Joint optimisation of price,warranty and recovery planning in remanufacturing of used products under linear and non-linear demand,return and cost functions

We investigate joint optimisation of remanufacturing, pricing and warranty decision-making for end-of-life products. A novel mathematical–statistical model is proposed where decisions involve pricing of returned used products (cores), degree of their remanufacturing, selling price and the warranty period for the final remanufactured products. The virtual age reliability improvement approach is chosen to model the upgrading of the cores to higher quality levels. We consider price- and warranty-dependent demand, price- and age-dependent return, and age-dependent remanufacturing cost in the model development. Both linear and non-linear forms of these functions are investigated. First, under some restrictive conditions of upgrade level and age distribution of received cores, special cases of the problem, which can be solved using a recently developed non-linear optimisation solver, are presented. We also implement a particle swarm optimisation algorithm for the solution of the original problem when all the restrictive assumptions are dropped. Finally, numerical experiments and sensitivity analysis are presented to address different aspects of the model and the solution approaches.     

Pricing and inventory policies for Hi-tech products under replacement warranty

Companies, especially in the Hi-tech (high-technology) industry (such as computer, communication and consumer electronic products), often provide a replacement warranty period for purchased items. In reality, simultaneously determining the price and inventory decisions under warranty policy is an important issue. The objective of this paper is to develop a joint pricing and inventory model for Hi-tech products under replacement warranty policy. In the first model, we consider a Hi-tech product feature in which the selling price is declining in a trend. We determine the optimal inventory level for each period and retail price for the first period while maximising the total profit. In the second model, we further determine the optimal retail price and inventory level for each period in the dynamic demand market. This study develops solution approaches to solve the problems described above. Numerical analysis discusses the influence of system parameters on the company's decisions and behaviours. The results of this study could serve as a reference for business managers or administrators.     

Determination of production run time and warranty length under system maintenance and trade credits

Manufacturers offer a warranty period within which they will fix failed products at no cost to customers. Manufacturers also perform system maintenance when a system is in an out-of-control state. Suppliers provide a credit period to settle the payment to manufacturers. This study considers manufacturer's production and warranty decisions for an imperfect production system under system maintenance and trade credit. Specifically, this study uses the economic production quantity to model the decisions under system maintenance and trade credit. These decisions involve how long the production run time and warranty length should be to maximise total profit. This study provides lemmas for the conditions of optimality and develops a theorem and an algorithm for solving the problems described. Numerical examples illustrate the solution procedures and provide a variety of managerial implications. Results show that simultaneously determining production and warranty decisions is superior to only determining production. This study also discusses the effects of the related parameters on manufacturer's decisions and profits. The results of this study are a useful reference for managerial decision-making and administration.     

Dynamic optimisation of the aroma production in brewing fermentation

Several key compounds for the final beer flavour (higher alcohols, esters, vicinal diketones) are produced during the alcoholic fermentation phase. The paper demonstrates the possibility of obtaining various desired final aroma profiles and reducing the total process time using dynamic optimisation of three control variables: temperature, top pressure and initial yeast concentration in the fermentation tank. The optimisation is based on a sequential quadratic programming algorithm, on a dynamic model of the alcoholic fermentation and on an aroma production model. The robustness of the optimal control profile with respect to model uncertainty is discussed.     

Dynamic joint pricing and production policy for perishable products

A joint dynamic pricing and production problem for perishable products without shortages is considered. The demand rate is price‐dependent and time‐varying. This paper constructs an optimal control model to maximize the total profit under a general nonlinear production cost function. The feature of the optimal joint dynamic pricing and production policy is analyzed by solving the corresponding optimal control problem on the basis of improved Pontryagin's maximum principle. Then, an effective algorithm is designed to obtain the optimal joint policy. The case of the joint static optimal policy is also investigated and compared with the dynamic one. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods, and some managerial implications are provided for the management of perishable items.     

Dynamic pricing and channel efficiency in the presence of the cost learning effect

This paper investigates the impacts of the supply‐side cost learning effect on dynamic pricing strategies and the channel efficiency in a decentralized supply chain consisting of a manufacturer and a retailer. The unit production cost incurred by the manufacturer declines as the cumulative output increases. With the manufacturer being the price leader, the interactions between the two channel members are modeled as a Stackelberg differential game, where the two channel members dynamically set the wholesale and retail prices over time to optimize their respective profits. We find that while the cost learning effect is beneficial to both channel members in terms of long‐term profitability, such an effect is detrimental to the channel inefficiency caused by price double marginalization. In a setting where the manufacturer sells through competing retailers, we show that the channel efficiency can be improved with the emergence of horizontal competition. Our result also indicates that the channel efficiency with a feedback pricing equilibrium is higher than that with an open‐loop equilibrium.     

Optimal maintenance policy and length of extended warranty within the life cycle of products

This paper investigates maintenance policy and length of extended warranty for repairable products from the seller’s viewpoint. When the product failed within the base and extended warranty periods, product failures are rectified using minimal repair. To reduce the number of product failures, the seller performs imperfect preventive maintenance (PM) actions when the age of the product reaches a controlled-limit within the base and extended warranty periods. After the base warranty period expires, the seller gives a discount of purchasing extended warranty expense if the consumer purchases the extended warranty for products. Under this maintenance scheme, the mathematical model of profit is constructed and then the optimal controlled-limit, the number and degree of PM and the length of extended warranty are obtained such that the expected total profit is maximized for the seller. Finally, numerical examples are given to illustrate the influences of the optimal length of the extended warranty and the maintenance policy for profit model.     

Robust incoherent control of qubit systems via switching and optimisation

A robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state. This scheme consists of two main steps: projective measurement on the initial mixed state and optimal control between two pure states. The first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states. The second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state. The connection between the two steps is accomplished by a switching strategy. To accomplish the second step, two approaches are presented in detail. These approaches are time-optimal transition with unbounded control and bang-bang control with minimal switches. The minimal time and minimal number of switches in these approaches can be calculated by simple analytical expressions. The proposed approaches provide two relatively straightforward optimal design methods.     

路径规划; 态势评估; 模糊逻辑; 贝叶斯网络

针对非线性动态系统辨识和控制的特点，对4层模糊神经网络进行了优化和改进，形成了动态模糊神经网络，提高了网络的稳定性和对动态系统的辨识能力，同时给出了基于Lyapunov函数稳定收敛定理的各权向量以及权矩阵学习速率的自适应调整算法．应用于非线性动态系统的辨识和控制仿真试验表明，改进后的动态模糊神经网络与模糊神经网络相比，可取得更好的辨识精度和跟踪控制效果。     

Multivariable norm optimal and parameter optimal iterative learning control: a unified formulation

This article investigates the two paradigms of norm optimal iterative learning control (NOILC) and parameter optimal iterative learning control (POILC) for multivariable (MIMO) ?-input, m-output linear discrete-time systems. The main result is a proof that, despite their algebraic and conceptual differences, they can be unified using linear quadratic multi-parameter optimisation techniques. In particular, whilst POILC has been naturally regarded as an approximation to NOILC, it is shown that the NOILC control law can be generated from a suitable choice of control law parameterisation and objective function in a multi-parameter MIMO POILC problem. The form of this equivalence is used to propose a new general approach to the construction of POILC problems for MIMO systems that approximates the solution of a given NOILC problem. An infinite number of such approximations exist. This great diversity is illustrated by the derivation of new convergent algorithms based on time interval and gradient partition that extend previously published work.     

On-line performance optimisation of aero engine control system

This paper is focused on on-line performance optimisation of gas turbine engine control systems. Practical problems of optimal engine control design and implementation are considered. An algorithm for on-line resolution of the engine control optimisation problem is proposed. The example of turbo-jet engine on-line specific fuel consumption minimisation is presented.     

Internet differential pricing: Effects on consumer price perception,emotions, and behavioral responses

Differential pricing is a strategy that retailers have used effectively in capturing sales and profits. The advent of the Internet is a new domain where this strategy can be applied conveniently and economically. This study examines the effects of various Internet differential pricing tactics (buyer identification, purchase quantity, purchase timing, and multi-channels) on consumers’ cognitive (i.e., perceptions of price fairness), emotional, and behavioral responses. A survey on 367 marketing students in Taiwan was carried out. Empirical findings show that perceived fairness is significantly related to emotions, and while emotions similarly affect behavioral responses, it also mediates the relationship between perceptions of price fairness and behavioral responses. Practical implications and future studies for internet pricing strategies are further discussed.     

Joint admission,production sequencing,and production rate control for a two-class make-to-order manufacturing system

Today's manufacturing industry faces a number of challenges related to the rapid delivery of products with a high degree of variety. Striking a balance between the effectiveness in capacity utilization and the rapidness in order-fulfillment is a substantial challenge for manufacturing companies. This work aims to provide a theoretical basis from which to address this practical question. To this end, we address the problem of coordinating the admission, production sequencing, and production rate controls for a two-class make-to-order manufacturing system. Formulating the problem as a Markov decision process model, we identify the structural properties of optimal control policies under both discounted and average profit criteria. We show that the cμ rule is optimal for production sequencing and the optimal admission and production rate control policies can be characterized by the state-dependent threshold levels, provided that the production times are not associated with customer class. We also show that the optimal production rates are monotone in the system state, as in the case of a single class queueing system, and that the lower priority class can be preferred to the higher priority class in order admission under a certain condition on the system parameters. Our numerical study demonstrates that a considerable economic benefit can be achieved if the production rate is dynamically controlled between the minimum and maximum rates rather than fixed to the mean rate of these values. Finally, we present a heuristic policy that is described by linear switching functions for the control of order admission and a selection rule for the control of production rate. We compare the performance of our heuristic to the optimal policy using a numerical experiment, revealing that the heuristic provides near optimal solutions to test example problems and is robust to the system parameters.     

Basis functions and parameter optimisation in high-order iterative learning control

In this paper a new parameter-optimal high-order Iterative Learning Control (ILC) algorithms is proposed to extend the work of Owens and Feng [Parameter optimisation in iterative learning control. International Journal of Control 14(11), 1059-1069]. If the original plant is positive, this new algorithm will result in convergent learning where the convergence is monotonic to zero tracking error. If the original plant is not positive, it can be shown that by adding a suitable set of basis functions into the algorithm, the tracking error will again converge monotonically to zero. This provides a considerable improvement to earlier work on parameter-optimal ILC as it opens up the possibility of globally convergent algorithms for any linear plant G. The number of parameters needed to ensure convergence could, however, become large. The paper shows that the use of low-order parameterisations is capable of achieving much of the benefit achieved in the ‘ideal’ case.     

Economics of Dynamic Pricing in a Reputation Brokered Agent Mediated Marketplace

We present a framework to study the microeconomic effects in a reputation brokered Agent mediated Knowledge Marketplace, when we introduce dynamic pricing algorithms. We study the market with computer simulations of multiagent interactions. In this marketplace, the seller reputations are updated in a collaborative fashion based on the performance of the user in the delegated tasks. To the best of our knowledge this is the first agent mediated marketplace where the agents use dynamic pricing based on dynamically updated reputations. The framework can be used to investigate the different equilibria reached, based on the level of intelligence of the selling agents, the level of price-importance elasticity of the buying agents, and the level of unemployment in the marketplace. Preliminary experiments addressing these issues are presented.     

A study on decisions of warranty,pricing, and production with insufficient information

It has been well-recognized that a better warranty term offered by the product producer can effectively increase the product sales, but how such the warranty and pricing decisions can be integrated into a marketing strategy with consideration of production planning as well has drawn relatively less attention in practice in terms of a systematic discussion. In addition, it is not uncommon that the manufacturer may not have sufficient historical data to estimate the deterioration of the new product, and thus the marketing decisions based on the conventional computation results may not be reliable. In such a case of scarce historical data, Bayesian analysis is a reasonable approach to additionally take expert opinions into account for better decision making. Accordingly, this paper proposes a Bayesian decision model by which the integrated optimal strategy can be obtained under the situation that the manufacturer does not have sufficient historical data. Moreover, in order to deal with the computing complexity of the proposed model, a heuristic algorithm is also provided, and finally, a practical application case is used to demonstrate the usefulness of the proposed model.     

Scheduling Under Common Due Date, A Single Resource and Precedence Constraints—A Dynamic Approach

This paper discusses dynamic methods for solving a class of multi-project scheduling problems in which rates of job performances are controllable and resources such as money, energy or manpower per time unit, are renewable and continuously divisible. The objective is to complete the projects as close to the common due date as possible. Two different ways of imposing sequential precedence relations between project jobs are explored by formulating two dynamic models and studying their relationships on the optimal solution. Efficient time-decomposition algorithms for finding either globally optimal schedules or lower bound guided near-optimal solutions are suggested and computationally tested.     

Two‐echelon manufacturer–retailer supply chain strategies with price,quality, and promotional effort sensitive demand

This study deals with the two‐layer supply chain model of one manufacturer and one retailer for a single commodity where market demand is assumed to be dependent on selling price, quality of the products, and promotional effort of the retailer. We investigate the behavior of the supply chain under centralized, manufacturer Stackelberg, conditional manufacturer Stackelberg, retailer Stackelberg, conditional retailer Stackelberg, and vertical Nash model structure. The nature of the above models provides great insights to a firm's manager for achieving optimal strategy in a competitive marketing system. Quite often, not all items produced in a firm are of perfect quality; some are perfect (conforming) quality and others are imperfect (nonconforming) quality. The nonconforming products are sold in a secondary shop or by other retailers. The procurement cost of finished products depends on the quality of the products due to more investment in advanced technology, better raw materials, and skilled labor, etc. The warranty policy for the products is also imposed to attract the customers to buy more. Here, both members (manufacturer and retailer) jointly share the cost of the warranty policy. The objective of this paper is to determine the optimal selling price and promotional effort of the retailer, while the optimal wholesale price and quality of the products are determined by the manufacturer so that the above strategies are maximized. Finally, numerical examples with sensitivity analysis of the key parameters are illustrated to investigate the proposed model.     

考虑异质需求的再制造系统最优产量与定价研究

考虑消费者对再制造品和新产品基于价格敏感的异质性需求特征,引入再制造品和新产品的需求函数,进而构建一个考虑单一再制造商并以该再制造商利润最大化为目标的最优产量及定价模型,分别求出了各期的再制造品与新产品的最优产量及价格策略。最后通过算例分析表明,随着消费者偏好系数的增加,企业越来越趋向于生产再制造品,再制造品与新产品的价格逐渐接近,企业实施再制造不仅能减少生产成本,同时企业的总利润也得到大幅提升。     

间歇过程最优迭代学习控制的发展:从基于模型到数据驱动

本文综述了间歇过程的基于模型的和数据驱动的最优迭代学习控制方法.基于模型的最优迭代学习控制方法需要已知被控对象精确的线性模型,其研究较为成熟和完善,有着系统的设计方法和分析工具.数据驱动的最优迭代学习控制系统设计和分析的关键是非线性重复系统的迭代动态线性化.本文简要综述了基于模型的最优迭代学习控制的研究进展,详细回顾了数据驱动的迭代动态线性化方法,包括其详细的推导过程和突出的特点.回顾和讨论了广义的数据驱动最优迭代学习控制方法,包括完整轨迹跟踪的数据驱动最优迭代学习控制方法,提出和讨论了多中间点跟踪的数据驱动最优点到点迭代学习控制方法,和终端输出跟踪的数据驱动最优终端迭代学习控制方法.进一步,迭代学习控制研究中的关键问题,如随机迭代变化初始条件、迭代变化参考轨迹、输入输出约束、高阶学习控制律、计算复杂性等.本文突出强调了基于模型的和数据驱动的最优迭代学习控制方法各自的特点与区别联系,以方便读者理解.最后,本文提出数据驱动的迭代学习控制方法已成为越来越复杂间歇过程控制发展的未来方向,一些开放的具有挑战性的问题还有待于进一步研究.