Effects of inflation and time value of money on an inventory system with deteriorating items and partially backlogged shortages

As the long arm of the grinding, deep financial crisis continues to haunt the global economy, the effects of inflation and time value of money cannot be oblivious to an inventory system. Inflation, defined as a general rise in the prices of goods and services over a period of time, has monetary depreciation as one of its major side effects. And, since inventories correspond to substantial investment in capital for any organization, it would be unethical if the effects of inflation and time value of money are not considered while determining the optimal inventory policy. Moreover, deterioration of items is a phenomenon which cannot be ignored, as it may yield misleading results. Further, under the inflationary conditions, the different cost parameters including the price are bound to vary from cycle to cycle over the planning horizon. Another important factor is shortages which no retailer would prefer, and in practice are partially backlogged and partially lost. In order to convert the lost sales into sales, the retailer offers such customers an incentive, by charging them the price prevailing at the time of placing an order, instead of the current inflated price. Therefore, bearing in mind these facts, the present paper develops an inventory model for a retailer dealing with deteriorating items under inflationary conditions over a fixed planning horizon. The objective is to derive the optimal number of cycles and cycle length that maximizes the net present value of the total profit over a fixed planning horizon. An appropriate algorithm has been proposed to obtain the optimal solution. Finally, a numerical example is provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some managerial inferences have been presented

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

Optimal inventory strategies for deteriorating items with price-sensitive investment in preservation technology

With recent developments in the technological world, the issue of deterioration has been addressed efficiently through preservation technology by numerous researchers. The fundamental concept of preservation technology involves an investment that is majorly dependent on the initial deterioration rate, irrespective of the selling price of the product. Owing to this, two different products having the same deterioration rate but different selling price requires equal investment, which is irrational. Further, the investment in preservation technology was considered to be per unit time irrespective of the number of units being held, which is again a major drawback of the existing literature. Thus, this paper attempts to bridge the gap by proposing a realistic way of implementing preservation technology, where not only the investment is per unit, but also depends on the selling price of that unit. The model jointly optimizes the selling price, the fraction of per unit profit to be invested in preservation technology, and cycle length to maximize the overall profit. The proposed model proves out to be economically more viable, through superior cost management, when compared with the existing model. The model is further illustrated with comparative numerical examples and graphical representations. Moreover, sensitivity analysis is performed to convey model characteristics

Economic order quantity model for deteriorating items with imperfect quality

En un modelo EOQ (tamaño económico del lote) es asumido tácitamente que el 100% de los ítems en un lote tiene una calidad perfecta. Esto es posible solo bajo situaciones muy ideales, pues prácticamente esta asunción debe ser no cierta. Entonces, la inspección del lote es indispensable en todas las organizaciones tanto públicas como privadas. Más aun, esto juega un rol muy significativo si los productos son deteriorables En este trabajo se ha hecho un intento de formular un modelo de inventario para ítems deteriorables con calidad imperfecta. La tasa de inspección se asume sea mayor que la demanda. Esta asunción ayuda a cumplimentar la demanda, fuera de los productos que fueron hallados con una calidad perfecta, junto con el proceso de valoración. Un ejemplo hipotético es considerado para validar el modelo y los resultados son obtenidos usando Matlab7.0.1. Un análisis comprensible de la sensibilidad es presentado también.In an EOQ model it is tacitly assumed that the 100% items in a lot are of perfect quality. This is possible only under very idealistic situation but practically this assumption may not be true. Thus, the inspection of lot becomes indispensable in all public and private sector organizations. Moreover, it plays a very significant role when the products are of deteriorating in nature. In this paper an attempt has been made to formulate an inventory model for deteriorating items with imperfect quality. The inspection/screening rate is assumed to be more than the demand. This assumption helps one to fulfill the demand, out of the products which are found to be of perfect quality, along with the screening process. A hypothetical example is considered to validate the model and results are obtained using Matlab7.0.1. Comprehensive sensitivity analysis has also been presented

Two echelon partial trade credit financing in a supply chain derived algebraically

Trade credit financing has become a powerful tool to improve sales & profit in an industry. In general, a supplier/retailer frequently offers trade credit to its credit risk downstream member in order to stimulate their respective sales. This trade credit may either be full or partial depending upon the past profile of the downstream member. Partial trade credit may be offered by the supplier/retailer to their credit risk downstream member who must pay a portion of the purchase amount at the time of placing an order and then receives a permissible delay on the rest of the outstanding amount to avoid non-payment risks. The present study investigates the retailer’s inventory problem under partial trade credit financing for two echelon supply chain where the supplier, as well as the retailer, offers partial trade credit to the subsequent downstream member. An algebraic approach has been applied for finding the retailer’s optimal ordering policy under minimizing the annual total relevant cost. Results have been validated with the help of examples followed by comprehensive sensitivity analysis

The relationship between nostalgia, social exclusion, and empathy

As a positive, social emotion, nostalgia has the potential to reduce the negative impact of social exclusion on empathy. I ran a series of experiments in order to establish the relationship between nostalgia, social exclusion, and empathy. In Studies 1 and 2, participants were instructed to recall either a nostalgic or ordinary autobiographical experience and then read an essay ostensibly written by another participant describing a physically painful ordeal. Afterwards, the participants were asked to report the level of empathy that they felt for the person who wrote the essay. Participants who had previously recalled a nostalgic event reported significantly higher levels of empathy than those who had recalled an ordinary event. In Studies 3 and 4, participants were given randomly assigned future alone, future belonging, or control feedback. Participants who were given future alone (compared to future belonging or control) feedback reported significantly higher levels of nostalgia. Study 5 examined nostalgia’s ability to directly counteract social threats. Individuals who were exposed to a future alone (compared to future belonging) feedback reported lower levels of empathy when they were instructed to recall an ordinary autobiographical experience. However, the future alone manipulation had no significant effect on empathy when participants recalled a nostalgic experience. The results suggest that nostalgia may function as an adaptive reaction to social exclusion, and can prevent people from becoming emotionally numb after being excludedEThOS - Electronic Theses Online ServiceGBUnited Kingdo

Effects of inflation and time value of money on an inventory system with deteriorating items and partially backlogged shortages

As the long arm of the grinding, deep financial crisis continues to haunt the global economy, the effects of inflation and time value of money cannot be oblivious to an inventory system. Inflation, defined as a general rise in the prices of goods and services over a period of time, has monetary depreciation as one of its major side effects. And, since inventories correspond to substantial investment in capital for any organization, it would be unethical if the effects of inflation and time value of money are not considered while determining the optimal inventory policy. Moreover, deterioration of items is a phenomenon which cannot be ignored, as it may yield misleading results. Further, under the inflationary conditions, the different cost parameters including the price are bound to vary from cycle to cycle over the planning horizon. Another important factor is shortages which no retailer would prefer, and in practice are partially backlogged and partially lost. In order to convert the lost sales into sales, the retailer offers such customers an incentive, by charging them the price prevailing at the time of placing an order, instead of the current inflated price. Therefore, bearing in mind these facts, the present paper develops an inventory model for a retailer dealing with deteriorating items under inflationary conditions over a fixed planning horizon. The objective is to derive the optimal number of cycles and cycle length that maximizes the net present value of the total profit over a fixed planning horizon. An appropriate algorithm has been proposed to obtain the optimal solution. Finally, a numerical example is provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some managerial inferences have been presented

Replenishment policy for non-instantaneous deteriorating items in a two storage facilities under inflationary conditions

The present study investigates an inventory model for non-instantaneous deteriorating items under inflationary conditions with partially backlogged shortages. In today’s market structure consumers are looking for goods for which there is a delay in deterioration. At the same time, the consumers’ willingness to wait has been decreased over time, which leads to lost sales. Moreover in financial decision-making, the effects of inflation and time value of money cannot be oblivious to an inventory system. In this scenario, managing inventory of goods remains a challenging task for the decision makers, who may also have to rent warehouse under different prevailing factors such as, bulk discount, limited space in the retail outlet, or increasing inflation rates. With a focus on reduction of costs and increasing customer service, warehouse decision models are crucial for an organization’s profitability. Hence a mathematical model has been developed in the view of above scenario, in order to determine the optimal policy for the decision maker, by minimizing the present worth of total cost. The optimization procedure has been illustrated by a numerical example and detailed sensitivity analysis of the optimal solution has been performed to showcase the effect of various parameters. Managerial implications has also been presented to aid the decision making process

Allocation game in a single period supply chain model

This paper considers a simple supply chain in which a single supplier sells to several downstream retailers and he may distinguish various retailers' demand by giving more importance to satisfying some categories of demand than others. The supplier has limited capacity. If the retailer orders exceed available capacity, the supplier allocates capacity using publicly known mechanism. After allocation if the supplier is left with inventory he can reallocate the demand. An algorithm has been developed for reallocation of demand using different allocation mechanism. It has been shown numerically, how reallocation mechanism can benefit the retailers as well as supplier causing higher supply chain profits. Further, we have tried to evaluate whether a retailer should use truth-inducing mechanism or he should use manipulable mechanism to increase his profit.Este trabajo considera una cadena simple de abastecimiento en la que un simple suministrador vende a varios intermediarios y puede distinguir varias de sus demandas dándole más importancia satisfaciendo algunas categorías de demanda que otras. El suministrador posee limitada capacidad.. Si las ordenes del intermediario exceden la capacidad disponible, el suministrador sitúa capacidades usando un mecanismo públicamente conocido. Después del suministro si el suministrador tiene sobrantes el re ubica la demanda. Un algoritmo ha sido desarrollado para reubicar la demanda usando diferentes mecanismos de reubicación. SE prueba numéricamente, como el mecanismo de reubicación puede beneficiar al intermediario incrementando sus ganancias.. Además, nosotros tratamos de evaluar si el intermediario debe usar un mecanismo que induzca lo verdadero o uno manipulable para incrementar sus ganancias