Shift-Level Decision on Reject Rates, Cost per Good Unit and Overtime
A small unit runs three shifts making the same machined component, each 8 hours long, and ships only good units. Shift A produces 1,200 units per day with 5.0% rejected, at a conversion cost of ₹40 per unit produced. Shift B produces 1,500 units per day with 8.0% rejected, at ₹38 per unit produced. Shift C produces 900 units per day with 3.0% rejected, at ₹45 per unit produced. A new customer contract requires 3,500 good units per day and specifies that no consignment may carry more than 4.0% defective pieces. Shift B is the only shift that can be extended, by up to 2 hours per day, at an overtime charge of ₹600 per hour; alternatively, the shortfall can be bought in from a job-work vendor at ₹55 per good unit. The plant manager wants the three shifts ranked on the right measure, the smallest quality improvement that satisfies the 4.0% clause, and a decision on overtime versus buying in.
1. Rank the three shifts on cost per good unit and state whether the highest-output shift is also the most efficient.
Read the worked answer
Good units: A = 1,200 × 0.95 = 1,140; B = 1,500 × 0.92 = 1,380; C = 900 × 0.97 = 873.
Cost per good unit = (units produced × cost per unit produced)/good units: A: 1,200 × 40 = 48,000 ÷ 1,140 = ₹42.11 B: 1,500 × 38 = 57,000 ÷ 1,380 = ₹41.30 C: 900 × 45 = 40,500 ÷ 873 = ₹46.39
Ranking: B (₹41.30) < A (₹42.11) < C (₹46.39).
B is both the highest-output and the cheapest per good unit, despite having the worst reject rate. That is the judgement the numbers force: B's low conversion cost (₹38) more than absorbs its extra scrap. C is the trap in the data - it has the lowest reject rate (3%) and looks like the 'quality' shift, but its high conversion cost makes each good unit ₹5 more expensive than B's, which at 3,500 units/day is about ₹17,500 per day. Ranking by reject percentage alone, or by output alone, gives the wrong answer; the correct denominator is good units shipped.
2. Current output already exceeds 3,500 good units per day. Does that mean the 4.0% defective clause is satisfied, and if not, what is the least disruptive fix?
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Output is not the issue; the defect clause is about the mix. Total produced = 1,200 + 1,500 + 900 = 3,600 units; rejects = 60 + 120 + 27 = 207, giving an overall defect rate of 207/3,600 = 5.75%, well above the 4.0% ceiling. Total good = 3,393, so volume is fine.
To reach 4.0% at 3,600 produced, rejects must fall to 0.04 × 3,600 = 144, i.e. eliminate 63 rejects.
Can any single shift do it alone? A to zero rejects: 207 − 60 = 147 > 144 - fails by 3. C to zero rejects: 207 − 27 = 180 > 144 - fails. B must therefore fall to 144 − 60 − 27 = 57 rejects, i.e. 57/1,500 = 3.8%.
Judgement: the whole burden falls on the shift with the worst quality, which is also the shift the manager least wants to disturb because it carries the volume. The improvement needed is 120 → 57 rejects, a 52.5% reduction in B's defect count - demanding but confined. Note how close A comes: driving A to near-zero defects leaves the unit 3 rejects short, so a 'fix the cheap problem first' instinct would consume effort and still fail the clause.
3. The customer needs 3,500 good units per day. Current good output is 3,393. Compare extending shift B with buying in the shortfall, and state the decision.
Read the worked answer
Shortfall = 3,500 − 3,393 = 107 good units.
Shift B's rate: 1,500 units/8 h = 187.5 units/h, of which 92% are good = 172.5 good units/h. Time needed = 107/172.5 = 0.62 h, comfortably inside the 2-hour cap.
Overtime cost = 0.62 × ₹600 = ₹372 of premium (the ₹38 conversion cost is incurred on those units either way, so it does not decide the comparison). Effective premium per good unit = 600/172.5 = ₹3.48.
Buy-in cost = 107 × ₹55 = ₹5,885.
Decision: extend shift B. It costs roughly ₹370 against ₹5,885 for job work - a saving of about ₹5,500 per day, and B's extra units stay under the unit's own quality control. Two caveats belong in the note to the manager: the shortfall grows if the 4.0% clause is met by scrapping rather than by repairing, because a reject must either be reworked or replaced; and if the 107 units are needed as a standing daily requirement, a 0.62 h daily extension is really a permanent capacity gap, so the ₹3.48/good-unit premium should be compared with the cost of a fourth shift or a process fix rather than treated as a one-off.