The data quality improvement plan: deciding on choice and sequence of data quality improvements

Abstract

With the rapid growth in the amount of data generated worldwide, ensuring adequate data quality (DQ) is increasingly becoming a challenge for companies: data are, among others, required to be timely, complete, consistent, valid, and accessible. Given this multidimensionality, DQ improvements (DQIs) need to be purposefully chosen and –as there can be path dependencies– arranged in an optimal sequence. Thus, this research contributes to performing the complex multidimensional task of ensuring adequate DQ in an economically reasonable manner by providing a formal decision model for identifying an optimal data quality improvement plan (DQIP). This DQIP comprises both an economically reasonable selection and execution sequence of DQIs based on existing interrelationships between different DQ dimensions. Furthermore, a comprehensive Monte Carlo simulation provides insights in implications to put the decision model into operation. For practitioners, the decision model enables efficient allocation of resources to DQIs. The model also gives advice on how to sequence DQIs and attracts attention to the complex problem context of DQ in order to support valid managerial decisions.

Appendix

Supplementing the chapter “Development of the Decision Model

”, a more detailed derivation of the objective function is given in the following.

The decision to consider a DQI ${v}_j^p$ in a DQIP is described formally using the decision variable ${x}_{v_j^p}$, whereas the binary variable ${x}_{v_j^p}$ is equal to 1 if DQI ${v}_j^p$ is part of the DQIP, and 0 if not. Thus, the resulting DQ level ${Q}_{d_{i,}{v}_j}^p$ of DQ dimension d _i , after applying DQI ${v}_j^p$, is calculated in the following manner:

$$ {Q}_{d_{i,}{v}_j}^p={Q}_{d_{i,}{v}_j}^{p-1}+\left\{\begin{array}{l}\left(1-{Q}_{d_{i,}{v}_j}^{p-1}\right)\cdot {I}_{d_i,{v}_j^p}\cdot {x}_{v_j^p}\kern0.5em if\kern0.5em {I}_{d_i,{v}_j^p}\ge 0\\ {}{Q}_{d_{i,}{v}_j}^{p-1}\cdot {I}_{d_i,{v}_j^p}\cdot {x}_{v_j^p}\kern0.5em if\kern0.5em {I}_{d_i,{v}_j^p}<0\end{array}\right.. $$

After remodelling and, for mathematical reasons, introducing the substitute variables ${f}_{d_i,{v}_j^p}$ and ${s}_{d_i,{v}_j^p}$, the resulting DQ level ${Q}_{d_{i,}{v}_j}^p$ can also be written as

$$ {Q}_{d_{i,}{v}_j}^p={Q}_{d_{i,}{v}_j}^{p-1}\cdot {f}_{d_{i,}{v}_j^p}+{s}_{d_{i,}{v}_j^p,}\kern0.5em \mathrm{with}\ {f}_{d_{i,}{v}_j^p}=\left\{\begin{array}{l}1-{I}_{d_{i,}{v}_j^p}\cdot {x}_{v_j^p}\; if\;{I}_{d_{i,}{v}_j^p}\ge 0\\ {}1+{I}_{d_{i,}{v}_j^p}\cdot {x}_{v_j^p}\; if\;{I}_{d_{i,}{v}_j^p}<0\end{array}\right.\mathrm{and}\ {s}_{d_i,{v}_j^p}=\left\{\begin{array}{l}{I}_{d_{i,}{v}_j^p}\cdot {x}_{v_j^p}\; if\;{I}_{d_{i,}{v}_j^p}\ge 0\\ {}\begin{array}{cc}\hfill 0\hfill & \hfill if\;{I}_{d_{i,}{v}_j^p}<0\hfill \end{array}\end{array}\right.. $$

Based on this, the DQ level ${Q}_{d_i}^m$ for dimension d _i , after applying a complete DQIP for m DQIs ${v}_j^p$ is calculated in the following manner:

$$ {\mathrm{Q}}_{{\mathrm{d}}_{\mathrm{i}}}^{\mathrm{m}}=\left(\left(\left(\dots \left(\left({\mathbf{Q}}_{{\mathbf{d}}_{\mathbf{i}}}^{\mathbf{p}=0} \cdot {\mathbf{f}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=1}}+{\mathbf{s}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=1}}\right) \cdot {\mathbf{f}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=2}}+{\mathbf{s}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=2}}\right)\cdot \dots \right) \cdot {\mathbf{f}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=\mathbf{m}-1}}+{\mathbf{s}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=\mathbf{m}-1}}\right) \cdot {\mathbf{f}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=\mathbf{m}}}+{\mathbf{s}}_{{\mathbf{d}}_{\mathbf{i}},{\mathbf{v}}_{\mathbf{j}}^{\mathbf{p}=\mathbf{m}}}\right) $$

The binary variables ${x}_{v_j^p}$, that are part of ${f}_{d_i,{v}_j^p}$ and ${s}_{d_i,{v}_j^p}$, neutralize the effect of DQI ${v}_j^p$ by taking the value 0 if a specific DQI ${v}_j^p$ is not part of the DQIP. Although term (3) contains all m DQIs ${v}_j^p$, a DQI selection is possible through this neutralization. Knowing the DQ level ${Q}_{d_i}^m$ for each DQ dimension d _i , the overall DQ level can be calculated. As there can be context-dependent differences between the DQ dimensions, an allocation of weights to different DQ dimensions is reasonable. Therefore, we use a weight ${w}_{d_i}$ (with $\sum_{i=1}^n{w}_{d_i}=1$) to weight the DQ dimensions in our decision model.

$$ {\sum}_{i=1}^n{w}_{d_i}\cdot {Q}_{d_i}^m $$

In contrast to former approaches that have been criticized in literature for not considering interrelationships when aggregating DQ dimensions to an overall DQ level, in this decision model, interrelationships between the DQ dimensions d _i are implicitly considered by the impacts ${I}_{d_i,{v}_j^p}$.

Since all DQIs are applied on the same dataset, which has a fixed size, and a DQIP is realized within one period (cf. A.3), the costs ${c}_{v_j}$ for applying DQI v _j are fixed. As a result, the overall DQIP costs are

$$ {\sum}_{j=1}^m{c}_{v_j}\cdot {x}_{v_j}. $$

According to assumption A.8, the costs of a DQIP must not exceed budget B; thus, the budget constraint for the decision model is

$$ {\sum}_{j=1}^m{c}_{v_j}\cdot {x}_{v_j}\le \mathrm{B} $$

In order to allocate a given budget in an economically reasonable manner to an available set of DQIs, all possible DQIPs need to be compared to each other. As a comparison criterion, we calculate the respective effectiveness E ^p = m of a DQIP in the way described in the chapter “Development of the Decision Model”. The objective function maximizes the effectiveness of a DQIP in the following manner:

$$ \mathrm{Maximize}{E}^{p=m}=\frac{\sum_{i=1}^n{w}_{d_i}\cdot \left({Q}_{d_i}^m-{Q}_{d_i}^{p=0}\right)}{1-{\sum}_{i=1}^n{w}_{d_i}\cdot {Q}_{d_i}^{p=0}}\mathrm{subject}\ \mathrm{t}\mathrm{o}\ {\sum}_{j=1}^m{c}_{v_j}\cdot {x}_{v_j}\le \mathrm{B} $$