# Dynamic Marketing Resource Allocation with Two-Stage Decisions

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## Abstract

**:**

## 1. Introduction

- What strategies can be utilized to link the customers’ preferences forecasting with capital/resource utilization maximization?
- How can we set a suitable marketing decision period that has the most noteworthy effect on sales?
- What techniques are utilized to forecast marketing demand facing short of historical sales data of new products?

#### 1.1. Key Results

- In the first stage of customer classification (targeting customers), we adopted three classic methodologies related to machine learning—distance-based method, K-nearest neighbors (KNN), and support vector machine (SVM)—over multiple heterogeneous features among potential customers. From the perspective of running time, the distance-based method used the shortest time to complete the classification process; KNN was the most stable in terms of predicted accuracy, although it cost twice as much time as that of the distance-based method. SVM showed a slightly higher predicted accuracy than that of the distance-based method, but it took a much long time to do classification due to finding its convex optimization results. Furthermore, as observations made in the training sample were all buyers/users who accepted a product that was very similar to the newly launched product, we had no information about customers who were uninterested in this new product. To deal with this issue, an online learning strategy was proposed. We found that the distance-based algorithm always reached its stable state after one episode, while KNN and SVM had a slower speed when learning.
- In the second stage of optimization of resource allocation, classification results were then taken as input parameters of resource optimization for allocation of resources. Experiments were also conducted to compare the optimal resource allocation with the marketing strategies currently adopted by the loan agency. Our simulation results showed that the higher predicted accuracy one algorithm yields, the greater the increase in final expected buyers/users, thus, the better the allocation proposal. Among the three classification algorithms, KNN outperformed others with a 22.42% increase in final expected customers. With more expected customers wanting to try new products under the scenario of limited promotion resources, the corresponding classification methodology together with optimal resource allocation plan are an improvement toward the promotion strategy that the company adopts at present.

#### 1.2. Literature Review

- Our research constructed a cost-effective solution through integrating the forecasting of preferences toward the promotion channel and the optimization of resource allocation, rather than solving them separately as typically performed.
- We derive a theoretical relationship between the preference probability and the optimization of a limited marketing budget.
- Academic studies overlook short-term decisions, while our proposed framework is flexible and can analyze in time to help making marketing decisions.
- Current forecast methods use sufficient sales data to predict a mid-range lifecycle. However, we generate practical steps for obtaining an accurate early lifecycle forecast.
- We conducted an online convex programming algorithm to analyze customers with no interest in the new product.
- We proposed a framework that can be adopted in different scenarios and is not restricted to industries.

## 2. Materials and Methods

#### 2.1. Customer Classification

#### 2.1.1. Distance-Based Method

#### 2.1.2. K-Nearest Neighbors

#### 2.1.3. Support Vector Machine

#### 2.1.4. On-Line Learning

#### 2.1.5. Evaluating Alternative Classification Algorithms

#### 2.2. Resource Allocation

- 1
- Some customers still do not receive any promotion even if all resources are consumed. We select potential customers randomly under resource constraints. Formulate the optimal problem as$$\begin{array}{cccc}\hfill \phantom{\rule{1.em}{0ex}}& max\hfill & \hfill \phantom{\rule{1.em}{0ex}}& {P}_{0}*\alpha \frac{R}{m}+{P}_{1}*(1-\alpha )\frac{R}{n}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \mathrm{s}.\mathrm{t}.\hfill & \hfill \phantom{\rule{1.em}{0ex}}& \alpha \frac{R}{m}\le {\omega}_{0}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & (1-\alpha )\frac{R}{n}\le {\omega}_{1}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & 0\le \alpha \le 1\hfill \end{array}$$The first-order condition (FOC) is $({P}_{0}/m-{P}_{1}/n)*R$.
- (a)
- When $FOC>0$, $1<\beta <{P}_{0}/{P}_{1}$.With $0\le \alpha \le {\omega}_{0}m/R$ or $1-{\omega}_{1}n/R\le \alpha \le {\omega}_{0}m/R$, optimal ${\alpha}^{*}={\omega}_{0}\beta n/R$and ${EU}^{*}={P}_{0}{\omega}_{0}+{P}_{1}(R/n-{\omega}_{0}\beta )$;With $0\le \alpha \le 1$ or $1-{\omega}_{1}n/R\le \alpha \le 1$, optimal ${\alpha}^{*}=1$ and ${EU}^{*}={P}_{0}R/m$.
- (b)
- When $FOC<0$, $\beta >{P}_{0}/{P}_{1}$.With $0\le \alpha \le {\omega}_{0}m/R$ or $0\le \alpha \le 1$, optimal ${\alpha}^{*}=0$ and ${EU}^{*}={P}_{1}*R/n$;With $1-{\omega}_{1}n/R\le \alpha \le {\omega}_{0}m/R$ or $1-{\omega}_{1}n/R\le \alpha \le 1$, optimal${\alpha}^{*}=1-{\omega}_{1}n/R$ and ${EU}^{*}={P}_{0}(R-n{\omega}_{1})/\left(n\beta \right)+{\omega}_{1}{P}_{1}$.

- 2
- Meet the demand of all customers with some promotion resources left if all resources focus on one certain promotion channel. Formulate the optimal problem as$$\begin{array}{cccc}\hfill \phantom{\rule{1.em}{0ex}}& max\hfill & \hfill \phantom{\rule{1.em}{0ex}}& {P}_{0}*{\omega}_{0}+{P}_{1}*{\omega}_{1}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \mathrm{s}.\mathrm{t}.\hfill & \hfill \phantom{\rule{1.em}{0ex}}& \alpha \frac{R}{m}\ge {\omega}_{0}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & (1-\alpha )\frac{R}{n}\ge {\omega}_{1}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & 0\le \alpha \le 1\hfill \end{array}$$When $\alpha $ meets the constraints above, we solve this inequality constrained optimization problem easily with its optimal solution ${EU}^{*}={P}_{0}*{\omega}_{0}+{P}_{1}*{\omega}_{1}$. In reality, situations such as this are uncommon, as resources are always limited.
- 3
- Resources in hand meet the demand of customers in urgent need of promotion by phone. However, when it comes to putting all resources to the channel of face-to-face promotion, we lack resources to meet the high demand. Describe the optimal problem as:$$\begin{array}{cccc}\hfill \phantom{\rule{1.em}{0ex}}& max\hfill & \hfill \phantom{\rule{1.em}{0ex}}& {P}_{0}*{\omega}_{0}+{P}_{1}*(1-\alpha )\frac{R}{n}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \mathrm{s}.\mathrm{t}.\hfill & \hfill \phantom{\rule{1.em}{0ex}}& \alpha \frac{R}{m}\ge {\omega}_{0}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & (1-\alpha )\frac{R}{n}\le {\omega}_{1}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & 0\le \alpha \le 1\hfill \end{array}$$Formulate the FOC of this inequality constrained optimization problem above as $FOC=-{P}_{1}*R/n$. As $FOC<0$, with $1-{\omega}_{1}n/R\le \alpha \le 1$, optimal ${\alpha}^{*}=1-{\omega}_{1}n/R$ and ${EU}^{*}={P}_{0}{\omega}_{0}+{P}_{1}{\omega}_{1}$; with ${\omega}_{0}m/R\le \alpha \le 1$, optimal ${\alpha}^{*}={\omega}_{0}m/R$, and ${EU}^{*}={\omega}_{0}{P}_{0}+{P}_{1}(R/n-{\omega}_{0}\beta )$.
- 4
- Resources in hand meet the demand of customers in urgent need of face-to-face promotion. However, when our optimization solution decides to put all resources to promoting by phone, we are short of resources. Describe the optimal problem as$$\begin{array}{cccc}\hfill \phantom{\rule{1.em}{0ex}}& max\hfill & \hfill \phantom{\rule{1.em}{0ex}}& {P}_{0}*\alpha *\frac{R}{m}+{P}_{1}*{\omega}_{1}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \mathrm{s}.\mathrm{t}.\hfill & \hfill \phantom{\rule{1.em}{0ex}}& \alpha \frac{R}{m}\le {\omega}_{0}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & (1-\alpha )\frac{R}{n}\ge {\omega}_{1}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}\hfill & & 0\le \alpha \le 1\hfill \end{array}$$The FOC of this inequality constrained optimization problem above is $FOC={P}_{0}*R/m$. As $FOC>0$, with $0\le \alpha \le {\omega}_{0}m/R$, optimal ${\alpha}^{*}={P}_{0}{\omega}_{0}+{P}_{1}{\omega}_{1}$; with $0\le \alpha \le 1-{\omega}_{1}n/R$, optimal ${\alpha}^{*}=1-{\omega}_{1}n/R$ and ${EU}^{*}={P}_{0}(R-n{\omega}_{1})/\left(n\beta \right)+{P}_{1}{\omega}_{1}$.

## 3. Results

- T + 1: the acquiring settlement is completed at a certain time of the next working day;
- In time: settlement is established once transaction occurs;
- T + 0: settlement is batched several times in the current working day.

- Approved time. The approved time lasting of an acquiring small businesses stands for how long he/she has been an acquired customer of the acquired agency, usually the longer the better, i.e., for small businesses with longer approved time, the more products they may experience, which would increase the accuracy of our classification process. Moreover, it may be easier to persuade small businesses approved earlier to use a new product as they know our product well and that the new product is beneficial to them.
- Gender. A $0-1$ variable indicates the gender of the legal representative of small businesses. Consider gender also has an impact on which channel they prefer to be promoted by.
- Age. Consider that small businesses at different life stages have different preferences for the promotion channel of a financial product. Furthermore, age may reflect a common pattern of a time period. For instance, young people today are used to reading messages in WeChat (a multi-function social media mobile application software) while the older generation may prefer making phone calls.
- Transaction amount. The transaction amount during the statistical period generally stands for which industry the small businesses are in and how much funds we may offer to them.
- Number of transactions. The number of transactions during the statistical period reflects the transaction frequency.
- Quality. Quality represents the kind of enterprise that the small businesses operates. Small businesses with different quality have different demands for funds.

^{®}Core (TM) i5-4200U CPU @ 1.60 GHz 2.30 GHz and RAM of 4 GB with R programming.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Saboo, A.R.; Kumar, V.; Park, I. Using big data to model time-varying effects for marketing resource (re) allocation. MIS Q.
**2016**, 40, 911–939. [Google Scholar] [CrossRef] - Rust, R.T.; Zeithaml, V.A.; Lemon, K.N. Customer-centered brand management. Harv. Bus. Rev.
**2004**, 82, 110–120. [Google Scholar] [PubMed] - Cao, X.; Zhang, J. Preference learning and demand forecast. Mark. Sci.
**2021**, 40, 62–79. [Google Scholar] [CrossRef] - Verhoef, P.C.; Venkatesan, R.; McAlister, L.; Malthouse, E.C.; Krafft, M.; Ganesan, S. CRM in data-rich multichannel retailing environments: A review and future research directions. J. Interact. Mark.
**2010**, 24, 121–137. [Google Scholar] [CrossRef] - Bodapati, A.V. Recommendation systems with purchase data. J. Mark. Res.
**2008**, 45, 77–93. [Google Scholar] [CrossRef] - Montgomery, A.L.; Smith, M.D. Prospects for Personalization on the Internet. J. Interact. Mark.
**2009**, 23, 130–137. [Google Scholar] [CrossRef] - Tong, S.; Luo, X.; Xu, B. Personalized mobile marketing strategies. J. Acad. Mark. Sci.
**2020**, 48, 64–78. [Google Scholar] [CrossRef] - Luo, X.; Andrews, M.; Fang, Z.; Phang, C.W. Mobile targeting. Manag. Sci.
**2014**, 60, 1738–1756. [Google Scholar] [CrossRef] [Green Version] - Andrews, M.; Luo, X.; Fang, Z.; Ghose, A. Mobile ad effectiveness: Hyper-contextual targeting with crowdedness. Mark. Sci.
**2016**, 35, 218–233. [Google Scholar] [CrossRef] - Li, C.; Luo, X.; Zhang, C.; Wang, X. Sunny, rainy, and cloudy with a chance of mobile promotion effectiveness. Mark. Sci.
**2017**, 36, 762–779. [Google Scholar] [CrossRef] [Green Version] - Ghose, A.; Kwon, H.E.; Lee, D.; Oh, W. Seizing the commuting moment: Contextual targeting based on mobile transportation apps. Inf. Syst. Res.
**2019**, 30, 154–174. [Google Scholar] [CrossRef] - Malthouse, E.C.; Derenthal, K.M. Improving predictive scoring models through model aggregation. J. Interact. Mark.
**2008**, 22, 51–68. [Google Scholar] [CrossRef] - Li, X.; Yin, Y.; Manrique, D.V.; Bäck, T. Lifecycle forecast for consumer technology products with limited sales data. Int. J. Prod. Econ.
**2021**, 239, 108206. [Google Scholar] [CrossRef] - Kumar, A.; Shankar, R.; Aljohani, N.R. A big data driven framework for demand-driven forecasting with effects of marketing-mix variables. Ind. Mark. Manag.
**2020**, 90, 493–507. [Google Scholar] [CrossRef] - He, P.; Zheng, F.; Belavina, E.; Girotra, K. Customer preference and station network in the London bike-share system. Manag. Sci.
**2021**, 67, 1392–1412. [Google Scholar] [CrossRef] - Thomas, J.S.; Sullivan, U.Y. Managing marketing communications with multichannel customers. J. Mark.
**2005**, 69, 239–251. [Google Scholar] [CrossRef] - Ansari, A.; Mela, C.F.; Neslin, S.A. Customer channel migration. J. Mark. Res.
**2008**, 45, 60–76. [Google Scholar] [CrossRef] - Neslin, S.A.; Shankar, V. Key issues in multichannel customer management: Current knowledge and future directions. J. Interact. Mark.
**2009**, 23, 70–81. [Google Scholar] [CrossRef] - Hwang, W.Y. Variable selection for collaborative filtering with market basket data. Int. Trans. Oper. Res.
**2020**, 27, 3167–3177. [Google Scholar] [CrossRef] - Perdikaki, O.; Kumar, S.; Sriskandarajah, C. Managing retail budget allocation between store labor and marketing activities. Prod. Oper. Manag.
**2017**, 26, 1615–1631. [Google Scholar] [CrossRef] - Ban, G.Y.; Rudin, C. The big data newsvendor: Practical insights from machine learning. Oper. Res.
**2019**, 67, 90–108. [Google Scholar] [CrossRef] [Green Version] - Luzon, Y.; Pinchover, R.; Khmelnitsky, E. Dynamic budget allocation for social media advertising campaigns: Optimization and learning. Eur. J. Oper. Res.
**2022**, 299, 223–234. [Google Scholar] [CrossRef] - Memarpour, M.; Hassannayebi, E.; Fattahi Miab, N.; Farjad, A. Dynamic allocation of promotional budgets based on maximizing customer equity. Oper. Res.
**2021**, 21, 2365–2389. [Google Scholar] [CrossRef] - Fischer, M.; Albers, S.; Wagner, N.; Frie, M. Practice prize winner—Dynamic marketing budget allocation across countries, products, and marketing activities. Mark. Sci.
**2011**, 30, 568–585. [Google Scholar] [CrossRef] - Koosha, H.; Albadvi, A. Allocation of marketing budgets to maximize customer equity. Oper. Res.
**2020**, 20, 561–583. [Google Scholar] [CrossRef] - Hanssens, D.M.; Parsons, L.J.; Schultz, R.L. Market Response Models: Econometric and Time Series Analysis; Kluwer Academic Publishers: Boston, UK, 2003. [Google Scholar]
- Kumar, V. Profitable Customer Engagement: Concept, Metrics and Strategies; Sage Publications: New Delhi, India, 2013. [Google Scholar]
- Salmani, Y.; Partovi, F.Y. Channel-level resource allocation decision in multichannel retailing: A US multichannel company application. J. Retail. Consum. Serv.
**2021**, 63, 102679. [Google Scholar] [CrossRef] - Li, H.; Shen, Q.; Bart, Y. Dynamic resource allocation on multi-category two-sided platforms. Manag. Sci.
**2021**, 67, 984–1003. [Google Scholar] [CrossRef] - James, G.; Witten, D.; Hastie, T.; Tibshirani, R. An Introduction to Statistical Learning; Springer: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Zinkevich, M. Online convex programming and generalized infinitesimal gradient ascent. In Proceedings of the 20th International Conference on Machine Learning, Washington, DC, USA, 21–24 August 2003; pp. 928–936. [Google Scholar]
- Metzen, J.H. Minimum regret search for single-and multi-task optimization. In Proceedings of the 33rd International Conference on Machine Learning, ICML, New York, NY, USA, 20–22 June 2016; pp. 192–200. [Google Scholar]
- Eduardo, C. A minimum expected regret model for the shortest path problem with solution-dependent probability distributions. Comput. Oper. Res.
**2017**, 77, 11–19. [Google Scholar] - Lee, J.; Jung, O.; Lee, Y.; Kim, O.; Park, C. A Comparison and Interpretation of Machine Learning Algorithm for the Prediction of Online Purchase Conversion. J. Theor. Appl. Electron. Commer. Res.
**2021**, 16, 1472–1491. [Google Scholar] [CrossRef] - Ma, L.; Sun, B. Machine learning and AI in marketing–Connecting computing power to human insights. Int. J. Res. Mark.
**2020**, 37, 481–504. [Google Scholar] [CrossRef] - Cui, D.; Curry, D. Prediction in marketing using the support vector machine. Mark. Sci.
**2005**, 24, 595–615. [Google Scholar] [CrossRef] - Huang, D.; Luo, L. Consumer preference elicitation of complex products using fuzzy support vector machine active learning. Mark. Sci.
**2016**, 35, 445–464. [Google Scholar] [CrossRef] [Green Version] - Dzyabura, D.; Jagabathula, S.; Muller, E. Accounting for discrepancies between online and offline product evaluations. Mark. Sci.
**2019**, 38, 88–106. [Google Scholar] [CrossRef] - Lemmens, A.; Gupta, S. Managing churn to maximize profits. Mark. Sci.
**2020**, 39, 956–973. [Google Scholar] [CrossRef]

R | The total mount of resources |

m | Unit consumption of resources for face-to-face promotion |

n | Unit consumption of resources for phone promotion |

$\beta $ | The proportion of m to n |

$\alpha $ | The proportion of resources allocated to face-to-face promotion |

${\omega}_{0}$ | The demand of customers who are preferred to face-to-face promotion |

${\omega}_{1}$ | The demand of customers who are preferred to phone promotion |

$EU$ | The number of expected buyers/users |

${P}_{0}$ | The probability that the customer is preferred to face-to-face promotion |

${P}_{1}$ | The probability that the customer is preferred to phone promotion |

True Promotion | Face to Face | Phone | of No Interest | |
---|---|---|---|---|

Predicted Promotion | ||||

face-to-face | ${x}_{11}$ | ${x}_{12}$ | ${x}_{13}$ | |

phone | ${x}_{21}$ | ${x}_{22}$ | ${x}_{23}$ | |

of no interest | ${x}_{31}$ | ${x}_{32}$ | ${x}_{33}$ |

**Table 3.**Evaluation index of different models with equal ${\theta}_{i}$ where ${\theta}_{1}=(1,1,1,1,1,1,1,1)$.

Distribution | Nor | Unif | Exp | Poi | Student’s t | Weibull | Logit | Lognormal | |
---|---|---|---|---|---|---|---|---|---|

Performance | Algorithm | ||||||||

Running time | D-B | 39.49 | 43.17 | 44.27 | 44.10 | 44.62 | 41.73 | 40.73 | 39.62 |

KNN | 83.43 | 84.14 | 84.35 | 84.38 | 83.20 | 80.27 | 79.43 | 78.75 | |

SVM | 316.80 | 310.04 | 278.44 | 229.26 | 173.11 | 274.73 | 343.42 | 251.26 | |

Predicted Accuracy | D-B | 66.22% | 63.82% | 89.74% | 79.07% | 80.16% | 87.81% | 60.86% | 75.06% |

KNN | 99.11% | 98.98% | 99.62% | 99.45% | 99.72% | 99.68% | 98.95% | 99.33% | |

SVM | 67.71% | 64.99% | 94.87% | 88.53% | 87.89% | 93.66% | 61.07% | 76.56% |

**Table 4.**Evaluation index of different models with unequal where ${\theta}_{2}=(5,5,10,20,20,1,1,1)$.

Distribution | Nor | Unif | Exp | Poi | Student’s t | Weibull | Logit | Lognormal | |
---|---|---|---|---|---|---|---|---|---|

Performance | Algorithm | ||||||||

Running time | D-B | 41.09 | 40.76 | 41.05 | 39.22 | 40.09 | 39.64 | 40.21 | 40.31 |

KNN | 83.89 | 83.11 | 84.08 | 83.95 | 84.77 | 80.78 | 84.00 | 83.05 | |

SVM | 365.51 | 364.34 | 370.81 | 374.16 | 387.24 | 362.89 | 361.69 | 369.24 | |

Predicted Accuracy | D-B | 87.86% | 87.97% | 89.98% | 90.02% | 90.19% | 90.38% | 85.01% | 76.22% |

KNN | 99.40% | 99.55% | 99.51% | 99.62% | 99.62% | 99.55% | 99.53% | 99.32% | |

SVM | 92.39% | 92.09% | 96.75% | 94.80% | 95.49% | 96.99% | 88.24% | 79.13% |

**Table 5.**Evaluation index of different models with unequal where ${\theta}_{3}=(5,50,20,20,20,1,10,1)$.

Distribution | Nor | Unif | Exp | Poi | Student’s t | Weibull | Logit | Lognormal | |
---|---|---|---|---|---|---|---|---|---|

Performance | Algorithm | ||||||||

Running time | D-B | 41.00 | 39.53 | 39.43 | 39.75 | 39.44 | 40.32 | 40.27 | 39.97 |

KNN | 84.23 | 82.91 | 81.40 | 85.32 | 85.11 | 81.72 | 81.85 | 81.33 | |

SVM | 75.78 | 81.68 | 71.17 | 59.41 | 53.46 | 67.60 | 76.91 | 63.35 | |

Predicted Accuracy | D-B | 97.18% | 97.20% | 97.45% | 98.24% | 98.10% | 97.73% | 96.76% | 90.99% |

KNN | 99.66% | 99.84% | 99.84% | 99.77% | 99.80% | 99.72% | 99.74% | 99.24% | |

SVM | 97.87% | 97.79% | 98.14% | 98.51% | 98.42% | 98.18% | 97.36% | 91.08% |

Algorithm | Round | ${\mathit{P}}_{0}$ | ${\mathit{P}}_{1}$ | Round | ${\mathit{P}}_{0}$ | ${\mathit{P}}_{1}$ |
---|---|---|---|---|---|---|

Distance-based | 2/10 | 92.85% | 90.72% | 2/50 | 93.22% | 93.15% |

KNN | 5/10 | 97.12% | 98.72% | 21/50 | 97.47% | 98.77% |

SVM | 6/10 | 98.33% | 98.93% | 20/50 | 98.10% | 98.55% |

Algorithm | Round | ${\mathit{P}}_{0}$ | ${\mathit{P}}_{1}$ | Round | ${\mathit{P}}_{0}$ | ${\mathit{P}}_{1}$ |
---|---|---|---|---|---|---|

Distance-based | 2/4 | 93.07% | 90.82% | 2/6 | 93.48% | 92.14% |

KNN | 4/4 | 97.72% | 99.13% | 6/6 | 97.54% | 99.05% |

SVM | 4/4 | 98.56% | 99.02% | 6/6 | 98.45% | 98.93% |

Optimal Resource Allocation | Random Allocation in Use | |||
---|---|---|---|---|

Algorithm | $\mathit{EU}*$ | Improvement | $\mathit{EU}*$ | Improvement |

Distance-based | 6638 | 21.60% | 5459 | Benchmark |

KNN | 6683 | 22.42% | 5835 | 6.89% |

SVM | 6654 | 21.89% | 5689 | 4.21% |

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## Share and Cite

**MDPI and ACS Style**

Zhang, S.; Liao, P.; Ye, H.-Q.; Zhou, Z.
Dynamic Marketing Resource Allocation with Two-Stage Decisions. *J. Theor. Appl. Electron. Commer. Res.* **2022**, *17*, 327-344.
https://doi.org/10.3390/jtaer17010017

**AMA Style**

Zhang S, Liao P, Ye H-Q, Zhou Z.
Dynamic Marketing Resource Allocation with Two-Stage Decisions. *Journal of Theoretical and Applied Electronic Commerce Research*. 2022; 17(1):327-344.
https://doi.org/10.3390/jtaer17010017

**Chicago/Turabian Style**

Zhang, Siyu, Peng Liao, Heng-Qing Ye, and Zhili Zhou.
2022. "Dynamic Marketing Resource Allocation with Two-Stage Decisions" *Journal of Theoretical and Applied Electronic Commerce Research* 17, no. 1: 327-344.
https://doi.org/10.3390/jtaer17010017