Two press lines, one deadline: costing the cheapest production plan
Phoenix Fabrication has won a contract for 1,200 acceptable MS brackets, to be delivered within three working days of eight hours each, giving 24 machine-hours per press line. The shop has two lines. Line A punches 40 brackets an hour but rejects 4% of them; its power and tooling cost is ₹110 per running hour. Line B is slower, at 30 brackets an hour with only 1.5% rejection, and its power and tooling cost is ₹40 per running hour. Each line needs its own operator at ₹120 per hour. Rejected brackets are scrapped with no salvage value and cannot be reworked. The foreman wants to run both lines flat out for all three days and 'sort the numbers out later'; the accountant wants the cheapest plan that still ships 1,200 good brackets on time. Overtime on Line B is available for up to six hours at 1.5 times the labour rate, and an outside vendor has offered to supply any shortfall at ₹22 per bracket.
1. Compute the cost per acceptable bracket on each line and state which line is cheaper. Explain why comparing hourly running cost or hourly output alone would give the wrong answer.
Read the worked answer
Compare on cost per acceptable piece, because only good brackets are paid for.
- Line A: 40 × 0.96 = 38.4 good brackets/h. Running cost = 110 + 120 = ₹230/h. Cost per good bracket = 230 / 38.4 = ₹5.99.
- Line B: 30 × 0.985 = 29.55 good brackets/h. Running cost = 40 + 120 = ₹160/h. Cost per good bracket = 160 / 29.55 = ₹5.41.
B is roughly 10% cheaper per shippable bracket, so it should be loaded first.
Two tempting shortcuts both fail. Ranking by hourly cost (₹160 vs ₹230) ignores that A converts its hours into more acceptable pieces. Ranking by output rate (40 vs 30) ignores that A also scraps 1.6 pieces an hour against B's 0.45, and that the scrapped pieces carry the operator's wage and the power bill with them. The rejection rate is part of the price, not a separate quality issue.
2. Find the cheapest schedule that delivers 1,200 good brackets within the 24 available hours, and compare it with the foreman's proposal of running both lines flat out.
Read the worked answer
Give the cheaper line every hour it has, then top up on the other.
- B for 24 h: 24 × 29.55 = 709.2 good brackets, cost = 24 × 160 = ₹3,840.
- Shortfall: 1,200 − 709.2 = 490.8. Hours on A = 490.8 / 38.4 = 12.78 h. Cost = 12.78 × 230 = ₹2,940.
- Total ≈ ₹6,780, with A running only about 12.8 of its 24 available hours.
The mirror plan (A full 24 h = 921.6 good, then 9.42 h on B) costs 5,520 + 1,507 = ₹7,027, i.e. ₹247 worse. Running both flat out produces 1,632 good brackets at a cost of 24 × (230 + 160) = ₹9,360 - 432 brackets of over-production that nobody pays for and that still consume material and operator time.
Because B is cheaper per acceptable piece, any hour given to A before B is exhausted simply adds cost. The schedule is driven by marginal cost per good piece, not by which machine is faster or which is idle.
3. Evaluate the two escape routes - six hours of overtime on Line B, or buying the shortfall from the vendor at ₹22 - and state what you would actually do, including where the real savings lie.
Read the worked answer
Overtime on B: at 1.5× labour, B costs 40 + 180 = ₹220/h, i.e. 220 / 29.55 = ₹7.45 per good bracket. That is worse than A's ₹5.99, so overtime loses to simply using more of A. Using the full 6 h: 177.3 extra good brackets for ₹1,320, leaving 313.5 to A at 8.16 h (₹1,877). Total = 3,840 + 1,320 + 1,877 = ₹7,037 - about ₹257 worse than the base plan.
Vendor at ₹22: 490.8 × 22 = ₹10,798, roughly 60% above the in-house cost. Rejected outright; it is only a fallback if the deadline were to slip.
Decision: run B for 24 h and A for about 12.8 h at roughly ₹6,780, and leave both overtime and bought-out supply unused.
The real money is in A's 4% rejection. Cutting it to 3% shortens A's requirement to 12.65 h, a trivial gain; the gain becomes material only if rejection is halved, which is a tool-die maintenance question, not a scheduling one. The accountant should be told that the schedule is already near-optimal and that further savings must come from the process.