Yield, scrap, and unfinished supply

A finished requirement is stated in good bottles. A machine start is a unit entering the process. These are not equal when some starts fail inspection. If expected yield is ninety seven percent, each start contributes an average of zero point nine seven good bottles across repeated comparable runs. To target twenty nine good bottles, divide twenty nine by zero point nine seven and round starts upward. The result is thirty starts. Expected good output is twenty nine point one. This is an average-based planning estimate; a single batch can produce fewer than twenty nine good bottles. Keep a service recovery option when the due date matters. Do not call a three percent yield loss the same thing as adding three percent to the desired output. Dividing by the retained fraction and multiplying by one plus a loss fraction are different conventions. Their difference grows with losses. Define the convention and denominator in the data dictionary rather than relying on a label such as scrap percent. Fixed startup scrap is another separate mechanism. If two input units are consumed before productive starts, add those two after calculating productive starts under this lesson’s convention. They are not also included in the observed yield. If the yield history already included setup loss, adding it again would overstate input needs. Rounding belongs at the physical decision boundary. You can calculate expected output as a decimal, because it is an expectation, but you cannot start a fraction of a bottle in this case. For multiple stages, determine whether intermediate units are indivisible and whether rounding occurs at each stage. State that rule before comparing answers. Use scenarios to expose the risk. A lower yield raises input needs and may also raise run time. A plan that covers material at the average yield can still fail on capacity. Keep the good-unit target unchanged while varying yield so the effect of the process assumption is visible. Work in process has passed some operations but is not yet available to ship. Its value in a plan depends on what remains, when that work can finish, and which inspections it must pass. Ten partly assembled bottles do not automatically equal ten usable bottles due tomorrow. Northstar records eight units after assembly and before final inspection. The remaining expected yield is ninety five percent, so expected good supply from that group is seven point six. Do not apply the earlier assembly loss again. The units already survived that stage, and their status is part of the starting information. Expected supply can be fractional, but a firm shipping promise is expressed in whole accepted bottles. For this planning exercise, use expected WIP output in the model and round only the new starts upward. The answer key shows the arithmetic. The decision memo must separately discuss uncertainty and avoid claiming that seven point six bottles can physically ship. WIP can also be late. If final inspection happens after the demand cutoff, exclude that batch from timely coverage even if it is almost complete. A small remaining operation is not proof of a short queue. A planner needs the resource slot and an agreed completion time, not only a percentage-complete estimate. Now pause and test the plan with your own hands. Draw a row for each week. Name the unit at the top of each row. Put the input in one place and the result in a new place. Keep a copy of the first plan. Change just one fact, then run the sums once more. Ask what moved, why it moved, and who must act. If a date is too late, say so. If a part is not there, show the gap. If a count is based on an average, do not call it a sure thing. A plan is useful when the next person can check it and act on it. Write a short note that states the need, the choice, the risk, and the next check. Read it out loud to a peer. Ask that peer to find one weak claim. Use the feedback to make the plan clear. Each number should have a unit, a time, and a source in the case. Each change should have a reason. Each open gap should have an owner. These habits help a small team see the same facts and make a sound choice.

1. The planning question

   Original card with the two lesson goals.

   • Translate good-output targets into starts without treating an expectation as a promise.
   • Assess unfinished supply by stage, timing, and remaining loss.
   • Northstar fictional case
2. Inputs and units

   Original table highlighting input quantities and dates.

   • Yield
   • Scrap
   • State timing
3. First calculation

   Original equation card showing the first worked case.

   • 97% starts[30,42,52,68]; expected good[29.1,40.74,50.44,65.96]; bodies[32,44,54,70].
   • 95% starts[31,43,53,69];90% starts[33,45,56,73].
   • For29 at90%,expected good29.7, productive rejects3.3, body input35 with fixed scrap.
4. Second calculation

   Original table showing the second worked case.

   • Base new starts[30,23,19,11]; combined expected output[29.1,29.91,29.83,29.67].
   • Late WIP means30 new starts in each case.
   • Confirmed accepted outputs yield new starts[30,23,20,12]; no remaining WIP yield is applied to accepted output.
5. Stress the plan

   Original side-by-side baseline and revised result cards.

   • Change one input
   • Recompute dependent rows
   • Expose the gap
6. Commit with evidence

   Original checklist with an owner and next review date.

   • Retain assumptions
   • Check the result
   • Name the next action