Economic losses are incurred by the US livestock industries because farm animals are raised in locations and seasons where effective temperature conditions venture outside their zone of thermal comfort. The objective of this review was to estimate economic losses sustained by major US livestock industries from heat stress. Animal classes considered were: dairy cows, dairy heifers (0 to 1 yr and 1 to 2 yr), beef cows, finishing cattle, sows, market hogs, broilers, layers, and turkeys. Economic losses considered were: 1) decreased performance (feed intake, growth, milk, eggs), 2) increased mortality, and 3) decreased reproduction. USDA and industry data were used for monthly inventories of each animal class in each of the contiguous 48 states. Daily weather data from 257 weather stations over a range of 68 to 129 yr were used to estimate mean monthly maximum and minimum temperatures, relative humidity, and their variances and covariances for each state. Animal responses were modeled from literature data using a combination of maximum temperaturehumidity index, daily duration of heat stress, and a heat load index. Monte Carlo techniques were used to simulate 1000 times the weather for each month of the year, for each animal class, for each state, and for each of four intensities of heat abatement (minimum, moderate, high, and intensive). Capital and operating costs were accounted for each heat abatement intensity. Without heat abatement (minimum intensity), total losses across animal classes averaged $2.4 billion annually. Optimum heat abatement intensity reduced annual total losses to $1.7 billion.

Various recommendations have been issued regarding the sampling schedule of diet components, especially forages. Their basis is unclear and none are justified from an economic standpoint. The objective of this research was to derive a general method for determining the optimal sampling design for forages. The process of forage removal from storage can be conceptualized as a quality control issue that can be monitored using a Shewhart X-bar chart. This procedure requires 3 control parameters: number of samples (n), sampling interval (h), and control limits (L). A quality cost function made of 4 parts is proposed: cost per cycle while the process is in-control (I); cost per cycle while the process is out-of-control (O); cost per cycle for sampling and analyses (A); and expected duration of a cycle (D). Thirteen inputs enter the cost function: the mean time that process is in control, the number of animals in the herd, the unit price of milk, the milk production loss due to white noise, the milk production loss from an abrupt change in forage composition, the time to sample and analyze one item, the expected time to discover the assignable cause, the expected time to fix the diet, the cost per false alarm, the cost to fix the diet, the fixed cost of sampling at each sampling time, the cost for each unit sampled, and the number of standard deviation slips when forage changes. The total quality cost per day C = (I + O + A)/D. The C function can be optimized with respect to n, h, and L to yield an optimal sampling schedule. Because n and h are discrete variables in a highly nonlinear function, parametric optimization algorithms cannot be used to optimize the function. A genetic algorithm was used for the minimization of C. Results showed that the optimal sampling designs are close to current practices in small herds of 50 cows, but very different in large herds of 1,000 cows, resulting in reduced total quality costs of $250/d. Total sensitivity of C was greatest for the number of cows in the herd, the shift in milk production when forage changes, the mean time that the process is in control, the price of milk, and the time to sample and analyze one item. Total sensitivities of n, h, and L were greatest for the mean time that the process is in control, the extent of the change in composition when there is a change in forage composition, the number of cows in the herd, the shift in milk production when forage changes, and the cost per unit sampled.

Monitoring the nutritional composition of forage can be conceptualized as a quality control process that can be accomplished using control charts such as the Shewhart X-bar chart. A sampling schedule for an X-bar chart is defined by 3 parameters: the number of samples n taken at each sampling time, the sampling interval h, and the control limits L. All 3 parameters affect the performance of the chart, and thus, the total quality cost (TQC). A TQC function consists of cost per cycle while the process is in-control, cost per cycle while the process is out-of-control, cost per cycle for sampling and analyses, and the expected duration of a cycle, with a cycle defined as the time between the start of successive in-control periods. A general TQC function was derived for a renewal reward process. Optimization of this TQC function allows for the determination of the optimal n, h, and L values that minimize the total daily quality costs. The model assumes an abrupt change in composition of the forage when the process goes out-of-control. It also assumes a normal distribution of the measurements when the process is in-control and an absence of outlier measurements. The objective of this research was to evaluate model robustness to departure from these 3 basic assumptions. A series of Monte Carlo simulations was performed while varying the average time that the process is in control from 5 to 90 d using 1) errors of measurements that follow a standard normal distribution (SN); 2) SN with +/- 3.5 SD outliers inserted with a frequency of 1, 5, and 10%; 3) log normal error of measurements with SD = 1; and finally 4) SN with a gradual shift of the mean from 0 to 1.5 SD over 7, 14, and 28 d. The model was very robust to the presence of outliers; the average change in TQC was less than 1%, even with a frequency of outliers of 10%. The model is also very robust to asymmetry in the distribution of the measurements (i.e., probability distribution function with a long right tail): the log normal distribution, as opposed to the assumed normal, resulted in an increase in TQC of less than 1.4%. Finally, the gradual shift in mean composition did not result in an increased TQC but in a 17.3% decrease compared with an abrupt change. The model appears very robust to departure from normality, presence of outliers, and a skewed distribution of measurements. Gradual changes in the process are readily detected by the optimum X-bar chart with the conventional decision criterion, and monitoring performance is not markedly improved by augmenting the number of decision criteria in the X-bar chart or by the addition of a cumulative sum chart. Because of its robustness, the model can be applied to optimize forage sampling on dairy farms, with expected savings ranging between $80 and $100/cow per yr.