A fuzzy optimization method to select marketing strategies for new products based on similar cases

Abstract

Successful new product launches are significant for company survival in intense competition environments. Companies generally divide customers into different marketing segments to increase profits due to the growing focus on customer relationship management (CRM). For new product launches, developing marketing strategies towards customers in different segments is a critical issue faced by companies. To address this issue, this paper proposes a fuzzy optimization method to select marketing strategies for new products based on similar cases. In the proposed method, a case database and a target case are constructed that consist of relevant data about historical products and a new product, respectively. Then, historical similar cases are retrieved based on similarities and adapted according to the current situation. Next, triangular fuzzy numbers are used to describe customers’ responses to the marketing strategies. Finally, a fuzzy integer linear model is constructed. By solving this model, marketing strategies for the new product towards customers in different segments can be obtained. A case study is provided to illustrate the potential for the practical application of the proposed methodology and several managerial implications are also noted.

Keywords

Fuzzy integer linear programming similar cases marketing strategy new product launch customer segment

1 Introduction

The rapid development of science and technology and their broad application in practice are accelerating updates to existing products and promoting the development of new products. Whether new products launch successfully in the process of product upgrading is related to the amount of market share a company occupies in an intensive market environment. Successful new product launches play an important role in increasing companies’ competitiveness. In the short term, a successful new product launch can bring immediate profits for companies. In the long run, new product success can promote brand extension, establish corporate image, and increase word-of-mouth promotion and customer loyalty. Hence, successful new product launches are critical for companies to survive under fierce market competition.

The successful launch of a new product is affected by external factors such as marketing strategies as well as by the intrinsic factors of the new product itself [1, 2]. For example, advertising can enhance the consumers’ perceptions of the new product efficiently and quickly, increase the store-entry ratio and further increase the probability that the products are purchased [3]. Discounts may stimulate consumers to purchase products and then increase product sales [4, 5]. Coupons can accelerate the purchase timing of the products, stimulate repeat purchases by consumers, and increase their purchase volume [6, 7]. The effects of these marketing strategies may be different with respect to different customers because customers generally differ in their feelings towards products and have heterogeneous perceptions of marketing strategies. In reality, companies generally divide customers into different marketing segments to increase profits due to their growing focus on customer relationship management (CRM). Several methods have been proposed to segment customers, such as “20/80 rules” –20% of customers produce 80% of sales to the company [8], the customer pyramid based on the profitability of each customer [9], the RFM model based on the recency, frequency, and monetary value [10], and so on. Therefore, it is necessary for marketers to develop a targeted marketing strategy for customers in each segment in the context of new product launches.

New products are categorized into different groups by the newness of new products in current literature. Micheal et al. [11] divide new products into new-to-the-market and new-to-the-firm products, new-to-the-firm but not new-to-the-market products, and products that are revisions to the firm and not new-to-the-market. Haji and Assadi [12] classify new products into really new products and slightly new products. The slightly new products are existing products that have minor variations in features. In practice, companies always develop new product versions on a regular basis. The new products in this paper refer to revisions of existing products, which can also be seen as the new generation of products [11]. Thus, similarities often exist between the new product and existing ones [13]. To analyse the marketing strategies for the existing products can help to develop marketing strategies for the new product due to the similarities between products.

A method considering similarities provides some insights to solve the problem of developing and selecting marketing strategies for the new product. The method based on similar cases originates from the idea that ‘from causes which appear similar we expect similar effects’ put forward by Hume [14]. Schank and Abelson [15] propose the idea of case-based reasoning (CBR) on the basis of this idea. CBR describes the process of solving current problems by recalling previous similar situations and reusing the knowledge and information learned from similar situations. This is very similar to people’s thinking habits and problem solving strategies. Additionally, the utilization of past knowledge and experiences can save time and economic costs that result from obtaining knowledge and experiences again. Due to these advantages, this method is widely applied in various areas such as human resources [16], fault diagnosis [17], supplier selection [18], risk analysis [19], production scheduling [20], medicine [21], emergency decisions [22, 23] and so on. In CBR, past events are described as historical cases that are stored in a case database and the current problem is described as a target case [24]. In general, each historical case is composed of three types of data that describe the problem’s features, its solution and the results after implementing the solution [25]. The target case only contains data regarding features of the new problem.

How to develop targeted marketing strategies for customers in different segments when a new product launches is an issue of great practical significance. However, existing studies rarely focus on this question. Therefore, the motivation of this paper is to address the gap in the literature by proposing a fuzzy optimization method to select marketing strategies for new products with respect to multiple customer segments based on similar cases. This motivation comes from two aspects: one is that new products are usually similar to the existing products, and the other is that customers’ responses to the marketing strategies are generally uncertain and vague in reality. The main contributions of this paper are concluded as follows. Firstly, a case database and a target case that consist of relevant data on historical products and the new product are constructed, respectively. Then, the similar historical cases are retrieved based on the similarities and then adapted according to current needs. Next, triangular fuzzy numbers are introduced [26 –28] to evaluate the fuzzy transition probabilities of customers across segments which can reflect customers’ uncertain responses to the marketing strategies. Finally, a fuzzy integer linear model [29 –31] is built to select the most appropriate marketing strategies for the new product towards different customer segments. The data about the new product, the customers, the marketing strategies, and their corresponding effects will be retained in the case database for future problem solving. Three managerial implications can be obtained through a case study. First, an optimal marketing budget exists for maximizing the profits. Second, greater profits can be gained by making a relatively detailed classification of the products. Third, the similarity threshold should be set with discretion for better use of the budget. The proposed method can also provide decision support for marketers making decisions about new product marketing as a practical application.

The reminder of this paper is organized as follows. Section 2 provides a literature review of related studies. Section 3 presents the proposed method for selecting marketing strategies for new products based on similar cases. Section 4 demonstrates the proposed method with an application to the cosmetics industry and presents discussions on the results. Conclusions and the directions for future work are offered in Section 5.

2 Literature review

The main function of marketing is to stimulate customer demand via a set of marketing strategies such as advertising, coupons, providing free samples or gifts of related products and price discounts, and thereby increase company profits [5]. Some studies have examined the impacts of different marketing strategies on company performance. Neslin and Shoemaker [32] put forward a user-oriented computer model to assess the profitability of coupon promotions. In marketing, a coupon is generally a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product. Subsequently, some researchers explore the impacts of various coupons on customers’ purchase behaviours [33 –36], examine how the duration of coupons’ validity can affect individual coupon redemption and purchase probabilities [37], and investigate the key difference between coupons and rebates and identify the conditions under which each is optimal [38]. In addition to coupons, price promotions as an important marketing strategy have been the subject of research attention. Price promotions are temporary price reductions offered to customers [39]. Kaltcheva et al. [40] show that price promotions influence consumers’ evaluations of a store’s regular prices. Nijs et al. [41] study the influence of price promotions on category demand in the short and the long run on the basis of empirical generalizations. Lam et al. [3] develop hypotheses that price promotions and new product promotions have a positive attraction effect on store performance and verify these hypotheses through an empirical analysis. Additionally, some researchers investigate the effects of other marketing strategies. Goić et al. [42] note that cross-market discounts as a promotion strategy can impact company profits and construct an analysis model to explore this impact. The results show that cross-market discounts can increase sales and company profits. Borza and Borza [43] analyse certain marketing actions using the SWOT method. According to the analysis, marketing actions, such as price discounts, advertising, promotion plans, and sales promotions can stimulate customer demand and affect their purchase behaviours. Pettigrew et al. [44] explore how in-store shopping experiences and sales promotion activities influence the alcohol choice of young drinkers and the quantity of alcohol purchased using exploratory approaches. Their results show that price discounts, give-aways, and special offers can influence the type, range, and quantity of alcohol purchased. To sum up, we can conclude that some marketing strategies such as coupons, price promotions, discounts, give-aways, and special offers have a significant influence on customers’ purchase behaviours and company profits.

Advertising is also an important marketing strategy which can deliver the product information to customers and motivate their purchase behaviours, especially in the context of new product launches for customers with limited product awareness. Some scholars study how to develop advertising strategies for new product marketing in different marketing environments. Nguyen and Shi [45] extend the Bass model considering the dynamics of the market share and market size and propose optimal advertising strategies for new products. Hariharan et al. [46] apply the dynamic optimization model to obtain advertising and segment-specific targeting strategies for new products with multiple consumer segments. Krishnan and Jain [47] use the generalized Bass model to draw up an optimal advertising plan for a new product under the influence of the diffusion phenomenon. Zhao [48] uses a signalling game to investigate firms’ optimal advertising and pricing strategies when introducing a new product. The results indicate that a high-quality firm will actually spend less on advertising than low-quality firms in the separating equilibrium.

Furthermore, most companies divide customers into multiple segments in CRM. Previous studies show that different customers should be rewarded and satisfied differently [49 –52]. Shaffer and Zhang [53] investigate the competitive effects of one-to-one promotions using a two-stage game. One-to-one promotions provide customized promotion strategies for different customers, such as price discounts, coupons, etc. The results show that one-to-one promotions always lead to an increase in price competition and influence the market shares of both sides. Zhang et al. [54] study which marketing strategies should be used in both variety-seeking and inertia markets. In their study, marketing strategies are divided into front-loaded and rear-loaded incentives. Front-loaded incentives are marketing strategies from which customers can receive immediate benefits when purchasing products, such as price packs and direct mail coupons. Rear-loaded incentives refer to marketing strategies from which customers can obtain promotion incentives on the next purchase occasion or later, such as in-pack coupons and participation in loyalty programmes. Their study shows that customers in different markets should be treated differently. In high variety-seeking markets, it is more profitable for a firm to rear-load, whereas in high inertia markets, it is more profitable to front-load. O’Cass et al. [55] argue that different marketing strategies should be adopted for the new customers versus existing customers as the perceptions of the two types of customers are different. To propose targeted marketing strategies for different customers, Kyun et al. [56] divide customers into six segments through cluster analysis and factor analysis and identify the purchase pattern of each segment. Wei et al. [57] segment customers of a Taiwanese hair salon into four groups using data mining techniques and the RFM model and develop targeted product recommendations and corresponding marketing strategies.

The studies cited make significant contributions to the study of marketing strategies and customer segments. According to the studies above, marketing strategies such as discounts, coupons, give-aways, etc., play a significant role in motivating customers’ purchase behaviours and increasing company profits. Advertising is also regarded as a key marketing tool, especially in the context of a new product launch. In addition, some researchers argue that different customers should be treated differently and focus on how to best segment customers. However, studies on how to develop appropriate marketing strategies for new products with respect to different segments are few. Meanwhile, in reality, how to launch a new product while focusing on customers in different segments to increase company profits is a critical issue. To address this issue, our paper proposes a fuzzy optimization method based on similar cases to select appropriate marketing strategies for new products that account for different customer segments. The proposed methodology attempts to help marketers to make decisions about new product marketing and to provide decision support for new product launches.

3 Methodology

The purpose of this study is to develop a methodology that provides guidance for decisions regarding new product marketing. This methodology consists of two main steps. First is finding similarities between historical products and the new product. The second step uses a fuzzy optimization model to select appropriate marketing strategies for customers in different segments. The general framework is presented in Fig. 1.

3.1 Construction of the case database and the target case

Today, more and more companies attach importance to CRM. CRM is an approach that can analyse historical customer data in order to improve business relationships with customers and drive sales growth. The prerequisite for the adoption of the CRM approach is to construct a database to store customer data. Generally, the database includes large amounts of historical data, such as product features, customers’ demographic characteristics, customers’ purchasing frequencies, etc. To provide decision support for new product marketing, a case database will be constructed.

The case database consists of many historical cases. Each historical case contains four types of data: product data, customer data, data about the marketing strategies, and data about the effects after implementing the marketing strategies. In our paper, let C ={ C₁, C₂, …, C_n } represent a finite set of n historical cases, where C_i denotes the ith historical case, i = 1, 2, …, n. The number of the historical cases in the case database is the same as the number of historical products because each historical case contains relevant data about each product. The product data are described as follows.

The product data comprise the product ID, product name, product category, product features, and the corresponding feature values. Let A_i denote the ith product, i = 1, 2, …, n, Ω_h denote the hth category, h = 1, 2, …, H. Thus, A_i ∈ Ω_h represents that the ith product belongs to the hth category. Let A_i,j denote the jth feature of the ith product, where j = 1, 2, …, m, and a_i,j denote the jth feature value of the ith product.

The customer data include the customer segments, the number of customers in each segment before the product launches, and the average incomes from the customer transitions. Let s denote the sth customer segment, where s = 1, 2, …, S and S is the number of customer segments. In practice, companies usually divide customers into different segments using several methods. For example, the customers can be classified into different segments according to customers’ cumulative consumption or points. Customers whose cumulative consumption is relatively low are classified in the lower segments, and vice versa. Specifically, customers can be categorized into four segments: platinum, gold, iron and lead. Among these segments, the platinum and gold customers are profitable while the iron and lead customers are less attractive. Customers in the gold segment may move to the platinum segment if their cumulative consumption reaches a certain amount. Let $N_{s}^{i}$ denote the number of customers in segment s before product A_i launches. Let $r_{s, s^{'}}^{i}$ denote the average income when the customers move from segment s to segment s′ after product A_i launches.

Targeted marketing strategies should be generally implemented for customers in different segments. For customers in lower segments, companies often provide discounts or coupons to persuade them to buy more products. For potential customers, advertising strategies are used to capture their eyes due to the lack of information about potential customers in the historical database. Thus, the marketing strategies for customers in each segment and the corresponding average implementation costs when products launch are included in the case database. In our work, M_i,s denotes the marketing strategy for customers in segment s when product A_i launches, and c_i,s denotes the average implementation cost of marketing strategy M_i,s for each customer in segment s. The effects after implementing the marketing strategies, which refer to customers’ responses to the marketing strategies in each segment, are also in the case database. Here, we use the number of customers who move from one segment to another to reflect the effects. Let $N_{s, s^{'}}^{i}$ denote the number of customers who move from segment s to segment s′ after product A_i launches.

To conveniently measure the similarities between the historical products and the new product, the target case, including the data about the new product, must be constructed. The target case includes only two types of data: product data and customer data. Let C₀ denote the target case, A₀ denote the product ID, A_0,j denote the jth product feature of the new product, and a_0,j denote the value of the jth product feature. $N_{s}^{0}$ and $r_{s, s^{'}}^{0}$ denote the number of customers in segment s before product A₀ launches and the average income of customers moving from segment s to segment s′ after product A₀ launches, respectively. All of the data in the case database and the target case are known except $r_{s, s^{'}}^{0}$ , and $r_{s, s^{'}}^{0}$ can be predicted by historical sales data [58].

3.2 Retrieval of similar historical cases

Similar results can be obtained when the same solutions are used to solve similar problems. In the problem of selecting marketing strategies for the new product, if a historical product is similar to the new product, then, for each customer segment, marketing strategies used for the historical product can be used for new product marketing. For the purpose of retrieving similar historical products, the similarities between the historical products and the new product should be calculated first. Then, a similarity threshold must be set as the screening benchmark. When the similarities are higher than the threshold, the historical products and their corresponding cases will be screened.

Products in the same category can be comparable since they have same or similar functions that can meet customers’ requirements. Thus, our paper sets product category as an indicator variable denoted as δ_i, i = 1, 2, …, n. When product A_i and the new product are in the same category, δ_i = 1, otherwise, δ_i = 0. The feature values of different products in the same category are usually different. Thus, the weighted sum of the similarities of each product feature is used to measure the similarity between the two products. Hence, the similarity can be calculated based on the following equation:

$\begin{matrix} Sim (A_{0}, A_{i}) & = & Sim (A_{i}, A_{0}) \\ = & δ_{i} \sum_{j = 1}^{m} w_{j} 1 pt Sim (A_{0, j}, A_{i, j}) \end{matrix}$ (1) where Sim (A₀, A_i) denotes the similarity between product A₀ and product A_i. If A_i ∈ Ω_h and A₀ ∈ Ω_h, then δ_i = 1, otherwise, δ_i = 0. Ω_h denotes the hth category, h = 1, 2, …, H. Sim (A_0,j, A_i,j) denotes the similarity between product A₀ and product A_i on the jth feature. w = (w₁, w₂, …, w_m) denotes the vector of feature weights, where w_j represents the weight of the jth feature and $\sum_{j = 1}^{m} w_{j} = 1$ , j = 1, 2, …, m. If Sim (A₀, A_i) ≥ Sim^*, then product A_i and its corresponding case C_i can be retrieved, where Sim^* denotes the similarity threshold.

In reality, the formats of the feature values are various and could be crisp numbers, interval numbers, random variables, sets and so on. For example, the capacity of refrigerators can be 150 L, 210 L, 280 L, and 500 L; these are crisp numbers. The expected rate of return on financial products can be 4.19% – 6.13%. The battery life of mobile phones is a random variable with a normal distribution. The composition of cosmetics may be a set of water, glycerine, dimethicone, carbomer, etc. Therefore, various methods for measuring similarity are given as follows with respect to the product feature values in the different formats:

(1) Similarity measurement methods for crisp numbers

Most methods for measuring the similarity between two crisp numbers are formulated based on the distance between them. In n-dimensional space, the basic idea of the similarity measurement methods is that the smaller the distance between two individuals is, the more similar the two individuals will be. Generally, the transforms between the similarity and the distance are as follows [59]: $dist (X, Y) = 1 - Sim (X, Y)$ (2) $dist (X, Y) = [1 - Sim (X, Y)] / Sim (X, Y)$ (3) $dist (X, Y) = \sqrt{1 - Sim (X, Y)}$ (4) where dist (X, Y) is the distance between X and Y, X, Y ∈ Rⁿ. Several methods for measuring the distance are given briefly below.

➀ Euclidean Distance. The Euclidean Distance is the most common method and measures the absolute distance between two individuals in n-dimensional space as follows: $dist (X, Y) = \sqrt{\sum_{i = 1}^{n} {(x_{i} - y_{i})}^{2}}$ (5) where x_i and y_i are the values in the ith dimension.

➁ Minkowski Distance. The Minkowski Distance is the extension of the Euclidean Distance: $dist (X, Y) = {(\sum_{i = 1}^{n} {| x_{i} - y_{i} |}^{P})}^{1 / p}$ (6)

When P = 2, the Minkowski Distance is the same as the Euclidean Distance.

➂ Manhattan Distance. The Manhattan Distance, which also refers to the city block distance, measures the rectilinear distance between two individuals in n-dimensional space as follows: $dist (X, Y) = \sum_{i = 1}^{n} | x_{i} - y_{i} |$ (7)

(2) Similarity measurement method for interval numbers

The similarity between two interval numbers [a₁, a₂] and [b₁, b₂] is defined as [60]:

$\begin{matrix} Sim ([a_{1}, a_{2}], [b_{1}, b_{2}]) \\ = 1 - \frac{\int_{a_{1}}^{a_{2}} \int_{b_{1}}^{b_{2}} | y - x | dydx}{(a_{2} - a_{1}) (b_{2} - b_{1}) (β - α)} \end{matrix}$ (8) where α and β are the lower bound and upper bound, respectively.

(3) Similarity measurement method for random variables

Assume that A and B are random variables, then the similarity between A and B can be defined as below [61]: $Sim (A, B) = exp [- \frac{1}{Δ_{max}} δ (F_{a} (x), F_{b} (x))]$ (9) where Δ_max = max{ δ (F_a (x) , F_b (x)) }, F_a (x) and F_b (x) are the cumulative distribution functions of random variables A and B, and their ranges are [α_a, β_a] and [α_b, β_b], respectively. δ (F_a (x) , F_b (x)) is the distance between cumulative distribution functions F_a (x) and F_b (x), and $δ (F_{a} (x), F_{b} (x)) = \sqrt{\int_{α^{*}}^{β^{*}} {[F_{a} (x) - F_{b} (x)]}^{2} dx}$ , where α^* = min{ α_a, α_b }, β^* = max{ β_a, β_b }.

(4) Similarity measurement method for sets

Assume that A and B are two sets that contain a number of elements. Jaccard’s coefficient can be used to measure the similarity between two sets as follows [62]: $Sim (A, B) = \frac{| A \cap B |}{| A \cup B |} = \frac{| A \cap B |}{| A | + | B | - | A \cap B |}$ (10) where | · | represents the number of elements in the set.

3.3 Adaptation of the retrieved cases

In the retrieved cases, the historical marketing strategies may be not suitable for the new product. For example, most companies generally provide customers with product information by email instead of regular mail due to the highly developed communications networks, which decreases the marketing cost. In addition, the cost of implementing the marketing strategy may need to be adapted even if the marketing strategy itself remains unchanged. For example, the implementation cost of advertising today may be several times that of a few years ago due to economic growth and/or inflation. Thus, it is necessary to adapt marketing strategies and their implementation costs according to the current situation.

There are some typical case adaptation methods in existing studies, such as non-adaptation, manual case adaptation, adaptation combined with RBR, knowledge-light adaptation, etc. Non-adaptation is applicable to problems involving complex conditions but with a simple solution [25]. Manual case adaptation can be used in situations where the relationships between problems and their solutions are complicated, and the solutions are also complex [63]. In the methods of adaptation combined with rule-based reasoning (RBR), rules and formulas that representing the accumulated knowledge of experts in the field are used to make the appropriate changes of the case solutions [64]. Knowledge-light adaptation methods are developed to overcome the challenge of acquiring sufficient programmable knowledge for case adaptation, and suitable for decomposable design problems, in particular formulation and configuration [65]. Among these methods, which method should be applied to do case adaptation is dependent on the specific issues and circumstances. In this paper, let $M_{i, s}^{'}$ denote the adapted marketing strategy and $c_{i, s}^{'}$ denote the adapted implementation cost.

3.4 Selection of the marketing strategies for maximum the profits from products

To obtain the optimal marketing strategies, an optimization model will be constructed with the objective function of maximizing the profits from products when the new product launches. To build the optimization model, a detailed analysis is presented below.

3.4.1 Calculation of the customers’ transition probabilities

Customers’ responses to marketing strategies are reflected in the transition probabilities of customers across segments after implementing the marketing strategies. The transition probability refers to the ratio of the number of customers moving from one segment to another to the number of customers in the segment before the transition. The calculation formula of the transition probability is defined by Equation (11): $p_{s, s^{'}}^{i} = N_{s, s^{'}}^{i} / N_{s}^{i}$ (11) where $p_{s, s^{'}}^{i}$ denotes the transition probability from segment s to segment s′ after product A_i launches. $N_{s, s^{'}}^{i}$ denotes the corresponding transition number. $N_{s}^{i}$ denotes the number of customers in segment s before product A_i launches.

Using the transition probabilities of customers with respect to each historical product in the retrieved cases and the similarity between the historical product and the new product, the transition probabilities of customers across segments after the new product launches can be predicted. The transition probabilities of customers after the new product launches will fluctuate close to those of the historical product. It is assumed that the fluctuation ranges are decided by the similarity between the historical product and the new product, and the centres of these ranges are the transition probabilities of customers with respect to the historical product. The larger the similarity is, the smaller the fluctuation ranges of the predicted transition probabilities will be. Because the most likely values of the transition probabilities are the centres of the ranges, the triangular fuzzy numbers herein are used to describe the transition probabilities with respect to the new product. Further, considering that the probability should be no more than 1, the fuzzy transition probabilities of customers with respect to the new product are expressed as follows:

$\begin{matrix} {\tilde{p}}_{s, s^{'}}^{0, i} = (p_{s, s^{'}}^{i} Sim (A_{0}, A_{i}), p_{s, s^{'}}^{i}, \\ \min [p_{s, s^{'}}^{i} (2 - Sim (A_{0}, A_{i})), 1]) \end{matrix}$ (12) where ${\tilde{p}}_{s, s^{'}}^{0, i}$ represents the fuzzy transition probability of customers from segment s to s′ with respect to new product A₀ when the adapted marketing strategy $M_{i, s}^{'}$ is used for product A₀, i ∈ Θ, and Θ denotes the set of the similar historical cases.

3.4.2 Construction of the fuzzy optimization model

The fuzzy optimization model is constructed to maximize profits with a limited budget. The objective function of the model is related to the customer transitions and the incomes arising from the transitions. Thus, the analysis of the customer transitions will be given briefly as follows.

When customers buy more products and their cumulative consumption reaches a certain amount on the basis of consumption points, customers may move to a higher segment. When customers buy some products or even no products and their cumulative consumption fails to reach a certain level, they remain in the initial segment. When customers do not buy products for a certain period, they may move to a lower segment. The first two situations will be considered in our paper as the customers in the last situation bring no profits to the company.

Based on the analysis above, the fuzzy optimization model to maximize the profits from products when the new product launches is constructed below: $\begin{matrix} max z (x) \\ = \sum_{s = 1}^{S} (\sum_{s^{'} \geq s}^{S} \sum_{i \in Θ} {\tilde{p}}_{s, s^{'}}^{0, i} x_{i, s} N_{s}^{0} r_{s, s^{'}}^{0} - \sum_{i \in Θ} x_{i, s} c_{i, s}^{'} N_{s}^{0}) \end{matrix}$ (13) $s . t . \sum_{s = 1}^{S} \sum_{i \in Θ} x_{i, s} c_{i, s}^{'} N_{s}^{0} \leq B$ (14) $\sum_{i \in Θ} x_{i, s} = 1 s = 1, 2, \dots, S$ (15) $x_{i, s} = 0, 1 i \in Θ, s = 1, 2, \dots, S$ (16)

In the model, objective function (13) maximizes the profits from products. Constraint (14) ensures the costs of implementing the marketing strategies meet the budget requirements. Constraint (15) ensures that only one marketing strategy is selected for customers in each segment. Constraint (16) is a binary mode indictor.

3.4.3 Solution of the fuzzy optimization model

It can be seen that the above model is a fuzzy integer linear model with imprecise coefficients in the objective function. The imprecise coefficients are described by triangular fuzzy numbers. Thus, the fuzzy integer linear model can be transformed into a bi-objective integer model by defuzzification. Then, the bi-objective integer model can be transformed into a conventional linear model using weight vectors [66]. The problem-solving procedure will be given below.

The above model can first be transformed to a bi-objective model expressed by model (17) through defuzzification. In the process of defuzzification, the level set of membership function of the fuzzy numbers, 1 - α, is involved, where α ∈ [0, 1].

$\begin{matrix} max z^{'} (α) = (z^{1} (x, α), z^{2} (x, α)) \\ s . t . Equations (14 - 16), and α \in [0, 1] \end{matrix}$ (17) where z¹ (x, α) and z² (x, α) can be defined as Equations (18) and (19), respectively. $\begin{matrix} z^{1} (x, α) & = & \sum_{s = 1}^{S} \sum_{s^{'} \geq s}^{S} \sum_{i \in Θ} \\ [p_{s, s^{'}}^{i} - α (p_{s, s^{'}}^{i} - p_{s, s^{'}}^{i} Sim (A_{0}, A_{i}))] \cdot \\ x_{i, s} N_{s}^{0} r_{s, s^{'}}^{0} - \sum_{s = 1}^{S} \sum_{i \in Θ} x_{i, s} c_{i, s}^{'} N_{s}^{0} \end{matrix}$ (18) $\begin{matrix} z^{2} (x, α) & = & \frac{1}{2} \sum_{s = 1}^{S} \sum_{s^{'} \geq s}^{S} \sum_{i \in Θ} \\ [α (\min [p_{s, s^{'}}^{i} (2 - Sim (A_{0}, A_{i})), 1] \\ + p_{s, s^{'}}^{i} Sim (A_{0}, A_{i}) - 2 p_{s, s^{'}}^{i}) \\ + 2 p_{s, s^{'}}^{i}] x_{i, s} N_{s}^{0} r_{s, s^{'}}^{0} \\ - \sum_{s = 1}^{S} \sum_{i \in Θ} x_{i, s} c_{i, s}^{'} N_{s}^{0} \end{matrix}$ (19)

Then, a weight vector β = (β₁, β₂) can be used to transform the bi-objective model (17) into a single-objective model (20) below, where β₁ + β₂ = 1.

$\begin{matrix} max z^{'} (α) = β_{1} z^{1} (x, α) + β_{2} z^{2} (x, α) \\ s . t . Equations (14 - 16), and α \in [0, 1] \end{matrix}$ (20)

Model (20) is a crisp linear programming problem that can be easily solved. Thus, by solving this model, the marketing strategies for new product launches can be obtained.

4 Applying the proposed methodology to the cosmetics industry

To investigate the potential for the practical application of the suggested methodology, the cosmetics industry is selected as a case study. The L’Oréal Group, headquartered in France, is the world’s largest cosmetics company. Its business scope covers more than 130 countries and regions. The L’Oréal Group has more than 280 branches, 40 factories, and 100 agents worldwide. The case study in our paper focuses on how to develop marketing strategies for customers in China. The relevant data for the following analysis are collected over the Internet and by interviews with sales representatives of L’Oréal.

To expand its market share and acquire more customers, L’Oréal takes customers who are not existing customers as the potential customers. Information on customer segments is given in Table 1. Customers in segment 1 are potential customers, and the number of the potential customers can be obtained based on the analysis of the market size, the expected market share, and the number of the existing customers. Customers in segment 2 to segment 5 are existing L’Oréal customers who are categorized based on their cumulative consumption in recent years.

4.1 Construct the case database and the target case

Generally, products in cosmetics industry can be divided into two categories, namely, skin care products and makeup products. When buying cosmetics, customers select products that are suitable for their skin type. There are generally five skin types catered to by existing products, namely, normal skin, dry skin, mixed skin, oily skin, and sensitive skin. The main ingredients in the products with respect to different skin types are always different. Thus, the skin type and ingredients are identified as product features.

After the identification of product features, the case database, which contains four types of data, is constructed. The database consists of 41 historical cases. The products in historical cases include essence water, moisturizing cream, emulsions and so on. The marketing strategies used in historical cases include television advertising, discounts, free samples, double points, etc. Table 2 shows data for an example historical case C₂.

The target case, which contains only product data and customer data, is shown in Table 3. In Table 3, the customer number is the number of customers in each segment just before the new product launches. The average incomes from customers who move across segments can be predicted by previous historical data.

4.2 Retrieve similar historical cases

In our paper, the similarities between historical products and the new product can be calculated considering product category and product features. The products can be categorized as skin care products or makeup products and the product categories are denoted as indicator variables. The product features are the skin type and ingredients, which are described by sets. Here, our paper assumes that the weights of the skin type and the ingredients are equal. Thus, taking Sim (A₀, A₂) as an example, the similarity between historical product A₂ and new product A₀ can be calculated according to Equations (1) and (10) as follows: $\begin{matrix} Sim (A_{0}, A_{2}) = δ_{2} \sum_{j = 1}^{2} w_{j} Sim (A_{0, j}, A_{2, j}) \\ = 1 \times (0.5 \times \frac{| a_{0, 1} \cap a_{2, 1} |}{| a_{0, 1} \cup a_{2, 1} |} + 0.5 \times \frac{| a_{0, 2} \cap a_{2, 2} |}{| a_{0, 2} \cup a_{2, 2} |}) \\ = 1 \times (0.5 \times 1 + 0.5 \times 0.6) = 0.8 \end{matrix}$

In addition to the similarities between historical products and the new product, the similarity threshold should be considered when retrieving similar cases. The similarity threshold can be set by the decision maker to determine how many historical cases can be retrieved. The retrieved similar cases may be different under different thresholds, as shown in Table 4.

4.3 Adapt data about marketing strategies in the retrieved similar cases

The marketing strategies in the retrieved similar cases are television advertising, outdoor advertising, newspaper advertising, messages, coupons, emails, discounts, gift-giving, free samples and double points. The implementation costs of these marketing strategies may need to be adapted and the manual case adaptation method is used in the adaptation process. Since adapting implementation costs of marketing strategies is a complicated issue in which many factors need to be considered, such as the economic growth or inflation, the average consumption or points in each segment, the current market prices of implementing these marketing strategies, etc. Thus, some experts are invited to do case adaptation. The detailed data on the adapted implementation costs by the expert panel meeting are shown in Table 5. Among these marketing strategies, advertising has much stronger effects on potential customers than on existing customers. Thus, it is assumed that the advertising strategy is only applied to customers in segment 1.

4.4 Construct the fuzzy optimization model

To construct the fuzzy optimization model, the fuzzy transition probabilities of customers after the new product launches are required. These probabilities can be calculated using the historical transition probabilities and the similarities via Equation (12). The historical transition probabilities can be obtained from the data in historical cases according to Equation (11). Taking case C₂ as an example, the transition probability $p_{1, 2}^{2}$ can be calculated as follows: $\begin{matrix} p_{1, 2}^{2} & = & N_{1, 2}^{2} / N_{1}^{2} \\ = & 588.9494 / 2863.1472 = 0.2057 \end{matrix}$

Then, the fuzzy optimization model to maximize the profits from products is constructed below: $\begin{matrix} max z (x) \\ = \sum_{s = 1}^{5} (\sum_{s^{'} \geq s}^{5} \sum_{i \in Θ} {\tilde{p}}_{s, s^{'}}^{0, i} x_{i, s} N_{s}^{0} r_{s, s^{'}}^{0} - \sum_{i \in Θ} x_{i, s} c_{i, s}^{'} N_{s}^{0}) \end{matrix}$ (21) $s . t . \sum_{s = 1}^{5} \sum_{i \in Θ} x_{i, s} c_{i, s}^{'} N_{s}^{0} \leq B$ (22) $\sum_{i \in Θ} x_{i, s} = 1 s = 1, 2, \dots, 5$ (23) $x_{i, s} = 0, 1 i \in Θ, s = 1, 2, \dots, 5$ (24)

The above model can be transformed into a simple linear model [66] according to Equations (17)–(20). The transformed model is expressed as follows:

$\begin{matrix} max z^{'} (x) = \sum_{s = 1}^{5} \sum_{s^{'} \geq s}^{5} \sum_{i \in Θ} x_{i, s} N_{s}^{0} r_{s, s^{'}}^{0} \frac{β_{2}}{2} {2 p_{s, s^{'}}^{i} (1 - α) \\ + α (p_{s, s^{'}}^{i} Sim (A_{0}, A_{i}) \\ + min [p_{s, s^{'}}^{i} (2 - Sim (A_{0}, A_{i})), 1])} \\ + \sum_{s = 1}^{5} \sum_{s^{'} \geq s}^{5} \sum_{i \in Θ} x_{i, s} N_{s}^{0} r_{s, s^{'}}^{0} β_{1} \\ {p_{s, s^{'}}^{i} - α [p_{s, s^{'}}^{i} - p_{s, s^{'}}^{i} Sim (A_{0}, A_{i})]} \\ - \sum_{s = 1}^{5} \sum_{i \in Θ} x_{i, s} c_{i, s}^{'} N_{s}^{0} \\ s . t . Equations (22 - 24), and α \in [0, 1] \end{matrix}$ (25) where 1 - α is the level set that is often designated as one of membership grades appearing in the fuzzy set [67]. In our paper, the value of α corresponds to the gap between the maximum and the minimum transition probabilities. A smaller α would lead to a narrower gap between the maximum and the minimum transition probabilities. Let β₁ and β₂ denote the weights of the two objectives, respectively. Here, we assume that the weights are equal, i.e., β₁ = β₂ = 0.5.

The solution of model (25) is related to marketing budget B, parameter α, and similarity threshold Sim^*. The optimal marketing strategies and profits may be different under different parameters. In the next section, the results and the sensitivity analysis will be shown to analyse the effects of these parameters on the selection of the marketing strategies for the new product.

4.5 Results and discussions

First, the effects of marketing budget B and parameter α on the profits will be analysed. The calculated results are shown in Fig. 2. According to Fig. 2, the profits will increase with budget B but decrease with α. This means that the greater the budget invested in new product marketing is, the greater the profits will be. Additionally, the smaller the value of α is, the greater the profits will be. The value of α corresponds to the ranges of the fuzzy transition probabilities which are dependent on the similarities. The similarities are calculated considering the product category and product features. Thus, greater profits can be obtained by making a detailed classification of the products.

Further, we try to examine whether there is an optimal budget to maximize the profits from products. From Fig. 3, it can be seen that profits initially increase with the budget and then maintain a stable level even if the budget continues to increase. This implies that the role of marketing strategies to stimulate customers’ purchasing behaviours is limited. Therefore, it is imperative to allocate the optimal budget for new product marketing in practice.

Finally, the influence of the similarity threshold on the profits is examined. From Fig. 4, it can be seen that profits are larger under the smaller thresholds, while profits are smaller under the larger thresholds. When the thresholds are larger, a few similar cases in the case database can be retrieved. Thus, some more effective marketing strategies for larger profits cannot be retrieved. When the thresholds are smaller, many similar cases can be retrieved. Significant time and costs may be required to adapt the retrieved cases. Therefore, the decision maker should set the similarity threshold with discretion when making real-life decisions on new product marketing.

5 Conclusions and future research

In this paper, a fuzzy optimization method is proposed to select appropriate marketing strategies with respect to customers in different segments for new product marketing. In the proposed method, the analysis of similar cases is used to retrieve historical marketing strategies, and the fuzzy optimization model is constructed to select targeted marketing strategies for different segments when a new product launches. The contributions of this paper are as follows. Firstly, a case database that can store the relevant data about historical products is constructed, in the same manner, a target case is constructed to store the data about the new product. Secondly, the similar historical cases are retrieved considering the similarities between the historical products and the new product and adapted according to the current needs. Thirdly, fuzzy transition probabilities are proposed to describe customers’ responses to the marketing strategies. Finally, a fuzzy integer linear model with the objective function of maximizing the profits from products is built. By solving this model, the marketing strategy for customers in each segment when launching a new product will be obtained.

The results and discussions of the case study generate several managerial implications for decision makers and marketers when developing targeted marketing strategies for customers in different segments in the context of a new product launch. First, greater profits can be obtained when a larger budget is invested in new product marketing and an optimal marketing budget exists for maximizing the profits. Thus, decision makers can allocate a reasonable budget for new product marketing. Second, making a detailed classification of the products can increase the profits. Third, the similarity threshold should be set with discretion when making real-life marketing decisions for better use of the marketing budget.

Future research could be carried out from the following aspects. First, to investigate interaction effects of the marketing strategies on customers’ behaviours, and then how the interaction effects influence marketing decisions may further improve the proposed methodology. Second, the adaptation costs should be considered if they are large when building the model, and thus the trade-off between the adaptation costs and the implementation costs should also be considered. Third, the information about customers’ responses to the marketing strategies is generally uncertain, and the uncertainty is usually described by an appropriate granule. Thus, it is worth of future research to apply the granular computing techniques [68 –79] to solve the problem of selecting marketing strategies for new products.

Footnotes

Acknowledgments

The authors express their gratitude to the anonymous reviewers for their valuable suggestions and comments. This work was partly supported by the National Science Foundation of China (Project No. 71471032), Research Fund for the Doctoral Program of Higher Education of China (Project No. 20130042110030) and Liaoning BaiQianWan Talents Program (Project No. [2015] 18).

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