ATM Service Cost Optimization Using Predictive ...

ATM Service Cost Optimization Using Predictive Encashment Strategy Vladislav Grozin1 , Alexey Natekin2,3,4 , and Alois Knoll4 1

4

ITMO University, Saint-Petersburg, Russia, [email protected] 2 Data Mining Labs, Saint-Petersburg, Russia, [email protected] 3 Deloitte Analytics Institute, Moscow, Russia Technical University Munich, Garching, Germany, [email protected]

Abstract. ATM cash flow management is a challenging task which involves both machine learning predictions and encashment planning. Banks employ these systems to optimize their costs and improve the overall device availability via reducing the number of device failures. Although cash flow prediction is a common task, complete design of the cost optimization system is a complex design problem. In this article we present our complete encashment strategy methodology. We evaluate the proposed system design on real world data from one of the Russian banks. We show that one can effectively achieve 18% cost reduction by employing such strategy. Keywords: atm, cash flow management, cost optimization, machine learning, regression.

1

Introduction

Cost saving has always been the cornerstone of business operations. There is no other industry but banking, where data-driven solutions to cost optimization have been so widely adopted. Some applications like risk management and fraud monitoring systems based on machine learning models, have been successfully used for several decades, whereas solutions like proactive customer retention modeling are only only finding their way to bank application portfolios. Nowadays banks pay a lot of attention to efficiency of cash management in their ATM networks [1]. ATM, or automated teller machines, are electronic telecommunication devices that enable the customers to perform financial transactions without the need for a human cashier, clerk or bank teller. It was estimated that improved inventory policies and cash transportation decisions for an ATM network can result in up to 28% cost reductions [2]. In order to employ ATM cash management, a complete system with both predictive analytics and business logic has to be designed. In this article we present our cost optimization methodology of an ATM network. This includes

proactive maintenance with proper predictions of the amount of money to replenish. We take into account both the fact that encashment costs money, and that additional costs are imposed due to excessive unused money in the devices. We evaluate our proposed system on real world data from one of the Russian banks and analyze the results with respect to the work of actual human experts. The paper proceeds as follows. Section 2 provides a literature review with the related work. Section 3 discusses the problem statement and the corresponding mathematical formulation. Section 4 describes our complete encashment strategy methodology. Section 5 outlines the architecture and technical details of the system. Section 6 reports the obtained results of our system on the real bank data. Section 7 concludes with a discussion about the potential technical and analytical improvements to the system design.

2

Related work

Cash management systems of ATM networks consist of two primary components: cash flow prediction part and a part with the set of rules for cash replenishment. The former part is typically based on machine learning approach, while the latter focuses on optimization and encashment plan design. Most of the published articles focus primarily on the prediction part of the problem. A popular way to approach this problem, followed by some authors [3, 4], is to apply time series-based methods, which provide decent accuracy on their tasks. Unfortunately these methods do not allow one to use additional non-temporal factors like ATM placement (e.g. shopping mall or bank). The second most popular way to predict cash flow is to build, or learn a functional relationship between the future cash flow and a set of independent factors which are likely to affect cash flow patterns. A common form of this relationship is a neural network [5–10] that also typically exploits time-series data of cash flows. With this approach one commonly uses factors like ATM operations in previous days, device placement, pay days, weekends etc. These methods are capable to capture complex relationships and take into account multiple factors from very different sources. Despite the fact that it is the replenishment part that actually provides the capability to reduce costs, there is significantly less material on this part of the overall cash management problem. Cash prediction alone does not solve cost minimization, thus additional calculations have to be made in order to create an optimal encashment plan. One approach to encashment plan design is based on fuzzy expert systems [11]. These systems imitate human reasoning and the development of such systems involves human experts. However a common problem of such method is the limitation of experts’ knowledge expressiveness in the form of fuzzy rule sets. Moreover, human input can be inconsistent and lead to unstable results. Another opportunity is to apply stochastic programming for cash management [12]. Author deals with discretized money chunks in order to exploit the stochastic approach for short and mid-term optimization. Limitation to this ap-

proach is that it is hard to reason on the properties of the solution to be globally optimal or suboptimal. Integer programming can also can be applied to solve ATM-optimization problem [3]. In this case authors combines travelling salesman problem solution via integer programming and time-series based approach for predictions. In our study we follow the machine learning approach of direct modeling an arbitrary functional relationship to get the future cash flow predictions. However for encashment planning we developed a greedy strategy based on cost balancing, which is different from the earlier discussed ones.

3

Business problem identification

We consider two types of ATM devices: cash-ins and dispensers. Cash-in devices support only debit operations and collect cash. Dispensers, on the contrary, support only credit operations and provide cash to the customers. These devices are placed across different locations of the city and suburbs. It is common that ATM devices come in couples, sometimes with more than one device of each type in one location. Data on the total amount of cash in each device is collected daily. Typical cash flow patterns for each device type, drawn from two real devices, are shown on Figure 1. Dotted lines correspond to encashment events, where money as either collected from the cash-in device, or was replenished in the dispenser.

Fig. 1. Cash flow dynamics examples for two device types.

Cash−in

cash

0.6M 0.4M 0.2M 0.0M Jul 01

Jul 15

Aug 01

Aug 15

Sep 01

Aug 15

Sep 01

date

Dispencer cash

2.0M 1.5M 1.0M 0.5M 0.0M Jul 01

Jul 15

Aug 01

date

Our key objective is to provide ATM encashment plans that will minimize annual costs incurred by management of the ATM network. Given that ATM network consists of K devices, we can write these costs as follows: AnnualCosts(D) =

K X 365 X

Costi (t)

i=1 t=1

K number of devices in network Costi (t) i-th device’s expense at moment t It is also important to keep the number of device failures minimal. By device failures we mean situations when the device is no longer operable. Dispenser can run out of money whereas cash-in can theoretically exceed its maximal volume. Considering the provided data, there were no registered cash-in failures, but dispensers indeed sometimes ran out of money. Unfortunately it is impossible to estimate the money equivalent of device failures, hence we will stick to the original objective of pure annual overall cost reduction. The business problem can be decomposed further if we describe the Costi (t) term in more detail. We have previously noted that incurred ATM costs consist of inventory costs of inefficiently used cash in the machines, and direct encashment costs. The former term equals to the amount of money that bank could have spent if kept it in turnover rather in devices while the latter is just the direct expense. The formula for costs can therefore be written as follows: Costi (t) = r · CashAmounti (t) + EncashmentCosti (t) · IsEncashedi (t), r bank lending rate, converted into percents per day CashAmounti (t) amount of money in i-th device at day t EncashmentCosti (t) encashment price of i-th device at day t IsEncashmenti (t) 1 if i-th is encashed at moment t, 0 otherwise In general, EncashmentCosti depends on time t because it is possible to save costs on efficient route planning. And routes are generated with different sets of devices daily thus for the same device i this cost can differ in between days. In our case most of the ATM devices were placed in the bank offices and didn’t involve logistical planning. This allows us to proceed with fixed daily costs for each device EncashmentCosti (t) = F ixedCosti , i ∈ 1, K.

4

Encashment strategy description

After we have defined the cost components that are to be optimized we can formulate the encashment strategy for cost optimization. Our strategy is based on one general principle: balance between inventory and fixed costs in between two encashments. If for a particular device i ∈ 1, K our cumulative inventory costs that start from previous encashment exceed

F ixedCosti , we can cut off this excess by ordering a new encashment. This idea of balancing costs components is illustrated on Figure 2, calculated for an artificially simulated cash-in device.

Fig. 2. Cost components.

6M

value

component 4M

fixed.price discount total

2M

10

20

30

40

period

Following this principle we seek a specific moment in time t > t0 that starts from previous encashment time with t0 = 0. This moment, defined as t˜ should be closest to the balance point when absolute difference between cumulative inventory cost and encashment cost is minimal: InventoryCosti (t) = r ·

t X

CashAmounti (j)

j=1

t˜i = argmin |InventoryCosti (t) − F ixedCosti | t

After we obtain t˜i we could set it as the desired encashment time and forward it to the bank operations office for execution. For strategy design we will assume that CashAmounti (t) are known ∀t ∀i. Despite being unrealistic in practice we deal with their predictions and estimations, thus letting us to substitute these predictions into the derived encashment rules. 4.1

Technical requirements

In the ideal world one could execute cash replenishment instantly. Unfortunately cash management suffers from a lag between the encashment decision of a particular device and the actual encashment execution. In our scenario with lag = 2 days, such decision of replenishment necessity of device i at time t could be executed no sooner than t˜i = t + 2. Despite the lag, in the ideal setting one can still make encashment decisions right away. However there is no encashment capability on weekends and holidays

which can render optimal t˜i evaluation impossible for device i. To deal with this issue we generate a set of candidates [t]w = t, t + w for further selection based on both cost balance and availability. First a set of encashment candidates [t] starting with t + 2 is defined: [t] = t + 2, t + 7. Then ∀t ∈ [t] we evaluate encashment capability of device i based T on holiday calendar Ci and match dates. Thus we get [t]ireal = [t] Ci . At time t we only need to make the encashment decision about the very first element of [t]ireal . We can then formulate encashment rule as follows: t˜i = argmin |InventoryCosti (t) − F ixedCosti | t∈[t]ireal

IF t˜i = [t]i1real then order encashment for device i at time t˜i , ELSE do nothing with device i and wait until tomorrow. 4.2

Device thresholds

Physical constraints on ATM device storage capacity have to be mitigated as an additional constraint on encashment planning. Both cash-in and dispenser devices have an upper limit on the amount of cash they store. Moreover, dispenser can run out of cash. Situations when these capacity requirements are not met are considered as device failures and should be evaded. Let us modify our strategy to the case of cash-in first. Without loss of generality put 0 as the moment of last encashment, t for current moment and lag as requirement input. Fig 3 illustrates the encashment process with complete money withdrawal at time t + lag. The line chart represents CashAmounti (t) while the filled red area corresponds to InventoryCosti (t) w.r.t. given r.

Fig. 3. Demonstration of cash-in withdrawal procedure. 0.08M

0.04M

t

0.02M

t+lag

Cash

0.06M

0.00M 0

10

20

30

40

Days

Although there were no registered breaches of cash-in storage limit in our data we will still define the threshold rule for them. The only time when threshold can impact our decision is when we chose to omit encashment execution but should instead have provided cash withdrawal.This applies to either very first candidate [t]i[1]real when we are already obliged to provide the encashment, or

to the second one [t]i[2]real when we see that it is the last moment before device failure. Thus given the U pperT hreshold our encashment rule modifies to: IF t˜i = [t]i1real OR CashAmounti ([t]i[1,2]real ) ≥ THEN order encashment for device i at time t˜i , U pperT hreshold ELSE do nothing with device i and wait until tomorrow. The procedure of choosing t˜i for dispenser devices has only one difference – a reversed threshold rule. We have to define the LowerT hreshold which serves as the indicator for necessary encashment: IF t˜i = [t]i1real OR CashAmounti ([t]i[1,2]real ) ≤ THEN order encashment for device i at time t˜i , LowerT hreshold ELSE do nothing with device i and wait until tomorrow. Fig 4 demonstrates the dispenser replenishment rule with threshold in consideration. It is worth noting that the slope of this chart is different from that of a cash-in because the sign of CashAmounti (t) is never positive. LowerT hreshold serves the purpose of device failure risk mitigation.

Fig. 4. Demonstration of dispenser replenishment procedure. 1.2M

0.6M

Threshold t t+lag

0.3M

k

Cash

0.9M

0.0M 0

20

40

60

Days

4.3

Encashment amount determination

The last component of our strategy is the amount of cash we have to leave in the device after the encashment execution. Cash-ins have a trivial answer to this problem given that we can always withdraw all cash from the device. For the case of dispensers we can do the following. Consider we have identified that we want to execute encashment at time t˜i . First, we have to predict one

whole next month of CashF lowi (t) = ∆CashAmounti (t) ∀t ∈ t˜i , t˜i + 30. This is done in order to define InventoryCostDispenseri (t) as:

CashAmountDispenseri (t) = LowerT hreshold +

t X

CashF lowi (t)

j=1

InventoryCostDispenseri (t) = r ·

t X

CashAmountDispenseri (j)

j=1

Now we can simulate the expected ATM behavior for the whole next month, taking into consideration a sequence of InventoryCostDispenseri (t), t ∈ t˜i , t˜i + 30. Due to the fact that the second condition of crossing the threshold is fulfilled by design, We can then find the point of expected texpected next encashment as simply the most optimal one in terms of cost balance:

texpected = argmin |InventoryCostDispenseri (t) − F ixedCosti | t∈t˜i ,t˜i +30

Finally, we can calculate this AmountDispenseri by taking into account that we will already have some cash remaining from the :

AmountDispenseri = CashAmountDispenseri (t˜i + texpected ) − − CashAmountDispenseri (t˜i )

5

Solution architecture

Solution of the cost optimization problem takes the form of a system which takes as input historical data and outputs optimal encashment plan for the next date. Plan comes in the form of a list of devices that require encashment and supplemented with dates and in case of dispenser devices with amounts of money to deposit. To make system viable we need to predict expected future cash flows and make decisions based on these forecasts. Thus, we have to create model that gives insight into future. Overall the system comprises of the following steps: 1. Data processing and feature extraction 2. Predictive model evaluation 3. Encashment plan provision

5.1

Data processing and feature extraction

In our study we were provided with historical about 115 devices from 2009-2013 years with the following information about each entry: – – – –

ATM device ID Date Daily cash flow Daily encashment (zero, if it didn’t take place)

Additional data about each device included it’s type (cash-in or dispenser), address and fixed encashment price. Due to the non-disclosure agreement we are unable to provide the raw data except for demo samples shown in figures. There is considerable freedom in the choice of features to use in our models. Those can be separated into three different groups: point-wise dealing only with current date info; point-wise which aggregate data across some time window; serialized representation of the time series. In terms of data domains we additionally extracted information about dates like in [13], holidays and weather. And besides initial raw time-series we also looked upon series of the closely correlated devices. For these series we extracted various aggregated summary statistics like mean, sd and quantile values. A complete map of all extracted features is presented in Figure 5. 5.2

Predictive model evaluation

In order to predict device cash flows we considered two families of models: linear ones with linear regression and lasso, ridge and elastic net regularizations; and nonlinear machine learning models like gradient boosted decision trees, random forests and svms. Each model was built separately to each device types and had it’s own built-in parameter selection procedures. We employed 10-fold cross-validation for hyperparameter selection in each of these models. Finally we compared the resulting models in order to get the best linear and best nonlinear model representatives. In terms of model goodness of fit criteria we chose the R2 metric. Model with higher R2 value doesn’t necessarily provide better cost decrease, however one might reason that with the increase in mode accuracy one could achieve better cost reduction result. 5.3

Encashment plan provision

We follow our proposed strategy of keeping balance between InventoryCosti and F ixedCosti for each device. Besides dispensers require exact amounts of cash to replenish if it reaches some critical threshold. The strategy is based on the predictions obtained from the considered linear and nonlinear machine learning models in discussion. Choosing dispenser threshold is trade-off between safety and additional incurred inventory losses. The higher the threshold value, the less we have our

Fig. 5. Map of extracted features. Day number in a week Day number in a month

Current Date This device

Month number

Serialized values 30 values

Is holiday Is weekend

Date specifics

Features Similar devices

30 values from 1 device

Temperature Pressure

Current weather

Aggregated date info

Serialized values

Across 30 days

Rain

Current date (single-value, non-spatial)

Number of holidays

Variance

Number of outliers

Quantiles

Current date, aggregated over time (single-value, spatial)

Serialized up to current date (multi-valued, spatial)

failure probability at the cost of some amount of money remaining permanently idle. In our system we chosen threshold equal to two standard prediction errors, however one might consider optimizing it as a stand-alone hyperparameter of the optimization algorithm. After we have the set of actions defined for each ATM device, this set of actions is compiled into a report for bank’s operations office.

6

Results

In order to estimate the quality of our solution We split our dataset into train set (2009-2012 years) and test set (2013 year). Daily discount r was set to 0.00035 since annual loan rate for this bank at this period in time was 12%. Table with F ixedCosti for each device was also provided by the bank. Test set was only used to evaluate both prediction quality and cost efficiency of our strategy. We compared 4 different solutions: 1. 2. 3. 4.

Original predictions given by human experts of the bank Proposed strategy based on best linear model Proposed strategy based on best non-linear model Proposed strategy based on ideal prediction. Solutions were compared based on 4 criteria resembling system objectives:

1. 2. 3. 4.

R2 for cash-in devices R2 for dispenser devices Number of device failures Cost reduction

To assure stable and sound results, bootstrap simulations were applied to objective criteria estimates. Each model was fit on a resampled with replacement train dataset. Predictions were evaluated on the complete test set. The boostrap was repeated for 20 times and the resulting average and standard deviations of resampled statistics were collected. The resulting criteria for complete systems are presented in Table 1. Table 1. System comparison based on objective criteria. Model name R2 cashin R2 dispenser Failures Cost decrease Human experts 172 0.00% Best linear (LM) 0.59±0.001 0.64±0.002 104±15.4 17.94±0.11% Best nonlinear (GBM) 0.59±0.028 0.64±0.005 98± 9.2 17.89±0.14% Ideal 1.00 1.00 0 27.12%

We can see that our strategy grants a reasonable 18% cost reduction compared to the schedules prepared by human experts. Moreover if we consider

ideally optimal predictions we see that the maximum cost reduction on this data is around 27%. This means that not only we achieved considerable results, but also the physical limit of productivity in this application is not far away. It is worth noting that the resulting systems of both linear and nonlinear models behave nearly the same. Although nonlinear models provide a slightly lesser amount of failures, neither their costs decrease nor R2 are significantly different from those of the linear model. It may be caused by the fact that the most important features of the resulting best nonlinear model (GBM) were very ARIMA-like (cash flow from previous 7,14,21 days) thus considering that the strong nonlinear model converged to a linear one.

7

Discussion

As noted in related works, there are many of articles on ATM cash flow prediction, but very few about actual optimization of ATM network costs. Authors usually deal with periodic data that is easy to predict. We have proposed a strategy that can decrease total expenses on ATM network management by 18% and can be adopted to bank operations and other industry-related tasks dealing with supply chain management. Our strategy however has considerable space for improvement. For example we can consider adaptive threshold selection for both types of devices and add additional hyperparameters on encashment decision support. It is the strategy that provides the cost reduction and potentially this would be the most fruitfull direction for future research of this problem. Predicting the amount of cash to replenish is a more challenging task than simple cash flow predictions. Many different approaches can be taken to solve this problem. For example one could apply quantile regression for predictive risk estimation. It is even remove the threshold necessity if the system was completely rewritten in terms of predictive risks.

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