Multi-Product Price Optimization With Reference Effects

The development of social economy and the advent of the Internet age have greatly improved the dominance of consumers.In order to adapt to the upgrading of consumer demand and satisfy heterogeneous consumer preferences,firms began to continuously enrich product categories,gradually changing from the production of a single product to the production of multiple products.The diversification of product categories can help firms better meet diversified and individualized consumer needs,but it also makes consumer behavior more difficult to analyze and predict.On the one hand,consumers’ preferences for product attributes are heterogeneous,so there are differences in consumers’ choice behaviors for diversified products.On the other hand,consumers’choice process of diversified products is influenced by reference effects.Specifically,the consumer reference effect refers to the fact that a certain attribute of a product or service is different from the consumer’s perception benchmark,resulting in a psychological "gain" or "loss" for the consumer,which in turn has an impact on the consumer’s purchasing behavior.A large number of studies have found that reference quality effect,reference price effect,and reference time effect can affect consumers’ choice behavior.The diversification of product categories,the heterogeneity of consumer preferences and the influence of reference effects make the pricing problem of firms face new challenges.Therefore,analyzing various reference effects that affect consumer behavior and making multi-product price decisions based on this can not only help firms analyze and predict consumer behavior more accurately,but also help firms improve business performance.In this thesis,on the basis of considering the influence of reference quality effect,reference price effect and reference time effect on consumer choice behavior,it deeply explores the problem of a firm’s multi-product price optimization.Firstly,considering the influence of reference quality effect on the choice behavior of consumers with heterogeneous preferences,the joint optimization problem of price and quality of multi-products of the firm is studied.By using a linear random utility framework that combines the reference quality effect with consumers’ vertical and horizontal heterogeneous preferences,the impact of the reference quality effect on the choice behavior of consumers with heterogeneous preferences is portrayed;subsequently,an optimization model is developed with the objective of maximizing the firm’s profit,and the optimal multi-product price and quality decisions are obtained by solving the model.The results of the thesis show that the degree of differentiation between product qualities will continue to increase as the influence of the reference quality effect increases.In addition,starting from the underlying logic of the influence of reference quality effect on consumer behavior,two production strategies are provided for the firm:a production strategy with a decoy product and a production strategy without a decoy product,so as to achieve the purpose of guiding consumers to choose according to the firm’s objectives;by analyzing the joint optimization problem of multi-product price and quality under the two strategies,the influence of reference quality effect on the optimal strategy selection of the firm is discussed.The findings indicate that the presence of the decoy product can increase the demand for non-decoy products.In addition,when the magnitude of the reference quality effect gradually increases,the difference between the optimal decisions and the demand of products under the two strategies gradually decreases.Finally,when the number of products is exogenous and the influence of the reference quality effect is relatively strong,or when the number of products can be determined endogenously,the firm should choose the production strategy with a decoy product;otherwise,the firm should choose the production strategy without a decoy product.Secondly,considering the influence of the reference price effect on the choice behavior of consumers with heterogeneous preferences,based on this,the joint optimization problem of the firm’s multi-product price,quality and number of products is explored.By establishing the utility function and the profit function including the reference price effect,the joint optimization problem of multi-product price and quality of the firm is analyzed when the number of products is exogenously given;subsequently,the joint optimization problem of multi-product price,quality and the number of products is analyzed.The results show that the existence of the reference price effect will cause a spillover effect on product quality;for the product with the lowest quality,its optimal quality will increase with the strengthening of the reference price effect;while the optimal quality of other products will show a tendency to increase first and then decrease with the strengthening of the reference price effect.In addition,a strong reference price effect or high fixed production costs may prompt the firm to abandon the production of diversified products and choose to produce a single product for sale.Based on the evaluation of the real data of the cooperative firm,it is found that compared with the demand model without the reference price effect,the demand model including the reference price effect proposed in this thesis can better fit and predict consumer choice behavior;meanwhile,the optimization strategy proposed in this thesis can increase the profit of the firm by 2.18%compared with the actual profit of the firm.Finally,considering the reference time effect caused by the firm’s deli very-time commitments,the influence of the reference time effect on the choice behavior of consumers with heterogeneous preferences is analyzed,and then the joint optimization of the firm’s multi-product price and delivery-time commitment is studied.The first step is to establish a consumer utility function including the reference time effect;then,an optimization model is established with the objective of maximizing the profit of the monopoly firm,and the model is solved to obtain the optimal price and delivery time commitment decision of the monopoly firm;then,establish the game model of competitive firms,and analyze the firms’ equilibrium prices and delivery-time commitments.The results show that the optimal delivery-time commitment of a product depends on the ratio of the firm’s marginal cost to the consumer’s marginal utility.Interestingly,as consumers’ perception of utility gains gradually increases,even when consumers are very price sensitive,it is still possible for firms to make more profits by raising the price of products.Moreover,for both monopolistic and competitive firms,when the consumer’s price sensitivity coefficient is greater than a certain threshold,if the firm can make a joint decision on product price and delivery-time commitment,the joint decision can lead to a win-win situation between the firm and consumers.By fitting the distribution function of the delivery time of the cooperative firm and estimating the parameters of the demand model,the prediction accuracy of the demand model including the reference time effect is tested;in addition,compared with the actual sales profit of the firm,the optimization strategy proposed in this thesis can increase the profit of the firm by 2.71%.Most of the existing studies on multi-product pricing ignore the reference effects and the influence of heterogeneous consumer preferences on consumer behavior.This study makes up for the shortcomings of the existing literature.For different types of reference effects,this thesis proposes corresponding demand models and model parameter estimation algorithms,which can help firms to test the existence of reference effects and predict consumer behavior more accurately.What is more,it also provides theoretical and practical guidance for firms’ multi-product pricing decisions as well as production,sales,and logistics service strategies that are closely related to product pricing.The research results of this thesis enrich the research on marketing and operations management,and provide new theoretical research perspectives and management suggestions for improving consumer surplus and social welfare.