Some Analytical and Numerical Bounds on the Renewal Function

Renewal-type equations are frequently encountered in the study of reliability, warranty analysis, replacement and maintenance policies, and inventory control. Renewal equations usually do not have analytical solutions, and hence, bounds or approximations are very useful. In this article, analytical bounds are studied based on a simple iterative procedure which provides some analytical results and nice convergence properties when the number of iteration increases. Bounds and approximations are also investigated for a recursive algorithm for numerical computation. In addition, some interesting monotonicity properties are introduced and discussed. The approximation error, which is important for determining the stopping rule of the iterative procedure and the numerical algorithm, is also studied.     

AN INVENTORY PROBLEM APPLIED TO A RENTAL SITUATION

An inventory problem, applied to a rental situation business, has been considered. If no item is in stock when a demand occurs, the company borrows the units from other concerns in the same line of business. The profit function has been calculated and it has been shown how the inventory level increases with penalty cost. A review of the literature on inventory control reveals that not much work has been done in holding inventories of rental items. In a recent paper, Tainiter (1964) considered the situation in which a company rents out items such as cars, trucks, farm equipment, books, furniture, etc., and obtained the profit function by taking “rental-out” time as a negative exponential and demand as a general random variable. The model is equally applicable to companies which rent out “service personnel”, repair men, taxi cabs, etc. “We consider a company renting out items to customers. The company starts its business by purchasing a total number of M items in the inventory. The term inventory, defined by Arrow, Earlin and Scarf (1958) as the stock of goods which is kept for future sale or production, is applicable here. Whenever a demand occurs the item is rented out immediately, if it is available in the stock. But if the inventory is zero, i.e. all the items are rented out, the demand will be satisfied by borrowing items from other companies which are dealing in the same line of business. For example, a manufacturer of refrigerators maintains and repairs his product at the customer's house after sale. If a complaint arrives when no repairmen are available, the company will “borrow” repairmen from elsewhere and will attend to the complaint immediately. The borrowing cost may be negative or positive, representing a penalty or a profit. On the other hand if the company does not borrow and the customer has to wait (and such situations occur very often) the loss of the customer's goodwill may occur. It is also not possible to keep large numbers of items because of the storage costs and tied up capital. The problem is then to devise an optimal policy such that the profits of the company are maximized.     

腾飞的翅膀：机场属地化改革与企业库存

良好的基础设施不仅包括投资增加或者技术进步，日常的维护和运营效率也至关重要。交通基础设施的分权化管理模式可以缩短监管者和经营者之间的监管距离，提高信息利用效率，从而提升基础设施运营效率，更好地发挥基础设施对于区域经济的推动作用。本文利用2003-2004年机场属地化改革这一自然实验，从基础设施运营效率的角度研究了分权治理对区域经济绩效的影响。本文发现，当机场由民航总局移交地方政府管理后，运营规模显著增加。基于企业库存反映企业经营绩效的视角，使用双重差分法，本文发现拥有机场的城市的企业在改革后库存水平显著下降8.5%。三重差分分析表明，更加依赖空运的企业在改革后库存下降更多。进一步研究发现，改革后基础设施建设投资并没有显著变化，但是与分权化有效利用本地信息、提升机场运行效率从而降低企业库存的假说一致的是，在沟通成本和库存异质程度更高的城市，机场属地化改革对企业库存的降低作用更大。安慰剂检验和各种稳健性检验排除了其他事件的影响，支持了本文的主要结论。研究结果表明，分权化治理可以改善交通基础设施运营效率，从而使其更好地适应区域本身情况，推动区域社会经济发展。     

Inventory Systems with Unreliable Suppliers

The aim of this article is to establish the optimal control of a periodic-review inventory system with two suppliers. One of them delivers orders immediately, the other one is unreliable delivering the orders immediately only with probability p ∈ (0, 1). Two cases are considered. In the first case, it is possible to order any inventory amount from each of suppliers. In the second case, the system budget is restricted.     

Stockouts and Restocking: Monitoring the Retailer from the Supplier’s Perspective

Suppliers and retailers typically do not have identical incentives to avoid stockouts (lost sales due to the lack of product availability on the shelf). Thus, the supplier needs to monitor the retailer’s restocking efforts with the available data. We empirically assess stockout levels using only shipment and sales data that is readily available to the supplier. The model distinguishes between store stockouts (zero inventory in the store) and shelf stockouts (an empty shelf but some inventory in other parts of the store), thereby identifying the cause of the stockout to be either a supply chain or a restocking issue. We find that, as suspected by the supplier, the average stockout rate is much higher than published averages. In addition, stockout rates vary widely between stores. Moreover, almost all stockouts are shelf stockouts. The model identifies stores that may have restocking issues.     

A property of the yule distribution and its applications

The relationship Y = RX between two random variables X and Y, where R is distributed independently of X in (0, l), is known to have important consequences in different fields such as income distribution analysis, Inventory decision models, etc.

In this paper it is shown that when X and Y are discrete random variables, relationships of similar nature lead to Yule-type distributions. The implications of the results are studied in connection with problems of income underreporting and inventory decision making.     

理性预期下宏观经济政策真的无效吗

本文在对理性预期模型评述的基础上,通过将宏观经济政策的有效性分为前期有效、当期有效与后期有效后发现,即便是在理性预期理论框架下,宏观经济政策总体上都是有效的,不同的是,在理性预期理论框架下,宏观经济政策仅表现为前期有效。在经验证据上,本文分别以我国和美国的相关实际数据为样本,利用实证分析的方法检验了货币政策的有效性。分析结果显示,我国的货币政策不仅是前期有效的,而且后期也是有效的,相比而言,美国的货币政策却表现出前期有效、后期无效的特点。究其原因,两者的差异主要在于政策信号传递以及公众对货币政策预期形成方式不同,但无论公众对宏观经济政策的预期符合什么形式,它都会对宏观经济经济运行产生影响,经济政策都是不可或缺的。     

ESTIMATION OF THE VECTOR MOVING AVERAGE MODEL BY VECTOR AUTOREGRESSION

We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the characteristic equation are well away from the unit circle, and more substantial where one or more roots have modulus near unity. We show that the representation estimated by this multivariate technique is consistent and asymptotically invertible. This estimator has significant computational advantages over Maximum Likelihood, and more importantly may be more robust than ML to mis-specification of the vector moving average model. The estimation method is applied to a VMA model of wholesale and retail inventories, using Canadian data on inventory investment, and allows us to examine the propagation of shocks between the two classes of inventory.     

Statistical measurement of the inventory shortage cost

In searching for the optimal inventory control policy, the objective is to minimize the expected total costs related, of which the shortage cost is an important element. Due to the difficulty in calculating the indirect cost of the loss of goodwill resulted from the shortage, practitioners and researchers often simply assume a fixed penalty cost on the inventory shortage or switch to the alternative method by assigning a specific customer service level. The development of an appropriate tool for measuring the shortage cost can help a business control the total costs and improve the productivity more effectively. This paper proposes probabilistic measurements of the shortage cost, based on mathematical relationship between the cost and the shortage amount. The derived closed-form estimates of the expected shortage cost value can then be applied to support the determination of the optimal inventory control policy.     

A NON-SEQUENTIAL INVENTORY MODEL WITH VARIABLE SUPPLY

In this paper an attempt has been made to determine an optimum order quantity for a two-period inventory model where demands for each period are completely known, but the supply in each period is a stochastic one with mean equal to the corresponding order size.     

Optimization of problems with multivariate multiple functional responses: A case study in air quality

Optimization of multi-response problems is a popular subject in the literature. However, the problem becomes complicated when the responses are functional due to the existence of signal factors. In this article, we have proposed a combined index to optimize multivariate multiple functional responses by considering functional specification limits and a target. The relation among the responses and controllable factors is characterized by polynomial equations to consider the curvature of the response functions. The validity of the proposed method is checked by a simulation example. To show the applicability of the proposed method, a real case about Tehran air quality is analyzed. Latitude and longitude are considered to be signal factors, and different pollutant values are responses of the experiment. Government policies in each time interval are considered as controllable factors. Finally, an optimization algorithm is used to find the best decisions for government policies.     

我国交通事故责任强制保险定价研究 ——来自北京、吉林、内蒙古和山东的经验证据

 本文运用北京、吉林、内蒙古和山东的交强险保单信息,研究我国交强险定价问题。研究发现：在费率水平方面,我国交强险定价除出租租赁和公路客运车型以外,总体上偏高;在作用机制方面,原有费率因子在影响交强险保费方面是显著的,但原理不尽相同;在费率结构方面,现有费率结构对于低风险的被保险人而言是不公平的。针对这些问题,本文建议监管当局和保险公司应与被保险人沟通,探索交强险的进一步改革,促进社会的稳定和谐发展。     

On parallel policies for ranking and selection problems

In this paper we develop and test experimental methodologies for selection of the best alternative among a discrete number of available treatments. We consider a scenario where a researcher sequentially decides which treatments are assigned to experimental units. This problem is particularly challenging if a single measurement of the response to a treatment is time-consuming and there is a limited time for experimentation. This time can be decreased if it is possible to perform measurements in parallel. In this work we propose and discuss asynchronous extensions of two well-known Ranking & Selection policies, namely, Optimal Computing Budget Allocation (OCBA) and Knowledge Gradient (KG) policy. Our extensions (Asynchronous Optimal Computing Budget Allocation (AOCBA) and Asynchronous Knowledge Gradient (AKG), respectively) allow for parallel asynchronous allocation of measurements. Additionally, since the standard KG method is sequential (it can only allocate one experiment at a time) we propose a parallel synchronous extension of KG policy – Synchronous Knowledge Gradient (SKG). Computer simulations of our algorithms indicate that our parallel KG-based policies (AKG, SKG) outperform the standard OCBA method as well as AOCBA, if the number of evaluated alternatives is small or the computing/experimental budget is limited. For experimentations with large budgets and big sets of alternatives, both the OCBA and AOCBA policies are more efficient.     

Seasonal Extraction in the Presence of Feedback

Time series seasonal extraction techniques are quite often applied in the context of a policy aimed at controlling the nonseasonal components of a time series. Monetary policies targeting the nonseasonal components of monetary aggregates are an example. Such policies can be studied as a quadratic optimal control model in which observations are contaminated by seasonal noise. Optimal extraction filters in such models do not correspond to univariate time series seasonal extraction filters. The linear quadratic control model components are nonorthogonal due to the presence of control feedback. This article presents the Kalman filter as a conceptual and computational device used to extract seasonal noise in the presence of feedback.     

Discussion: The Recent Reappearance of the Homotheticity Restriction on Preferences

A model linking final demand (sales) with intermediate manufactures is estimated and simulated over the course of a business cycle. The results show that prices fluctuate more for early-stage manufactures than for later-stage products at the manufacturing and retail level. This is found to be largely due to inventory and unfilled orders fluctuations, particularly those of inventories of primary manufactured products held by finished goods manufacturers. Since these inventory fluctuations lead the cycle in final demand, prices of primary manufactures lead business activity. Another result is that inventories of materials and supplies, including those of retailers for resale, exhibit more instability than producers' inventories of finished goods.     

蒙代尔——弗来明模型在中国的扩展分析

蒙代尔-弗来明模型的理论和结论已经逐渐成为各国制定宏观经济政策的基础。但是因为中国的经济体制和实际情况与蒙代尔-弗来明模型中的基本假设不完全符合,将模型的结论简单地作为制定宏观调控政策的决策依据是不够的。文章通过对中国多年实证数据的检验,建立了一个中国的蒙代尔-弗来明模型,研究了在中国特殊的情况下蒙代尔-弗来明模型的运用。     

对外贸易与制造业机器人使用:行业开放促进技术进步的新证据

本文基于国际机器人联盟提供的制造业分行业机器人数据,以2009年六部委联合出台的汽车出口促进政策作为“准自然实验”,利用双重差分法评估了行业对外贸易对机器人使用规模的影响。研究表明:在汽车出口促进政策实施以后,汽车生产行业及与汽车生产关系紧密的行业,机器人存量和增量规模相比其他行业有更大幅度提高,证明行业对外贸易水平提高,会显著增加机器人使用规模,并且无论出口还是进口水平提高,都会同样促进机器人存量和增量增长。结论通过了一系列稳健性检验。本文进一步的研究还发现,行业开放提高机器人使用规模,依靠用工替代和研发鼓励两条路径实现。本研究为行业开放促进技术进步提供了新的理论和证据,也为国家制定人工智能发展计划提出了有益建议。     

The demographic transformation--a challenge to labor market and social policies

The implications of future demographic trends for labor market and social policies in the Federal Republic of Germany are discussed. The focus is on how trends such as demographic aging and declining fertility will affect the labor market, employment, and old-age security.