The Flat-Pack Desk and the CNC Router Queue
A Year 12 student is producing 120 flat-pack laptop desks for a school fundraiser. The design uses 18 mm birch plywood panels joined with a slot-and-tab system and no fasteners. The school has one three-axis CNC router with a 1,200 x 2,400 mm bed, a single 6 mm upcut spiral bit, and a feed rate that cuts 18 mm plywood at 1.8 m/min. Each desk requires 2.6 m of cutting path and 14 minutes of setup and panel handling per sheet. A sheet yields four desks. The fundraiser deadline is 11 school days away, and the workshop is available for 4 hours per day. The student also needs two days for sanding and finishing.
1. Calculate whether the CNC schedule can meet the deadline, showing your working, and identify the binding constraint.
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Total desks: 120. Sheets required: 120 / 4 = 30 sheets. Cutting time per sheet: 4 desks x 2.6 m = 10.4 m of path; at 1.8 m/min that is 10.4 / 1.8 = 5.78 minutes. Add 14 minutes handling and setup per sheet: 19.78 minutes per sheet. For 30 sheets: 30 x 19.78 = 593.4 minutes, or about 9.89 hours. Available machining time: 11 days minus 2 finishing days = 9 machining days, at 4 hours per day = 36 hours. So machining fits comfortably within 36 hours. The binding constraint is not the router but the single 6 mm bit and the sheet count: 30 sheets must be processed one at a time, and any bit breakage or panel defect adds a full 19.78-minute cycle. The real risk is the two finishing days being consumed by sanding 120 desks, which is labour-bound rather than machine-bound.
2. Recommend how the student should manage the project to protect the deadline, including at least two specific contingencies.
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The student should build a Gantt-style schedule that front-loads machining and overlaps sanding with cutting, rather than treating finishing as a separate two-day block at the end. Specific actions: cut a test panel first to confirm the 6 mm bit and feed rate produce clean edges in the actual plywood, since plywood voids can cause tear-out and rework. Nest two desks per sheet where geometry allows to reduce handling time, or negotiate a larger batch to justify a second bit. Contingencies: keep two spare 6 mm upcut bits on hand, because a single broken bit stops production entirely; and pre-cut 10 percent extra sheets (three additional sheets, 12 desks) so a defective panel does not delay the whole run. The student should also book the workshop in two-hour blocks with a teacher supervisor to satisfy safe-work requirements, and record daily progress against the schedule so slippage is visible early enough to add a weekend session or reduce the order to 100 desks.