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Advanced product platform and product family design methods are needed to define and optimize the value they bring to a company. Maximizing platform commonality and individual product performance often fails to realize the most valuable product family during optimization; however, few examples exist in the literature to explore these trade-offs. This paper introduces a novel industry case study to explore the differences between “traditional” multidisciplinary design optimization (MDO) and value-driven design (VDD) approaches to product family design. The case study involves a family of five commercially-available washing machines and integrates multidisciplinary analyses, simulations, mathematical models, and response surface models to obtain ratings for individual product attributes. These attributes are then aggregated into a value function for the product family using a novel approach to estimate sales volume and a demand sensitivity curve derived from publicly available data. We then formulate and solve a “traditional” MDO product family design problem using a multi-objective genetic algorithm to minimize performance deviation and a product family penalty function. A novel VDD formulation is then introduced and solved to maximize the net present value (NPV) for the firm producing the family of products. Visualization and comparison of the results illustrate that the “traditional” MDO formulation can find several promising solutions for the product family, but it fails to find solutions that maximize the value to the firm. The results also provide a benchmark for researchers to explore alternative value function formulations and solution approaches for product family design using the novel industry case study.

Methods for evaluating the strength of design dependencies in a product architecture have been widely studied in the literature; however, evaluating the effects of direct and indirect interactions between components/modules remains a challenge. In fact, indirect connections between components/modules are often overlooked in many cases when evaluating design dependencies. Having a more consistent way of defining a product architecture that considers both its direct and indirect connections is important, especially when analyzing redesign complexity and change propagation. In this study, we propose a systematic method to evaluate direct and indirect design dependencies between components in product architectures. Interfaces are classified into six different types based on a thorough review of the literature, and a method for evaluating design dependencies is introduced to estimate the relative importance of interfaces directly from a set of comparable products. Using an electrical circuit analogy, the proposed method can quantify both direct and indirect design dependencies between components within a product architecture. We compare design dependency results for different wireless computer mice to validate the effectiveness of the proposed method. The results show that using the proposed design dependency measure including direct and indirect effects provides more reliable design dependency results.

This research presents a method of optimizing the consolidation of parts in an assembly using metal additive manufacturing (MAM). The method generates candidates for consolidation, filters them for feasibility and structural redundancy, finds the optimal build layout of the parts, and optimizes which parts to consolidate using a genetic algorithm. Results are presented for both minimal production time and minimal production costs, respectively. The production time and cost models consider each step of the manufacturing process, including MAM build, post-processing steps such as support structure removal, and assembly. It accounts for costs affected by part consolidation, including machine costs, material, scrap, energy consumption, and labor requirements. We find that developing a closed-loop filter that excludes consolidation candidates that are structurally redundant with others dramatically reduces the number of candidates, thereby significantly reducing convergence time. Results show that when increasing the number of parts that are consolidated, the production cost and time at first decrease due to reduced assembly steps, and then increase due to additional support structures needed to uphold the larger, consolidated parts. We present a rationale and evidence justifying that this is an important tradeoff of part consolidation that generalizes to many types of assemblies. Subsystems that are smaller, or can be oriented with very little support structures or have low material costs or fast deposition rates can have an optimum at full consolidation; for other subsystems, the optimum is less than 100%. The presented method offers a promising pathway to minimize production time and cost by consolidating parts using MAM. In our test-bed results for an aircraft fairing produced with powder-bed electron beam melting, the solution for minimizing production cost (time) is to consolidate 17 components into four (two) discrete parts, which leads to a 20% (25%) reduction in unit production cost (time).

This research presents a method of evaluating and optimizing the consolidation of parts in an assembly using metal additive manufacturing (MAM). The method generates candidates for consolidation, filters them for feasibility and structural redundancy, finds the optimal build layout of the parts, and optimizes which parts to consolidate using a genetic algorithm. Optimal results are presented for both minimal production time and minimal production costs, respectively. The production time and cost model considers each step of the manufacturing process, including MAM build, post-processing steps such as support-structure removal, and assembly. It accounts for costs affected by parts consolidation, including machine costs, material, scrap, energy consumption, and labor requirements. We find that developing a closed-loop filter that excludes consolidation candidates with structural redundancy dramatically reduces the number of candidates to consider, thereby significantly reducing convergence time. Results show that, when increasing the number of parts that are consolidated, the production cost and time at first decrease due to reduced assembly steps, and then increase due to additional support structures needed to uphold the larger, consolidated parts. We present a rationale and evidence justifying that this is an inherent tradeoff of parts consolidation that generalizes to most types of assemblies. Subsystems that can be oriented with very little support structures, or have low material costs or fast deposition rates can have an optimum at full consolidation; otherwise, the optimum is likely to be less than 100%. The presented method offers a promising pathway to minimize production time and cost by consolidating parts using MAM. In our test-bed results on an aircraft fairing produced with powder-bed electron-beam melting, the solution for minimizing time is to consolidate 48 components into three discrete parts, which leads to a 33% reduction in unit production time. The solution for minimizing production costs is to consolidate the components into five discrete parts, leading to a 28% reduction in unit costs.

Nonassembled products, which are produced from a raw material and post-processed to a final form without any assembly steps, form a large and potentially growing share of the manufacturing sector. However, the design for manufacturing literature has largely focused on assembled products and does not necessarily apply to nonassembled products. In this paper, we review the literature on design for nonassembly (DFNA) and the broader literature on design for manufacturing that has design guidelines and metrics applicable to nonassembled products, including both monolithic single-part products and nonassembly mechanisms. Our review focuses on guidelines that apply across multiple manufacturing processes. We identify guidelines and metrics that seek to reduce costs as well as provide differentiated products across a product family. We cluster the guidelines using latent semantic analysis and find that existing DFNA guidelines fall into four main categories pertaining to (1) manufacturing process, (2) material, (3) tolerance, and (4) geometry. We also identify existing product family metrics that can be modified for nonassembled products to measure some aspects of these categories. Finally, we discuss possible future research directions to more accurately characterize the relationships between design variables and manufacturing costs, including investigating factors related to the complexity of operations at particular process steps and across process steps.

Modularity indices based on Design Structure Matrices (DSMs) have been utilised to help measure modularity and cluster a product’s architecture into independent or coordinated modules, but many metrics have difficulty (a) measuring the modularity of different types of architectures in real-world products such as bus-type architectures and (b) optimising module boundaries in architectures. After reviewing existing modularity indices and clustering algorithms, we introduce new modularity indices that can capture the degrees of (1) connection strengths within each independent module and between different modules, (2) density of connections within each module and between modules, (3) proximity of interactions to the diagonal of the DSM, and (4) density of connections between buses and other components. Moreover, the proposed metrics can serve as objective functions to obtain optimal DSMs to maximise modularity. A comparative analysis of the proposed modularity index shows that the proposed metric can ...

In this study we investigate how we can effectively redesign a product family using additive manufacturing (AM). Specifically, we propose an integrated approach to product family redesign using platform metrics for a product family that uses AM. The proposed approach can help identify what to platform and how to platform with AM. We employ a variety metric to measure the amount of redesign for each component, a commonality metric to capture different types of commonality, and Design Structure Matrix (DSM) to analyze a platform architecture. After integrating these metrics, we can optimize balancing the tradeoffs between commonality and differentiation of components. Components that offer little variety for the market can be made common and part of the platform while components that must be varied to achieve market requirements should not be platformed and may be easily customized with AM. In order to facilitate customization of AM components, we can evaluate redesign of platform interfaces to help embed flexibility and modularity into the product family. To investigate the impact of the integrated approach, we apply the proposed approach to a family of Unmanned Aerial Vehicles (UAVs) as a case study. The results show the proposed approach can be effectively employed to identify ways to redesign the UAV family to improve the balance of commonality and variety of future product offerings.Copyright © 2018 by ASME

In order to determine target market and price, and design products/components for a family of front-loading washing machines, the coordination for decision-making from the corporate level down to the product and ultimately component levels is required. However, existing design research for many products focuses on analyzing single or multiple disciplines, even though optimizing local performance does not guarantee minimizing total cost at the product line level or maximizing value at the company level. In this work, we apply a multi-level value-driven design (VDD) approach to optimize a family of front-loading washing machines using a discipline-based decomposition. The VDD solutions obtained using discipline-based decomposition (DD) are compared with those obtained using product-based decomposition (PD). Consequently, the multi-level VDD approach based on DD for the washer family provides better performance for attributes than PD, but we observed that DD for the washer family does not guarantee maximizing the value function compared to PD because of the larger numbers of subsystems and consistency-related variables. Ongoing and future work to address this problem are discussed.

Companies usually launch families of products into the market to provide value to different segments based on different customer needs; however, most of the research on Value-Driven Design (VDD) in the literature has focused on modeling value functions and optimizing the design of single products, not families of products. In order to increase profit and minimize total cost for product design and manufacturing, VDD should be applicable to product family design. In this work, we propose a multi-level VDD approach for product family design by extending multidisciplinary design optimization methods. The multi-level VDD is applied to a family of front-loading washing machines to validate the effectiveness of the proposed approach. With this example, we demonstrate that design problems that optimize traditional objective functions (e.g., cost, performance) at each level do not necessarily maximize value when compared to an appropriate VDD formulation. On the other hand, when the value function is set as an objective function throughout the organization (company, product family, and product level), we find that the VDD formulation provides the best value. Future work based on these promising findings is also discussed.

Existing research on the design and analysis of front-loading washing machines has primarily focused on maximizing performance of a single product based on specific disciplinary analyses (e.g., vibration, dynamics). This design approach does not necessarily guarantee low costs, high sales, and maximum profit. Moreover, in order to target a variety of different customer needs, washing machines should be thought of and designed as a product family. In this paper, we suggest a value-driven design approach for a family of front-loading washing machines to identify promising solutions based on stakeholder’s preference. To create a value function, the sales volume for front-loading washers is estimated based on sales rank data, and then the net present value (NPV) is formulated by using the estimated sales volume and a demand sensitivity curve derived from the literature and publicly available data. The result shows that we can determine product family design candidates that maximize NPV, performance, and commonality of scalable and platform (i.e., shared) variables in the washer family. We also investigate the effectiveness of reducing the complexity of the value function based on rank ordering and parametric studies of the attributes used to compute NPV.

In the past decade, the market share of front-loading washing machines has seen explosive growth in the United States. As a result, many companies are now offering families of front-loading washing machines with a variety of features and options. Understanding the tradeoffs within these product families is challenging as existing research has focused primarily on a single disciplinary analysis (e.g., dynamic analysis, strength analysis); few models exist for cleanliness, reliability, energy efficiency, etc. In this paper, we introduce a new integrated multidisciplinary analysis using simulations, mathematical models, and response surface models based on the ratings of product attributes. In order to determine feasible design solutions for a front-loading washer family, we formulate a product family design problem using deviation functions and a product family penalty function. A multi-objective genetic algorithm is applied to solve the proposed formulation, and the results indicate that designers can successfully determine solutions for the best performance, most common, and compromise families of front-loading washers.

In order to improve the efficiency of the branch-and-bound method for mixed-discrete nonlinear programming, a nonuniform convergence tolerance scheme is proposed for the continuous subproblem optimizations. The suggested scheme assigns the convergence tolerances for each continuous subproblem optimization according to the maximum constraint violation obtained from the first iteration of each subproblem optimization in order to reduce the total number of function evaluations needed to reach the discrete optimal solution. The proposed tolerance scheme is integrated with five branching order options. The comparative performance test results using the ten combinations of the five branching orders and two convergence tolerance schemes show that the suggested non-uniform convergence tolerance scheme is obviously superior to the uniform one. The results also show that the branching order option using the minimum clearance difference method performed best among the five branching order options. Therefore, we recommend using the "minimum clearance difference method" for branching and the "non-uniform convergence tolerance scheme" for solving discrete optimization problems.

We present a new dual sequential approximate optimization (SAO) algorithm called SD-TDQAO (sequential dual two-point diagonal quadratic approximate optimization). This algorithm solves engineering optimization problems with a nonlinear objective and nonlinear inequality constraints. The two-point diagonal quadratic approximation (TDQA) was originally non-convex and inseparable quadratic approximation in the primal design variable space. To use the dual method, SD-TDQAO uses diagonal quadratic explicit separable approximation; this can easily ensure convexity and separability. An important feature is that the second-derivative terms of the quadratic approximation are approximated by TDQA, which uses only information on the function and the derivative values at two consecutive iteration points. The algorithm will be illustrated using mathematical and topological test problems, and its performance will be compared with that of the MMA algorithm.

Redesigning a product family entails carefully balancing the trade-offs between commonality and differentiation that are governed by the underlying platform architecture. Numerous metrics for commonality and variety exist to support product family and product platform design; however, rarely are they used in concert to help redesign platforms and families of products effectively. In this paper, we introduce an integrated approach that uses multiple product family metrics to establish an effective platform redesign strategy. Specifically, we present a detailed procedure to integrate the generational variety index, product line commonality index, and design structure matrix to prioritize components for redesign based on variety and commonality needs in a family of products. While all three of these tools exist in the literature and have been used extensively to support product family design, the novelty in our work lies in their integration to establish a redesign strategy for platform architectures that achieves a better balance between the commonality and variety within a product family. To demonstrate the proposed approach, case studies involving two generations of wireless computer mice and two families of dishwashers are presented. Ongoing and future work is also discussed.

Structural representations for interfaces between modules and components in a product vary widely in the literature. After reviewing several structural approaches to interface definition, a new weighted design dependency measure is described. The new representation takes into account both six different types of interfaces as well as their relative strength and frequency within a product architecture. The resulting design dependency measure provides a means for designers to quantify the change resistance in a product. In this paper, we investigate the use of this new design dependency measure to drive module identification. Specifically, we compare the resulting modules obtained by optimizing Design Structure Matrices (DSMs) using standard 0-1 representations of the interfaces to those obtained using the new design dependency measure. The results indicate that the weighted design dependency measure leads to more a logical definition of modules that maximizes within module dependencies and minimizes interactions between modules.Copyright © 2014 by ASME

Module definition entails clustering an original product architecture into independent or coordinated modules. Clustering algorithms based on Design Structure Matrices (DSMs) for defining modules have been widely studied. After reviewing existing clustering algorithms, we introduce simple new metrics that can be used as modularity indices bounded between 0 and 1 and also utilized as the objective functions to obtain optimal DSMs including the maximized interactions within modules and the minimized interactions between modules. As a search strategy for clustering modules, a combinatorial genetic algorithm using a new extended chromosome approach and modified operators for the chromosome is suggested. The module definition results indicated that the proposed clustering method using new modularity indices and genetic algorithm helps obtain optimal modular product architectures more logically.

Many practical design problems are multidisciplinary and typically involve the transfer of complex information between analysis modules. In solving such problems, the method for performing multidisciplinary analyses greatly affects the speed of the total design time. Thus, it is very important to group and order a multidisciplinary analysis (MDA) process so as to minimize the total computational time and cost by decomposing a large multidisciplinary problem into several subsystems and then processing them in parallel. This study proposes a decomposition method that exploits parallel computing, including the determination of an optimal number of subsystems by using a multi-objective optimization formulation and a messy genetic algorithm (GA) modified to handle discrete design variables. In the suggested method, an MDA process is decomposed and sequenced for simultaneously minimizing the feedback couplings within each subsystem, the total couplings between subsystems, the variation of computation times among subsystems, and the computation time of each subsystem. The proposed method is applied to the decomposition of an artificial complex system example and a multidisciplinary design problem of a rotorcraft with 17 analysis modules; promising results are presented using this proposed method.

A Broyden-Fletcher-Goldfarb-Shanno (BFGS) update formula is a standard technique for updating the Hessian matrix of a Lagrangian function in a sequential quadratic programming (SQP). The initial Hessian of the SQP is usually set to an identity matrix, because the previous information of the Hessian does not exist at the first iteration and it is extremely expensive to evaluate the exact Hessian of the real Lagrangian function. The inaccuracy of the identity matrix, however, is propagated to the next iterations in the SQP using BFGS update formula. In this study, we develop a new method that can generate more accurate approximate Hessian than that using the BFGS update formula even if the identity matrix is employed at the first iteration. In this method, the inaccuracy of the identity matrix is not propagated to the next iterations. Since the approximate Lagrangian obtained by using an enhanced two-point diagonal quadratic approximation method can be expressed as an explicit function of the design variables, the Hessian of the approximate Lagrangian can be analytically evaluated with negligible computational cost.

New Keynesian economic has attempted to justify nominal price rigidity with the "menu cost hypothesis". However, the nature of the menu cost is vague and has not been investigated> I set up an information search model in which firms face information scarcity to set the state-contingent prices in an input-output system. This paper shows that the cost of price adjustment stems from firms information search in a complex input-output system. The model is also able to explain the differing price stickiness across industries and the observed considerable price stickiness of the final goods. This implies that price rigidity accumulates when individual prices pass through an input-output system. Therefore, the model and empirical evidence support the "cumulation hypothesis" as an explanation for nominal price rigidity.

The gradual adjustment of the aggregate price level has been attributed to the driving force of fluctuation of output in Keynesian macroeconomics. The staggering timing pattern in price adjustment contributes to the inertia in the aggregate price level. This paper incorporates input-output relation into price setting firms in order to demonstrate that the staggered price setting is a stable equilibrium. The timing pattern in price setting is explained by two elements: heterogeneous inputs and information asymmetry. The result suggests that an input-output system has a hierarchical structure when staggering pattern arises. On the other hand, staggering is not likely to take place when each industry is not linked to other industries.

In the manufacturing process for the lens system of a mobile phone camera, various types of assembly and manufacturing tolerances, such as tilt and decenter, should be appropriately allocated. Because these tolerances affect manufacturing cost and the expected optical performance, it is necessary to choose a systematic design methodology for determining optimal tolerances. In order to determine the tolerances that minimize production cost while satisfying the reliability constraints on important optical performance indices, we propose a tolerance design procedure for a lens system. A tolerance analysis is carried out using Latin hypercube sampling for evaluating the expected optical performance. The tolerance optimization is carried out using a function-based sequential approximate optimization technique that can reduce the computational burden and smooth numerical noise occurring in the optimization process. Using the proposed design approach, the optimal production cost was decreased by 28.3% compared to the initial cost while satisfying all the constraints on the expected optical performance. We believe that the tolerance analysis and design procedure presented in this study can be applied to the tolerance optimization of other systems.