ATM cassette mix and the cost of a second weekly refill
An urban cooperative bank runs 12 off-site ATMs in one district. Each ATM has four note cassettes, and each cassette holds a maximum of 2,200 notes. The district's combined withdrawal demand is Rs 1.44 crore a week, spread evenly across the 12 machines. The bank currently loads three Rs 500 cassettes and one Rs 200 cassette per ATM, and its cash vendor charges Rs 1,800 per ATM per replenishment visit. Historical analysis shows that 70% of the value withdrawn is in Rs 500 notes and 30% in Rs 200 notes, and the bank currently calls for two refills a week per ATM as a precaution. The operations head wants to cut vendor cost without risking a dry ATM, and has asked for the numbers before the board's cost review. Clean-note and cassette-mix norms are to be treated as already satisfied; only capacity, demand and cost are in question.
1. Work out the weekly demand per ATM and the number of notes of each denomination the 70:30 value mix requires, then compare that with the current cassette configuration.
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Per-ATM weekly demand: Rs 1,44,00,000 / 12 = Rs 12,00,000.
Value split at 70:30: Rs 500 notes must carry Rs 8,40,000; Rs 200 notes must carry Rs 3,60,000.
Notes required per ATM per week:
- Rs 500: 8,40,000 / 500 = 1,680 notes.
- Rs 200: 3,60,000 / 200 = 1,800 notes.
Capacity available today:
- Rs 500: 3 cassettes x 2,200 = 6,600 notes = Rs 33,00,000.
- Rs 200: 1 cassette x 2,200 = 2,200 notes = Rs 4,40,000.
- Total capacity = Rs 37,40,000 against a weekly draw of Rs 12,00,000.
Utilisation: the Rs 500 side uses 1,680 of 6,600 notes (25.5%); the Rs 200 side uses 1,800 of 2,200 notes (81.8%).
The important finding is the asymmetry: capacity is not remotely the constraint in aggregate - the machine is loaded with more than three weeks of demand - but the single Rs 200 cassette is already over four-fifths full on one week's demand. Any analysis that looks only at total capacity will conclude 'plenty of room' and miss the binding cassette.
2. The head proposes moving to two cassettes per ATM (one Rs 500, one Rs 200) and a single weekly refill. Test whether that survives current demand, and find the demand growth at which it fails.
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Two-cassette capacity per ATM: Rs 500 cassette = 2,200 x 500 = Rs 11,00,000; Rs 200 cassette = 2,200 x 200 = Rs 4,40,000; total Rs 15,40,000 per week.
Against Rs 12,00,000 of weekly demand:
- Rs 500 requirement 8,40,000 (1,680 notes) fits in 2,200 notes - 76.4% used.
- Rs 200 requirement 3,60,000 (1,800 notes) fits in 2,200 notes - 81.8% used.
So a single weekly refill on two cassettes does cover current demand, with the Rs 200 cassette again the tighter one.
Where it breaks. Solve for the demand at which each cassette saturates:
- Rs 200 cassette: 4,40,000 / 0.30 = Rs 14,66,667 per ATM per week - about 22.2% above today's Rs 12,00,000, i.e. district demand of roughly Rs 1.76 crore a week.
- Rs 500 cassette: 11,00,000 / 0.70 = Rs 15,71,429 per ATM per week - about 31% growth.
Conclusion: the scheme fails first on the Rs 200 cassette, at roughly 22% demand growth, not at 31%. Practical caveat: a 22% margin on an average week is thin, because demand is not flat - festival weeks, salary dates and weekends concentrate withdrawals, and an ATM that empties on a Saturday is out for the rest of the weekend. A single weekly refill should therefore be piloted rather than switched on district-wide.
3. Recommend a refill policy to the board, quantify the saving, and state the binding constraint and the main risk.
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Recommendation: move from two refills a week to one, keeping four cassettes loaded for now, and reduce to two cassettes only where the local mix and footfall are stable.
Quantified saving. Two refills a week = 12 ATMs x 2 x Rs 1,800 = Rs 43,200 per week. One refill a week = Rs 21,600. Saving = Rs 21,600 per week, or Rs 21,600 x 52 = Rs 11,23,200 a year.
Why four cassettes still earn their place even though two would fit. The saving comes from halving visits, not from removing cassettes - the vendor charges per visit, so a two-cassette machine costs exactly the same to service. But four cassettes give a buffer of Rs 37,40,000 against a weekly draw of Rs 12,00,000, which absorbs a demand spike or a missed vendor visit. Cutting cassettes buys no money and removes the buffer; the cassette reduction should be treated as a separate decision about redeploying cassettes to new sites, not as a cost saving.
Binding constraint: the Rs 200 cassette at 81.8% utilisation on one week's demand - the first thing to run dry, and the reason a 22% demand rise would break the single-refill plan.
Main risk and mitigation: dry-out during festival or salary weeks, which is a reputational cost far larger than Rs 11.23 lakh. Mitigate by keeping four cassettes, tracking per-ATM dry-out incidents for one quarter, pre-loading extra Rs 200 notes before known peak weeks, and writing into the vendor SLA a same-day response for any ATM reported empty.