Product line selection and pricing under a share-of-surplus choice model

Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today’s competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs.We address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share-of-surplus choice model. A customer’s surplus is defined as the difference between his utility (willingness to pay) and the price of the product. Under the share-of-surplus model, the fraction of a customer segment that selects a product is defined as the ratio of the segment’s surplus from this particular product to the segment’s total surplus across all offered products with positive surplus for that segment.We develop a heuristic procedure for this non-concave, mixed-integer optimization problem. The procedure utilizes simulated annealing to handle the binary product selection variables, and a steepest-ascent-style procedure that relies on certain structural properties of the objective function to handle the non-concave, continuous portion of the problem involving the prices. We also develop a variant of our procedure to handle uncertainty in customer utilities. In computational studies, our basic procedures perform extremely well, producing solutions whose objective values are within about 5% of those obtained via enumerative methods. Our procedure to handle uncertain utilities also performs well, producing solutions with expected profit values that are roughly 10% higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities.     

Integrated Production and Distribution Planning for Södra Cell AB

In this paper we consider integrated planning of transportation of raw material, production and distribution of products of the supply chain at Södra Cell AB, a major European pulp mill company. The strategic planning period is one year. Decisions included in the planning are transportation of raw materials from harvest areas to pulp mills, production mix and contents at pulp mills, distribution of pulp products from mills to customer via terminals or directly and selection of potential orders and their levels at customers. Distribution is carried out by three different transportation modes; vessels, trains and trucks. We propose a mathematical model for the entire supply chain which includes a large number of continuous variables and a set of binary variables to reflect decisions about product mix and order selection at customers. Five different alternatives regarding production mix in a case study carried out at Södra Cell are analyzed and evaluated. Each alternative describes which products will be produced at which pulp mills.     

Dynamic zigzag pricing of resalable goods with no depreciation and intergroup externalities

This paper addresses the pricing policy of durable value goods that do not depreciate over time. This implies that demands for this type of goods fluctuate with respect to their market price and social interactions between customers rather than with respect to the time elapsed since they have been produced or created. We suggest an analytical approach for optimally setting durable value product prices with respect to the interdependency between two customer groups characterized by asymmetric intergroup externalities. We demonstrate that cyclic pricing policies of harmonic form become optimal when the company is prepared to compromise its short-run net profit to ensure its lasting reputation. Furthermore, we show that the greater the difference between the product of the price and the externality effect of the two customer groups, the greater the frequency of the harmonic fluctuation.     

双寡头垄断下全渠道竞争优化策略

引入包含线上购买线下取货(buy online and pick up in store, BOPS)的全渠道策略,在随机和确定性需求下分别构建双寡头Nash均衡博弈模型,得出在线下-线上和BOPS-线上等不同渠道下双寡头企业的最优库存策略。通过分析不同的渠道,进一步探讨了双寡头企业产品定价的差异对最优线下库存的影响。结果表明,BOPS作为一种新的零售模式,通过提供库存的可用性信息,显著降低了顾客承担的缺货风险,既可以增加顾客的访问量,还可以增加交叉收益;同时,零售商是否提供BOPS,将显著影响顾客的渠道选择。     

Rational Abandonment from Tele-Queues: Nonlinear Waiting Costs with Heterogeneous Preferences

We consider the modelling of abandonment from a queueing system by impatient customers. Within the proposed model, customers act rationally to maximise a utility function that weights service utility against expected waiting cost. Customers are heterogeneous, in the sense that their utility function parameters may vary across the customer population. The queue is assumed invisible to waiting customers, who do not obtain any information regarding their standing in the queue during their waiting period. Such circumstances apply, for example, in telephone centers or other remote service facilities, to which we refer as tele-queues. We analyse this decision model within a multi-server queue with impatient customers, and seek to characterise the Nash equilibria of this system. These equilibria may be viewed as stable operating points of the system, and determine the customer abandonment profile along with other system-wide performance measures. We provide conditions for the existence and uniqueness of the equilibrium, and suggest procedures for its computation. We also suggest a notion of an equilibrium based on sub-optimal decisions, the myopic equilibrium, which enjoys favourable analytical properties. Some concrete examples are provided to illustrate the modelling approach and analysis. The present paper supplements previous ones which were restricted to linear waiting costs or homogeneous customer population.     

Customer choice prediction based on transfer learning

Choice behaviour prediction is valuable for developing suitable customer segmentation and finding target customers in marketing management. Constructing good choice models for choice behaviour prediction usually requires a sufficient amount of customer data. However, there is only a small amount of data in many marketing applications due to resource constraints. In this paper, we focus on choice behaviour prediction with a small sample size by introducing the idea of transfer learning and present a method that is applicable to choice prediction. The new model called transfer bagging extracts information from similar customers from different areas to improve the performance of the choice model for customers of interest. We illustrate an application of the new model for customer mode choice analysis in the long-distance communication market and compare it with other benchmark methods without information transfer. The results show that the new model can provide significant improvements in choice prediction.     

Question selection responding to information on customers from heterogeneous populations to select offers that maximize expected profit

The advent of Internet broking pages allows customers to ‘apply’ to a number of different companies at one time, leading to multiple offers made to a customer. The saturated condition of the personal financial products has led to falling ‘take’ rates. Financial institutions are trying to increase the ‘take’ rates of their personal financial products. Applicants for credit will have to provide information for risk assessment, which can be used to assess the probability of a customer accepting an offer. Interactive channels such as the Internet and telephone allow questions that are asked to depend on previous answers. The questions selected need to provide information to assess the probability of acceptance of a particular variant of financial product. In this paper, we investigate a model to predict the best offer to extend next to a customer based on the response for the questions, as well as the question selection itself.     

Assortment and inventory decisions with multiple quality levels

We consider the assortment and inventory decisions of a retailer under a locational consumer choice model where products can be differentiated both horizontally (e.g., color of a product) and vertically (e.g., quality of a product). The assortment and quantity decisions affect customer choice and, hence, the demand and sales for each product. In this paper, we investigate two different environments where product availability and assortment affect consumer choice and demand in different ways: make-to-order (MTO) and make-to-stock (MTS). In the MTO environment, customers order and purchase their most preferred product; that is, stockouts do not occur. In the MTS model, customers buy their most preferred product if it is in stock or do not buy if it is out of stock. In both environments we find conditions under which it is optimal to carry assortments of only a single quality level. In the MTS case, we show that an assortment of mixed quality levels can be optimal only within a narrow range of parameters.     

基于分类服务机制的可预约排队系统设计和服务定价研究

采取合理有效的服务机制和服务定价是确保服务型企业持续有效运行的重要方式,服务提供商设计合理的服务策略可以使得服务收益达到最优。本文以服务可预约的排队系统为研究背景,对服务提供商分类服务机制选择和服务定价策略进行研究。通过考虑由两种服务策略下顾客之间的平均等待时间的对比和顾客等待厌恶心理参数形成的全新顾客服务效用模型,给出服务提供商在不同服务机制下的最优服务策略以及顾客市场规模对其服务策略选择的影响。研究表明,当预约顾客的市场规模相对较小时,服务提供商可以采取分类服务机制,即同时服务预约顾客和未预约顾客以增加服务收益,反之亦然。此外,预约顾客等待厌恶程度能够显著增大服务提供商的服务定价。     

Tracking customer portfolio composition: A factor analysis approach

In this paper, we address the changing composition of a customer portfolio taking into account actions undertaken by the company to adapt its service offer to market conditions and/or technological innovations. We present a specific methodology to identify clusters of customers in different periods and then compare them over time. The classification process takes into account both qualitative and quantitative aspects of the consumption levels of the services or products offered by the company. The possibility of period‐to‐period variation in the customer portfolio and the service or product offer is also considered, in order to achieve a more realistic scenario. The core of the proposed methodology is related to the family of exploratory factorial and cluster techniques. The customers are classified by using a bicriterial clustering methodology based on ‘tandem’ analysis (multiple factor analysis+cluster analysis of the main factors). The bicriterial approach allows for a compromise between customers' consumption levels (a quantitative criterion) and their consumption/non‐consumption pattern (a qualitative criterion). The evolution of the customer portfolio composition is explored through multiple correspondence analysis. This technique allows visual comparison of the position of different clusters against time and the identification of key changes in customer consumption behavior. The methodology is tested on realistic customer portfolio scenarios for a major telecommunication company. We simulate various scenarios to show the strengths of our proposal. Copyright © 2009 John Wiley & Sons, Ltd.     

The gravity p-median model

In this paper we propose a new model for the p-median problem. In the standard p-median problem it is assumed that each demand point is served by the closest facility. In many situations (for example, when demand points are communities of customers and each customer makes his own selection of the facility) demand is divided among the facilities. Each customer selects a facility which is not necessarily the closest one. In the gravity p-median problem it is assumed that customers divide their patronage among the facilities with the probability that a customer patronizes a facility being proportional to the attractiveness of that facility and to a decreasing utility function of the distance to the facility.     

Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands

We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers according to a particular customer order. The demands of the customers for each product are assumed to be random variables with known distributions. Each product type is stored in its dedicated compartment in the vehicle. Using a suitable dynamic programming algorithm we find the policy that satisfies the demands of the customers with the minimum total expected cost. We also prove that this policy has a specific threshold-type structure. Furthermore, we investigate a corresponding infinite-time horizon problem in which the service of the customers does not stop when the last customer has been serviced but it continues indefinitely with the same customer order. It is assumed that the demands of the customers at different tours have the same distributions. It is shown that the discounted-cost optimal policy and the average-cost optimal policy have the same threshold-type structure as the optimal policy in the original problem. The theoretical results are illustrated by numerical examples.     

顾客参与研发过程的价值共创机理与策略研究

顾客参与企业研发是产品价值创造的最初始过程,不仅提高产品接受度、满足顾客需求,而且为企业增加收入,但同时也产生相应成本。文章探究顾客参与研发的系统中,顾客、企业和产品的价值共创行为以及企业决策如何影响三者价值;立足多目标视角,充分考虑企业与顾客的收益、成本,采用系统动力学方法建立顾客参与研发过程的动态价值共创模型,全面探究系统内部共创机理。在模型基础上,重点就企业产品价格、交互次数以及激励资金比例等策略进行仿真,使企业、顾客及产品实现价值共创。结论如下:(1)随着顾客、企业交互次数的增多,顾客参与研发过程同样具备一般产品生命周期导入期、成长期、成熟期以及衰退期的特点。(2)系统存在最优交互次数;且最优交互次数随着研发投入比例减少而增加。(3)在不考虑参与顾客获取激励资金的情况下,企业针对不同顾客群(参与研发顾客与普通购买顾客)进行定价,在最优交互次数状态下,统一定价模式优于差别定价模式,将为企业带来更大的收益。     

Improved bid prices for choice-based network revenue management

One of the latest developments in network revenue management (RM) is the incorporation of customer purchase behavior via discrete choice models. Many authors presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories. However, in many implemented RM systems—most notably in the hotel industry—bid price control is being used, and this entails the problem that the recommended combination of products as identified by these policies might not be representable through bid price control. If demand were independent from available product alternatives, an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network. But under dependent demand, this is not necessarily the case. In fact, it seems that these bid prices are typically not restrictive enough and result in buy-down effects.We propose (1) a simple and fast heuristic that iteratively improves on an initial guess for the bid price vector; this first guess could be, for example, dynamic estimates of the marginal value of capacity. Moreover, (2) we demonstrate that using these dynamic marginal capacity values directly as bid prices can lead to significant revenue loss as compared to using our heuristic to improve them. Finally, (3) we investigate numerically how much revenue performance is lost due to the confinement to product combinations that can be represented by a bid price.The heuristic is not restricted to a particular choice model and can be combined with any method that provides us with estimates of the marginal values of capacity. In our numerical experiments, we test the heuristic on some popular networks examples taken from peer literature. We use a multinomial logit choice model which allows customers from different segments to have products in common that they consider to purchase. In most problem instances, our heuristic policy results in significant revenue gains over some currently available alternatives at low computational cost.     

On the management of life insurance company risk by strategic choice of product mix,investment strategy and surplus appropriation schemes

The aim of this paper is to analyze the impact of management’s strategic choice of asset and liability composition in life insurance on shortfall risk and the shareholders’ fair risk charge. In contrast to previous work, we focus on the effectiveness of management decisions regarding the product mix and the riskiness of the asset side under different surplus appropriation schemes. We propose a model setting that comprises temporary life annuities and endowment insurance contracts. Our numerical results show that the effectiveness of management decisions in regard to risk reduction strongly depends on the surplus appropriation scheme offered to the customer and their impact on guaranteed benefit payments, which thus presents an important control variable for the insurer.     

The open vehicle routing problem with time windows

In this paper, we consider the open vehicle routing problem with time windows (OVRPTW). The OVRPTW seeks to find a set of non-depot returning vehicle routes, for a fleet of capacitated vehicles, to satisfy customers’ requirements, within fixed time intervals that represent the earliest and latest times during the day that customers’ service can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns. The model is solved using a greedy look-ahead route construction heuristic algorithm, which utilizes time windows related information via composite customer selection and route-insertion criteria. These criteria exploit the interrelationships between customers, introduced by time windows, that dictate the sequence in which vehicles must visit customers. Computational results on a set of benchmark problems from the literature provide very good results and indicate the applicability of the methodology in real-life routing applications.     

Staffing a service system with appointment-based customer arrivals

Appointment systems are widely used to facilitate customers’ access to services in many industries such as healthcare. A number of studies have taken a queueing approach to analyse service systems and facilitate managerial decisions on staffing requirements by assuming independent and stationary customer arrivals. This paper is motivated by the observation that the queueing-based method shows relatively poor performance when customers arrive according to their appointment times. Because customer arrivals are dependent on their appointment times, this study, unlike queueing-based methods, conducts a detailed analysis of appointment-based customer arrivals instead of making steady-state assumptions. We develop a new model that captures the characteristics of appointment-based customer arrivals and computes the probability of transient system states. Through the use of this model, which relaxes stationary and independent assumptions, we propose a heuristic algorithm that determines staffing requirements with aims to minimizing staff-hours while satisfying a target service level. The simulation results show that the proposed method outperforms the queueing-based method.     

A discrete long-term location–price problem under the assumption of discriminatory pricing: Formulations and parametric analysis

We consider a competitive location problem in which a new firm has to make decisions on the locations of several new facilities as well as on its price setting in order to maximise profit. Under the assumption of discriminatory prices, competing firms set a specific price for each market area. The customers buy one unit of a single homogeneous price-inelastic product from the facility that offers the lowest price in the area the consumers belong to. Three customer choice rules are considered in order to break ties in the offered prices. We prove that, considering long-term competition on price, this problem can be reduced to a problem with decisions on location only. For each one of the choice rules the location problem is formulated as an integer programming model and a parametric analysis of these models is given. To conclude, an application with real data is presented.     

A Reconciliation Among Discrete Compromise Solutions

The application of compromise solutions to discrete multi-objective problems brings about some technical flexibilities, such as the selection of distance function for computing both normalized attribute ratings and distances between two alternatives, and the choice between the ideal and negative-ideal alternatives for implementing the axiom of choice. These flexibilities are undesirable, since the method may yield conflicting preference-alternative rankings, depending on parameter choice. This paper introduces a credibility measurement of distance function and takes a broader concept of the axiom of choice in order to reconcile disagreement among compromise solutions.     

Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.