Introduction: Dietary protein comes from foods with greatly different compositions that may not relate equally with mortality risk. Few cohort studies from non-Western countries have examined the association between various dietary protein sources and cause-specific mortality. Therefore, the associations between dietary protein sources and all-cause, cardiovascular disease, and cancer mortality were evaluated in the Golestan Cohort Study in Iran. Methods: Among 42,403 men and women who completed a dietary questionnaire at baseline, 3,291 deaths were documented during 11 years of follow up (2004-2015). Cox proportional hazards models estimated age-adjusted and multivariate-adjusted hazard ratios (HRs) and 95% CIs for all cause and disease-specific mortality in relation to dietary protein sources. Data were analyzed from 2015 to 2016. Results: Comparing the highest versus the lowest quartile, egg consumption was associated with lower all-cause mortality risk (HR=0.88, 95% CI=0.79, 0.97, ptrend=0.03). In multivariate analysis, the highest versus the lowest quartile of fish consumption was associated with reduced risk of total cancer (HR=0.79, 95% CI=0.64, 0.98, ptrend=0.03) and gastrointestinal cancer (HR=0.75, 95% CI=0.56, 1.00, ptrend=0.02) mortality. The highest versus the lowest quintile of legume consumption was associated with reduced total cancer (HR=0.72, 95% CI=0.58, 0.89, ptrend=0.004), gastrointestinal cancer (HR=0.76, 95% CI=0.58, 1.01, ptrend=0.05), and other cancer (HR=0.66, 95% CI=0.47, 0.93, ptrend=0.04) mortality. Significant associations between total red meat and poultry intake and allcause, cardiovascular disease, or cancer mortality rate were not observed among all participants. Conclusions: These findings support an association of higher fish and legume consumption with lower cancer mortality, and higher egg consumption with lower all-cause mortality. (C) 2016 American Journal of Preventive Medicine. Published by Elsevier Inc. All rights reserved.

The continuous-review (r,Q) inventory model with lost sales and stochastic lead-time is considered. It is assumed that Qr, so that at most a single order may be outstanding at any time. This model is much treated in the literature, beginning with Hadley and Whitin (1963) and there are many heuristics, but no simple exact algorithm. We derive the model for both continuous and discrete (Poisson) demand and stochastic lead-time, and devise a simple iterative algorithm that is certain to locate the global minimum if the lead-time demand distribution function is log-concave. It iterates between a square-root formula for Q and a simple equation for r. The algorithm is applicable to discrete demand when amended by a final comparison between two adjacent policies. We finally show that the model is applicable without the constraint Qr, but then lead-time demand is a function of r and Q, the investigation of which is left to future research.

The probability distribution of customer waiting times due to stock-outs and backlogging is studied, including mean and variance, when demand follows a compound Poisson process and the inventory is governed by an (nQ,R) inventory policy under continuous review. Existing results are reviewed and new exact contributions are presented, particularly covering the case when R<–1, a case that quite often may be optimal for central warehouses, but is missing in the literature. Waiting times are investigated for two cases: For an average unit of demand, assuming partial deliveries, and for a customer demanding

d units, assuming full deliveries only. Here d may be interpreted as the constant order size from a specific customer/retailer. The results are easily generalized to the waiting time of an average customer. Besides exact formulae, various approximations and simple heuristics are suggested for calculation of means and variances. The results should be valuable for approximately optimal inventory control in distribution

This paper investigates the delay experienced by retailers in a distribution system due to shortages at the central warehouse. Simple formulae are developed to estimate the mean and variance of this delay. The formulae are based on replacing the stochastic lead-time demand with a stochastic demand rate, and they differ in how this demand rate is estimated. An extensive numerical study shows improved accuracy compared to existing methods with similar computational complexity. The numerical study also shows that the batch quantities and the service level have a large influence on the delay. Both the mean and variance of a retailer’s delay decrease with the service level and increase with the batch quantities used at the warehouse and at the retailer. No other variables seem to have a significant impact on the delay.

The discounted continuous-review (R,Q) inventory model with continuous and stochastic demand is investigated.  New optimality conditions are derived, clarifying the difference to the average cost case, also graphically. Supported by depreciation theory, applied to the value of a setup, the results suggest an insightful and very precise approximation – The Shrewd Accountant’s Heuristic – based on a new average-cost model. It deepens and extends the work of Hadley (1964). Three examples are worked out in detail and the model is generalized to Poisson demand and to stochastic lead-times.

Customer waiting time is a critical variable in heuristic modelling of multi-echelon inventory systems. It is not sufficiently investigated in the literature, which is large.

The paper reviews and comments the literature and extends it by investigating customer waiting times in (nQ,R) inventory systems with continuous review and compound Poisson demand and with R+1<0 allowed. Two basic cases are considered: the waiting time for an average unit of demand assuming partial deliveries, and the waiting time for a customer demanding d units when only full deliveries are allowed.

The probability distributions are characterized and exact and approximate formulae are derived for means and variances. There are some computational results of various heuristics for the mean and variance of waiting time in each of the cases.

It is well known that longer and more uncertain lead-times in a distribution system increase the need for safety stock and/or reduce the service level at lower levels. It is also well known that ordering decisions at higher level of the supply chain have an impact on the lead-time. Yet not much research has been devoted to increasing the knowledge of how exactly these decisions do influence the lead-time and there is a lack of simple methods to estimate the expected value and variance of the lead-time. Recent research that strongly indicates that it is optimal to provide a low service level at the earlier stages only emphasizes the importance of shedding a light on this issue. This as lower service levels leads to prolonged and more frequent stock outs and hence longer and more uncertain lead-time

In this paper we provide a large simulation study of a two-level distribution system where different decision parameters as well as external parameters influence the lead-time are investigated. Not surprisingly, the study shows that the service level at a higher, not surprisingly, has a positive effect on both the length and variability of the lead time, i.e. they decrease with an increasing service-level. More interestingly though, is that of the other parameters it is only the order quantities that has a significant impact on the lead-time. Both the expected value and variance of the lead-time increase with the retailer’s as well as the central warehouse’s order quantity. This can be describe as an inverted bullwhip effect as the lead-time variability increase as one moves down the supply chain towards the end customer.

In the paper we also develop simple methods to estimate the mean value and variance of the lead-time. The methods are based on replacing a stochastic lead-time demand at the central warehouse with a stochastic demand rate. For a given inventory position and demand rate it is shown how to compute the delay at the central warehouse due to stock-outs in a straight forward manner. These delays are then weighted together based on the probability for each combination of inventory position and demand rate to attain the estimates. The difference between the developed methods lay in how the stochastic demand rate is estimated. The above mentioned simulation study shows that the estimates exhibit a good accuracy and constitutes an improvement compared to existing methods with similar computational complexity.

The discounted continuous-review (R,Q) inventory model with continuous and stochastic demand is investigated, generalizing and refining Hadley's (1964) work. A new optimality condition is derived, clarifying the difference to the average cost case. Based on depreciation theory, applied to the value of a set-up,a very easy and extremly precise approximation is suggested, based on the average cost model- The Shrewd Accountant's Heuristic. A few examples are worked out in detail.