ATM Cash Replenishment: Cost Against Stock-out Risk
Your branch runs two on-site ATMs and draws cash only from the district currency chest, 30 km away. Cash is issued in sealed cassettes of ₹2,00,000 each, and a magazine can be loaded only with whole cassettes. ATM-1 dispenses ₹4,80,000 on an average day; ATM-2 dispenses ₹2,40,000. Demand is steady across the week and the averages are reliable in normal months. Each ATM magazine holds a maximum of six cassettes.
The chest permits at most one replenishment run in 48 hours, and an ATM cannot be opened between runs. Each run costs ₹3,000 in transport and cash-handling charges, whatever the number of cassettes moved. Cash sitting in an ATM earns nothing for the bank, while funds retained at the chest earn 5% per annum.
Last month ATM-1 ran dry on a Friday evening and the branch logged three complaints. The regional office has asked for a written note covering the next 12 months. Assume 365 days, and 183 runs in a 48-hour cycle and 365 runs in a 24-hour cycle.
1. Test a 48-hour replenishment cycle against each ATM's requirement. Show the arithmetic and state whether a straightforward 'fill to requirement' loading is safe.
Read the worked answer
ATM-1, 48 hours: 4,80,000 × 2 = ₹9,60,000 needed. In cassettes of ₹2,00,000 that is 4.8 cassettes, so the minimum legal load is 5 cassettes = ₹10,00,000, leaving a cushion of ₹40,000 - one-twelfth of a day's demand, roughly two hours.
ATM-2, 48 hours: 2,40,000 × 2 = ₹4,80,000, i.e. 2.4 cassettes, so 3 cassettes = ₹6,00,000, cushion ₹1,20,000, about half a day.
Verdict: loading ATM-1 with exactly 4 cassettes (₹8,00,000) would be an outright failure - it does not even cover two average days. Even the 5-cassette load is not 'safe' in a risk sense: it is dimensioned to the average with a two-hour cushion, so any Friday, salary-day or festival spike exhausts the machine before the next permitted run. That is precisely what happened last month. ATM-2 is comfortably stocked. The fix is not more cash at ATM-1 alone; the maga zine limit of six cassettes caps it at ₹14,00,000, so the cycle length, not the load, is the variable to manage.
2. Compare a 24-hour cycle with a 48-hour cycle on total annual cost - transport plus the carrying cost of average cash held in the machines. Which is cheaper and by how much?
Read the worked answer
24-hour cycle
- Runs: 365 × ₹3,000 = ₹10,95,000.
- ATM-1 needs 2.4 cassettes → load 3 (₹6,00,000), ends the day at ₹1,20,000, so average holding ₹3,60,000.
- ATM-2 needs 1.2 cassettes → load 2 (₹4,00,000), ends at ₹1,60,000, average ₹2,80,000.
- Total average cash ₹6,40,000 × 5% = ₹32,000.
- Total: ₹11,27,000.
48-hour cycle, prudent loading (6 cassettes at ATM-1, 3 at ATM-2)
- Runs: 183 × ₹3,000 = ₹5,49,000.
- ATM-1: ₹12,00,000 down to ₹2,40,000, average ₹7,20,000.
- ATM-2: ₹6,00,000 down to ₹1,20,000, average ₹3,60,000.
- Total average ₹10,80,000 × 5% = ₹54,000.
- Total: ₹6,03,000.
Conclusion: the 48-hour cycle is cheaper by ₹11,27,000 − ₹6,03,000 = ₹5,24,000 a year, about 46% of the 24-hour cost. The extra carrying cost of ₹22,000 is trivial against ₹5,46,000 of saved transport. The economic answer is to keep the 48-hour cycle and treat the ATM-1 stock-out as a loading and cushioning problem, not a frequency problem.
3. Recommend a cassette configuration for each ATM for the coming year and justify it in cost terms. Then say what you would do if ATM-1's average daily dispense rises by 20%.
Read the worked answer
Recommendation now: 6 cassettes at ATM-1 (₹12,00,000, cushion ₹2,40,000 ≈ 12 hours of demand) and 3 cassettes at ATM-2 (₹6,00,000, cushion about half a day). Annual cost ₹5,49,000 transport plus ₹54,000 carrying = ₹6,03,000, against ₹11,27,000 for daily replenishment. The cushion at ATM-1 is the cheapest insurance available: one extra cassette adds roughly ₹5,000 a year in carrying cost and removes an exposure that produced three complaints in a single month.
If ATM-1 rises 20% to ₹5,76,000 a day, the 48-hour requirement becomes ₹11,52,000. Six cassettes (₹12,00,000) still fit, but the cushion collapses to ₹48,000 - about two hours - and the magazine is already full, so no further cushion can be bought.
The options are: (a) a 36-hour cycle - 243 runs × ₹3,000 = ₹7,29,000 transport, plus carrying on averages of ₹5,68,000 (ATM-1, 5 cassettes) and ₹2,20,000 (ATM-2, 2 cassettes), i.e. ₹39,400, total about ₹7,68,000, an extra ₹1,65,000 a year; (b) a daily cycle at ₹11,27,000. Option (a) buys a five-to-six-hour cushion for less than a sixth of the cost of option (b), so recommend renegotiating the chest window to 36 hours rather than reverting to daily runs.