring job identities. A total of twelve without that breakdown would not show whether the extra time came from switching, longer jobs, or a different initial condition.

Replay a grouped sequence

Now examine A, C, B with exactly the same jobs and costs. A uses two, the X-to-X transition adds zero, C uses two, the X-to-Y transition adds three, and B uses two. Service remains six; transitions total three; occupied time is nine.

Only one type change occurs instead of two. Nothing about A or C became easier, and no job disappeared. Keep the original and grouped ledgers together so the difference can be traced to that changed adjacency. Calling the grouped plan better overall would still exceed the calculation, because the toy omits other considerations.

Bound any claim about the minimum

There are six orders for these three identified jobs. ACB, CAB, BAC, and BCA each place the two X jobs together and incur one type change, costing nine. ABC and CBA separate them and incur two changes, costing twelve.

Under this complete tiny fixture, nine is the minimum and four orders attain it. The calculation does not select one of those four as uniquely best. Nor does it prove that grouping every type is optimal when transition costs differ by direction, an initial configuration matters, or other requirements constrain order. Preserve the cost table and assumptions behind any minimum claim.

Inspect the proposed operational tradeoff

A real request may need B earlier, or someone may have to prepare materials for the type change. Those conditions belong in a revised model. This exercise has no deadlines; do not import the completion-deadline result from another worksheet without recalculating the combined constraints.

Ask another reader to recompute both totals and explain what stayed fixed. If they attribute the difference to faster service, restore the separate entries. The finish artifact is a transition-by-transition cost ledger, candidate orders, and unresolved real-world costs. It supports a bounded discussion of preparation overhead, not an automatic Kiguri batching feature or a measured improvement for any team.