Optimal government scrappage subsidies in the presence of strategic consumers

Many countries have introduced vehicle scrappage programs to motivate consumers to replace their old cars earlier. Since these programs are generally offered over a given period of time, policy makers need to plan for inter-temporal subsidies. Considering a two-period game between strategic consumers and the government, we determine the optimal scrappage subsidy levels. Our results demonstrate that the subsidy level in the second period is higher than in the first, allowing the government to discriminate on price (or subsidy) between consumers with different valuations. In addition, we show that subsidy levels increase with the government’s targeted replacement level. However, when the government target level changes from intermediate to high, the first-period subsidy drops while the second-period subsidy remains unchanged.     

Optimal warranty policies for systems with imperfect repair

We investigate a system whose basic warranty coverage is minimal repair up to a specified warranty length. An additional service is offered whereby first failure is restored up to the consumers’ chosen level of repair. The problem is studied under two system replacement strategies: periodic maintenance before and after warranty. It turns out that our model generalizes the model of Rinsaka and Sandoh [K. Rinsaka, H. Sandoh, A stochastic model with an additional warranty contract, Computers and Mathematics with Applications 51 (2006) 179–188] and the model of Yeh et al. [R.H. Yeh, M.Y. Chen, C.Y. Lin, Optimal periodic replacement policy for repairable products under free-repair warranty, European Journal of Operational Research 176 (2007) 1678–1686]. We derive the optimal maintenance period and optimal level of repair based on the structures of the cost function and failure rate function. We show that under certain assumptions, the optimal repair level for additional service is an increasing function of the replacement time. We provide numerical studies to verify some of our results.     

Hitting probabilities and hitting times for stochastic fluid flows

Recently there has been considerable interest in Markovian stochastic fluid flow models. A number of authors have used different methods to calculate quantities of interest. In this paper, we consider a fluid flow model, formulated so that time is preserved, and derive expressions for return probabilities to the initial level, the Laplace–Stieltjes transforms (for arguments with nonnegative real part only) and moments of the time taken to return to the initial level, excursion probabilities to high/low levels, and the Laplace–Stieltjes transforms of sojourn times in specified sets. An important feature of our results is their physical interpretation within the stochastic fluid flow environment, which is given. This allows for further implementation of our expressions in the calculation of other quantities of interest.Novel aspects of our treatment include the calculation of probability densities with respect to level and an argument under which we condition on the infimum of the levels at which a “down–up period” occurs.Significantly, these results are achieved with techniques applied directly within the fluid flow model, without the need for discretization or transformation to other equivalent models.     

碳减排补贴与碳税下的供应链碳减排决策优化与协调

针考虑碳税政策和政府对制造商的碳减排技术创新投入补贴,构建了供应链博弈模型,根据协调条件给出了相应的契约形式及参数。通过对供应链模型的求解,得到了碳税和碳减排技术创新投入补贴下的最优碳减排量和最优订货量。数值分析结果表明:碳减排技术创新投入的补贴比例变化对供应链的最优碳减排量、订货量及期望利润的影响有较大影响,而且是成正向变化关系,而且在其他参数不变及供应链碳减排量一定的情况下,碳税与碳减排补贴比例呈反向变化关系,进而可为政府碳减排补贴政策制定及供应链碳减排优化提供科学的决策依据。     

考虑顾客使用行为的汽车租赁容量分配策略研究

随着物联网技术的发展, 租赁公司通过智能技术可以实时监测顾客的使用行为, 因此可以根据顾客使用行为设计补贴策略以激励顾客在使用过程中保持良好的行为习惯。本文将租赁价格作为顾客行为的函数, 构建随机动态规划模型, 研究了多产品、多周期下汽车租赁公司的容量分配决策和补贴机制。考虑到所构建模型的状态变量维度较高, 因此提出两种近似算法对模型进行求解, 并通过数值仿真验证了模型的相关性质。在考虑顾客行为可以转变的前提下, 得到相关结论:租赁公司以机会成本作为容量分配决策的重要依据;当所需等级汽车缺货时, 由于低等级汽车的机会成本低于高等级汽车的机会成本, 因此满足升级条件时, 租赁公司总是按照等级顺序进行升级;在合理的补贴策略下, 公司的总收益将会随着补贴的增加而增加。     

A Model of Medical Record Storage

A model is developed to describe the growth of a medical records store subject to rules for microfilming or disposing of record files when they have not been used within a given period of time. Separate projections are given for the number of files in the system and for the volume of file contents. The model allows different microfilm policies to be compared and aids the long term planning of storage facilities.     

Optimal order-replacement policy for a phase-type geometric process model with extreme shocks

A system is subject to random shocks that arrive according to a phase-type (PH) renewal process. As soon as an individual shock exceeds some given level the system will break down. The failed system can be repaired immediately. With the increasing number of repairs, the maximum shock level that the system can withstand will be decreasing, while the consecutive repair times after failure will become longer and longer. Undergoing a specified number of repairs, the existing system will be replaced by a new and identical one. The spare system for the replacement is available only by sending a purchase order to a supplier, and the duration of spare system procurement lead time also follows a PH distribution. Based on the number of system failures, a new order-replacement policy (also called $(K\text{,}N)$ policy) is proposed in this paper. Using the closure property of the PH distribution, the long-run average cost rate for the system is given by the renewal reward theorem. Finally, through numerical calculation, it is determined an optimal order-replacement policy such that the long-run expected cost rate is minimum.     

Two time-delay dynamic model on the transmission of malicious signals in wireless sensor network

Deployed in a hostile environment, motes of a Wireless sensor network (WSN) could be easily compromised by the attackers because of several constraints such as limited processing capabilities, memory space, and limited battery life time etc. While transmitting the data to their neighbour motes within the network, motes are easily compromised due to resource constraints. Here time delay can play an efficient role to reduce the adversary effect on motes. In this paper, we propose an epidemic model SEIR (Susceptible–Exposed–Infectious–Recovered) with two time delays to describe the transmission dynamics of malicious signals in wireless sensor network. The first delay accounts for an exposed (latent) period while the second delay is for the temporary immunity period due to multiple worm outbreaks. The dynamical behaviour of worm-free equilibrium and endemic equilibrium is shown from the point of stability which switches under some threshold condition specified by the basic reproduction number. Our results show that the global properties of equilibria also depends on the threshold condition and that latent and temporary immunity period in a mote does not affect the stability, but they play a positive role to control malicious attack. Moreover, numerical simulations are given to support the theoretical analysis.     

Minimising the number of aircraft for a transportation network

A case is presented of a transportation problem involving eight locations. Known for each location is the quantity of goods to be shipped by air to the other seven locations and the travel time between locations. The transport can be directly to each destination or via other locations. The capacity of the aircraft is specified. The transportation has to be completed between 10 p.m. and 5 a.m.This problem was solved in three stages. First a lower bound for the number of aircraft was determined. Secondly a network was established by mixed integer programming which minimizes the total travel time to transport all the goods to their respective destinations without violating the capacity constraints. Thirdly, the individual aircraft were assigned to part of the network in such a way that the total travel time per aircraft is within the specified time period.     

Modeling of financial supply chain

The research work on supply-chain management has primarily focused on the study of materials flow and very little work has been done on the study of upstream flow of money. In this paper we study the flow of money in a supply chain from the viewpoint of a supply chain partner who receives money from the downstream partners and makes payments to the upstream partners. The objective is to schedule all payments within the constraints of the receipt of the money. A penalty is to be paid if payments are not made within the specified time. Any unused money in a given period can be invested to earn an interest. The problem is computationally complex and non-intuitive because of its dynamic nature. The incoming and outgoing monetary flows never stop and are sometimes unpredictable. For tractability purposes we first develop an integer programming model to represent the static problem, where monetary in-flows and out-flows are known before hand. We demonstrate that even the static problem is NP-Complete. First we develop a heuristic to solve this static problem. Next, the insights derived from the static problem analysis are used to develop two heuristics to solve the various level of dynamism of the problem. The performances of all these heuristics are measured and presented.     

Pricing Fixed-Income Securities in an Information-Based Framework

Abstract

The purpose of this article is to introduce a class of information-based models for the pricing of fixed-income securities. We consider a set of continuous-time processes that describe the flow of information concerning market factors in a monetary economy. The nominal pricing kernel is assumed to be given at any specified time by a function of the values of information processes at that time. Using a change-of-measure technique, we derive explicit expressions for the prices of nominal discount bonds and deduce the associated dynamics of the short rate of interest and the market price of risk. The interest rate positivity condition is expressed as a differential inequality. An example that shows how the model can be calibrated to an arbitrary initial yield curve is presented. We proceed to model the price level, which is also taken at any specified time to be given by a function of the values of the information processes at that time. A simple model for a stochastic monetary economy is introduced in which the prices of the nominal discount bonds and inflation-linked notes can be expressed in terms of aggregate consumption and the liquidity benefit generated by the money supply.     

The decomposition method for a control problem for an underactuated Lagrangian system

The control problem for an underactuated Lagrangian system is considered. A system of smooth non-linear functions of the generalized coordinates is introduced into the treatment and the number of functions is equal to the number of generalized control forces. The aim of the control is to bring the system in a finite time to a terminal set specified by the level lines of the selected functions, and it is required that the motion at the terminal instant occurs along the level lines. As a result, a development and extension of Chernous’ko's decomposition method is given. This method was proposed for designing feedback control for Lagrangian systems when the number of controls in a system is equal to the number of its degrees of freedom.     

Subsidy Competition in Networks

This paper investigates a competitive location model on a network with free entry and exit. The given network consists of regions that represent independent jurisdictions. Market entry and exit are sequential. In each stage of the multi-stage game, the regions simultaneously decide what subsidy to offer to a firm should it located within its boundaries. The paper delineates three distinct classes of subsidy policies and examines their effects in a series of computational tests.     

自保护相依多部件系统的预防维修建模及策略优化

自保护技术作为自愈技术的一种,能够使系统在环境或工况条件变化的干扰下以较高可靠性运行。本文构建了一个新的具有相依主要部件和辅助部件的系统可靠性模型,其中主要部件的退化速率与工作中的辅助部件的数量有关。此外,基于定期检测和预防维修策略,本文利用半再生过程技术求解了系统的长期运行平均成本,并以长期运行平均成本最小化为目标给出了系统的最优预防维修策略。最后,以镗刀系统为例,利用所提方法给出了预防更换阈值和检测周期的最优值,以期望为实际维修行为决策提供理论参考。     

碳补贴和时滞效应下低碳供应链微分博弈研究

在政府低碳补贴政策下,本文考虑技术的时滞效应,构建政府、制造商和零售商的微分博弈模型,在分散决策下分析了制造商采用远视策略和短视策略时各方的最优决策,并将结果与集中决策下的对应情形进行了比较分析。研究发现滞后效应与政府的最优补贴比率负相关。制造商的短视策略并不一定会损害收益,若滞后时间超过特定阈值,那么企业将不会投资低碳技术。集中决策下减排努力、宣传努力、减排稳定值、商誉稳定值均高于分散决策,但满足一定条件时集中决策的供应链利润会低于分散决策。     

Optimal number of minimal repairs before ordering spare for preventive replacement

This paper presents a model for determining the optimal number of minimal repairs before ordering spare for preventive replacement. By introducing the costs of ordering, repair, downtime, replacement, and the salvage value of an un-failed system, the expected long-term cost rates and cost effectiveness are derived. It is shown that, under certain conditions, the optimal number of minimal repairs, which minimizes the cost rate or maximizes the cost effectiveness, is given by a unique solution of an equation. A numerical example is also given for illustration of the proposed model.     

Modelling impact of advertising and optimizing advertising policy: an application in recreation

This paper deals with the problem of the desirable level of advertising expenditure, the optimal distribution of this expenditure in time and the allocation over the media: TV, radio and newspaper for a recreation park in the Netherlands.Although the model id developed for the specific situation of this park, in principle it can be applied in all situations where the interest is in short-term (day-by-day) effects of promotional activities on sales. Examples are: other situations in the recreation and leisure business, cultural events (theatre, cinema) and sales promotions (e.g. weekend offerings) for products in supermarkets.First a model was specified and estimated that relates number of visitors to advertising effort. It also takes into account non-advertising variables that effect the number of visitors.Then this model was used in a heuristic advertising planning procedure, which by means of incremental analysis, for a given budget level searches for the optimal allocation of the advertising budget over media and time.With this procedure, ways to readjust the advertising policy were found: by allocating the budget differently over media and time and by changing the overall budget level.Several recommendations were made to the management of the park, a number of which have already been implemented.     

Developing an integrated model of an aluminium smelter incorporating sub-models with different time bases and levels of aggregation

In this paper an integrated production model of an aluminium smelter is discussed. The core model, i.e., the model involving the largest time base and highest level of aggregation of the production process, is a nonlinear bilevel programming problem. A number of smaller intermediate product modelling type mixed integer sub-models involving smaller time bases and lower levels of aggregation of the production process are important components of the overall integrated production model. It is shown that in order for the core integrated model of the smelter to be able to be specified with respect to some capacities, etc., and for the results of the integrated model to be implemented, these sub-models are necessary.     

A shift scheduling model for employees with different seniority levels and an application in healthcare

This paper addresses the problem of scheduling medical residents that arises in different clinical settings of a hospital. The residents are grouped according to different seniority levels that are specified by the number of years spent in residency training. It is required from the residents to participate in the delivery of patient care services directly by working weekday and weekend day shifts in addition to their regular daytime work. A monthly shift schedule is prepared to determine the shift duties of each resident considering shift coverage requirements, seniority-based workload rules, and resident work preferences. Due to the large number of constraints often conflicting, a multi-objective programming model has been proposed to automate the schedule generation process. The model is implemented on a real case in the pulmonary unit of a local hospital for a 6-month period using sequential and weighted methods. The results indicate that high quality solutions can be obtained within a few seconds compared to the manually prepared schedules expending considerable effort and time. It is also shown that the employed weighting procedure based on seniority levels performs much better compared to the preemptive method in terms of computational burden.     

A general age-replacement model with minimal repair under renewing free-replacement warranty

A general age-replacement model in which incorporates minimal repair, planned and unplanned replacement, is considered in this paper for products under a renewing free-replacement warranty policy. For both warranted and non-warranted products, cost models from the user’s perspective are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of a product warranty on the optimal replacement model are investigated analytically. Furthermore, we show that the optimal replacement age for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, numerical examples are given for illustration.