Elsevier

Neurocomputing

Volume 142, 22 October 2014, Pages 4-15
Neurocomputing

Multi-objective new product development by complete Pareto front and ripple-spreading algorithm

https://doi.org/10.1016/j.neucom.2014.02.058Get rights and content

Abstract

Given several different new product development projects and limited resources, this paper is concerned with the optimal allocation of resources among the projects. This is clearly a multi-objective optimization problem (MOOP), because each new product development project has both a profit expectation and a loss expectation, and such expectations vary according to allocated resources. In such a case, the goal of multi-objective new product development (MONPD) is to maximize the profit expectation while minimizing the loss expectation. As is well known, Pareto optimality and the Pareto front are extremely important to resolve MOOPs. Unlike many other MOOP methods which provide only a single Pareto optimal solution or an approximation of the Pareto front, this paper reports a novel method to calculate the complete Pareto front for the MONPD. Some theoretical conditions and a ripple-spreading algorithm together play a crucial role in finding the complete Pareto front for the MONPD. Simulation results illustrate that the reported method, by calculating the complete Pareto front, can provide the best support to decision makers in the MONPD.

Introduction

New product development plays an extremely crucial role in company survival and success in the modern increasingly competitive global market; every year, billions of dollars are invested in various new product development projects (NPDPs) worldwide [1], [2], [3], [4], [5]. Obviously, not all NPDPs are successful, and there never lack examples where a big-brand company collapses after an NPDP because it misjudges market trends and/or consumes considerable of capital. To avoid such a tragedy, an effective practice is “not to put all eggs in one basket”. Therefore, a company may often have several NPDPs proceeding at one time. Each NPDP has both a profit expectation and a loss expectation, and such expectations vary according to the resources allocated to the NPDP. Basically, the greater the allocated resources the higher the profit expectation is. Increased allocated resources may reduce the failure possibility during the development stage of an NPDP, but cannot necessarily provide a better guarantee of market success. If anything goes wrong during the marketing stage due to many external, uncertain and uncontrollable factors, the larger resource allocation only means a bigger loss. Common sense in the financial sector predicts that a high profit expectation usually comes with a big loss expectation [6]. Therefore, decision makers often have to make a choice between high-profit-big-risk options and low-profit-small-risk options, based on their risk taking willingness and understanding of a market environment. Since available resources are always limited, decision makers usually need to optimize their investment portfolio, in order to maximize the profit expectation while minimizing the loss expectation – two conflicting objectives. In this paper, we are particularly concerned with the problem of allocating limited resources among several NPDPs, so that the overall profit expectation can be maximized while the overall loss expectation can be minimized. This clearly fits in the scope of a multi-objective optimization problem (MOOP), and hereafter we call the concerned problem multi-objective new product development (MONPD).

To resolve the MONPD, we need to make use of the Pareto front. As the most important concept in MOOPs, the Pareto front originates from the concept of Pareto efficiency proposed to study economic efficiency and income distribution [7]. In general MOOPs, a solution is called Pareto optimal if there exists no other solution that is better in terms of at least one objective and is not worse in terms of all other objectives [8], [9]. The projection of a Pareto optimal solution in the objective space is called a Pareto point. All Pareto points, i.e., the projections of all Pareto optimal solutions, compose the complete Pareto front of an MOOP.

The history of such problems is long resulting in the development of many methods for resolving various MOOPs. Basically, most methods can be classified into three categories: aggregate objective function (AOF) based methods [10], [11], [12], [13], [14], Pareto-compliant ranking (PCR) based methods [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], and constrained objective function (COF) based methods [26], [27], [28], [29], [30]. An AOF method combines all of the objectives of an MOOP to construct a single aggregate objective function, and then resolve the single-objective problem to get a Pareto optimal solution. However, it involves subjectiveness in constructing an AOF, and it often fails to find some Pareto optimal solutions if the Pareto front is not convex. A PCR method may overcome such drawbacks of AOF methods by operating on a pool of candidate solutions and favoring non-dominated solutions. Population-based evolutionary approaches (such as genetic algorithms, particle swarm optimization and ant colony optimization) often play a key role in PCR methods to identify multiple Pareto optimal candidate solutions. It should be noted that, due to the stochastic nature of PCR methods, their outputs are Pareto optimal candidate solutions, not necessarily real Pareto optimal solutions. Theoretically, COF methods, by optimizing only one single objective while treating all other objectives as extra constraints, may avoid both the subjectiveness of AOF methods and the loss of Pareto optimality in PCR methods.

Calculating complete Pareto front is a relatively less discussed topic in the study of MOOPs. Theoretically, some nonlinear AOF based methods can prove that for any Pareto point on the Pareto front a set of AOF coefficients definitely exists which can lead to that Pareto point. However, the difficulty is that there lacks a practicable method to find those sets of coefficients that will help to identify the complete Pareto front [28]. For PCR methods, guaranteeing the complete Pareto front is theoretically a mission impossible, largely because of the stochastic nature of employed population-based approaches [15]. COF methods, given well posed objective function constraints, may theoretically guarantee the finding of the complete Pareto front but like AOF methods, the practicality of finding proper constraints is a big issue [30]. Therefore, most existing methods can only produce an incomplete or approximate Pareto front [10], [15], [26], [27], [28], [29], [30]. In particular, as pointed out in [26], very few results are available on the quality of the approximation of the Pareto front for discrete MOOPs.

We have recently proposed a deterministic method which can, theoretically and practically, guarantee the finding of complete Pareto front for discrete MOOPs [31]. Some theoretical conditions and a general methodology were reported in [31], and a case study on a multi-objective route optimization problem (ROP) was used to prove the correctness and practicability. In this paper, we will particularly apply the method of [31] to the MONPD. Actually, there is a substantial body of literature on optimizing investment portfolios [6], [32], [33], [34], [35], [36], [37], [38] similar to MONPD, but little work has been reported to calculate complete Pareto front of such investment portfolio optimization problems. To calculate the complete Pareto front for MONPD, firstly, we will improve the theoretical conditions and the methodology reported in [31]. The most challenging part in the method of [31] is to design an algorithm that is capable of finding the global kth best solution for any given k in terms of a given single objective. Designing such an algorithm is largely problem-dependent, and is often difficult because most optimization algorithms only calculate the global 1st best solution. MONPD is quite different from the ROP in [31]. For example, in the ROP, every objective needs to be minimized; however, in MONPD, the profit expectation needs to be maximized although the loss expectation is to be minimized. Therefore, MONPD demands a new algorithm to calculate the general kth best (rather than only the kth smallest) single-objective solution. By successfully developing a new ripple-spreading algorithm for MONPD, this paper will further prove the practicability and the potential of the methodology of resolving discrete MOOPs by calculating complete Pareto front.

The remainder of this paper is organized as following. Section 2 gives some theoretical results for calculating complete Pareto front for discrete MOOPs. Section 3 describes mathematically the details of MONPD. Section 4 reports a ripple-spreading algorithm for MONPD. Simulation results are given in Section 5, and the paper ends with some conclusions and discussions on future work in Section 6.

Section snippets

Theoretical results for calculating the complete Pareto front

We have recently reported some theoretical results and a general methodology to guarantee, theoretically and practicably, the finding of the complete Pareto front for discrete MOOPs [31]. The work in [31] is the theoretical foundation of this application paper. In this section, we will introduce some improvements to the work of [31], in order to better apply to MONPD later.

First of all, we need a general mathematical formulation of discrete MOOPs as following:minx[g1(x),g2(x),,gNObj(x)]T,

A mathematical formulation of MONPD

Basically, MONPD is to allocate limited resources among several different new product development project (NPDPs), in order to maximize the profit expectation and minimize the loss expectation. Here we give a mathematical description of the MONPD as following, which is illustrated by Fig. 1.

Suppose we have limited resources, X¯, to support NP NPDPs. Let x denote an allocation strategy, and 0≤x(i)≤X¯ denote the resources allocated to NPDP i, for i=1,…,NP. With allocated resources x(i), the

Basic idea of ripple-spreading algorithm (RSA)

It is well known that many successful computational intelligence techniques are actually inspired by certain natural systems or phenomena [39]. For instance, genetic algorithms are inspired by natural selection and evolutionary processes, artificial neural networks by the animal brain, particle swarm optimization by the learning behavior within a population, and ant colony optimization by the foraging behavior of ants. Following the common practice of learning from nature in the computational

Simulation results

In this section, we present some simulation results to demonstrate the practicability and effectiveness of the proposed method to calculate the complete Pareto front for MONPD. There are three parts of simulation results: (i) comparative results with a brute-force search (BFS) method to prove the discovery of the complete Pareto front; (ii) comparative results with an aggregate objective function (AOF) based method and a Pareto-compliant ranking (PCR) based method to show the advantage of new

Conclusions and future work

Profit expectation and loss expectation are two concerns of decision makers in front of several new product development (NPD) projects. The decision of how to allocate limited resources among projects in order to maximize the profit expectation and minimize the loss expectation (a challenging task) falls in the scope of a multi-objective optimization problem (MOOP). As a key concept in the study of MOOPs, the Pareto front can theoretically provide the best support to decision makers, but

Xiao-Bing Hu received the B.S. degree in aviation electronic engineering from the Civil Aviation Institute of China, Tianjin, China, in 1998, the M.S. degree in automatic control engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2001, and the Ph.D. degree in aeronautical and automotive engineering from Loughborough University, Leicestershire, U.K., in 2005.

He currently holds an Experienced Marie Curie Fellowship with both the State Key Laboratory of Earth

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    Xiao-Bing Hu received the B.S. degree in aviation electronic engineering from the Civil Aviation Institute of China, Tianjin, China, in 1998, the M.S. degree in automatic control engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2001, and the Ph.D. degree in aeronautical and automotive engineering from Loughborough University, Leicestershire, U.K., in 2005.

    He currently holds an Experienced Marie Curie Fellowship with both the State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, China, and the School of Engineering, University of Warwick, UK. His major fields of research include integrated risk governance, complex networks, artificial intelligence, and air traffic management.

    Ming Wang received the B.S. degree in civil engineering from Tsinghua University, Beijing, China, in 2000, the M.S. and Ph.D. degrees in structural engineering from University of Maryland, USA in 2005 and 2006.

    He currently holds a position of Professor with the State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, China. His major fields of research include risk modeling and simulation, integrated risk governance, and complex networks.

    Qian Ye received the B.S. and the M.S. degrees from Beijing University, Beijing, China, in 1983 and 1985, and Ph.D. degree in the Oregon State University, USA, in 1993.

    He currently holds a position of Professor with the State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, China. His major field of research includes risk modeling and simulation, integrated risk governance, and policy and decision making.

    Zhangang Han received the B.S. and the M.S. degrees from the Beijing Normal University, Beijing, China, in 1987 and 1990, and Ph.D. degree in the Chinese Academy of Sciences, Beijing China, in 1997.

    He currently holds a position of Professor with the School of Systems Science, Beijing Normal University, China. His major fields of research include evolutionary computation, agent-based modeling, complex systems.

    Mark S. Leeson received the degrees of B.Sc. and B.Eng. Electrical and Electronic Engineering from The University of Nottingham in 1986, and was awarded a Ph.D. in Optoelectronics by The University of Cambridge (Sidney Sussex College) in 1990, UK.

    He is currently a Reader with the School of Engineering, University of Warwick, UK. His major fields of research include molecular communications, optical communications, communication systems, intelligent systems, information theory and coding.

    This work was supported in part by the National Basic Research Program of China under grant 2012CB955404, the project grant 2012-TDZY-21 from Beijing Normal University, China, and the Seventh Framework Programme (FP7) of the European Union under Grant PIOF-GA-2011-299725.

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