Rush Order on the Bottleneck Lathe
A job shop runs three product families on a single CNC lathe that is the plant bottleneck. Committed weekly demand is family A at 500 units (1.5 min cycle), B at 400 units (2.0 min), and C at 200 units (2.5 min). The lathe is staffed 2,400 min per week across two shifts. Every changeover costs 45 min regardless of family, and the scheduler currently runs two campaigns per family per week - six changeovers - to hold work-in-process down and match daily shipment patterns. On Monday morning sales lands a rush order for 100 units of family A promised for Friday. Raw material is on hand, the lathe can be run on overtime at a $2.40/min premium, a qualified subcontractor quotes a $450 premium for the 100 units, and carrying one extra week of B and C output is estimated at $65.
1. Determine the lathe's committed load and state precisely how much capacity the rush order does or does not have.
Read the worked answer
Run time at standard
| Family | Units | min/unit | Minutes |
|---|---|---|---|
| A | 500 | 1.5 | 750 |
| B | 400 | 2.0 | 800 |
| C | 200 | 2.5 | 500 |
| Run total | 2,050 |
Changeover time: 6 campaigns x 45 min = 270 min
Committed load = 2,050 + 270 = 2,320 min
Slack = 2,400 - 2,320 = 80 min
Rush order: 100 x 1.5 = 150 min of run time.
- Added to an existing A campaign (no extra setup): 150 min needed vs 80 min available -> short 70 min.
- Run as a separate third A campaign: 150 + 45 setup = 195 min -> short 115 min.
So the order does not fit as things stand; it is short by 70 min at best. Note the 80 min of slack is nominal - it assumes zero unplanned downtime, no scrap/rework on the lathe, and that the 2,400 min is truly available machine time rather than paid time including breaks and shift handover. Before committing to the promise date, confirm the slack is real; if historical downtime is even 3%, the slack is already gone.
2. Evaluate the four options available - (i) add the 100 units to an existing A campaign on overtime, (ii) run A as a third campaign, (iii) subcontract, (iv) collapse to one campaign per family - and recommend one.
Read the worked answer
Option (i) - fold into an existing A campaign
Overrun = 150 - 80 = 70 min -> 70 x $2.40 = $168. No extra setup, since it rides inside a campaign already scheduled.
Option (ii) - third A campaign
Overrun = 195 - 80 = 115 min -> 115 x $2.40 = $276.
Option (iii) - subcontract
Premium = $450. It also removes 150 min from the lathe, so no overtime is incurred - but it is 2.7x the cost of option (i).
Option (iv) - collapse from six campaigns to three
Saves 3 x 45 = 135 min -> load becomes 2,185 min. Add the rush order (150 min, inside the single A campaign) -> 2,335 min. Overrun = 15 min.
Cost = 15 x $2.40 + $65 carrying = $36 + $65 = $101.
Recommendation: Option (iv), at about $101, is the cheapest and it also builds slack back into the week. But it is the only option that changes a scheduling policy, so it should not be adopted blindly:
- The two-campaign-per-family pattern was presumably set for a reason (daily ship patterns, floor-space limits for B and C, or a shelf-life/oxidation limit). Confirm the reason before collapsing - if it is a customer daily-ship commitment, option (iv) may violate a delivery window even though it is cheapest in dollars.
- Longer campaigns also raise WIP on B and C; the $65 estimate should be checked against actual holding cost, not a rule of thumb.
- If the two-campaign rule cannot be broken this week, take option (i) at $168 rather than option (ii); there is no justification for paying $108 for an extra 45-min setup.
- Subcontract only if the A campaign cannot be stretched (e.g., A raw material is committed to another order) or if the strategic value of a guaranteed Friday ship outweighs the $349 premium over option (iv).
3. The rush-order customer is the plant's largest account and has hinted at more volume. How does that change your analysis, and what would you commit to?
Read the worked answer
Strategic value legitimately changes the answer, but only by changing the risk you are willing to carry, not by changing the arithmetic.
What does not change: the lathe still only has 2,400 min, and the bottleneck is still the bottleneck. If this account grows, the shop cannot absorb the growth with clever scheduling - the constraint has to be broken. Accepting growth without a capacity plan converts a one-week problem into a permanent late-delivery problem, which is a worse outcome than losing the order.
What does change:
- The cost gap between options is small relative to the value of the account ($101 vs $450 is a rounding error against a lost major customer). Buy certainty: option (iv) plus the 15 min of overtime, or option (i) if (iv) is infeasible, and do not subcontract a strategic customer's product to a competitor's supplier.
- Institutionalize the change rather than firefighting it: move permanently to one campaign per family if the ship-pattern check passes, which recovers 135 min/week - a 5.6% capacity gain with no capital.
- Quantify the growth case before committing: if the account adds, say, 100 A units per week, that is another 150 min on a machine with 80 min of slack. That is a capital decision (second shift, second machine, or outsourcing a mature family), not a scheduling decision, and it belongs in the next capacity review.
Commitment: a Friday ship date, achieved by option (iv) with the 15-min overtime, provided planning confirms the B and C ship patterns survive a single campaign. If that check fails, ship via option (i) at $168 and raise the campaign-policy question separately. Do not promise growth volume until the 135 min/week recovered here is verified in practice.