A Fuzzy Inventory System with Deteriorating Items under Supplier Credits Linked to Ordering Quantity

Fuzzy set theory has a remarkable progress in the field of research. It initiates many areas in both practical & theoretical studies. It is really useful for several people engaged in research and development including medical researchers, mathematician, businessman, social scientists, natural researchers etc. This field of mathematics has introduced new life into technical and scientific fields that have been undeveloped for a long period. Thousands of scholars are operating and working with fuzzy set theory and presented a lot of research papers. In this paper latest review of existing literature & numerous types of fuzzy EOQ inventory models under shortage situation. It assists to categorize how the concept of fuzzy sets theory has been applied in inventory models which motivate researchers to concentrating on new technique in study of inventory control models in fuzzy environment. In this review, we study desirable constraints of existing models in fuzzy environment under shortage of supplies. A lot of effort is attempted to deliver the latest review of existing literature of inventory and fuzzy models. The purpose of the work is to obtain a continuous and comprehensive assessment of existing literature and recognize upcoming research guidelines. This review helps other researchers to draft an outcome during the situation of short supplies. This will also help to manage inventory according to the situation & reduce the loss during shortage of supplies, this review also helps to reduce loss with proper inventory management in real-life applications and marketable products.

Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number

In many inventory models uncertainty is due to fuzziness and fuzziness is the closed possible approach to reality. In this paper, we proposed a fuzzy inventory model with acceptable shortage which is completely backlogged. We fuzzily the carrying cost, backorder cost and ordering cost using Triangular and Trapezoidal fuzzy numbers to obtain the fuzzy total cost. The purpose of our study is to defuzzify the total profit function by Graded Mean Integration Value Method. Further a numerical example is also given to demonstrate the developed crisp and fuzzy models.

The present paper proposes a fuzzy economic order quantity (EOQ) model for deteriorating items with stock dependent demand rate where shortages are not allowed. The cycle time is divided into two parts. The first interval demand is considered as stock dependent and the second part is assumed to be constant. We first develop a crisp model. Since most of the parameters of the inventory model are uncertain, we consider the demand, holding cost, deterioration cost and deterioration rate as triangular fuzzy numbers. Graded mean representation, signed distance method and centroid method are used to defuzzify the total cost function. The results obtained by these methods are compared with the help of a numerical example. Sensitivity analysis is also carried out to explore the effect of changes in the values of the system parameters.

In the present paper fundamental changes in monetary policy strategy, especially in leading industrialized countries, from concentrating on development of the quantity of money to focusing strictly on developments of interest rates and interest rate levels is analysed in the case of the European Central Bank. The goal of research is to show that this change in monetary policy is one important reason for expansions of the European debt crisis since 2010. Within this new monetary policy regime, interest rate levels on the one hand and the transmission of interest rate policy measures to the interest rates of the other financial markets on the other hand, have become a very important role in central banking policies of today. For example to guarantee a sure and strict transmission of interest rate policy measures, which have its starting point on the short-term money market, and which should radiate to long-term interest rates on the capital market the ECB, if necessary, uses outright monetary transactions in secondary markets for sovereign bonds in the euro area. The main reason for acting in that manner is to avoid rising of long-term interest rates and to guarantee low levels of interest rate in the sovereign bonds markets. It is argued in the present paper that in focusing to guarantee low interest rate levels especially to overcome economic crisis you can find one important reason for expansions of the European debt crisis. This is so, because in view of current European economic policy rising interest rates in the European bonds markets above a level of 6 or 7 percent have become an unmistakeable proof of a severe debt problem.

A systematic approach is required to analyze present worth by incorporating annual interest rate fluctuations. This is a key factor in attracting local and foreign investors and maintaining a level of economic advancement. This study primarily focuses on the domain of the State Bank of Pakistan (SBP) and contributes towards achieving three major objectives. The first objective includes modeling interest rate values as triangular fuzzy numbers, and using the Analytic Hierarchy Process (AHP), a Multi-criteria Decision-Making technique (MCDM). Second, the triangular fuzzy interest rates are forecasted over a future timespan. Subsequently, the last objective includes the use of the Present Worth Analysis (PWA) to calculate the final net present value. The results demonstrate a trend in interest rates with net present values of specific future years. This research is a good initiative for the SBP and helpful for both foreign and local investors. The study is novel in that it involves the merging of qualitative and quantitative data. Furthermore, the combination of the forecasting technique, the AHP, fuzzy set theory, and present worth criteria renders a unique approach to formulating present worth. There is no previous research of this magnitude that has been conducted on this topic in a developing country such as Pakistan. This study delves into the annual interest rate fluctuations, providing valuable insights for present worth calculations.

The target of monetary policy is generally set as to create an environment of manageable employment and affordable long-term interest rates. However, priorities of central banks may differ depending on economic and financial circumstances of individual countries. Modern approaches to monetary policy transmission can be grouped under two headings, Money View and Credit View. The money view concentrates on interest rates to explain the effects of monetary policy on aggregate spending by creating an interest rate channel. The credit channel transmission approach focuses on the supply of credits by banks following a monetary policy shift in interest rates. In 2010, the Central Bank of Turkey (CBT) developed an interest rate corridor shaped by one-week and overnight repo lending to the financial banks to absorb excessive volatility caused by short-term capital inflows. Under this framework, the CBT implements its monetary policy in two ways; firstly it can alter the interest rates of weekly repo as well as O/N lending rate. Secondly, it can configure the funding structure it provides to the financial intermediaries. In such a framework, the interest rate transmission mechanism has been operated by two benchmark interest rates, one of which is the weighted average of the cost of funds provided by the CBT and the other is the interest rate in Borsa Istanbul (BIST) money market transactions at an overnight maturity. There is a strong co-movement between the interest rates and they are affected by the movements in the CBT lending rate in both directions. Interest rates applied to deposits and loans by banks are affected by the policy rate (CBT Average Funding Rate) and the market rate (BIST O/N Repo Rate).

INTERRELATIONSHIP OF INFLATION, EXCHANGE RATE AND INTEREST RATES IN THE CONTEXT OF HUNGARY'S STRATEGIC POLICY

The paper examined the interest rate operations and processes in Nigeria and examined the role of financial development in incentivizing central bank monetary policies from the monetary policy rate to the money market rates, lending rates, and deposit rates. The analysis covered the period from 1981 to 2021 with sub-samples for 1981 to 2011 and 1991 to 2021 to test the consistency of the findings. The findings confirmed that interest rate pass-through is incomplete for Nigeria, albeit to a lower degree in the short run compared to the long run. The reasons for this may be due to interest rate stickiness, problems of asymmetric information, and bank switching costs. Also, the findings confirmed that financial development weakens the impact of monetary policy on the interest rate pass-through process, while the analysis of the asymmetric mean adjustment lags confirmed that changes in the policy rate are transmitted to the deposit and lending rates within the year it was announced. The analysis confirmed that the results across each sub-sample and the robustness tests are consistent with the main analysis. Therefore, it is imperative that policymakers should account for financial development when designing monetary policy effectiveness since it can hinder or strengthen the interest rate monetary policy channel.

In this study, the author focuses on modeling and optimizing a freight routing problem in a road-rail intermodal transportation network that combines the hub-and-spoke and point-to-point structures. The operations of road transportation are time flexible, while rail transportation has fixed departure times. The reliability of the routing is improved by modeling the uncertainty of the road-rail intermodal transportation network. Parameters that are influenced by the real-time status of the network, including capacities, travel times, loading and unloading times, and container trains’ fixed departure times, are considered uncertain in the routing decision-making. Based on fuzzy set theory, triangular fuzzy numbers are employed to formulate the uncertain parameters as well as resulting uncertain variables. Green routing is also discussed by treating the minimization of carbon dioxide emissions as an objective. First of all, a multiobjective fuzzy mixed integer nonlinear programming model is established for the specific reliable and green routing problem. Then, defuzzification, linearization, and weighted sum method are implemented to present a crisp linear model whose global optimum solutions can be effectively obtained by the exact solution algorithm run by mathematical programming software. Finally, a numerical case is given to demonstrate how the proposed methods work. In the case, sensitivity analysis is adopted to reveal the effects of uncertainty on the routing optimization. Fuzzy simulation is then performed to help decision makers to select the best crisp route plan by determining the best confidence level shown in the fuzzy chance constraints.

Decision-making in contemporary inventory systems frequently faces uncertainties in parameters such as demand rate, deterioration, and cost. Conventional deterministic models are inadequate in addressing such imprecision. This study develops a triangular fuzzy inventory model for deteriorating products with time and quality reliant demand under complete backlogging, considering triangular fuzzy number with an analytical optimization approach for deriving the optimal solution. The model assumes that demand varies with both time and product quality, which is influenced by deterioration, while holding cost, deterioration rate, and demand parameters are represented as triangular fuzzy numbers. The primary objective is to minimize the total inventory cost per unit time, comprising ordering, holding, deterioration, and shortage costs. The analytical optimization method, employing the Signed Distance Method (SDM), is used to defuzzify the total cost and determine the optimal cycle time and ordering quantity. A detailed numerical illustration and sensitivity analysis validate the model’s effectiveness. The results show that the fuzzy-analytical optimization framework outperforms the crisp environment by yielding more robust and adaptive decisions in uncertain conditions.

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

The global Economic meltdown has effect on all the countries in the world. The Indian economy is also not exception to this situation because world economy cannot perform in seclusion in today's faster growing world. All the economies are interlinked to each other and any major ebb and flow in economic conditions causes numerous impacts for all other economies. The global economic crisis started with Subprime disaster in the US. Many strong economies are suffering from the crisis of credit and liquidity due to the interconnectedness of each other in international trade relations. This situation has the negative impacts on GDP, Employment, exports, FDI and economic development of the nation. Government and Policy makers are always taking precautionary measures for maintaining the economic stability and corrective actions in inflationary and recession situations. The striking balance of Monetary and Fiscal policies may help to overcome the situation to some extent. Monetary and Fiscal policies can be framed and implemented according to the economic situations. Central Banks of countries can influence the economy through the use of monetary policy by controlling the monetary variables such as rate of interest, the money supply and the volume of credit. The fiscal policy can be used to help on economy out of recession or reduce demand pressures in a boom. Monetary and fiscal policies are complementary to each other. Monetary policy influences the level of aggregate income and spending in the economy by influencing the money supply and cost of borrowing. Fiscal policy affects income and spending through its effects on size, composition and timing of government revenue and spending. These two policies can play the role in a perfect balancing for promotion of inclusive growth. This paper will focus on the important and balanced role of monetary and fiscal policy in economy with reference to the current scenario in Indian Economy.

In this chapter, a fuzzy inventory model for deteriorating items with shortages under fully backlogged condition is formulated by utilizing uncertain, vague and imprecise data. Fuzzy set theory has been used for handling the uncertainty in the data and hence the corresponding inventory parameters are assumed to be triangular fuzzy numbers. The main purpose of this work is to find out the quantity lot size (Q) and reorder point (R) level, which minimize the total annual inventory cost function in fuzzy environment. During the formulation of the model, the lead time is considered to be zero and the reorder level follows the different types of distribution namely uniform, exponential and Laplace distribution. Graded mean representation is used to defuzzify the total cost function and results obtained by these methods are compared with the crisp and the numerical results. A numerical example is given in order to show the applicability of the proposed model for different values of defective rate \( \left( \theta \right) \) and the backorder ratio \( \left( \beta \right) \). Finally, sensitivity analysis is carried out to explore the effect of changes in the values of some of the system parameters.KeywordsFuzzy setsInventory modelsLead timeProbability

Cet article examine l’art du central banking de la BCE en reprenant la distinction proposée par Goodfriend [2009] entre les trois politiques qui sont du ressort d’une banque centrale : la politique monétaire qui consiste à faire varier la taille de son bilan ; la politique du crédit qui consiste à en modifier la structure et la politique de taux d’intérêt qui consiste à modifier les taux sur la facilité de prêt marginal et sur la facilité de dépôt. La « littérature » théorique souligne l’existence d’un principe de séparation entre la première, orientée vers la stabilité monétaire, et les deux autres politiques, orientées vers la stabilité financière identifiée au bon fonctionnement du marché monétaire interbancaire ; elle montre en particulier qu’une banque centrale non seulement a la possibilité mais doit s’efforcer de séparer la conduite de sa politique monétaire, qui doit être fondée sur la recherche de la stabilité des prix à moyen et long terme, de sa politique du crédit, qui obéit à des impératifs de court terme et consiste à approvisionner le système bancaire en liquidité en cas de chocs transitoires sur la demande de monnaie. Le principe de séparation, qui a guidé l’action de la BCE durant la première phase de la crise, est devenu de plus en plus difficile à maintenir quand les taux d’intérêt se sont rapprochés de zéro. Les mesures non conventionnelles adoptées par la BCE ont en effet créé une interférence entre sa politique monétaire, sa politique du crédit et sa politique de taux d’intérêt.