Optimal Product Line Research Articles

A profit maximizing mathematical model for pricing and selecting optimal product line

Variety among products is manifested in terms of different attributes or features present in a product. Each attribute in its turn, may be built-in in the product at different levels, giving rise to an increased choice for the customer. However, higher level of an attribute, yielding higher utility for the customers, typically requires higher costs and commands higher price. Increasing price results in higher profit margin but lowers the attractiveness of the product to the customers. In this regard, product line optimization is concerned with the offering of a set of product variants to a large customer base, such that, certain objectives like maximization of buyers’ utility, seller’s return can be met. In this paper, a mathematical programming model has been developed, to determine the optimal product combination that fetches the maximum profit from a potential targeted market segment. Contrary to the existing formulations on product line optimization, where the pricing decision is determined exogenously, we consider simultaneous decision on pricing and product line optimization. Price is considered as a decision variable along with other attributes. Another major departure from the past models is the incorporation of costs associated with each level of attributes. These costs, used as input data, are justified, as the manufacturers typically use combinations of different modules to create different levels of the attributes. The resulting model became computationally complex and hence a greedy heuristic is developed for the purpose. An example is provided to illustrate the working of the heuristic. The same example has been solved for optimality, yielding identical solution to the heuristic results. Finally, a proposition has been presented to show the condition under which the heuristic will give the optimal solution.

Consumer Deliberation and Product Line Design

This paper studies optimal product line design when consumers need to incur costly deliberation to uncover their valuations for quality. To induce deliberation, a firm must maintain quality dispersion and cut the price of the high-end product so that consumers are motivated to deliberate in the hope that high-end consumption fits their needs. To prevent deliberation, the firm may have to offer downgraded quality at a low price so that an impulsive purchase will not appear too wasteful. Whether the firm should induce deliberation depends on how much surplus it creates by aligning the supply of quality with heterogeneous demand for quality and how much surplus it captures during this process. Interestingly, equilibrium firm profit, consumer surplus, and social welfare can all increase with the cost of deliberation. We extend the model to accommodate consumers' heterogeneous prior beliefs of their valuations for quality. We also discuss how market research could benefit from taking into account the endogeneity of consumer deliberation.

Positioning and Pricing of Horizontally Differentiated Products

We provide structural results and a solution method for designing horizontally differentiated product lines – optimizing product positions and prices – under fairly general consumer choice behavior. Our choice model is a generalization of the basic Hotelling-Lancaster locational choice model: Consumer tastes (ideal products) follow a general distribution; substitution disutility (transportation cost) can be an asymmetric convex function of product-spatial distance; and the market may not be fully covered. We formalize the notion that a shift of consumer tastes toward one end of the product space cannot result in a shift of the optimal product line in the opposite direction. For a unimodal taste distribution, we show that with respect to the product that covers the mode (or one of two products adjacent to it) prices and market shares drop toward the tails. Hence, higher popularity is always associated with higher price – although pricing, positioning, relative market share and popularity of products are all endogenous in our model. Our solution method is exact for discrete consumer taste distributions. Whereas, for continuous distributions, it requires lower and upper bounds, which can be computed efficiently using shortest path formulations and they asymptotically converge to the optimal profit.

Optimization of extrusion production lines for EPDM rubber vulcanized with sulphur: A two-phase model based on Finite Elements and kinetic second order differential equation

A numerical two-phase approach, based on experimental curometer charts and aimed at predicting the optimal production line parameters (exposition time and cure temperature) for extruded thick rubber items cured with accelerated sulphur is presented.In the first phase, a simple kinetic model based on the actual reticulation reactions occurring during sulphur curing is utilized to fit experimental curometer data. The model is able to predict the degree of crosslinking at successive curing times and at different controlled temperatures and it requires the calibration of only three kinetic constants. The variation of such parameters with temperature is then evaluated by means of three experimental cure curves performed at three different temperatures. Both the case of indefinite increase of the torque and reversion can be handled.In the second phase, considering the same rubber compound of step one, kinetic reaction parameters are implemented in a Finite Element (FE) software, specifically developed to perform thermal analyses on complex 2D geometries. As an example, an extruded cylindrical thick EPDM item is considered and meshed through four-noded isoparametric plane elements. Several FE simulations are repeated by changing exposition time tc and external cure temperature Tn, to evaluate for each (tc,Tn) couple the corresponding mechanical properties of the item at the end of the thermal treatment. An alternating tangent approach (AT) is used to drastically reduce the computational efforts required to converge to the optimal solution associated with the maximization of the average tensile strength.

An approach to competitive product line design using conjoint data

In today’s highly competitive environment, where market oriented firms aim to maximize profits through customer satisfaction, there is an increasing need to design a product line, rather than a single product. The main goal of designing a profit maximizing product line is to target the ‘right product’ to the ‘right customer’. Although conjoint analysis has turned out to be one of the most widely used techniques for product line design, it falls to explicitly consider retaliatory reactions from competitors. In this paper, we propose a new conjoint-based approach to competitive new product line design, employing the Nash equilibrium concept. The optimal product line design problem for each firm is formulated as a nonlinear integer programming problem. In the absence of a closed-form solution, to compute the Nash equilibrium and to determine the optimal product line, we propose a two-phase procedure: a sequential iterative procedure in the first phase, and backward induction in the second. To solve the optimization problem in each of the iterations of the sequential procedure, we used the branch-and-bound method. The proposed approach is illustrated under several scenarios of competition using previously published conjoint data.

Product Line Design for Consumer Durables: An Integrated Marketing and Engineering Approach

Product line design for consumer durables often relies on close coordination between marketing and engineering domains. Product lines that evolve as optimal from marketers’ perspective may not be optimal from an engineering viewpoint, and vice versa. Although extant research has proposed sophisticated techniques to handle problems that characterize each individual domain, the majority of these developments have not addressed the interdependent issues across marketing and engineering. The author presents a product line optimization method that enables managers to simultaneously consider factors deemed important from both marketing and engineering domains. One major advantage of this method is that it takes into account the strategic reactions from the incumbent manufacturers and the retailer in the design of the product line. The author demonstrates in a simulation study that this method is applicable to problems with a reasonably large scale. Using data collected in a power tool development project undertaken by a major U.S. manufacturer, the study illustrates that the proposed method leads to a more profitable product line than alternative approaches that consider requirements from these two domains separately.

Comment: A conceptual framework for studying the interaction of demand, supply and the market environment in product line optimization

This paper examines the work of Michalek et al. (2011) and Tsafarakis, Marinakis and Matsatsinis (2011), published in this issue of the International Journal of Research in Marketing, within a strategic framework. This framework allows a consideration of how the powerful tools that the two papers propose can be harnessed within the overall direction and activity of the firm. On reviewing these two papers, one could concentrate on the algorithms and heuristics that make the complex problem of product line optimization tractable. Such an analysis would be valuable. Instead I concentrate on the strategic environment in which the optimization decision takes place to allow a consideration of applications and extensions within a managerial context. I do that by suggesting a framework for product line decisions after a brief overview of both articles. That enables me to examine managerial issues that arise in implementing such an approach in practice, many of which are addressed in the two papers. For those issues not addressed in the papers, I propose a set of research questions which would be valuable to managers.

Comment: New developments in product-line optimization

Comment: New developments in product-line optimization

Enhancing marketing with engineering: Optimal product line design for heterogeneous markets

Successful product line design and development often require a balance of technical and market tradeoffs. Quantitative methods for optimizing product attribute levels using preference elicitation (e.g., conjoint) data are useful for many product types. However, products with substantial engineering content involve critical tradeoffs in the ability to achieve those desired attribute levels. Technical tradeoffs in product design must be made with an eye toward market consequences, particularly when heterogeneous market preferences make differentiation and strategic positioning critical to capturing a range of market segments and avoiding cannibalization. We present a unified methodology for product line optimization that coordinates positioning and design models to achieve realizable firm-level optima. The approach overcomes several shortcomings of prior product line optimization models by incorporating a general Bayesian account of consumer preference heterogeneity, managing attributes over a continuous domain to alleviate issues of combinatorial complexity, and avoiding solutions that are impossible to realize. The method is demonstrated for a line of dial-readout scales, using physical models and conjoint-based consumer choice data. The results show that the optimal number of products in the line is not necessarily equal to the number of market segments, that an optimal single product for a heterogeneous market differs from that for a homogeneous one, and that the representational form for consumer heterogeneity has a substantial impact on the design and profitability of the resulting optimal product line — even for the design of a single product. The method is managerially valuable because it yields product line solutions efficiently, accounting for marketing-based preference heterogeneity as well as engineering-based constraints with which product attributes can be realized.

Two heuristics to the share-of-choice product line design problem

Two heuristics are proposed in this paper to solve the problem of constructing an optimal product line using partworth estimates from conjoint analysis. The objective of this NP-hard problem is to choose a level for each attribute to construct a product line so that the line’s share-of-choice is maximised. Existing solution approaches include heuristics that have been only tested on small simulated problems and an exact method that requires long run times when tested on a large commercial problem. Computational results demonstrate that one of our heuristics is capable of finding near optimal solution to large simulated and commercial problems in seconds. The performance of the other heuristic fluctuates with the degree of consumer heterogeneity in a sample.

Analysis and optimization of a bakery production line using ARENA

Production planning in German bakeries is mainly based on the experience of the responsible production manager. As a result production planning happens more or less chaotic, which often results in bottle-necks, deficient dimensioning, ineffective staff allocation and operational problems. The aforementioned points cause a production environment in which factories are not able to achieve the best possible economical and ecological performance. As shown in several industry branches, it is highly advantageous to use virtual models in order to detect and improve suboptimal processes. Models behave like the real system and provide the possibility to predict the changes that may occur to the real production, if the specifications of the production change. For those reasons, virtual modelling supplies the user with a powerful tool for production planning. In this case study ARENA was used as the modelling and simulation tool to analyse a bakery production line. (Received in August 2010, accepted in October 2010. This paper was with the authors 1 month for 1 revision.).

Optimization of acrylic dry spinning production line by using artificial neural network and genetic algorithm

AbstractAcrylic fibers are synthetic fibers with wide applications. A couple of methods can be utilized in their manufacture, one of which is the dry spinning process. The parameters in this method have nonlinear relationships, making the process very complex. To the best of the authors' knowledge, no comprehensive study has yet been conducted on the optimization of acrylic dry spinning production using computer algorithms. In this study, such parameters as extruder temperature in and around the head, solution viscosity, water content in the solution, formic acid content of the solution, and the retention time of the solution in the reactor were measured in an attempt to predict the behavior of the dry spinning process. The color index of the manufactured fibers was used as an indicator of production quality and statistical methods were employed to determine the parameters affecting the process. An artificial neural network (ANN) using the back propagation training algorithm was then designed to predict the color index. ANN parameters including the number of hidden layers, number of neurons in each layer, adaptive learning rate, activation functions, number of max fail epochs, validation and test data were optimized using a genetic algorithm (GA). The trial and error method was used to optimize the GA parameters like population size, number of generations, crossover or mutation rates, and various selection functions. Finally, an ANN with a high accuracy was designed to predict the behavior of the dry spinning process. This method is capable of preventing the manufacturing of undesired fibers. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Simulation and Optimization of the Camshaft Production Line Based on Petri Net

With the development of scientific and technology, the automotive industries competition is becoming more and tougher. The camshaft production system is an important part of the engine manufacturing. The production line productivity and characteristic are affected by many practical factors of the workshop. It’s a complex discrete manufacturing system somehow. In this paper, the production line model is presented based on Petri net. Then the mapping relationship is established between the Petri net model and the eM-Plant discrete system model. The discrete simulation model of production line is constructed by using eM-plant software. Based on the simulation, the reasonable simulation experimental are carried out with the determined simulation boundary and objectives under the different input conditions such as orders, the working stations' processing time, the working stations’ fault distribution, and the production line layout. The simulation experimental results are discussed on condition that the shifts, equipment operation condition, production line capacity and WIP in detail. These results could provide the theory basis for decision-making of the production plan of the automotive industries.

Leadtime-Variety Tradeoff in Product Differentiation

The literature on mass customization generally focuses on the tradeoff between higher revenues from better matching customer preferences with product specifications, and higher costs of offering a broader—possibly fully customized—product line. Less well understood is the tradeoff between the increased ability to precisely meet customer preferences and the increased leadtime from order placement to delivery often associated with customized products. In this paper, we use a locational customer choice model to formulate a firm's integrated product line design problem that involves variety, leadtime (or inventory), and pricing decisions. We propose a dynamic programming based solution procedure that amounts to solving a shortest path problem on an acyclic network, and derive some structural results on the optimal product line design. We find that unimodal preferences generally result in hybrid product lines, with standard products clustering around the mode and custom products covering the tails, in contrast with the all-custom or all-standard product lines that are optimal under uniform preferences. We also numerically examine how the firm should adjust its leadtime and variety in response to changes in parameters such as customer dispersion and operational scale. We find that the tradeoff between leadtime and variety is sometimes nonintuitive and complex.

Fuzzy product line design model while considering preference uncertainty: A case study of notebook computer industry in Taiwan

Enterprises evaluate customers’ preferences of high-tech products to appropriately adjust product lines when the technologies are ready for commercialization. Conjoint analysis (CA) is usually applied to measure customers’ preferences while the product line design model (PLDM) is used to simulate customers’ purchase decisions based on these preferences. The optimal product line extension scheme (PLES) can then be found. For customers unfamiliar with a new technology, it is difficult to precisely appraise preferences for new products. This paper proposes fuzzy PLDM that combines fuzzy theory with CA to take preference uncertainty into consideration. To precisely apply fuzzy preferences, fuzzy rating is used to simulate customers’ purchase decisions. This paper focuses on the notebook industry in Taiwan. Optimal PLES are obtained under Fuzzy and Crisp scenarios. The results show that customers with high preference uncertainty have different purchase decisions under above scenarios, which leads to a great inconsistency between the optimal PLES obtained from Fuzzy and Crisp scenarios. The Fuzzy scenario takes preference uncertainty into consideration and uses stricter standards to judge whether customers buy products with new technology.

Particle swarm optimization for optimal product line design

Designing optimal products is one of the most critical activities for a firm to stay competitive. Except for genetic algorithms, previous approaches that solve the optimal product line design problem provide the decision maker with a single best solution. Furthermore, they assume a static market, in which the incumbent firms will not respond to the entrance of a new player. In this paper we apply a new population-based algorithm called particle swarm optimization to the problem and employ a Monte Carlo simulation to compare its performance to that of genetic algorithms. The results indicate that the proposed particle swarm optimization algorithm constitutes an attractive alternative for solving the optimal product line design problem because its performance is comparable to that of genetic algorithms concerning the best solution found while it outperforms genetic algorithms regarding the diversity of the final set of provided solutions. Furthermore, we use concepts from game theory to illustrate how the algorithm can be extended to incorporate retaliatory actions from competitors. The dynamic approach is illustrated through a real-world case in which a firm intends to enter the Greek retail milk market. While employing highly simplifying assumptions, the incorporation of the Nash equilibrium concept provides useful insights, such as the attribute levels that may be resistant to competitive reactions and the incumbent firms that will benefit most in the long term.

On the Optimal Product Line Selection Problem with Price Discrimination

Product line design decisions are determinant for a firm's market success and, simultaneously, very costly to implement and change. To evaluate the profitability of a design, a number of mathematical programming approaches have been proposed in the last three decades—typically nonlinear integer optimization problems that can only be tackled heuristically for real-world instances. Recently, Chen and Hausman (2000) efficiently exploited the fractional programming properties of a stylized model for product line and price selection with the objective to maximize contribution given homogeneous customer behavior by an aggregate multinomial logit choice model. We extend the approach of Chen and Hausman (Chen, K. D., W. H. Hausman. 2000. Technical note: Mathematical properties of the optimal product line selection problem using choice-based conjoint analysis. Management Sci. 46(2) 327–332) to determine an optimal product line under a personalized or group pricing strategy in markets with multiple heterogeneous consumers such that total profit (including fixed costs) is maximized. Personalized/group pricing is a growing discrimination strategy that more and more businesses are realizing is not only very profitable, but also often implementable in the era of e-business. Our problem formulation allows to incorporate commonly applied attraction choice models including the multinomial logit, the Bradley–Terry–Luce, and approximately the first choice model. Though the problem is generally nonlinear, we show that the fractional substructure resulting from attraction choice models can still be exploited to globally solve real-world instances in reasonable time.

Metaheuristics for assortment problems with multiple quality levels

The assortment planning problem involves choosing an optimal product line, as defined by a set of products with specific attributes, to offer consumers. Under a locational choice model in which products are differentiated both horizontally (by variety attributes) and vertically (by quality attributes), an optimal assortment, whose attributes have only been partially characterized, may consist of multiple quality levels. Using previous analytical results, we approximate the optimal assortment for make-to-order and static substitution environments. We test the appropriateness and compare the performance of three metaheuristic methods. These metaheuristics can easily be modified to accommodate different consumer preference distribution assumptions.

The implications of costs, capacity, and competition on product line selection

We consider a situation in which a manufacturer has to select the product(s) to sell as well as the selling price and production quantity of each selected product. There are two substitutable products in the consideration set, where product 2 has a higher quality and reservation price than that of product 1. By considering the cannibalization effect that depends on the selling price of each product, the manufacturer needs to evaluate the profit function associated with three different product line options: sell both products or only one of the 2 products. In order to examine the impact of costs, capacity, and competition on the optimal product line selection, optimal price, and optimal production quantity analytically, we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal.

A Branch-and-Price Approach to the Share-of-Choice Product Line Design Problem

We develop a branch-and-price algorithm for constructing an optimal product line using partworth estimates from choice-based conjoint analysis. The algorithm determines the specific attribute levels for each multiattribute product in a set of products to maximize the resulting product line's share of choice, i.e., the number of respondents for whom at least one new product's utility exceeds the respondent's reservation utility. Computational results using large commercial and simulated data sets demonstrate that the algorithm can identify provably optimal, robust solutions to realistically sized problems.