Bar Stock, Kerf and a Two-Day Fabrication Deadline
Your section must fabricate 12 identical window grilles for a newly constructed barrack block. Each grille needs 4 vertical bars of 1.20 m and 3 horizontal bars of 0.90 m, all cut from standard 6 m mild-steel square bars held by the supply depot. Every cut consumes about 3 mm of bar as kerf, and the depot issues only full 6 m lengths. One length costs Rs 480, and the fabrication norm is 2 complete grilles per worker per day. Three fitters are available and the block must be handed over in exactly two working days. On day one a four-hour power failure is expected because the feeder is being shifted. The depot clerk has already indented 17 bars, arrived at by adding a rough 8 per cent wastage to the straight total length.
1. Calculate the minimum number of 6 m bars actually required and set out a cut plan that justifies the figure.
Read the worked answer
Straight total length. Per grille: (4 × 1.20) + (3 × 0.90) = 4.8 + 2.7 = 7.5 m. For 12 grilles: 90 m, or 15 bars if cutting waste is ignored. That figure is wrong because it ignores kerf and length-matching.
Vertical bars, 48 pieces of 1.20 m. Five pieces would need 6.00 m plus 4 kerfs = 6.012 m, which exceeds a 6 m bar. So at most 4 pieces per bar: 4 × 1.20 + 4 kerfs = 4.812 m, leaving a 1.188 m remnant. 48/4 = 12 bars, giving 48 verticals plus 12 remnants.
Use the remnants. Each 1.188 m remnant yields one 0.90 m piece (0.9 + 0.003 = 0.903 m), so 12 of the 36 horizontal pieces come free.
Remaining horizontal pieces, 24 of 0.90 m. Six per bar: 6 × 0.90 + 5 kerfs = 5.415 m, so 4 bars.
Total = 12 + 4 = 16 bars, costing 16 × 480 = Rs 7,680, a saving of Rs 480 on the indent.
2. Was the clerk's 17-bar indent sound? What do you tell the clerk, and what practical caveat do you attach?
Read the worked answer
The indent is one bar more than the mathematically minimum requirement. The method behind it is not defensible: adding a flat percentage of wastage to a straight length ignores the fact that kerf and piece-length matching, not a percentage, decide bar count. A 16-bar indent with this cut plan is sufficient.
Tell the clerk: cut the verticals and horizontals exactly as listed, keep the 1.188 m remnants separately labelled for the horizontal cuts, and do not allow offcuts to be thrown into the scrap bin.
Caveat. The calculation assumes clean, straight stock and square ends. Inspect the bars on issue; a bent bar or a damaged end can destroy one piece. If the depot permits, take 17 and return the unused length with a written receipt, or keep one length as a spare and record it in the store ledger; if the depot does not permit returns, take 16 and pre-check every length before cutting. State the chosen option in the fabrication register so that the choice is auditable.
3. Can three fitters meet the two-day deadline despite the four-hour power failure? Show the numbers and recommend an action.
Read the worked answer
Nominal capacity. 3 fitters × 2 grilles per day = 6 grilles per day; two days gives 12 grilles. That is exactly the target with zero slack.
Effect of the outage. Assuming an 8-hour shift, a 4-hour failure removes half of day one's productive time: day one output falls to about 3 grilles, so total becomes 3 + 6 = 9 grilles, three short.
Options, with numbers. (i) Sanction 4 hours of overtime on day one for the same three fitters: 3 workers × 0.5 day × 2 grilles = 3 extra grilles, total 12. (ii) Bring three additional fitters for half a day on day one: also 3 grilles. (iii) Do all cutting by hand hacksaw during the outage so that day one's powered hours are used only for welding; this recovers part, not all, of the loss because the norm of 2 grilles per day already includes cutting.
Recommendation. Pre-cut as much stock as possible during the outage, book 4 hours of overtime on day one, and inform the supervisor in writing on day one morning rather than on day two evening. Record the extra labour in the work order.