The bullwhip effect under count time series: The case of first order integer auto-regressive demand processes

This is the final version. Available from the IEOM Society via the link in this recordThe impact of fast moving items, modeled by auto-regressive moving average (ARMA) type processes, on the bullwhip effect is well known. However, slow moving items that can be modeled using integer ARMA processes have received little attention. Herein, we measure the impact of bullwhip effect under a first order integer auto-regressive, INAR(1), demand process. We consider a simple two-stage supply chain consisting of a retailer and a manufacturer. We assume that the retailer employs a base stock inventory policy when the demand is forecasted using a minimum mean squared error method. We investigate the impact of the INAR(1) demand process parameter, α, and the replenishment lead time, L, on the bullwhip effect generated by the order-up-to replenishment policy. We show that the bullwhip effect is increasing with the lead-time L

On the order-up-to policy with intermittent integer demand and coherent forecasts

This is the author accepted manuscript.We measure the impact of a first-order integer auto-regressive, INAR(1), demand process on order-up-to (OUT) replenishment policy dynamics. We obtain a unique understanding of the bullwhip behavior for slow-moving integer demand. We forecast this integer demand in two ways; with a conditional mean and a conditional median. We investigate the impact of the two forecasting methods on the bullwhip effect and inventory variance generated by the OUT replenishment policy. While the conditional mean forecasts result in the tightest inventory control, they result in real-valued orders and inventory levels which is incoherent with the integer demand. However, the conditional median forecasts are integer-valued and produce coherent integer order and inventory levels. The conditional median forecasts minimize the expected absolute forecasting error, but it is not possible to obtain closed forms for the variances. Numerical experiments reveal existing results remain valid with high volume correlated demand. However, for low volume demand, the impact of the integer demand on the bullwhip effect is often significant. Conditional median bullwhip can be both lower and higher than the conditional mean bullwhip; indeed it can even be higher than a known conditional mean upper bound (that is valid for all lead times under real-valued, first-order autoregressive, AR(1), demand), depending on the auto-regressive parameter. Numerical experiments confirm the conditional mean inventory variance is a lower bound for the conditional median inventory variance

Forecasting: theory and practice

Forecasting has always been in the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The lack of a free-lunch theorem implies the need for a diverse set of forecasting methods to tackle an array of applications. This unique article provides a non-systematic review of the theory and the practice of forecasting. We offer a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts, including operations, economics, finance, energy, environment, and social good. We do not claim that this review is an exhaustive list of methods and applications. The list was compiled based on the expertise and interests of the authors. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of the forecasting theory and practice

Forecasting: theory and practice

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases

Population and fertility by age and sex for 195 countries and territories, 1950–2017: a systematic analysis for the Global Burden of Disease Study 2017

Background: Population estimates underpin demographic and epidemiological research and are used to track progress on numerous international indicators of health and development. To date, internationally available estimates of population and fertility, although useful, have not been produced with transparent and replicable methods and do not use standardised estimates of mortality. We present single-calendar year and single-year of age estimates of fertility and population by sex with standardised and replicable methods. Methods: We estimated population in 195 locations by single year of age and single calendar year from 1950 to 2017 with standardised and replicable methods. We based the estimates on the demographic balancing equation, with inputs of fertility, mortality, population, and migration data. Fertility data came from 7817 location-years of vital registration data, 429 surveys reporting complete birth histories, and 977 surveys and censuses reporting summary birth histories. We estimated age-specific fertility rates (ASFRs; the annual number of livebirths to women of a specified age group per 1000 women in that age group) by use of spatiotemporal Gaussian process regression and used the ASFRs to estimate total fertility rates (TFRs; the average number of children a woman would bear if she survived through the end of the reproductive age span [age 10–54 years] and experienced at each age a particular set of ASFRs observed in the year of interest). Because of sparse data, fertility at ages 10–14 years and 50–54 years was estimated from data on fertility in women aged 15–19 years and 45–49 years, through use of linear regression. Age-specific mortality data came from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 estimates. Data on population came from 1257 censuses and 761 population registry location-years and were adjusted for underenumeration and age misreporting with standard demographic methods. Migration was estimated with the GBD Bayesian demographic balancing model, after incorporating information about refugee migration into the model prior. Final population estimates used the cohort-component method of population projection, with inputs of fertility, mortality, and migration data. Population uncertainty was estimated by use of out-of-sample predictive validity testing. With these data, we estimated the trends in population by age and sex and in fertility by age between 1950 and 2017 in 195 countries and territories. Findings: From 1950 to 2017, TFRs decreased by 49\ub74% (95% uncertainty interval [UI] 46\ub74–52\ub70). The TFR decreased from 4\ub77 livebirths (4\ub75–4\ub79) to 2\ub74 livebirths (2\ub72–2\ub75), and the ASFR of mothers aged 10–19 years decreased from 37 livebirths (34–40) to 22 livebirths (19–24) per 1000 women. Despite reductions in the TFR, the global population has been increasing by an average of 83\ub78 million people per year since 1985. The global population increased by 197\ub72% (193\ub73–200\ub78) since 1950, from 2\ub76 billion (2\ub75–2\ub76) to 7\ub76 billion (7\ub74–7\ub79) people in 2017; much of this increase was in the proportion of the global population in south Asia and sub-Saharan Africa. The global annual rate of population growth increased between 1950 and 1964, when it peaked at 2\ub70%; this rate then remained nearly constant until 1970 and then decreased to 1\ub71% in 2017. Population growth rates in the southeast Asia, east Asia, and Oceania GBD super-region decreased from 2\ub75% in 1963 to 0\ub77% in 2017, whereas in sub-Saharan Africa, population growth rates were almost at the highest reported levels ever in 2017, when they were at 2\ub77%. The global average age increased from 26\ub76 years in 1950 to 32\ub71 years in 2017, and the proportion of the population that is of working age (age 15–64 years) increased from 59\ub79% to 65\ub73%. At the national level, the TFR decreased in all countries and territories between 1950 and 2017; in 2017, TFRs ranged from a low of 1\ub70 livebirths (95% UI 0\ub79–1\ub72) in Cyprus to a high of 7\ub71 livebirths (6\ub78–7\ub74) in Niger. The TFR under age 25 years (TFU25; number of livebirths expected by age 25 years for a hypothetical woman who survived the age group and was exposed to current ASFRs) in 2017 ranged from 0\ub708 livebirths (0\ub707–0\ub709) in South Korea to 2\ub74 livebirths (2\ub72–2\ub76) in Niger, and the TFR over age 30 years (TFO30; number of livebirths expected for a hypothetical woman ageing from 30 to 54 years who survived the age group and was exposed to current ASFRs) ranged from a low of 0\ub73 livebirths (0\ub73–0\ub74) in Puerto Rico to a high of 3\ub71 livebirths (3\ub70–3\ub72) in Niger. TFO30 was higher than TFU25 in 145 countries and territories in 2017. 33 countries had a negative population growth rate from 2010 to 2017, most of which were located in central, eastern, and western Europe, whereas population growth rates of more than 2\ub70% were seen in 33 of 46 countries in sub-Saharan Africa. In 2017, less than 65% of the national population was of working age in 12 of 34 high-income countries, and less than 50% of the national population was of working age in Mali, Chad, and Niger. Interpretation: Population trends create demographic dividends and headwinds (ie, economic benefits and detriments) that affect national economies and determine national planning needs. Although TFRs are decreasing, the global population continues to grow as mortality declines, with diverse patterns at the national level and across age groups. To our knowledge, this is the first study to provide transparent and replicable estimates of population and fertility, which can be used to inform decision making and to monitor progress. Funding: Bill & Melinda Gates Foundation

On the order-up-to policy with intermittent integer demand and logically consistent forecasts

This is the author accepted manuscript.We measure the impact of a first-order integer auto-regressive, INAR(1), demand process on order-up-to (OUT) replenishment policy dynamics. We obtain a unique understanding of the bullwhip behaviour for slow moving integer demand. We forecast the integer demand in two ways; with a conditional mean and a conditional median. We investigate the impact of the two forecasting methods on the bullwhip effect and inventory variance generated by the OUT replenishment policy. While the conditional mean forecasts result in the tightest inventory control, they result in real-valued orders and inventory levels which is inconsistent with the integer demand. However, the conditional median forecasts are integer-valued and produce logically consistent integer order and inventory levels. The conditional median forecasts minimise the expected absolute forecasting error, but it is not possible to obtain closed form variance expressions. Numerical experiments reveal existing results remain valid with high volume correlated demand. However, for low volume demand, the impact of the integer demand on the bullwhip effect is often significant. Bullwhip with conditional median forecasts can be both lower and higher than with conditional mean forecasts; indeed it can even be higher than a known conditional mean upper bound (that is valid for all lead times under real-valued, first-order auto-regressive, AR(1), demand), depending on the auto-regressive parameter. Numerical experiments confirm the conditional mean inventory variance is a lower bound for the conditional median inventory variance

Neural network approach to lumpy demand forecasting for spare parts in process industries

Accurate demand forecasting is one of the most crucial issues in inventory management of spare parts in process industries. The problem of modeling future consumption becomes especially difficult for lumpy patterns, which characterized by intervals in which there is no demand and, periods with actual demand occurrences with large variation in demand levels. However, many of these methods may perform poorly when demand for an item is lumpy. Furthermore, traditional time-series methods may not sometimes capture the nonlinear pattern in data. Artificial neural network modeling is a logical choice to overcome these limitations. In this study recurrent neural network has been used for lumpy demand forecasting of spare parts. In order to evaluate the performance of the proposed approach, their forecasts were compared to those obtained by using two conventional methods, namely, Crostonpsilas method and Syntetos & Boylan approximation, recently employed multi-layered perceptron neural network and generalized regression neural network in this area. The models were applied to forecast future demand of spare parts of Arak Petrochemical Company in Iran, using 30 types of real data sets. The results indicate that the forecasts obtained by using our proposed mode are superior to those obtained by using other methods

Demand forecasting in supply chains:a review of aggregation and hierarchical approaches

Demand forecasts are the basis of most decisions in supply chain management. The granularity of these decisions lead to different forecast requirements. For example, inventory replenishment decisions require forecasts at the individual SKU level over lead time, whereas forecasts at higher levels, over longer horizons, are required for supply chain strategic decisions. The most accurate forecasts are not always obtained from data at the 'natural' level of aggregation. In some cases, forecast accuracy may be improved by aggregating data or forecasts at lower levels, or disaggregating data or forecasts at higher levels, or by combining forecasts at multiple levels of aggregation. Temporal and cross-sectional aggregation approaches are well established in the literature. More recently, it has been argued that these two approaches do not make the fullest use of data available at the different hierarchical levels of the supply chain. Therefore, consideration of forecasting hierarchies (over time and other dimensions), and combinations of forecasts across hierarchical levels, have been recommended. This paper provides a comprehensive review of research dealing with aggregation and hierarchical forecasting in supply chains, based on a systematic search. The review enables the identification of major research gaps and the presentation of an agenda for further research