Bottleneck flow and product mix

A narrow doorway can limit how fast people leave a hall even when the stairs beyond it are wide. Widening the stairs does little until the doorway changes. But if the doorway is widened, the stairs may become the next limit. A bottle route has the same pattern. What matters is the flow that crosses every required stage before its due time, not the largest capacity number displayed beside one machine.

In the simplified Northstar route, the supplier supports twenty four good bottles, manufacturing supports thirty two, and shipping supports thirty. All three figures refer to the same week and the same finished good equivalent. The maximum new completed flow is the smallest of the three, twenty four. The net requirement is twenty nine, so the route leaves a five bottle shortfall. These capacities are good-unit ceilings for this example; do not apply the ninety seven percent yield factor again to them.

Local spare capacity is useful only if it can help the constrained route. Adding four manufacturing units changes its ceiling to thirty six but leaves the route at twenty four. Adding five supplier units raises the supplier limit to twenty nine, enough for the stated requirement. Adding ten supplier units makes shipping, at thirty, the next limit. The identity of a bottleneck can therefore change as recovery actions change the feasible set. Always recalculate the whole route after each action.

The minimum rule assumes one product, a common time window, compatible units, no usable intermediate stock, and stages that can pass the required flow on time. If a pallet waits between stages or a truck leaves before production ends, the weekly minimum is only an upper bound. Flow conservation also matters: upstream releases should not be mistaken for customer shipments. Label starts, good production, packed bottles, and shipped bottles separately. This helps reveal where work is waiting and where a promise can actually be made.

Two recipes may use the same oven but very different amounts of preparation time. Baking only the quick recipe can make oven capacity look generous while the cook struggles. A mixed menu needs a resource table rather than one average cooking time. Northstar faces the same issue when a plain bottle and a decorated bottle share equipment. Changing the mix changes which resource fills first, even when the total number of bottles is unchanged.

Call the plain bottle A and the decorated bottle B. A uses ten machine minutes and six labor minutes. B uses twenty machine minutes and four labor minutes. The shift supplies two hundred machine minutes and one hundred twenty labor minutes. With demand caps of twelve A and ten B, a proposed mix of twelve A and four B uses all two hundred machine minutes but only eighty eight labor minutes. That mix is feasible. The machine is binding while labor has thirty two minutes of headroom.

Now compare ten A and five B. Machine load remains two hundred minutes, while labor falls to eighty minutes. Equal machine load does not imply equal product counts or value. If contribution is six currency units per A and fourteen per B, twelve A plus four B contributes one hundred twenty eight, while ten A plus five B contributes one hundred thirty. This value comparison assumes contribution already subtracts the relevant variable costs. It says nothing by itself about promised customer service.

A single average time is risky when the product mix moves. Fifteen A need one hundred fifty machine minutes and ninety labor minutes; fifteen B need three hundred machine minutes and sixty labor minutes. Both are fifteen bottles but have very different feasibility. Resource use per product should remain visible in the model. Contribution per bottleneck minute can guide a simple one-resource comparison, but it does not replace checking all constraints, product demand caps, or a policy that protects a minimum allocation.

In your lab, change the limits across four weeks, then test a new mix in three shifts. Do not stop when one resource fits. Follow the flow to the last stage and check the due date. Say which action raises shipped output, which action adds only spare time, and why. End with a choice that states both its value goal and its service rule. A good answer explains the constraint that makes the choice useful.

1. Define the case

   Original card shows the two lesson titles, fictional business, and planning goal.

   • Northstar case
   • Explicit scope
   • Check the units
2. Read the inputs

   Original table highlights the first lesson’s supplied quantities with unit and timing labels.

   • Given quantities
   • Usable dates
   • Stated limits
3. Trace the first check

   Original arithmetic flow follows the first lesson’s worked calculation to its checked answer.

   • Calculate load
   • Find the gap
   • State the result
4. Add the second view

   Original paired cards show how the second lesson adds a new constraint or decision policy.

   • New condition
   • Same discipline
   • No hidden assumptions
5. Compare scenarios

   Original three-column table uses the lesson lab baseline, stress case, and response.

   • Baseline
   • Stress case
   • Feasible response
6. Release the decision

   Original decision card links result, uncertainty, owner, and next verification gate.

   • Explain tradeoffs
   • Name the owner
   • Verify before release