The nested three-layer decision faced by a multi-ATM bank: (a) each ATM's daily opening cash level, (b) replenishment frequency and quantity, (c) the armoured cash-in-transit (CIT) vehicle's route. Balancing the customer-complaint cost of an empty ATM against the immobilisation (interest opportunity) cost of an over-full ATM. Academic name: ATM Cash Management; foundational Simutis et al. (2008), Castro (2009).
In plain words
Sound familiar?
- We are a mid-size commercial bank operating 500-3,000 ATMs; the daily opening cash level per ATM is decided by a branch planner on intuition or a simple arithmetic average — no systematic demand forecasting.
- We are a participation bank with 100-500 in-city ATMs; shopping centre, bus station, campus, office district give very different withdrawal patterns, but all ATMs are filled with the same 'rule-based' cash.
- CIT (armoured cash-transit) routes are planned by the night operations centre; the same ATM is overfull one day and empty the next — replenishment frequency is observation-driven, not data-driven.
- We have never computed the annual interest opportunity cost of idle cash inside our ATMs; finance reports 'this much cash in circulation' but the fact that this number can be cut by 20-40% has never been on the table.
- Empty-ATM customer complaints show in weekly operations reports as 50-300 incidents; the average cost per incident (lost transaction fee + brand damage) is not numerically computed.
- On anomaly days (month-end, before public holidays, payday) empty-ATM incidents multiply; the demand forecasting framework does not include these patterns.
- Banking regulator CIT-monitoring obligations and insurer route-confidentiality clauses pull in one direction while existing planning assigns all routes to a single operator — a single-supplier lock-in risk is present.
Why it matters
How it's solved
Technical depth
How it's solved
Technical depthIn one sentence: Forecast each ATM’s daily withdrawals; set its opening cash level via a chance-constrained inventory rule (keep stock-out probability below 1-5%); then plan the armoured-vehicle nightly VRP with a different route every night (security) — minimise idle cash + vehicle km + empty-ATM penalty together.
This problem is studied in Operations Research (the discipline that uses math and computers to solve business decisions) literature as ATM Cash Management or Cash-in-Transit Routing and Replenishment. ATM Cash Management differs from classical VMI/IRP (#048): IRP is the general industrial-gas/fuel delivery joint inventory-routing; ATM Cash Management is cash-specific (denomination mix — small/medium/large banknotes, security/insurance cost, location-specific demand patterns, CIT-monitoring regulation). It also differs from VRPTW (#002) — not only routing, but a three-layer decision of demand forecasting + inventory + routing. Solution in three stages:
1. Modelling. Inputs: (a) ATM set — per ATM, location code (mall, bus stop, campus, office, neighbourhood market etc.), cassette capacity (typically 2,500-4,000 notes/cassette, 4-6 cassettes/ATM, 10K-25K notes total), daily withdrawal history (at least 12-24 months of time series), denomination mix (share of small/medium/large notes demanded), (b) CIT (armoured cash-transit) parameters — vehicle count, per-vehicle capacity (TRY or banknote count), average speed, shift length (typically 22:00-06:00 night), depot location (bank central vault), security rules (route confidentiality, max ATMs/vehicle), (c) financial parameters — reference rate (TRY money market), inside-ATM cash insurance premium (typically 0.5-2 per mille/year), empty-ATM complaint cost (typical 8-20 TRY/event), per-transaction fee, (d) regulation — banking-regulator CIT-monitoring requirements, data-protection rules (no customer identification from withdrawal pattern), denomination-distribution rules. Decision variables jointly: (i) per ATM, daily opening cash level (by denomination), (ii) which ATM is replenished how often (daily service-level parameter β = 0.95-0.99 with chance constraint), (iii) CIT vehicle daily routes (each night which ATMs in which order). Constraints: ATM cassette capacity (no overflow), minimum service level (chance constraint — daily stock-out probability < 1-5%), CIT vehicle capacity, shift length, route confidentiality (different route each night — predictability dampening). Objective: weighted sum — immobilisation cost (inside-ATM + in-transit cash × interest) + CIT operations cost (km + hourly) + expected stock-out penalty + insurance premium.
2. Solver-driven decision. Three layers jointly: (a) Demand forecasting — Holt-Winters triple exponential smoothing (seasonal + trend + level), ARIMA(p,d,q) time series, location-specific calibration, anomaly days (month-end, payday, before holiday, weekend) as additional regressors; group-demand forecasting — cluster similar-pattern ATMs and forecast at the group level (more accurate than the single-ATM forecast). (b) Stochastic inventory — per ATM use an (s, S) or newsvendor-type model for the opening cash level, service level β = 0.95-0.99 enforced as a chance constraint (probabilistic constraint — “stock-out probability under 5%”); rolling-horizon (daily re-planning) re-solves the model as telemetry data (actual withdrawals) updates. (c) CIT routing — VRP (Vehicle Routing Problem) variant; each-night armoured vehicle pool, capacitated, shift-bounded; at the 50-200 ATM scale, MIP (Mixed-Integer Linear Programming — optimisation with some 0/1 variables and some continuous) solves directly; at 200-1,000 ATMs, ALNS (Adaptive Large Neighborhood Search — intelligent search method) or branch-and-cut. Integrated solution: VMND (Variable MIP Neighborhood Descent) for joint inventory + distribution MIP in an ATM network — at the 100-500 ATM scale, good practical quality in hours.
3. Field integration. Output in four layers: (a) planning-centre dashboard — per ATM the daily opening cash recommendation (by denomination), service-level report, actual-vs-forecast withdrawal report, (b) CIT operator mobile app — night-shift ordered ATM list + per-ATM amount to drop + denomination, per-night route variation (for security), (c) real-time monitoring — per ATM telemetry (cassette fill, transaction count, fault status), central monitoring, ‘critical low’ alert, (d) financial reporting — daily immobilisation cost, CIT operations cost, stock-out event count, KPI deviation report. Upstream integration: core banking (withdrawal data), central vault management (depot stock), banking-regulator reporting, insurer interface. Quarterly operations committee: per-ATM immobilisation vs forecast accuracy, CIT operator performance (route time, ATMs/hour productivity), stock-out reduction trend, denomination-mix analysis.
Alternatives
Manual + fixed rule (every ATM the same amount, weekly refill)
FreeZero license
Who it fits: Small operator (50-200 ATMs), single-city coverage
- + Zero software cost
- + Easy rule for the planner
- + IT integration simple
- − No demand forecasting — high-demand ATMs stock-out, low-demand ATMs immobilise
- − CIT route inefficient — fixed weekly schedule ignores ATM priority
- − Service level is observation-driven, not numerical
- − Annual 15-30M TRY saving missed at 200+ ATM scale
Local bank operations software + basic reporting
Enterprise1-4M TRY license + 300K-1M TRY/year maintenance (TR market observation)
Who it fits: Mid commercial bank (200-800 ATMs), single-region operation
- + Close to local financial regulation (banking-regulator, anti-money-laundering reporting)
- + Mature core-banking integration
- + Local-language UI and support
- − Demand-forecasting module typically simple (weekly average); no Holt-Winters / ARIMA / group-demand
- − Stochastic inventory (chance-constrained) usually absent
- − CIT VRP module typically absent — routing is manual
- − Three decisions not integrated, separate modules
International banking-operations platform + ATM cash module
Enterprise5-20M EUR license + 1-4M EUR/year maintenance (large platforms)
Who it fits: Large commercial bank (1,000+ ATMs), multi-region, high-volume
- + Mature demand forecasting (ARIMA, machine learning, anomaly detection)
- + Stochastic inventory + chance-constrained service level
- + CIT VRP + security-aware routing integrated
- + Telemetry + real-time re-planning standard
- − High license + long (18-30 month) rollout
- − Local-regulation customisation adds project time
- − Operations-team training is a wide programme
- − Single-platform lock-in (long contract, high exit cost)
Open-source solver + custom ATM cash management module
Open SourceLicense free; in-house build 30-50 weeks or 1.5-4M TRY consultancy
Who it fits: Bank with tech team, integration with existing core banking + CIT required
- + No license cost
- + Demand forecasting + stochastic inventory + dynamic routing well-defined for open-source solvers
- + Demand forecasting + stochastic inventory + CIT VRP designed flexibly
- + Three-layer integrated solution has open-source reference implementations
- − Internal OR specialist + banking operations team required
- − Academic prototype to production 12-18 months
- − Regulatory compliance managed internally
- − CIT operator API integration is a separate module
Recommendation
Ask in the meeting
- Which approach does the demand-forecasting module support — Holt-Winters, ARIMA, group-demand clustering, machine learning? How are anomaly days (month-end, payday, holiday) modelled?
- Is stochastic inventory (chance-constrained service level β = 0.95-0.99) supported? Is it an (s, S) or newsvendor formulation, or just a fixed min/max rule?
- Are ATM cash management + CIT routing solved as one integrated model, or sequentially (inventory first, routing later)? Is there an approach where inventory and routing are optimised in the same solve?
- How is denomination mix (small/medium/large notes) modelled — is per-ATM denomination forecast available, is the cassette-fill decision made by denomination?
- How is CIT route confidentiality (a different route each night, predictability dampening) implemented — randomisation parameter, fixed-pattern-breaking rule?
- How are banking-regulator CIT-monitoring and insurer reporting integrated — is automatic report generation available, how is the audit trail kept?
- In a pilot with real operational data (12-16 weeks), what saving report against the prior manual/fixed-rule solution can be produced — immobilisation cost, stock-out events, CIT operations cost?
- If we end the contract, in which standard format (CSV, JSON, Parquet) can we export ATM withdrawal history, CIT route archive, demand-forecasting model and service-level reports?
Technical details
Editor’s note
This problem is known on the operations desk as “ATM cash planning”, “cash-transit routing” or “ATM cash management”. In the academic literature its canonical name is ATM Cash Management or Cash-in-Transit Routing and Replenishment. The foundational approach is Simutis, Dilijonas, Bastina, Friman and Drobinov (2008) and Castro (2009); the modern survey is Wagner and Bachner (2018) in International Journal of Banking, Accounting and Finance. This problem joins three interlocking decision layers — not only routing, not only inventory, not only forecasting; all three at once.
Distinction from #048 (IRP): #048 is the general industrial-gas / fuel delivery VMI — customer tank monitored, supplier decides. This problem is cash-specific: (a) denomination mix (small/medium/large notes) means the tank is not a single commodity — each cassette is a separate note, demand differs by denomination, (b) security / insurance cost — cash inside ATMs and cash in transit are physically at risk, (c) location-specific demand pattern — malls, bus stops, campuses, offices show very different withdrawal profiles (homogeneity is higher in general VMI), (d) regulation — banking-regulator CIT-monitoring, customer-data protection, insurer route-confidentiality clauses (the general VMI regulatory load is not this dense).
Distinction from #002 (VRPTW): VRPTW routes already-ordered goods within time windows — a single-layer routing decision. This problem is three-layer: demand forecasting + inventory + routing. An approach that only does CIT routing (classical VRP) does not solve ATM cash management; questions of how much cash each ATM receives and how often it is replenished remain unanswered.
Most-skipped point in the sector: the immobilisation-cost vs replenishment-cost trade-off. Practitioner banks fill ATMs ‘generously’ to avoid customer complaints — to prevent any chance of a stock-out, each ATM is topped at 80-100% of cassette capacity. The hidden cost of this approach is immobilisation cost: idle cash inside an ATM costs annual 5-15% reference interest opportunity + insurance premium + security risk. In a 1,000-ATM bank this line is 4-30M TRY/year — a cost finance does not close the book on, but operations has never computed. Real-time demand forecasting + chance-constrained inventory + dynamic replenishment can cut annual immobilisation cost by 20-40%; at the same time stock-out events do not increase, they fall (high-demand ATMs refilled more often, low-demand ATMs hold less cash). Second skipped point: anomaly days (month-end payday, before public holidays, weekend mall peaks, weekly market days) — a simple average-based forecast misses these days and stock-out events multiply. Holt-Winters seasonal + anomaly flags, or Ekinci-Lu-Duman (2015) group-demand forecasting, captures the pattern.
Third skipped point: CIT route confidentiality and security. Giving a single operator the same weekly route produces predictability; this raises heist/robbery risk. Insurers put route-confidentiality clauses into the contract. An optimised solution must produce a different (and still cost-effective) route each night; a fixed weekly schedule is weak both on cost and on security.
Step-by-step path for an SMB bank
Stage 1 — Measure first, plan later. At least 18 months of ATM withdrawal data: per ATM the daily withdrawal amount (total and by denomination), transaction count, intra-day hourly profile, stock-out event history. Location-type tagging: mall, campus, office, neighbourhood market. CIT operations data: nightly ATMs visited, vehicle-hours, km, total cash dropped, route time. Financial: TRY reference rate, insurance premium, insured limit, stock-out complaint cost estimate.
Stage 2 — Build the knowledge capital. ATM segmentation map (high-demand / mid / low; seasonal / stable; anomaly-day sensitive / not). Demand-forecast model calibration (Holt-Winters seasonal + anomaly flags, or Ekinci-Lu-Duman group-demand). Immobilisation vs stock-out cost trade-off curve (effect of service level β across 0.90-0.99). CIT vehicle productivity (current vehicle-hours per ATM, target).
Stage 3 — Pilot. 12-16 weeks. For a single region (e.g. one city, 50-200 ATMs) run integrated demand forecasting + stochastic inventory + CIT VRP in parallel with the current manual solution. The planning centre keeps the final call; the system makes a recommendation. Success criteria in writing, beforehand: immobilisation cost down 15% minimum, stock-out events down 30% minimum, CIT vehicle productivity up 10% minimum.
Stage 4 — Rollout. 12-18 months to full ATM network + CIT integration. Telemetry-triggered real-time re-planning (hourly critical-low alert, daily full re-plan). Quarterly operations committee: actual vs planned immobilisation, forecast accuracy, stock-out trend, CIT operator performance, regulator / insurer reporting compliance.
Risks — what can go wrong
Demand-forecast deviation (especially on anomaly days). If payday, before-holiday, weekly-market and mall-campaign days are not flagged in the forecasting model, stock-out events multiply. The anomaly calendar must be refreshed every year, the model recalibrated with last-12-month + last-3-month weighting. Academic reference: Ekinci-Lu-Duman (2015) group-demand forecasting.
CIT vehicle heist/robbery risk. Fixed weekly route and fixed vehicle-crew assignment generate predictability; this opens the attack vector. Fix: a different route each night (randomisation parameter), vehicle-crew rotation, real-time GPS monitoring, insurer route-confidentiality clause. An inside-ATM cash limit (per ATM max 200-500K TRY) is a further control.
ATM machine fault (note jam, cassette error). No stock-out has occurred yet customers cannot withdraw — the system flags this as ‘stock-out’ and triggers unnecessary replenishment. Fix: ATM telemetry that separates fault from cassette state (fill level vs machine status), real-time fault monitoring, technical-service SLA (4-12 hour response).
Single-supplier ATM-management platform lock-in. Without a contract clause for ‘annual standard-format export (CSV, JSON, Parquet) of ATM withdrawal history, CIT route archive, demand-forecasting model and service-level reports’, leaving the system means losing operational memory. The CIT operator contract must also keep route-data ownership with the bank; a CIT operator change should not restart the forecasting from zero.
Solution method — technical view
| Approach | Typical scale | Solve time | Guaranteed optimum? |
|---|---|---|---|
| Manual + fixed rule (every ATM the same amount) | Small operator, <200 ATMs | instant | No, 40-60% optimum |
| Demand forecasting (Holt-Winters, ARIMA) + fixed (s, S) | Mid, 200-500 ATMs | minutes | Partial — forecast good, inventory+routing decoupled |
| Group-demand forecasting (Ekinci-Lu-Duman 2015) | Mid-large, 300-1,000 ATMs | minutes-hours | Forecast accuracy +10-20% |
| Stochastic inventory (Castro 2009) + separate VRP | Mid, 200-800 ATMs | hours | Inventory exact, routing sequential |
| Integrated VMND (Larrain-Coelho-Cataldo 2017) | Mid-large, 100-500 ATMs | hours | Yes (within bound) |
| Adaptive Large Neighborhood Search (ALNS) — large scale | Large, 800-3,000 ATMs | hours | No, good practical quality |
| Rolling-horizon re-planning (telemetry-triggered) | Continuous operation | minutes | Transitional quality |
Objective function choice:
- Objective 1 — Total cost minimum: Classical formulation — immobilisation cost + CIT operations + expected stock-out penalty as weighted sum.
- Objective 2 — Stock-out event count minimum (max service level): Customer-satisfaction driven; immobilisation cost is given low weight.
- Objective 3 — Immobilisation cost minimum: Finance-driven; chance-constrained stock-out probability cap preserved.
- Objective 4 — CIT operations cost minimum: Logistics-driven; inventory fixed, only routing optimised.
Multi-objective: weighted sum or hierarchical (regulation + security constraints first, then stock-out service level, finally immobilisation + CIT total).
ATM Cash Management variants — pick by the field:
- Classic ATM Cash Management (Castro 2009): Single bank, deterministic / mildly stochastic demand, static weekly planning.
- Group-demand forecasting (Ekinci-Lu-Duman 2015): Clustering similar-pattern ATMs to lift forecast accuracy.
- Integrated inventory + distribution VMND (Larrain-Coelho-Cataldo 2017): Joint inventory + CIT routing MIP.
- Stochastic ATM Cash Management: Chance-constrained service level + scenario-based demand.
- Multi-bank shared CIT: Several banks share the same CIT operator; route optimisation cross-bank.
- Real-time replenishment (telemetry-triggered): Hourly critical-low alert, intra-night re-routing.
Academic references
Listed in the page frontmatter under sources. Simutis et al. (2008) and Castro (2009) foundational; Wagner-Bachner (2018) modern survey; Ekinci-Lu-Duman (2015) group-demand forecasting; Larrain-Coelho-Cataldo (2017) integrated inventory + distribution VMND.
Sources
- Simutis, R., Dilijonas, D., Bastina, L., Friman, J. and Drobinov, P. (2008). Optimization of cash management for ATM network. Information Technology and Control, 36(1A), 117-121. Foundational approach for ATM-network cash management.
- Castro, J. (2009). A stochastic programming approach to cash management in banking. European Journal of Operational Research, 192(3), 963-974. Canonical stochastic-programming formulation for cash management in banking.
- Wagner, D. and Bachner, M. (2018). Bank cash management — a review of recent literature. International Journal of Banking, Accounting and Finance, 9(2), 169-189. Comprehensive modern literature survey.
- Ekinci, Y., Lu, J.-C. and Duman, E. (2015). Optimization of ATM cash replenishment with group-demand forecasts. Expert Systems with Applications, 42(7), 3480-3490. Group-demand forecasting for replenishment.
- Larrain, H., Coelho, L. C. and Cataldo, A. (2017). A Variable MIP Neighborhood Descent algorithm for managing inventory and distribution of cash in automated teller machines. Computers & Operations Research, 85, 22-31. Integrated inventory + distribution in an ATM network.
- YÖK Thesis Center — keywords: ‘ATM nakit yönetimi’, ‘para taşıma’ or ‘CIT’ — 15+ theses from TR academia. tez.yok.gov.tr
Glossary
- ATM Cash Management
- OR problem of forecasting each ATM's cash demand, deciding replenishment timing and amount, and balancing the immobilisation cost (interest opportunity + security risk) of idle in-ATM cash against the stock-out cost (customer complaints + lost transactions) of an empty ATM; joins forecasting + stochastic inventory + cash-in-transit (CIT) routing.
- Cash-in-Transit Routing
- Operational routing of armoured cash-transport vehicles visiting a bank's ATMs and branches for refill. A VRP variant shaped by security (route unpredictability), tight time windows, denomination considerations and regulatory monitoring.
- VRP
- The decision of which vehicles, leaving from one or more depots, visit which customers in which order.
- MIP
- An optimization model where some decision variables are forced to be whole numbers (e.g. number of trucks, number of shifts).
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