Foundry Recovery Plan: Overtime, Subcontract or a One-Day Delay
A foundry has accepted an order for 4,000 machined castings to be delivered in 12 working days. The contract carries a late-delivery penalty of Rs 8,000 per working day. Two machining lines run one 8-hour shift each: Line A averages 25 saleable castings per hour, Line B averages 18. Deferred preventive maintenance has now been scheduled, so Line B will be down for days 7, 8 and 9 inclusive. Overtime is sanctioned only for days 10, 11 and 12 because the crew is committed elsewhere earlier. On those days Line A may run at most 1 hour of overtime (tooling cooldown) and Line B at most 2 hours, and a single setter can supervise only 2 hours of overtime in total per day. Overtime is paid at a premium of Rs 450 per hour on A and Rs 380 per hour on B. A local vendor can supply up to 250 interchangeable castings at Rs 210 each with 4 working days' notice. The planner argues: Line A is the faster machine, so put every overtime hour on A - one hour on A is worth more castings than one hour on B.
1. Compute the output achievable by day 12 with no intervention, showing the day-by-day arithmetic, and state the shortfall.
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Break the 12 days into the three regimes created by the Line B shutdown.
| Period | Days | Lines running | Calculation | Output |
|---|---|---|---|---|
| Days 1-6 | 6 | A and B | (25 + 18) x 8 x 6 | 2,064 |
| Days 7-9 | 3 | A only | 25 x 8 x 3 | 600 |
| Days 10-12 | 3 | A and B | (25 + 18) x 8 x 3 | 1,032 |
| Total | 12 | 3,696 |
Shortfall = 4,000 - 3,696 = 304 castings.
Two arithmetic traps to avoid: (a) applying the shutdown to the whole 12 days instead of three, and (b) treating the 12 days as 12 x 43 x 8 = 4,128, which ignores the shutdown entirely and would falsely show the order closing. The lost capacity from the shutdown is not just B's 3 x 8 x 18 = 432 castings - it is 432 castings of output that the schedule had already counted on.
2. Evaluate the planner's reasoning and select the cheapest feasible recovery, comparing overtime, subcontracting and accepting a one-day delay. Show cost per casting.
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On the claim: the conclusion is right, the reasoning is incomplete. One hour of A does yield 25 castings against 18, but the decision variable is cost per casting, not castings per hour:
- Line A: 450 / 25 = Rs 18.00 per casting
- Line B: 380 / 18 = Rs 21.11 per casting
A wins on both output and unit cost, so it should be loaded first - but only because the arithmetic happens to agree, not because speed alone settles it. Had B's premium been Rs 250, B would have been the cheaper hour (Rs 13.89) despite being slower.
Maximum overtime in days 10-12: the setter constraint caps the total at 2 h/day, with A at 1 h and B at 1 h (B's own 2 h cap is not reachable).
- Line A: 3 x 25 = 75 castings, cost Rs 1,350
- Line B: 3 x 18 = 54 castings, cost Rs 1,140
- Overtime covers 129, leaving 175.
Remaining 175:
- Subcontract: 175 x 210 = Rs 36,750 (within the 250 cap)
- One-day delay: penalty Rs 8,000, and day 13 delivers a full 344 castings, which covers 175 easily
Delay is cheaper by Rs 28,750. Choose the delay unless the customer's downstream cost of a late day exceeds about Rs 28,750 - which, for an assembly line, it often does. Subcontracting is the right answer only if that downstream cost is high.
3. Given the vendor's 4-day lead time, state the latest day by which the subcontract must be released, and explain what information is and is not available at that point. Is waiting an option?
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Latest release: the start of day 8 (lead time of 4 working days, needed on site by day 12).
What is known by then: days 1-6 output is actual, not forecast - (25 + 18) x 8 x 6 = 2,064. Days 7-9 are deterministic because the Line B shutdown is planned, contributing 600. Days 10-12 are capacity, not yet production, contributing 1,032 plus up to 129 of overtime. So the 304 shortfall is knowable on the evening of day 6, which gives the planner a full day of slack before the day-8 deadline. There is no information argument for waiting.
What is not known at day 8: whether days 10-12 will actually hit capacity (absenteeism, tool breakage). That is the only reason to order more than 175. Ordering the full 250 buys 75 castings of insurance for Rs 15,750 - poor value against a Rs 8,000 delay penalty, unless overtime is genuinely at risk.
Waiting past day 8 is not an option: it silently forecloses the subcontract route and makes the one-day delay the default, which is a commercial decision the planner is not authorised to take by inaction. If the delay is chosen, notify the customer on day 8, not on day 12 when the shortfall is confirmed - notification lead time is usually what the customer actually prices into the penalty.