Multivariate tolerance design for a quadratic design parameter model

The determination of tolerance allocations among design parameters is an integral phase of product/process design. Such allocations are often necessary to achieve desired levels of product performance. Parametric and nonparametric methods have recently been developed for allocating multivariate tolerances. Parametric methods assume full information about the probability distribution of design parameter processes, whereas, nonparametric methods assume that only partial information is available, which consists of only design parameter process variances. These methods currently assume that the relationship between the design parameters and each of the performance measures is linear. However, quadratic response functions are increasingly being used to provide better approximations of the relationships between performance measures and design parameters. This is especially prevalent where there is a multivariate set of performance measures that are functions of a common set of design parameters. In this research we propose both parametric and nonparametric multivariate tolerance allocation procedures which consider the more general case where these relationships can be represented by quadratic functions of the design parameters. We develop the corresponding methodology and nonlinear optimization models to accommodate and take advantage of the presence of interactions and other nonlinearities among suppliers.     

Strategically decentralise when encroaching on a dominant supplier

A manufacturer may encroach on his suppliers by developing substitutable components. In the presence of encroachment, the manufacturer could assemble products using (high-end) components purchased from the supplier, and assemble products using (low-end) components produced in-house. Thus, the manufacturer must deliberate on how to manage the expanded organisation consisting of competing product divisions. In this paper, we examine the quintessential organisational structure decision – the centralisation versus decentralisation choice – from the perspective of the manufacturer. Our model assumes that the supplier is a dominant player, moving first by pricing the high-end component, and consumers have a higher willingness-to-pay of the product containing the high-end component. In such a context, we find that the manufacturer may encroach on the supplier even if producing the low-end component costs more than producing the high-end one. The supplier should strategically price to deter or accommodate downstream encroachment contingent on the manufacturer’s organisational structure decision. If the unit cost of low-end components is high enough, product-based decentralisation is preferred to centralisation due to the supplier’s lower wholesale price. Furthermore, the manufacturer’s strategic decentralisation always hurts the supplier, always benefits the customers and could benefit or hurt the entire supply chain under certain conditions.     

Incentives for quality improvement efforts coordination in supply chains with partial cost allocation contract

In this paper, we consider quality improvement efforts coordination in a two-stage decentralised supply chain with a partial cost allocation contract. The supply chain consists of one supplier and one manufacturer, both of which produce defective products. Two kinds of failure cost occur within the supply chain: internal and external. The supplier and the manufacturer determine their individual quality levels to maximise their own profits. We propose a partial cost allocation contract, under which the external failure cost is allocated between the manufacturer and the supplier at different rates based on information derived from failure root cause analysis. If the quality levels of the supplier and the manufacturer are observable, we show that the partial cost allocation contract coordinates the supply chain, provided that the failure root cause analysis does not erroneously identify the manufacturer’s fault as the supplier’s, and the supplier does not take responsibility for the manufacture’s fault. In the single moral hazard model, where only the quality level of the supplier is unobservable, the optimal share rates require the supplier to take some responsibility for the manufacture’s fault. However, in the double moral hazard model, where quality levels of the supplier and the manufacturer are unobservable to each other, the optimal share rates require the supplier not to take responsibility for the manufacturer’s fault. It is noted that the root cause analysis conducted by the manufacturer may have its disadvantage in attributing the fault to the supplier when both sides are at fault. We also propose a contract based on the dual root cause analysis to reduce the supplier’s penalty cost. Numerical results illustrate that the partial cost allocation contract satisfies the fairness criterion compared with the traditional cost allocation contract.     

ROBUST TOLERANCE ALLOCATION USING STOCHASTIC PROGRAMMING

Abstract

Tolerance allocation in manufacturing is a prominent industrial task for enhancing productivity and reducing manufacturing costs. The classical tolerance allocation problem can be formulated as a stochastic program to determine the assignment of component tolerances such that the manufacturing cost is minimized. However, tolerance design is a prerequisite to the overall quality and cost of a product; robust tolerance design is particularly important and should be considered. In this paper, robustness is considered in formulating the tolerance allocation problem by minimizing the manufacturing cost's sensitivity. Moreover, from a practical perspective, the process capability index for each component and the upper bound of the manufacturing cost are also considered. To effectively and efficiently resolve the robust tolerance allocation problem, a sequential quadratic programming algorithm embedded with a Monte Carlo simulation is developed. To demonstrate this design method's robustness, two commonly used test problems are solved. The designs devised in this paper have lower manufacturing costs and smaller variations in manufacturing costs than those in previous studies, indicating that the proposed method is highly promising in the robust tolerance design.     

Policy and cost approximations of two-echelon distribution systems with a procurement cost at the higher echelon

This paper investigates a two-echelon (warehouse-retailer) inventory system with stochastic demand and a pull system of inventory allocation. We assume that ordering costs are charged at the warehouse for procuring the item from a supplier. However, the internal costs of ordering the item from the warehouse by the retailers are considered negligible. For this problem, the lower echelon uses a single critical number, an order-up-to-level policy, whereas a (s, S) inventory system is followed at the upper echelon. We develop a cost model for this problem and provide a simple algorithm for estimating the optimal policy. Simulation is used to test the accuracy of the model.     

Economic tolerance design for quality

This paper provides a few general mathematical models for determining product tolerances which minimize the combined manufacturing costs and quality loss. The models contain quality cost with a quadratic loss function and represent manufacturing costs with geometrical decay functions. The models are also formulated with multiple variables which represent the set of characteristics in a part. Applications of these models include minimizing the total cost with effective tolerance allocation in product design.     

Horizontal cooperation and information sharing between suppliers in the manufacturer–supplier triad

In this paper, we analyse a collusion and information-sharing problem between two suppliers in a manufacturer–supplier triad. The manufacturer treats one supplier as a strategic supplier and the other as a backup. While the strategic supplier offers modules of good quality but longer lead times, the backup supplier offers modules with inferior quality but shorter lead times. If there are urgent orders, the manufacturer must turn to the backup supplier. However, it is difficult for the manufacturer to estimate whether the urgent supplier has put extra effort into their production. We formulate this problem by assuming that the urgent supplier has either low or high production costs. To take advantage of the competition between two suppliers, the manufacturer can design a contract menu that defines total payment and lead times, under which both suppliers may be worse off. Meanwhile, it is possible for the suppliers to tacitly form a coalition, and to even share the private cost information. We study this problem by formulating it as a three-stage game. Furthermore, we investigate the variation of profits for each part of the supply chain. We find that the manufacturer is worse off when suppliers cooperate or share private information. Both suppliers, however, can benefit from cooperation and information sharing.     

Achieving product variety through optimal choice of module variations

The trade-off in designing products typically involves consideration of manufacturing and development costs, and the potential market share. Modular design of products has been identified as one way of providing firms with a competitive advantage. In the context of modular product design, some of the pertinent questions are: (i) how many product varieties in a product group should be introduced in the market; and (ii) what is the minimum number of module-options required to support this variety? In this paper we study the optimality of such decisions related to modularization in two separate scenarios: (i) the module supplier is an independent operator whose decisions are not coordinated with that of the firm; and (ii) the module supplier is a wholly owned subsidiary of the firm. For these scenarios, we show how the choice of module-options affects product variety, total sales, product development cost, and hence, the firm's profit. We establish that the module-options can be rank ordered, based on profit margin and customer rating, and that the optimal set of module-options to be acquired or developed would include only the top ranked options. We also show how to determine the number and type of module-options a firm should acquire to maximize its profit. Finally, we discuss how our algorithm can be extended to the case of firms that deal with products having multiple module-types.     

基于讨价还价博弈的ATO供应链零部件生产及补货策略

通过建立ATO供应链中最终产品制造商与其两个供应商间的讨价还价合作模型,研究了ATO供应链的零部件生产补货策略和相应的利润分配策略,并探讨了供应链中各合作主体议价能力对最优解的影响。研究发现,ATO供应链应随着最终产品销售价格的提高而增加零部件产量,随最终产品组装成本或零部件生产成本的提高而减少零部件产量;随着最终产品制造商对其中一个供应商议价能力的增强,该供应商零部件的转移价格及其利润会降低,而另外一个供应商的零部件转移价格和利润会提高;若最终产品制造商比另外一个供应商的议价能力强,其期望利润会得到提高,反之,则会降低。     

A new tolerance design method for a secondary rechargeable battery using design of experiments with mixture

Mixing errors in the manufacturing process of a mixture may cause a sizeable variation in the performance of the product, leading to the need for the tolerance design. Even though a variety of procedures have been proposed for the optimal tolerance design based on quality loss and manufacturing costs, there are no available tolerance design methods when mixing errors exist in the manufacturing process of a mixture. In this article, we propose a new tolerance design method for the case where mixing errors are involved in massive manufacturing process of a secondary rechargeable battery. Using an approximation method, we derive quality loss function, reflecting the effects of mixing errors on the product performances. Statistical design of mixture experiments is applied to build empirical models of performances as functions of component proportions in the corresponding quality loss function. A real‐life case study on the tolerance design of a secondary battery is provided for the illustration of the proposed method. The results show the efficiency of the proposed method in designing the tolerances to minimize the quality loss and manufacturing costs. Copyright © 2008 John Wiley & Sons, Ltd.     

Multiobjective capital allocation for supplier development under risk

Supplier development is increasingly important due to the complexity of today’s supply chains and the globalisation of businesses. Since manufacturers have only limited resources, they need to make an informed decision about which suppliers to develop. Moreover, the returns from investment in supplier development are uncertain, so manufacturers have to take this risk into account when choosing their suppliers for development programmes. In this paper, we propose a multi-objective model for capital allocation for supplier development under risk. We apply it to an example of a global car manufacturer and support the decision-making process with data downloaded from the Bloomberg database. We use stock market returns and cost of capital of suppliers to assess their performance. Our model supports an informed decision, which is that tradeoffs exist between risk and cost of supplier development programme. Depending on the risk aversion of the manufacturer, we demonstrate different allocation schemes for supplier development.     

Joint effects of remanufacturing channel design and after-sales service pricing: an analytical study

We conduct an analytical study on remanufacturing channel design and after-sales service pricing, which jointly affect the sustainability and profitability of the supply chain. We model a supply chain with one manufacturer and one independent retailer. The manufacturer, as the Stackelberg game leader, engages in remanufacturing to take advantage of production cost savings. The collection of the used products can be carried out by either the manufacturer or the retailer. After-sales service, for example, extended warranty, is offered with the product and is sold separately. The service provider can be either the manufacturer or the retailer. We use game theoretic models to answer an important research question: How do remanufacturing and after-sales service jointly affect channel selection decisions? We explore the benefits of joint decision making in terms of remanufacturing efficiency and after-sales service performance. We find that it is most efficient for the retailer to collect the used product for remanufacturing and to offer after-sales service, because the retailer simultaneously makes decisions regarding remanufacturing and after-sales service and thus reduces double marginalisation in the supply chain. We also demonstrate numerically how the costs of collecting used products and providing after-sales service impact channel selection decisions.     

Concurrent optimal allocation of geometric and process tolerances based on the present worth of quality loss using evolutionary optimisation techniques

Concurrent tolerancing becomes an optimisation problem to find out the optimum allocation of the process tolerances in the given design function constraints. In traditional optimisation methods, finding out the optimum solution for this advanced tolerance design problem is complex. The proposed algorithms (elitist non-dominated sorting genetic algorithm) and differential evolution extensively do better than the previous algorithms for attaining the optimum result. The aim of this paper is to suggest a model for optimal tolerance allocation by considering both tolerance cost and the present worth of quality loss such that the total manufacturing cost/loss is minimised. The suggested model takes into account the time value of money for quality loss and product degradation over time and consists of two new parameters: the planning horizon and the product user’s discount rate. From the outcome of this study, a longer planning horizon results in an increase in both tolerance cost and quality loss; however, a larger value of discount rate gives up a decrease in both tolerance cost and quality loss. Finally, a practical example is brought into reveal the effectiveness of the suggested method.     

Development of a sequential optimization procedure for robust design and tolerance design within a bi-objective paradigm

Many practitioners and researchers have implemented robust design and tolerance design as quality improvement and process optimization tools for more than two decades. Robust design is an enhanced process/product design methodology for determining the best settings of control factors while minimizing process bias and variability. Tolerance design is aimed at determining the best tolerance limits for minimizing the total cost incurred by both the customer and manufacturer by balancing quality loss due to variations in product performance and the cost of controlling these variations. Although robust design and tolerance design have received much attention from researchers and practitioners, there is ample room for improvement. First, most researchers consider robust design and tolerance design as separate research fields. Second, most research work is based on a single quality characteristic. The primary goal of this paper is to integrate a sequential robust design–tolerance design optimization procedure within a bi-objective paradigm, which, the authors believe, is the first attempt in the robust design and tolerance design literature. Models are proposed and numerical examples along with sensitivity analysis are performed for verification purposes.     

紧急订单成本信息不对称下的激励契约设计

在正常订单和紧急订单供应商共存情况下.分析制造商的最优订货策略.正常订单供应商采购提前期较长.需在销售期前进行订货.紧急订单供应商交货期较灵活.但交货期长短与成本相关且该成本信息为其私有信息.考虑在此条件下制造商的订货策略(与正常订单供应商)和激励合同设定问题(与紧急订单供应商).最后,比较了紧急订单供应商的存在与否对制造商的订货以及利润的影响.     

Optimal reliability, warranty and price for new products

The success of a new product depends on both engineering decisions (product reliability) and marketing decisions (price, warranty). A higher reliability results in a higher manufacturing cost and higher sale price. Consumers are willing to pay a higher price only if they can be assured about product reliability. Product warranty is one such tool to signal reliability with a longer warranty period indicating better reliability. Better warranty terms result in increased sales and also higher expected warranty servicing costs. Warranty costs are reduced by improvements in product reliability. Learning effects result in the unit manufacturing cost decreasing with total sales volume and this in turn impacts on the sale price. As such, reliability, price and warranty decisions need to be considered jointly. The paper develops a model to determine the optimal product reliability, price and warranty strategy that achieve the biggest total integrated profit for a general repairable product sold under a free replacement-repair warranty strategy in a market and looks at two scenarios for the pricing and warranty of the product. The model assumes that the sale rate increases as the warranty period increases and decreases as the price increases. The maximum principle method is used to obtain optimal solutions for dynamic price and warranty situations. Finally, numerical examples are given to illustrate the proposed model.     

Simultaneous configuration of platform products and manufacturing supply chains

The product platform concept represents a powerful approach for manufacturers to compete cost-effectively in a global market that requires diverse product range, quick time to market, and rapid responses to supply sources. A key challenge is how to strike a balance between platform commonality and modularity. When a manufacturer outsources its raw materials or module options, the supplier capabilities and production costs should be considered. This paper discusses optimizing decision variables for simultaneously configuring not only platform-based product variants but also their supply chain. We develop a mixed-integer programming model that integrates both platform product design and material purchase decisions based on cost drivers sensitive to commonality and modularity. Theoretical analysis of the model yields two properties, allowing us to further simplify the model and thus help in developing an effective solution algorithm. A numerical example is presented to illustrate how manufacturers strive to dynamically adjust their product design strategies in response to changes in the market demands and/or supply base.     

Concurrent optimal allocation of design and process tolerances for mechanical assemblies with interrelated dimension chains

Concurrent tolerance allocation has been the focus of extensive research, yet very few researchers have considered how to concurrently allocate design and process tolerances for mechanical assemblies with interrelated dimension chains. To address this question, this paper presents a new tolerance allocation method that applies the concept of concurrent engineering. The proposed method allocates the required functional assembly tolerances to the design and process tolerances by formulating the tolerance allocation problem into a comprehensive model and solving the model using a non-linear programming software package. A multivariate quality loss function of interrelated critical dimensions is first derived, each component design tolerance is formulated as the function of its related process tolerances according to the given process planning, both manufacturing cost and quality loss are further expressed as functions of process tolerances. And then, the objective function of the model, which is to minimize the sum of manufacturing cost and expected quality loss, is established and the constraints are formulated based on the assembly requirements and process constraints. The purpose of the model is to balance manufacturing cost and quality loss so that concurrent optimal allocation of design and process tolerances is realized and quality improvement and product cost reduction is achieved. The proposed method is tested on a practical example.     

Simultaneous tolerance synthesis for manufacturing and quality

Tolerance allocation affects product design, manufacturing, and quality. No existing technique has been found by the authors that takes product design, manufacturing, and quality into account simultaneously. This paper introduces a new concurrent engineering method for tolerance allocation. A nonlinear optimization model was constructed to implement the method. The model minimizes the combination of quality loss and manufacturing cost simultaneously in a single objective function by setting both process tolerances and design tolerances simultaneously. The purpose of the model is to balance manufacturing cost and quality loss to achieve near-optimal design and process tolerances simultaneously for minimum combined manufacturing cost and quality loss over the life of the product. Compared to other models, this model shows significant improvements. Electronic Publication     

基于共同代理的多方协调下物流成本节约合同

对制造商、供应商和第三方物流组成的供应物流环节展开研究,以制造商和供应商为委托人,第三方物流为代理人,建立了基于共同代理的成本节约合同.得出了第三方物流观测到的物流成本与所选择的上下游企业努力水平的函数关系,并进一步讨论了上下游企业在合作与非合作模式下努力水平存在的差异.最后通过数值分析对研究成果进行了验证,研究结果表明该物流成本节约合同可以披露出第三方物流真实成本信息,有效激励制造商、供应商积极参与降低物流成本.