Insert Grade Choice Under a Fixed Due Date
A job shop must deliver 240 machined 316L stainless flanges in five working days. Each day has one 8-hour shift, and planned availability is 85%, giving 408 productive minutes per day. Two insert grades are quoted. Grade A (PVD carbide) runs at 90 m/min: cycle time 9.0 min, tool life 15 min, tool-change time 2.5 min, insert cost Rs 380 for four usable edges. Grade B (CVD carbide) runs at 130 m/min: cycle time 6.2 min, tool life 8 min, change time 2.5 min, insert cost Rs 520 for four edges. Both meet the 1.6 µm Ra requirement, but Grade B has shown notch wear on the work-hardened skin and the supplier will not guarantee tool life on the first 1 mm depth. The shop has no second shift; overtime costs Rs 1,200 per hour and is limited to two hours per day by labour rules. A subcontractor can machine flanges at Rs 260 each, but quality rejects have averaged 3%.
1. Calculate the time per part and total time for each grade, and determine whether either grade meets the five-day schedule in regular time.
Read the worked answer
Regular capacity = 408 min/day × 5 days = 2,040 min.
Grade A: Tool-change time per part = (cycle time/tool life) × change time = (9.0/15) × 2.5 = 1.50 min. Time per part = 9.0 + 1.50 = 10.50 min. Total = 240 × 10.50 = 2,520 min. Shortfall = 2,520 − 2,040 = 480 min (8.0 h). Grade A misses the schedule.
Grade B: Tool-change time per part = (6.2/8) × 2.5 = 1.9375 min. Time per part = 6.2 + 1.9375 = 8.1375 min. Total = 240 × 8.1375 = 1,953 min. Slack = 2,040 − 1,953 = 87 min. Grade B meets the schedule.
The decision is not close on time: Grade B is the only grade that fits the five-day window without overtime.
2. Compare the total machining cost for both grades, including overtime, and recommend a grade while addressing the tool-life risk on the work-hardened skin.
Read the worked answer
Grade A: Edges required = 240/15 = 16 edges. Insert cost = 16 × (380/4) = 16 × 95 = Rs 1,520. Overtime = 8.0 h × 1,200 = Rs 9,600. Total = Rs 11,120.
Grade B: Edges required = 240/8 = 30 edges. Insert cost = 30 × (520/4) = 30 × 130 = Rs 3,900. Overtime = 0. Total = Rs 3,900.
Grade B is much cheaper despite the higher insert cost. Test the risk: if tool life falls to 5 min on the work-hardened skin, time per part = 6.2 + (6.2/5) × 2.5 = 9.30 min. Total = 2,232 min, an overtime shortfall of 192 min = 3.2 h. Cost = 48 edges × 130 + 3.2 × 1,200 = Rs 6,240 + Rs 3,840 = Rs 10,080, still below Grade A.
Recommend Grade B, but run a first-article trial, monitor notch wear and keep Grade A as fallback.
3. The customer adds 60 flanges. Compare in-house overtime with subcontracting all 60, using the costs given, and recommend an option.
Read the worked answer
In-house with Grade B: Total time for 300 parts = 300 × 8.1375 = 2,441.25 min. Regular capacity = 2,040 min. Shortfall = 401.25 min = 6.69 h. Overtime limit = 2 h/day × 5 days = 10 h, so 6.69 h is feasible. Insert edges = 300/8 = 37.5, so 38 edges. Cost = 38 × 130 + 6.69 × 1,200 = Rs 4,940 + Rs 8,025 = Rs 12,965.
Subcontracting 60 parts: The 3% reject rate means more than 60 must be supplied to obtain 60 good parts. Effective cost per good part = 260/0.97 = Rs 268. Cost = 60 × 268 = Rs 16,080, ignoring any expediting and inspection burden.
In-house overtime is cheaper by about Rs 3,100 and keeps quality control in-house. The overtime is within the labour limit, so it is the recommended option. The decision would reverse if overtime were unavailable or if Grade B tool life deteriorated beyond the trial value.