For continuous-review inventory systems with ADI, Buzacott and Shanthikumar (1994) consider production-inventory systems with ADI and evaluate policies that use two parameters: a **base**-**stock** level and a release leadtime. Hariharan and Zipkin (1995) introduced the notion of demand leadtime in a system where orders are announced a fixed amount of time before they are due. For constant supply leadtimes and Poisson order arrivals, they show that there is an **optimal** **base**-**stock** **policy** with a fixed **base**-**stock** level. Karaesmen et al. (2002) analyze a discrete-time model with constant demand leadtimes that is similar to our SDD model with no due-date updating (see Section 5). They prove the optimality of state-dependent **base**-**stock** policies. Gallego and ¨ Ozer (2002, Section 2.4) consider a system similar to a special case of our SDD setting, but with exogenous load-independent supply leadtimes. Gayon et al. (2009) study a system similar to our IDD scheme but with multiple demand classes, lost sales, and no due-date updates. Other papers that deal with continuous-review systems include Liberopoulos et al. (2003) and Karaesmen et al. (2004).

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tribution with service time distribution in some class, which is discussed in Chandhiry and Gupta [6], and the probability distribution on the order unit corresponding to an item each unit of the demand requires, which is obtained in Zhao [3], are used in our analysis. The ana- lytical method for deriving the waiting time distribution of demand is developed. Through numerical experiments properties of the waiting time distributions are discussed. It is used for finding the **optimal** number of **base** stocks, which is a minimal number of **base** stocks satisfying the condition that the fraction of demand who waits for items for period less than or equal to a predetermined time must be greater than a pre-specified value.

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The previous models dealt in the instantaneous order arrival case, the following literature deals with models with lead time. Due to the complex nature of the single period lead time **optimal** **policy**, many approximations have been developed to solve the lost sales penalty cost model. Morton (1971) created a myopic critical fractile procedure that works well for short lead times. Zipkin (2008b) provides a comprehensive overview of many approximations that have been developed to solve this problem. One common assumption is that the **policy** takes on a **base** **stock** **policy** structure because it is easy to implement. The total cost function for the penalty cost setting is convex in the **base** **stock** level S, making the search for the **base** **stock** level relatively simple (Janakiraman and Roundy 2004). The literature suggests that lost sales models with penalty costs have complex ordering policies that can easily be approximated by simpler **base** **stock** policies without a large increase in cost. For example, Huh et al. (2009) proved that as the penalty cost grows large in relation to other costs, a **base** **stock** **policy** asymptotically approaches the **optimal** solution. In the perturbed demand case, an approximation is developed to speed up the solution procedure. Additionally, as this paper will show, even if we force the instantaneous order arrival structure on the lead time model, it is not easy to solve for the best **policy**, nor does this always provide a close approximation. The advantage, however, is that is the **policy** is easier to implement once determined.

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The rest of the paper is organized as follows: In the next section, the one-for-one replenishment **policy** and its assumptions are described and a problem formulation is presented in detail. Then, we show how the result of the one-for-one replenishment **policy** in a two-level inventory system can be used for the exact evaluation of the **base** **stock** **policy**. Following that, the batch-ordering **policy** in a two-level inventory system is extended by considering order costs for both retailer and supplier. Setting the inventory position at the supplier to a certain value, a search algorithm for nding the **optimal** solution of a (R; Q) **policy** is presented. Then, for demonstrating the applicability of the proposed method, we resort to solving an example. Finally, some remarks concerning possible extension are made.

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Two versions of expectations formation were envisioned: ratio- nal expectations and VAR-based expectations. Rational expectations means that agents are assumed to understand and take fully into ac- count the entire structure of the model, including monetary **policy** formulation, in arriving at their decisions. VAR-based expectations follows a parable quite like the Phelps-Lucas “island paradigm”: the model’s agents live on diﬀerent islands where they have access to a limited set of core macroeconomic variables, knowledge they share with everyone in the economy. The core macroeconomic variables are the output gap, the inﬂation rate, and the federal funds rate, as well as beliefs on the long-run target rate of inﬂation and what the equilibrium real rate of interest will be in the long run. In addi- tion, they have information that is germane to their island, or sector. Consumers, for example, augment their core VAR model with infor- mation about potential output growth and the ratio of household income to GDP.

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If the basic purpose of institutional constraints is to keep spillover effects in check, then corrective taxes on variables associated with these spillovers constitute the theoretically most appealing response. Tradeable permits for such variables are an alternative. Assuming the severity of the spillover effects to depend on the EU-averages of the source variables, uniform corrective taxes across countries, or multilateral markets for tradeable permits, suffice for an effi- cient arrangement. Naturally, a system of Pigouvian taxes or, to an even larger extent, tradeable permits, could only be implemented in a rough, less than ideal manner, due to informational limitations and various imperfections in the political process. But even in a less than ideal form, such an arrangement would significantly dominate the SGP as well as many proposed reforms of the Pact, for at least two reasons. First, it could account for all important spillovers. The latter do not only, or even mainly, occur via national budget deficits but also via output gaps (alternatively unemployment rates), inflationary pressure, and the **stock** of public debt. Sec- ond, it could more efficiently regulate these spillovers, due to the symmetry and continuity of the incentive structure induced by Pigouvian taxes, which leads to an equalization of costs and benefits of spillover reductions across countries.

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Productivity shocks: The same considerations are relevant for understand- ing dynamic responses to productivity. In figure 6, panel A, we see that the dynamic response to the productivity shock under a constant money growth rule is similar to the responses suggested by Gali. Consumption can rise only to the extent that prices are flexible, so that it increases by about .2% (in contrast to 1% under the **optimal** **policy**). Labor input must fall, since the small output response (with higher productivity) mandates fewer units of work eﬀort. Again, this diﬀerence in the response of real quantities carries over to eﬀects on the real interest rate: it initially rises in the face of the productivity shock, rather than falling, because there is sustained growth in consumption over the first few periods of the response. But, as with the aggregate demand shock, there are nearly oﬀsetting movements in the price level which make the nominal interest rate largely invariant to the shock. 16

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In section 7, we describe the near-steady state dynamics of the model under **optimal** **policy**. Looking across a battery of specifications, we find that these dynamics display only minuscule variation in the price level. Thus, we document that there is a robustness to the Fisherian conclusion in King and Wolman [1999], which is that the price level should not vary greatly in response to a range of shocks under **optimal** **policy**. In fact, the greatest price level variation that we find involves less than a 0.5% change in the price level over twenty quarters, in response to a productivity shock which brings about a temporary but large deviation of output from trend, in the sense that the cumulative output deviation is more than 10% over the twenty quarters. Across a range of experiments, output under **optimal** **policy** closely resembles output which would occur if all prices were flexible and monetary distortions were absent. We refer to the flexible price, nonmonetary model as our underlying real business cycle framework. Although the deviations of quantities under **optimal** **policy** from their real business cycle counterparts are small, because these deviations are temporary, they give rise to larger departures of real interest rates from those in the RBC solution. We relate the nature of these departures to the nature of constraints on the monetary authority’s **policy** problem. Section 8 concludes.

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Coordination The apparent solution to problems associated with a lack of international co- ordination is, of course, to coordinate. In practice, however, coordination that is sufficiently far-reaching to solve the problems associated with international economic dependencies is hardly the **optimal** solution, since it creates a number of new problems. For once, far-reaching coordi- nation by governments of different countries might, in the presence of **policy** failures, turn into coordination against citizens, a point made by Persson and Tabellini (1995) or, in the presence of credibility problems of governments, into coordination against the ECB, a point made by Giavazzi (2004). More generally, the substantial transfers of power to officials required for suc- cessful coordination bear significant risks, in particular of abuse of power and of misjudgement due to insufficient information among decision makers (a Hayek-type argument). The obvious way of minimizing these risks is to limit government intervention on the supra-national level to those issues for which coordination is expected to be particularly beneficial. Such partial coordination might be a more “robust” arrangement than far-reaching coordination, since it limits the danger of large-scale political mistakes. Moreover, it is in better accord with visions of decentralization of power, citizens’ political participation, and political accountability. 9

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The oxidation stability of **base** stocks in the presence of some synthesized Benzothiazoles derivatives, 2- (benzothiazol-2-ylthio)-N-butylacetamide (Ia), 2-(benzo-thiazol-2-ylthio)-N-octyl-acetamide (Ib) and 2- (benzothiazol-2-ylthio)-N-dodecylaceta-mide(Ic), as oxidation inhibitors has been studied. The structures of these prepared compounds are elucidated by the common tools of analysis, Elemental analysis, I.R. and 1 H-NMR spectroscopy. The oxidation reaction of these compounds with one of the **base** stocks that used in the formulation of the local lubricating oil was investigated, using the change in Total Acid Number (TAN), Viscosity, and Infra- Red (IR) spectroscopy. The data obtained, reveals that these prepared compounds gave good results. The efficiency order is shown as follows Ib and Ic > Ia.

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A fascinating point to note here is that apart from the different contexts in which optimality of a **policy** has been seen by various studies, it is also interesting to recognize that for the same context, the parameter of optimality has been different. Ferrero (2009) showed that **optimal** monetary **policy** should be flexible inflation targeting, while taking an opposite line, Nakov and Thomas (2011) ar- gued that **optimal** monetary **policy** should only be strict inflation targeting. Hence, in these two ex- amples, there is a difference of opinion on the optimality of monetary **policy** for achieving the same objective, i.e. price stability. One reason for this difference could be the constraints which should also be satisfied. In this study, we are analysing the optimality of macroeconomic policies in the context of financial stability. There is very few, yet sufficient evidence to support the importance of analysing optimality of **policy** combination for financial stability. For example, a recent study by Benigno et al. (2012) showed that **optimal** fiscal **policy** (taxes) is effective in restoring financial stability. This study used capital flows as the measure of financial stability. However, this study measures financial sta- bility using **stock** and bond markets. In this regard, this is associated with Kontonikas and Montagnoli (2006) who argued that **optimal** monetary **policy** should positively affect **stock** market and house prices due to the wealth effects of these assets. In other words, this study considers a macroeco- nomic **policy** combination as **optimal** which positively influences our objective function, e.g. **stock** prices without negatively affecting the bond market (constraint) and vice versa. The **optimal** **policy** combination for financial stability is to some degree unique as mostly **optimal** **policy** has been seen as a single **policy** in context of the real economy. The difference of this study from any other is to take it further by taking fiscal **policy** and bond markets on board. Furthermore, this study also tests the optimality of our **policy** mix in various contexts (discussion on **policy** combinations and state dependencies in separate section) as a robustness measure.

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Abstract: In a recent paper, Soni and Shah [Soni, H., Shah, N. H., 2008. **Optimal** ordering **policy** for **stock**-dependent demand under progressive payment scheme. European Journal of Operational Research 184, 91-100] developed a model to find the **optimal** ordering **policy** for a retailer with **stock**-dependent demand and a supplier that offers a progressive payment scheme to the retailer. This note corrects some errors in the formulation of the model of Soni and Shah. It also extends their work by assuming that the credit interest rate of the retailer may exceed the interest rate charged by the supplier. Numerical examples illustrate the benefits of these modifications.

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The move from EU to EMU thus has various, and potentially opposing, consequences for the extent of domestic **policy** failure and thus for macroeconomic stability and intergenerational redistribution. The net effects are unclear from a theoretical point of view. Nor is the empirical evidence conclusive. Fat´as and Mihov (2003) report signs of a “fatigue” in fiscal consolidation efforts after the introduction of the common monetary **policy** in 1999. But whether this fatigue, reflected in laxer fiscal policies, is related to changed strategic incentives or rather represents a reaction to the preceding exceptional efforts to qualify for EMU membership, remains unclear. Summary How important are these potential problems in EMU? The prevalence and impor- tance of domestic **policy** failure is widely acknowledged. In contrast, there is less consensus on the importance of international repercussions of fiscal policies, although it seems clear that the move from EU to EMU most likely rendered these effects quantitatively more important. The existence, and strength of these direct spillover effects is also crucial for the importance of spillover effects transmitted by fiscal **policy** responses. In contrast, it is not crucial for the importance of spillover effects transmitted by monetary **policy** responses. These effects already arise if the arguments of the ECB’s objective function, e.g. average inflation in the EMU area, are affected by fiscal **policy** choices. Clearly, an assessment of the importance of spillover effects transmitted via monetary **policy** responses depends on one’s view about the ECB’s **policy** strat- egy, in particular whether inflation is the ECB’s sole target variable, and whether the ECB is fully committed. As emphasized, in our view, the ECB can neither commit, nor is it perfectly insulated against political pressures to pursue objectives other than inflation targeting. To the extent that fiscal **policy** makers exploit these features of central bank behavior, an inflationary bias or a dynamic common-pool problem might arise. Under the alternative assumption that the ECB can actually commit, and is only concerned about inflation, such an inflationary bias or dynamic common-pool problems cannot arise.

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decision is to enforce the credit constraint. Since the volume of loans o¤ered by the lender is proportional to capital **stock**, the smaller the current **stock** the smaller will be the available credit. In this way the maximizing behavior of the RZ …rm can initiate a vicious circle. During a phase of economic recession the …rm reduces its capital endowment. This hurts the …rm in the next period because it owns less collateralizable assets. In the presence of credit rationing this reduces the demand for capital. From this point of view, credit rationing is caused not only by **optimal** decisions on the supply side ( Hodgman, (1960)), but also by forward-looking expectations on the demand side.

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3 The economic experience of the ASEAN-5 in the last 15 years provides an excellent testing ground for assessing the interaction of monetary **policy** shocks with the financial sector and subsequent effects on the real economy. ASEAN financial markets generally experience higher volatility than their OECD counterparts, and comparatively lower liquidity. During the float of the Thai bhat in July 1997, all of these markets experienced significant **stock** market falls, rapid withdrawal of funds by foreign investors and local currency depreciation. For Malaysia, Thailand, Indonesia and the Philippines substantial economic recession followed. The crisis was severe enough to significantly impact monetary **policy** mechanisms for many of these countries; Thailand moved from a fixed to floating exchange rate regime with inflation targeting, Malaysia reverted to a fixed exchange rate regime, Indonesia removed its managed float and adopted inflation targeting, and the Philippines removed its remaining few impediments to a freely floating exchange rate regime but retained its combined monetary growth/inflation targeting monetary **policy** stance, moving to inflation targeting in 2002. Singapore, the most developed and least affected of the ASEAN- 5 markets, retained its managed currency throughout. In the 21st century the relatively high growth and high interest rate environments of these economies has again attracted capital inflow, excess liquidity, and a perceived higher risk of emerging price bubbles (Shimada and Yang, 2010; Hong and Tang, 2010).

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processes. Given a pixel group of n pixels and the desired embedding bits k, the first process determines an **optimal** **base** (OB) which provides minimal pixel distortion for message concealment. The second process adopts the aggressive bit encoding and decomposition (ABED) scheme to produce n secret digits. The third process embeds these n secret digits into a pixel group of n pixels producing a stego HDR image. An aggressive bit encoding and decomposition scheme (ABED) is proposed,

800 In real scenarios however, those factors acting as attrac- 801 tors for users tend also to inﬂuence **base** station locations, 802 so that actual **base** stations tend to cluster where users 803 cluster, typically to supply capacity in periods of peak traf- 804 ﬁc around places such as tall buildings, stadiums, etc. In 805 order to characterize the impact of the correlation between 806 user locations and **base** station locations, we have run 807 numerical evaluations assuming **base** stations to be dis- 808 tributed according to a Matern clustered point process. 809 For these evaluations, for BS we have assumed the same 810 parent nodes and cluster regions as the user point process. 811 In Fig. 10 the line with square markers is the energy opti- 812 mal BS density for cluster regions of 2500 m 2 . We see that 813 when the attractors for users are also attractors for **base** 814 stations locations, the energy **optimal** **base** station density 815 is very close to the **optimal** density for the case of uniform 816 user and BS distribution, for the same value of mean user 817 density. These results suggest that the estimations of the 818 energy **optimal** **base** station densities and of the potential 819 energy savings derived with our analysis are valid also 820 for more realistic scenarios, where both users and **base** sta- 821 tions distributions are non uniform, and clustered around 822 the same attractors.

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An enormous work has been done in the field of trade-credit. Many previous economic order quantity inventory models are developed with trade-credit, a very few production inventory models are developed under allowable delay in payment. In addition, the inventory models for perishable items with imperfect production, **stock** dependent demand under trade-credit in which production rate depends on demand factor are much rare. Therefore, the present model is developed with these unique features. This model is an extension of the model Sarkar (2012) by considering deterioration and demand dependent production. The most favorable solution of the proposed model not only exists but also is unique. To obtain the **optimal** solution some lemmas are provided and with the help of sensitivity analysis, the effect of change in the parameters on the **optimal** **policy** is also disclosed.

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Monetary systems and policies receive little attention when economies are performing well. Until recently, there was not much interest in Japanese monetary **policy**. Through most of the postwar period, Japanese economic performance was strong. Low inflation with high and relatively steady output growth won the Bank of Japan (BOJ) plaudits from all quarters. Keynesians praised the Bank for following Keynesian policies while Milton Friedman characterized BOJ policymakers as “closet monetarists.” Not many economists outside of Japan were very interested in the actual workings of Japanese monetary **policy**. Most economists simply assumed—and a few even set out to prove—that Japan’s monetary system was built on a strong institutional platform. For most, it was enough to know that monetary **policy** worked. If economists had bothered to look deeper, perhaps they would have wondered how it could have worked so well.

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The licensing of a patented technology is one of the most important sources of revenue for many innovators, particularly, when they do not participate in the production in the final market. A licensing contract typically includes a royalty payment that comprises two components: a royalty rate and a royalty **base**. Most attention in the economic literature has been devoted to the **optimal** determination of the royalty rate. Much less work has been done in studying the scope of the royalty **base**. This scope can be determined in two principal ways. One option is the value of the components of the infringing product that incorporate the patented technology. This is the so-called apportionment rule. Alternatively, the scope of the royalty **base** can be given by the value of the sales of the entire product – the entire market value rule. These two rules give raise to the usage of per-unit royalty rates (a constant payment based on the units sold) and ad-valorem royalty rates (a payment comprising a percentage of the value of the sales of the product), respectively.

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