John P. Norback

Linear facility location — Solving extensions of the basic problem

Abstract The basic problem is to locate a linear facility to minimize the sume of weighted shortest Euclidean distances from demand points to the facility. We extend the analysis to locating a constrained linear facility, a radial facility, a linear facility where distances are rectangular and a linear facility under the minimax criterion. Each case is shown to admit a simple solution technique.

Predicting Pathogen Growth during Short-Term Temperature Abuse of Raw Pork, Beef, and Poultry Products: Use of an Isothermal-Based Predictive Tool

A computer-based tool (available at: www.wisc.edu/foodsafety/meatresearch) was developed for predicting pathogen growth in raw pork, beef, and poultry meat. The tool, THERM (temperature history evaluation for raw meats), predicts the growth of pathogens in pork and beef (Escherichia coli O157:H7, Salmonella serovars, and Staphylococcus aureus) and on poultry (Salmonella serovars and S. aureus) during short-term temperature abuse. The model was developed as follows: 25-g samples of raw ground pork, beef, and turkey were inoculated with a five-strain cocktail of the target pathogen(s) and held at isothermal temperatures from 10 to 43.3 degrees C. Log CFU per sample data were obtained for each pathogen and used to determine lag-phase duration (LPD) and growth rate (GR) by DMFit software. The LPD and GR were used to develop the THERM predictive tool, into which chronological time and temperature data for raw meat processing and storage are entered. The THERM tool then predicts a delta log CFU value for the desired pathogen-product combination. The accuracy of THERM was tested in 20 different inoculation experiments that involved multiple products (coarse-ground beef, skinless chicken breast meat, turkey scapula meat, and ground turkey) and temperature-abuse scenarios. With the time-temperature data from each experiment, THERM accurately predicted the pathogen growth and no growth (with growth defined as delta log CFU > 0.3) in 67, 85, and 95% of the experiments with E. coli 0157:H7, Salmonella serovars, and S. aureus, respectively, and yielded fail-safe predictions in the remaining experiments. We conclude that THERM is a useful tool for qualitatively predicting pathogen behavior (growth and no growth) in raw meats. Potential applications include evaluating process deviations and critical limits under the HACCP (hazard analysis critical control point) system.

Integrating Hazard Analysis and Critical Control Point (HACCP) and sanitation for verifiable food safety.

Reliable, verifiable food safety requires the application of technologically correct methods in a systematic way. This requires making a distinction between sanitation and Hazard Analysis and Critical Control Point (HACCP) and integrating these two systems into one food safety system. Although sanitation and HACCP share the same goal of producing safe food products, the focus of sanitation is on the environment surrounding the food to prevent contamination, whereas the focus of HACCP is on controlling hazards intrinsic to food materials. Together they provide the organizational base for applying the correct methods and procedures to ensure and verify that food served is safe for foodservice clients. These approaches also provide records that demonstrate that food safety measures have been planned and completed as planned. One way to demonstrate a responsible approach to food safety is to understand the differences between sanitation and HACCP and to build approaches to food safety that use both of these systems. The resulting integrated system has a better chance of controlling all the hazards than either system by itself.

Fitting hyperplanes by minimizing orthogonal deviations

Hyperplanes withm + 1 parameters are fitted by minimizing the sum of weighted orthogonal deviations to a set ofN points. There is no inverse regression incompatibility. For unweighted orthogonall1-fits essentially the same number of points are on either side of an optimal hyperplane. The criterion function is neither convex, nor concave, nor even differentiable. The main result is that each orthogonallp-fit interpolates at leastm + 1 points, for 0 <p ≤ 1. This enables the combinatorial strategy of systematically trying all possible hyperplanes which interpolatem + 1 data points.

Predicting pathogen growth during short-term temperature abuse of raw sausage.

Lag-phase duration (LPD) and growth rate (GR) values were calculated from experimental data obtained using a previously described protocol (S. C. Ingham, M. A. Fanslau, G. M. Burnham, B. H. Ingham, J. P. Norback, and D. W. Schaffner, J. Food Prot. 70:1445-1456, 2007). These values were used to develop an interval accumulation-based tool designated THERM (temperature history evaluation for raw meats) for predicting growth or no growth of Salmonella serovars, Escherichia coli O157:H7, and Staphylococcus aureus in temperature-abused raw sausage. Data (time-temperature and pathogen log CFU per gram) were obtained from six inoculation experiments with Salmonella, E. coli O157:H7, and S. aureus in three raw pork sausage products stored under different temperature abuse conditions. The time-temperature history from each experiment was entered into THERM to predict pathogen growth. Predicted and experimental results were described as growth (> 0.3 log increase in CFU) or no growth (< or = 0.3 log increase in CFU) and compared. The THERM tool accurately predicted growth or no growth for all 18 pathogen-experiment combinations. When compared with the observed changes in log CFU values for the nine pathogen-experiment combinations in which pathogens grew, the predicted changes in log CFU values were within 0.3 log CFU for three combinations, exceeded observed values by 0.4 to 1.5 log CFU in four combinations, and were 1.2 to 1.4 log CFU lower in two combinations. The THERM tool approach appears to be useful for predicting pathogen growth versus no growth in raw sausage during temperature abuse, although further development and testing are warranted.

Data Structures for Integrating Quality and Cost Factors in a Foodservice Operation

The information requirements for proper management of product quality and safety in a foodservice call for organization and manipulation of large amounts of data. This requires a structural organization to the data, which has large capacity while simultaneously being flexible enough to rapidly deliver information developed from the data. A matrix data structure meets these requirements and conveniently integrates new procedures and new products into a well - structured management information system. Such a structure is a convenient computational device, especially when implemented on a computer, and can be used for immediate feedback of information to the manager. Product quality and safety management requires that these functions be integrated into such a system and related to cost. Only in this way will the resource utilization impact of these control functions on the overall foodservice operation be apparent. Although in this paper the data structures are applied to foodservice operations, other applications are possible. In particular, dairy processing operations, meat and other food processing operations as well as food distribution systems, could all benefit from applications of such structures.

Predicting behavior of Staphylococcus aureus, Salmonella serovars, and Escherichia coli O157:H7 in pork products during single and repeated temperature abuse periods.

Tools for predicting growth of Staphylococcus aureus, Salmonella, and Escherichia coli O157:H7 (THERM; temperature history evaluation for raw meats) have been developed using ground pork and sausage. THERM tools have been tested with three types of pork sausage but not with other pork products or during sequential temperature abuse periods. We conducted inoculation studies (five strains each of S. aureus and/or Salmonella plus E. coli O157:H7) with simulated cooling of warm sausages, inprocess warming of bratwurst, isothermal temperature abuse of pork frankfurter batter, and two sequential periods of 13, 15.6, or 21.1 degrees C temperature abuse of breakfast sausage, natural (additive-free) chops, and enhanced (phosphate solution-injected) loins. In sequential temperature abuse studies, a temperature abuse period (> or =24 h) occurred before and after either refrigeration (5 degrees C for 24 h), or freezing (-20 degrees C for 24 h) and thawing (24 h at 5 degrees C). Pathogen growth predictions from THERM developed using ground pork and sausage were compared with experimental results of 0 to 3.0 log CFU of growth. Across all temperature abuse conditions, qualitative predictions (growth versus no growth) made using the pork tool (n = 133) and the sausage tool (n = 115) were accurate (51 and 50%, respectively), fail-safe (44 and 50%), or fail-dangerous (5 and 0%). Quantitative predictions from the two tools were accurate (29 and 22% , respectively), fail-safe (59 and 73%), or fail-dangerous (12 and 5%). Pathogen growth was greater during the second sequential temperature abuse period but not significantly so (P > 0.05). Both THERM tools provide useful qualitative predictions of pathogen growth in pork products during isolated or sequential temperature abuse events.