Impulsive optimal control with finite or infinite time horizon

We consider a dynamical system subjected to feedback optimal control in such a way that the evolution of the state exhibits both sudden jumps and continuous changes. Previously obtained necessary conditions (Ref. 1) for such impulsive optimal feedback controls are generalized to admit the case of infinite time horizon; this generalization permits application to a wider class of problems. The results are illustrated by application to a version of the innkeeper's problem.Dedicated to G. Leitmann     

非平衡指派模型及其在航空机务维修中的应用

非平衡指派问题是最优平衡指派问题的推广与深化,在航空机务维修工作中,维修任务的合理配置对及时完成维修任务,保障训练作战计划非常重要.本文从装备完好率和人力资源的优化配置角度出发,按照不考虑维修任务等待时间和考虑维修任务等待时间两种情况分别建立了非平衡指派优化模型,并给出了这两种情况下效益矩阵的构造方法,进而将优化模型转化为最优平衡指派模型进行求解,从而为航空机务维修工作中维修人员的优化配置提供了一种科学、合理的决策方法.     

Considerations for building knowledge-based expert systems in highway maintenance planning

Genuine, nontrivial planning problems in pavement and bridge maintenance are generally beyond the capabilities of expert systems. However, the diagnostic, interpretive and predictive features of such systems can be combined with algorithmic planning tools to produce comprehensive maintenance planning and management systems.After a discussion of the relevant issues, this paper addresses the potential application areas for knowledgebased expert systems in highway maintenance planning. The foxus is on how and where expert systems can interface with optimization models to yield meaningful results.     

Optimal scheduling of non-perfect inspections

^** Corresponding author. Email: romulo.zequeira{at}utt.fr^*** Email: christophe.berenguer{at}utt.fr In this paper, we study the determination of optimal inspectionpolicies when three types of inspections are available: partial,perfect and imperfect. Perfect inspections diagnose withouterror the system state. The system can fail because of threecompeting failure types: I, II and III. Partial inspectionsdetect without error type I failures. Failures of type II canbe detected by imperfect inspections which have non-zero probabilityof false positives. Partial and imperfect inspections are madeat the same time. Type III failures are detectable only by perfectinspections. If the system is found failed in an inspection,a repair is made which renders the system in a good-as-new condition.The system is preventively maintained following an age-basedpolicy. Preventive maintenance actions return the system toa good-as-new condition. We consider cost contributions of inspections,repairs, preventive maintenance and periods of unavailability.The model presented permits to determine the optimal (constant)inter-inspection period for partial, imperfect and perfect inspectionsand the optimal times of preventive maintenance actions.     

Resale price maintenance in supply chains with general multiplicative demand

We analyze a supply chain with a Resale Price Maintenance (RPM) contract in which the manufacturer sets the retail price with a general multiplicative price–demand function and prove the existence/uniqueness of an equilibrium. We also compare the equilibrium prices and quantities, consumer surplus and total system welfare for the RPM and wholesale price contracts. We conclude that a manufacturer may capture a smaller share of the total supply chain profit despite her ability to set the retail price.     

考虑更新延长两阶段保修的二手产品维修策略优化

针对二手产品的维修问题,给出了二手产品生命周期的定义,提出了考虑更新延长两阶段保修的维修策略模型。该策略综合考虑了产品的年龄变化、延保折扣、小修和生产损失费用等因素,从顾客的角度出发,建立以顾客期望总费用率最小化为目标的免费更换保修和按比例更换保修两种策略模型,并给出模型最优化的相关理论证明。算例研究验证了模型的有效性,并对参数的灵敏度进行了分析,文中结论可为顾客进行产品维修计划提供决策依据。     

Optimization of maintenance policy under warranty length‐based demand with consideration of both manufacturer and buyer satisfaction

This study proposes a model to optimize postsale services consisting of four factors: (a) the basic warranty length, (b) the extended warranty length, (c) the preventive maintenance level, and (d) the preventive maintenance interval. Furthermore, consumer demand for the product and extended warranty are considered as functions of the length of the basic warranty and extended warranty periods, respectively. Because buyer dissatisfaction with a product can lead to the loss of potential buyers and the switch of current customers to the competitors, both manufacturer and buyer satisfaction are considered in the model. Three comparative studies are done for showing the effectiveness of the model. The first one compares the results of simultaneous optimization from the two perspectives of manufacture and customer with the single‐objective optimization results from each of the mentioned viewpoints. The second comparison studies the provision of extended warranty contract in the proposed model, and the third comparison investigates the effect of preventive maintenance actions on the results of the model.     

A single-machine scheduling problem with maintenance activities to minimize makespan

We study a single-machine scheduling problem with periodic maintenance activity under two maintenance stratagems. Although the scheduling problem with single or periodic maintenance and nonresumable jobs has been well studied, most of past studies considered only one maintenance stratagem. This research deals with a single-machine scheduling problem where the machine should be stopped for maintenance after a fixed periodic interval (T) or after a fixed number of jobs (K) have been processed. The objective is to minimize the makespan for the addressed problem. A two-stage binary integer programming (BIP) model is provided for driving the optimal solution up to 350-job instances. For the large-sized problems, two efficient heuristics are provided for the different combinations of T and K. Computational results show that the proposed algorithm Best-Fit-Butterfly (BBF) performs well because the total average percentage error is below 1%. Once the constraint of the maximum number of jobs (K) processed in the machine’s available time interval (T) is equal or larger than half of jobs, the heuristic Best-Fit-Decreasing (DBF) is strongly recommended.     

Availability analysis of crank-case manufacturing in a two-wheeler automobile industry

The paper describes the availability of crank-case manufacturing system in an automobile industry. The units discussed here fail either directly from normal working state or indirectly through partial failure state. The machines are subjected to both preventive and corrective maintenance. Failure and repair times of the units are independent. The problem is formulated using probability consideration and supplementary variable technique. The system of equations governing the working of system consists of ordinary as well as partial differential equations. Lagrange method and Runge–Kutta method is used to solve partial differential equation and ordinary differential equation respectively. The study reveals that successful program of preventive and routine maintenance will reduce equipment failures, extend the life of the equipment, and increase the system availability to considerable margin.     

A polynomial expression for the Owen value in the maintenance cost game

The class of maintenance cost games was introduced in 2000 to deal with a cost allocation problem arising in the reorganization of the railway system in Europe. The main application of maintenance cost games regards the allocation of the maintenance costs of a facility among the agents using it. To that aim it was first proposed to utilize the Shapley value, whose computation for maintenance cost games can be made in polynomial time. In this paper, we propose to model this cost allocation problem as a maintenance cost game with a priori unions and to use the Owen value as a cost allocation rule. Although the computation of the Owen value has exponential complexity in general, we provide an expression for the Owen value of a maintenance cost game with cubic polynomial complexity. We finish the paper with an illustrative example using data taken from the literature of railways management.