Scientific modeling of blended meat products

8 Scientific modeling of blended meat products R. A. LaBudde, Least Cost Formulations Ltd, USA and T. C. Lanier, North Carolina State University, USA

Abstract: This chapter discusses the history and practice of least-cost formulation (LCF), with particular emphasis on the science-based formulation (SBF) models needed to control blended meat product properties. These properties include chemical, compositional, nutritional, functional, physical and flavor attributes. The current state of modeling of these properties is discussed, and the methodology illustrated by examples. Finally, the lack of continuing research and material characterization in the development of SBF technology is identified as the principal impediment to future progress in this important area of the application of meat science. Key words: least-cost formulation (LCF), science-based formulation (SBF), formulation, bind, linear programming.

8.1 Introduction This chapter deals with the subject of requirements-oriented formulation of blended meat products (fresh, cooked, dry and semi-dry sausage, mixed foods, pumped or marinated muscle foods). It does not, in general, apply to single-ingredient meat products that meet all requirements with a fixed formulation (steaks, chops, roasts) with no substitutability or level of use issues.

8.1.1 Requirement-oriented formulation The requirements for an acceptable formulated product derive from various sources. These include governmental regulations, safety, sensory qualities, producibility, logistics and cost. Governmental regulations apply in detail in many ways to formulation:

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nutritional content and claims; order of predominance labeling; use of non-meat extenders (proteinaceous), binders and fillers; control of crude chemistry (fat, moisture, protein); and control of additive use (e.g., nitrite, erythorbate, phosphates).

Food safety is influenced by formulation by: (a) levels of key ingredients added specifically or partially for anti-microbial effect (salts, nitrite, essential oils, lactates, acetates, etc.); (b) non-inclusion of unlabeled allergens; and (c) impact of formula upon the ability to achieve lethality in processing (cf. ‘producibility’ below). Sensory qualities include internal color, external color, gel strength (e.g., peak stress or force to failure at fixed deformation rate), gel ductility (e.g., peak strain or deformation to failure at fixed deformation rate), saltiness, sweetness, pepperiness (heat), meatiness (meat flavor), juiciness and other flavor notes. Producibility requirements relate to the ability to make a particular meat product consistently, reliably and efficiently in practice. Such requirements include: • • • • • •

emulsion stability prior to gelation (‘cooking’); smoke acceptance; product strength (gel strength generally, peelability, sliceability); dimensional stability (non-bloating); syneresis stability (post-packaging exudate); and shelf-life stability.

Logistical requirements involve making sure that particular ingredients and lots of ingredients are selected from those expected to be available at the time of production. Finally, cost has played, and will continue to play for some time to come, a critical role in the acceptability of processed meat products to institutional customers and to consumers. The meat industry remains highly competitive, with a plethora of processors soliciting the business of a limited number of key customers. Cost determines profit in a competitive environment where sales prices and order volumes are fixed.

8.1.2

Science-based formulation (SBF), computer-assisted formulation (CAF) and least-cost formulation (LCF) We will primarily be interested here in ‘science-based formulation’ (SBF), where the role of requirements is dominant, and quantification and modeling of such requirements in order to achieve control are key issues. However, the calculations necessary for these activities inevitably brings a connection to ‘computer-assisted formulation’ (CAF), and the important commercial issue of optimizing profit has inexorably linked SBF and CAF to ‘least-cost formulation’ (LCF). The CAF tool for implementing SBF has traditionally

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been LCF. LCF also deals with more complex and wider issues of purchasing selections, production scheduling, quality control and materials management, none of which will be discussed here other than tangentially. SBF as defined here involves three primary tasks: 1. Reducing requirements to (at least theoretically) measurable quantitative variables. 2. Modeling the requirement variables by (typically linear) functions of the formula input variables (viz., the ingredient proportions or weights). 3. Setting critical limits on the requirement variables such that any formula which meets such limits is considered satisfactory in production. Once this ‘product specification’ is set, a tool such as LCF (described in more detail below) is used to down-select to a specific formula meeting these and other requirements.

8.1.3 History of LCF and SBF in the meat industry Wars have always been the impetus for the greatest strides in food science because, in the words of Napoleon, ‘une armée marche à son estomac’. The fermented dry sausage may have been the end product of a search for portable, shelf-stable rations by the Roman legions. Hard tack and salt pork were staples of armies from the seventeenth to the nineteenth centuries. Canned food was an outgrowth of the Napoleonic wars. The roots of modern SBF and LCF were in World War II. This war encompassed the world with multiple theaters of action, and was a nightmare of logistics. There were three key inventions that grew out of WWII that are germane to the discussion here: 1. The first coherent statement of SBF. 2. The invention of ‘linear programming’ problem solution methods. 3. The digital computer. Exposition of these inventions, which were ‘secret’ during the war, did not occur until 1945–1947. George Stigler (later to receive a Nobel prize in economics) and his group worked on the optimization of nutrition for the diets of soldiers. In Stigler (1945), the ‘Diet Problem’ for human nutrition was discussed and formulated. He presented the first LCF solutions published, calculated by hand. George Dantzig and his group worked on solving logistics problems related to distribution of supplies and factory scheduling. Just after WWII he developed the ‘simplex method’ algorithm for solving large-scale ‘linear programs’ (i.e., optimization problems phrased as systems of linear inequalities, ‘program’ = ‘schedule’). Dantzig (1963) presents an extensive history of events and publications in this area. Interestingly, he also relates how Jack Laderman of the Mathematical Tables Project of the US National

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Bureau of Standards (now National Institute of Standards and Technology) had a team of nine clerks solve Stigler’s Diet Problem with hand calculators. It took the team 120 man-days of effort to find an optimum solution. The digital computer was invented during WWII in order to perform simulations of nuclear fission chain reactions (in order to verify that an atomic bomb test would not ignite the atmosphere of the Earth in a fusion reaction). The inventors of the ‘ENIAC’ computer, Drs Eckert and Mauchley, went on to found the Univac Corporation to commercialize their invention. Their first ‘UNIVAC’ computer was delivered to the US Census Bureau (which since the nineteenth century has been a driver of computing technology) at a cost of US $1 million. There is an anecdotal story that Univac in the early 1950s decided that the market for digital computers in industry was too small (projected at 10 units per year at a $10 million price tag each), and the product was too unreliable (using 20,000+ vacuum tubes with random lifetimes). So Univac decided to get out of the computer business. At the same time, IBM, looking forward to transistor technology (another outgrowth of research of WWII), decided to get into the computer business. (In fact, IBM had been involved with the invention of the digital computer during WWII, and had systematically been continuing attempts to commercialize the device, so the story is probably apocryphal or distorted.) Progress was fast: in 1951 IBM released the 701 model, and the FORTRAN scientific ‘high-level’ program language followed. In 1956, the 704 model incorporated floating-point arithmetic, which, together with the FORTRAN language for programming, allowed practical solutions of reasonable size linear programming problems. Because of the cost of digital computers during this era, IBM used its new scientific capabilities and the new LCF methodology to sell computers across a wide range of blending industries as a way to cut cost of materials by 5–10%, doubling a typical company’s net profit, and thereby getting the accounting and payroll departments a computer for ‘free’. Use of LCF in the blending industries increased rapidly along with lowered costs of digital computers due first to transistor technology, and then integrated circuits in the 1960s. These events are chronicled in Charnes and Cooper (1961) and Danø (1974). During the period 1955–1975, LCF became solidly entrenched throughout the larger companies in the meat industry for solving sausage formulation problems. The need for SBF became evident early on, as some candidate meat ingredients were very high in connective tissue and low in functionality, and others were high in contractile muscle tissue and functionality, so substitutability was restricted. The postulation and solution of LCF problems for sausage and other blended meat products could not be done reliably until the general texture (gel strength) of the cooked batter could be predicted. This property was traditionally known as the ‘bind’ or ‘binding ability’ of a meat, and known

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to be high in skeletal muscle meat and low in ‘filler’ or high connective tissue meat. To a lesser extent, predicting the ‘color’ (pigment) of the resulting blend was also desirable. Very occasionally, the term ‘bite’ was used to indicate the shear stress needed to break the skin or casing of a link sausage product, but ‘bite’ was primarily a property of the processing schedule in cooking and of the type of casing used. To a sausagemaker, both fat and water binding were encompassed in the term ‘bind’. The first attempts at SBF to provide predictors of ‘bind’ and ‘color’ were based upon ad hoc subjective estimates of the quality of different meat sources relative to a standard of comparison, typically bull meat, which was judged the most functional meat commonly available for sausage applications. Anderson and Clifton (1967) provides one such scale, where bull meat is denoted by the value 1.00 for either ‘bind’ or ‘color’, and other meats are assigned values in multiples of 0.05. The Anderson–Clifton tables are reproduced in Pearson and Tauber (1984). Perhaps surprisingly, such ad hoc assignment of values to a functional attribute actually works sufficiently well to control the needed function in LCF. All that is needed is a reasonable degree of correctness in assessing the ratio scale of measurement among the candidate ingredients. In the 1960s, the ‘emulsion’ theory of sausage products became in vogue. It was believed that salt-soluble protein ‘encapsulated’ fat globules, providing ‘stability’ to the fat-in-water emulsion of the sausage product, and this was the basis of product texture (‘bind’). So the search for a SBF attribute to use for ‘bind’ focused on salt-soluble protein and emulsion stability. Swift et al. (1961) and Swift (1965) provided an ad hoc method that allowed oil titration of emulsion stability. This was followed by a well-designed series of experiments by Saffle and coworkers, reviewed in Saffle (1968). The laboratory methods are particularly well-described in Carpenter and Saffle (1964). The ‘Saffle’ or ‘University of Georgia’ bind and color models rapidly became the norm for LCF of sausage products, and were viewed as a triumph of SBF modeling. (For a historical and scientific review, with an extensive table of values, see LaBudde and Lanier, 1995, also Anon, 1970, Porteous, 1979, LaBudde, 1991, Gordon and Barbut, 1992.) Beginning in the 1980s, it became increasingly clear that the ‘emulsion stability’ model for sausage products was of limited value in explaining cooked product properties, such as texture and water and fat binding (Comer and Dempster, 1981, Lanier, 1985, Regenstein, 1988, 1989). The ‘gel’ theory of cooked meat products became ascendant (see review in LaBudde, 1992, also Lanier and LaBudde, 1993, and Lanier et al. 1993). In LaBudde and Lanier (1995), a framework for SBF is postulated, based upon statistical analysis of linear mixture models and upon finished product measurements. From a standardized series of experiments on different mixtures, the effect of a particular ingredient can be inferred based on an input–output model. Using a torsion gelometer, the ultimate gel strength and ultimate gel strain were measured, and coefficients determined for more than a dozen different

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meat ingredients in multiple lots. The Saffle ‘bind’ constants were found to correlate well with the coefficients derived from finished product ultimate gel strength, and with non-collagen soluble protein, the underlying connector between the emulsion and gelation theories. The new approach was found to have four principal scientific benefits: 1. Causality. The strength and strain coefficients are based on measurements of a finished product (highly predictive of actual smokehouse product), not results of testing a model system. The test system derives from recognition that protein gelation and entrapment of constituents, rather than emulsification of fat, is the primary determinant of product stability and texture. 2. Validity. Rather than a vague ‘bind assessment’, prediction of actual product attributes (texture, liquid retention) are made by the new ‘coefficients’. Predicted results can be easily validated by measurements on the actual finished product. 3. Applicability. Not only meat ingredients, but all other ingredients can have their effects estimated by the new methodology. Even the effects of processing variables can be assessed. 4. Reproducibility. The new methodology is based on well-defined, fundamental test methods derived from material science and engineering, capable of being reproducibly performed in independent laboratories. SBF was extended in the 1990s to water-holding capacity (WHC), meat flavor, thermal properties, and response to certain processing variables (LaBudde, 1991; LaBudde and Lanier, 1995). Sporadic work continues in some of these areas, particularly WHC (see Pouttu and Puolanne, 2003).

8.2 The least-cost formulation (LCF) model Although the focus of this chapter is on SBF, this depends upon a foundation of the well-established methodology of LCF to achieve solutions in practice. So it is necessary to first understand the principles of LCF and its assumptions and limitations before going into the more specific details of SBF of blended meat products.

8.2.1 Central assumptions The reduction to practice of a new process involves traditionally three stages: research; development; and manufacturing. Research answers the questions ‘Is it possible and, if so, how?’ A search for optimum parameters is generally involved, and the use of science (modeling, experimentation and analysis). Sometimes nonlinear models (e.g., response surface methodology) are needed to find reasonable starting sets of parameters and a region for subsequent investigation.

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Development (‘engineering’) answers the question ‘How can it be done best?’ Established engineering models, almost invariably linear, are used to fine-tune parameters, such as blend formulae or process variables. Manufacturing deals with the question ‘Can it be done the same way, batch after batch, day after day?’ Management and specifications are used to get employees and materials to accomplish consistent and predictable production. Manufacturing models are characterized by very flat optima, where modest changes in parameters result in near identical results. If this were not true, management of the process and personnel would be extremely difficult. LCF is a type of ‘engineering’ (linear modeling) that unfortunately intrudes upon ‘manufacturing’ (constant procedures) on a batch-by-batch basis, requiring changes in blend formulae. Because of the variability of the different lots of materials (particularly meats), a fixed (constant) blend formula will result in variable product qualities as different material lots are used. Constant product quality can only be attained by variable blend formulae. Material variation must be ‘blended out’ if the product batches are to be consistent in quality. Conservation: ‘What goes in is what comes out.’ The principal assumption in LCF is that product quality is due (for the most part) to material attributes. That is, the product attributes are predictable from the blend formula and the material attributes. This is obviously not true for certain quality attributes, which may be heavily influenced, e.g., by processing. Consider, for example, bacterial contamination of a unit of finished product. For raw product, such as ground beef or fresh pork sausage, the bacteria present in materials will carry forward into the final product. But there may be modulation due to handling or cryogenic chilling and certainly to storage conditions. For cooked product, the ingoing load of bacteria in raw materials is almost unimportant compared with degree of cooking and post-cook environmental recontamination. So, generally, microbiological contamination is not a ‘formulatable’ attribute of a product. (Here we define ‘formulatable’ as predictable via a linear input–output model based upon blend formula proportions and material attributes.) This assumption does hold true for a remarkably large set of attributes, including chemistry (moisture, fat, protein, salt), nutrients and functional properties. Some of these (e.g., moisture, salt) are typically modulated to some extent by processing variables, which sometimes must be dealt with explicitly in LCF. Linearity Traditionally, LCF has been used with only linear models, which makes the constraints weighted averages of material attributes, e.g., the protein content of the finished product is the weighted average of the protein content of each material used. The places LCF in the ‘engineering model’ regime.

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Although LCF could be performed using quadratic or more nonlinear models (see, e.g., Hsu et al., 1996), there are many reasons why this is impractical or undesirable. Firstly, such models are difficult to understand and interpret, which therefore makes it difficult to train manufacturing personnel to use on a daily basis or even to train food technologists to use for development work. Secondly, models nonlinear in parameters are unstable with respect to starting conditions and incremental changes. A small change in a parameter may result in a large change in result. Thirdly, models nonlinear in parameters may not have an easily found optimum, particularly if initial guesses as to formula proportions and parameters are not accurate enough. Fourthly, solving nonlinear optimization models is timeconsuming and troublesome, and this increases dramatically with the size of the model. Problems solved routinely in manufacturing in a meat processing facility may involve hundreds of variables and hundreds of constraints, and this size of nonlinear problem is generally impractical to deal with on a recurring basis. Finally, nonlinear models, even those linear in parameters, rarely have enough robustness or external validity to generalize to the variations and substitutions present in practical application. Linear models are much more likely to be valid in modest extrapolation. It should be noted that the great majority of food science research articles published involve linear (in both variables and parameters) models analyzed, e.g., by multiple linear regression or analysis of variance techniques. When a process is further optimized by engineering development and reduced to practice in manufacturing, the process parameters are typically positioned at some type of optimum where variation in parameters induces only a slight change in output. For manufacturable products, a linear model is thus sufficiently accurate to control quality. Continuity Another traditional assumption made in LCF is that material weights in a blend are continuous variables and not, say, limited to integral values. This assumption greatly simplifies the search for a solution. The most common case where this assumption is limiting is where frozen meats are used in a small batch size. Frozen meat is used in ‘box’-sized increments, typically 20 kg or 60 lb. If the batch size is less than 10 times this unit of measure, the solution based on continuous weights may be inaccurate. The problem is exacerbated if several such ingredients are present in the blend. Typically, when the unit of measure is only a small fraction of the blend weight, the problem is dealt with approximately by ‘rounding after formulation’ the ingredient weights to the nearest multiple of the box size. Incorporation of discrete material weights into the model requires solution by integer programming techniques, essentially involving a collection of linear programming solutions whose number increases exponentially with the number of discrete combinations possible.

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8.2.2 Product formula input–output model Let ‘A’ denote some attribute per kg of a raw material (input), and wi denote the mass in the blend formula of the ith material. Within the framework of the above assumptions, the linear product formula input–output model for the kg of attribute ‘A’ of the blend (output) is then kg A = w1 A1 + w2 A2 + ... + wn An

8.1

This form, although basic to the LCF model, requires adjustment in many cases for process losses to be practically useful, and needs to be scaled to a mass base to apply problem-level constraints. As an example of this, eq. (8.1) gives the basic input–output model for the situation in which the process of conversion of materials to a blended product conserves kg of A, e.g., a simple blend step. But in practice the model must have a greater reach to be representative of a real finished product. In particular, cooked meat products are significantly affected by moisture loss (so-called ‘shrink’) in the process. Such cook losses range from 1–3% for large diameter permeable casings (e.g., bologna) to 25% or more for dry sausage and small diameter casings (e.g., snack sticks). Large shrink losses must be included explicitly in the model to obtain accurate predictions. Shrink loss or gain Let ‘GW’ denote the gross blend mass, or ‘gross weight’, GW = w1 + w2 + ... + wn

8.2

Typically it is assumed that the shrink loss for a given process is a constant fraction ‘s’ of the blend weight GW. (If there were an interaction between the shrink loss and the masses wi of the materials, the model would become nonlinear due to cross-terms.) Suppose further that a fraction γA of the shrink mass loss is lost from the attribute A. Then eq. (8.1) needs to be modified to kg A = w1 A1 + w2 A2 + ... + wn An − γA s GW

8.3

in order to estimate the kg of A post-process in the finished product batch. Finally, the total kg of attribute A in the finished product batch is not as relevant in specification units as the amount of attribute A in the finished product, per kg of some specified mass base. The mass bases of most interest are generally gross weight (GW), finished weight (FW), meat weight (MW) or serving weight (SW). GW is defined by eq. (8.2) above, and the others typically by FW = (1 − s) GW

8.4

MW = w1 μ1 + w2 μ2 + ... + wn μn

8.5

SW = η FW

8.6

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where μi = 1 if the material is a ‘meat’ and 0 otherwise, s is the shrink fraction defined above, and η is the conversion factor from a kg to the specific nutritional labeling serving size for the product, e.g., for a 57 g serving, η = 57/1000 = 0.057. Now the attribute A content of the product blend can be phrased more accurately and per mass base via, e.g., w1 A1 + w2 A2 + … + wn An − γ A s GW 8.7 FW Suppose the fat content (as a fraction) is denoted by F. For a typical meat product, the fraction γF = 0 (although exceptions might be cooked ground beef, cooked pork sausage or cooked bacon), so the fat content of the finished product would be modeled by A=

F=

w1 F1 + w2 F2 + … + wn Fn FW

8.8

Similarly, for protein content P, the fraction γP = 0, and P=

w1 P1 + w2 P2 + … + wn Pn FW

8.9

For permeably cased product, where the cook loss is dominated by moisture, the moisture content M has fraction γM = 1, and M=

w1 P1 + w2 P2 + … + wn Pn − s GW FW

8.10

Occasionally the process increases weight instead of reducing it, so ‘loss’ is a misnomer. For example, in the steam extrusion or immersion cooking in water of some foods, a net weight can occur, and either s < 0 or γM < 0. In sausage production which incorporates a brine chill post-cook, frequently salt (i.e., NaCl) pickup occurs if the salt activity of the brine exceeds that of the product itself (typically +0.3% weight for a 10–15% brine), so γS < 0 (or −0.03 for a 10–15% brine and a product with s = 0.10 loss). If the total ‘shrink’ loss or gain is divided among various components of chemistry, there is a constraint that the total multiplication factor: γ = γ M + γ F + γ P + γ S +…

8.11

must equal 1.0 for the shrink loss or gain s to give the correct total weight change in GW. Conceptually, it is simplest to think of s giving the total fractional weight loss (+) or gain (−) in GW, and γA chosen such that γA s GW gives the total kg loss (+) or gain (−) in attribute ‘A’. Other process effects There are other situations besides processing losses (gains) where the postulate of conservation might be violated, and so which must be handled explic-

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itly as a model adjustment. So far, such features have not been generally necessary to formulate blended meat products. Examples might include the impact of thermal treatment on microbiology or labile nutrients (e.g., microbiology, vitamin C, nitrite). Typically these are assumed to be subject to a constant effect, and dealt with separately from formulation for simplicity. 8.2.3 Prices LCF is an optimization problem. It assumes that orders (sales) are known, therefore production volume is known, and the way to maximize profits is to minimize the cost of production. In a typical blended meat product, meat comprises typically 50–70% of total direct costs. The other direct costs (labor, labels, packaging, equipment usage) can reasonably be assumed constant per unit of production, and so are not important in LCF. There are a number of economic assumptions implicit in the previous paragraph, which are important to the use of LCF as a management tool, but not to SBF, which is our principal focus here, so details of economicsbased modeling for LCF will not be given further. However, one thing must be said about the ‘costs’ used in least-‘cost’ formulation. Although traditionally the word ‘cost’ has been used in terminology, LCF is a planning tool, and therefore operates prospectively, not retrospectively. Under the assumption that the producing entity is a ‘going concern’, the ‘cost’ that must be minimized is the cost of obtaining of materials and the replenishment of stores after the planned production takes place. Thus the issue is one of ‘replacement’ cost, not ‘historical’ cost. In English-speaking countries, the word ‘cost’ generally connotes an auditable value for a transaction that took place in the past, and ‘price’ as the prospective value that would be paid if a future transaction were to take place. ‘Prices’, and not ‘costs’, are generally what are of interest in LCF. The use of prospective vs. retrospective is critical, because otherwise the real cost of production may be increased rather than reduced in the optimization. An example of this would be in the usage of stored inventories of frozen meat. If use does not occur, a holding cost will be incurred. Accounting principles require that this holding cost be added to the cost of the material. However, from an LCF point of view, if the material were to be used, the cost will be saved, and so the cost is properly to be subtracted from the cost of the material in formulation. This reversal of policy is characteristic of the difference between retrospective accounting and prospective decision-making. Following the accounting policy in this example would result in diminished usage when increased usage would have been the correct decision. 8.2.4 Availabilities Every real problem involves limited resources. This must be taken into account in LCF as well. A scarce material may be available at low cost, but

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only in very limited quantities. If cost alone is used as a deciding point, a formula with high percentage of that material will be chosen by LCF, and the formula will be unsustainable in practice. Similarly, materials in inventory, such as frozen meat, may temporarily appear to be in great supply, but excessive use in formulae will result in ‘feast and famine’ cycles of replenishment. Generally only materials available on short notice in the open market should be viewed as freely available. Other materials (in-house trimmings, frozen inventories, low volume lots) are best handled by capping their usage in the formula. As an example, suppose that frozen beef is expected to have an approximate 24 week usable lifetime in storage, calculated as 48 weeks from kill, minus 12 weeks for product shelf-life, minus 12 weeks for acquisition and delivery. Then one method of physical flow is to force a minimum usage of exactly 1/24 of the amount in inventory each week of production. The upper limit on usage would depend upon the ability of production to properly stage and temper the meat before use.

8.3 Linear science-based models for meat product properties The heart of the use of SBF is the characterization of the attributes of raw materials and the use of these attributes, as well as logical relationships among materials, to set product requirements such that automatic formulation results in a practically acceptable formula. In setting a product specification, there are generally three methods of controlling product attributes. The most primitive is to attempt to fix the usage of individual ingredients within some range that generally results in acceptable product batches. This is conceptually easy to do, and appeals to the unsophisticated modeler, but ignores the substitutability of materials and severely restricts choice. So control is poor using this method, unless the material constrained has obviously constant unique properties, unlike those of any other material. This method is used in practice for controlled ingredients (such as curing agents and accelerators), starter culture, seasonings, etc., but is not advisable for meats. A more acceptable method of setting a product requirement is to constrain the usage, not of individual materials, but of a group of similar-acting materials. This categorical grouping of materials works well for labeling, where, e.g., all meats labeled ‘beef’ are considered equivalent by a regulatory agency, but ignores differing functional or chemical effects among different ingredients. The most precise and scientific (i.e., model- and evidence-based) method of control is to base a product requirement upon material attributes, which allows the weighted average of all material effects to be controlled.

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As an example, consider one of the first major issues in SBF of blended meat products: the control of the ‘firmness’ (‘gel strength’) of finished cooked sausage. Sausage makers had long known that some meats (such as lean skeletal meat) had good ‘binding’ ability (i.e., their inclusion creates firmer texture) and others (such as high connective tissue meat) had poor ‘binding’ ability, and were considered simply ‘fillers’. So the first attempts at LCF limited ingredients such as snouts, lips and head meat individually to, say, 10% of the total blend. But if all three meats entered a formula, the individual limits still allowed 30% of the formula from the combination of them. Obviously the next step would be to place a 10% usage limit on the ‘group’ of ‘filler’ meats, so that the combination of them would never exceed 10% of the formula. Later, through the pioneering work of Saffle (see Section 8.3.5 below), these compositional controls were replaced with more scientific ones based upon experimentally measured coefficients for each meat’s ‘binding ability’ attribute, termed ‘bind values’, ‘bind indices’ or ‘bind coefficients’.

8.3.1 Mixture models The conservation model form of eq. (8.1) is identical to that of the linear statistical ‘mixture’ model (Cornell, 2002): E[y] = a1 x1 + a2 x2 + a3 x3 + ... + an xn

8.12

where E[y] is the expected value of y, y is some measured attribute, a1 ... an are coefficients, and x1 ... xn are a set of values of predictor variables constrained by, e.g., x1 + x2 + ... + xn = 1

8.13

With the right-hand side of eq. (8.13) being 1.0, the x1 ... xn are fractional composition variables. In eq. (8.1) as written, the w1 ... wn would total instead the GW in kg. The two forms are equivalent in the sense that they are simply scaled versions of each other, i.e., xi = wi/GW

8.14

A typical experiment (as in LaBudde and Lanier, 1995) would be to make blends with linearly independent formulae (i.e., {xi}), make measurements of the response variable y for each, and statistically reduce the data using the mixture model form of eq. (8.12). This is most conveniently done by multiple linear regression with no intercept, which is eliminated by the constraint eq. (8.13). The values of the attribute ‘A’ used in the SBF model for the raw materials would be the fitted coefficients {ai} in eq. (8.12). A nonlinear mixture model would include, e.g., interaction terms of the form xi xj and quadratic terms of the form xi2. As mentioned on pages 191–2, models nonlinear in variables or parameters are rarely necessary in modeling products reduced to manufacturing practice, and are difficult enough to

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deal with and interpret even in a research setting. A crude linear model at the manufacturing operating point is generally preferable to a more accurate nonlinear model for most practical purposes. Interaction terms in formulation are typically necessary only when ingredients chemically react or interact, and such issues are antithetic to manufacturability. As an example, consider a meat product that contains both a starch and a gum. If the starch composition were raised to 90% of the blend, there would obviously be insufficient moisture present (moisture must be 100% − 90% = 10% or less) to hydrate the starch, let alone the gum. If the gum were raised to 90%, the same problem would recur, this time more severely, as the gum would likely have an even greater affinity for water. Clearly there must be interaction terms present between the starch, gum and moisture fractions in the blend. If we allow the entire range of variability (0 to 100%), these interactions will likely be present at high orders. But if we keep in mind the product involved is supposed to be a meat product of a known type, it is highly unlikely that either starch or gum will be allowed to be present at more than a few percent of the blend. Otherwise the fundamental character of the product would shift. By the very nature of manufacturability and the maintenance of product identity, all changes possible by allowed shifts in material fractions must cause relatively small shifts in product character. This makes the situation by definition a first-order effects model, typically represented by a linear model by virtue of Taylor’s theorem in mathematics. It is not that nonlinear models are not possible, it is just that they are not allowed in manufacturing. If a meat product is manufacturable, it must be controllable by a linear model. Otherwise it has not yet been reduced to manufacturing, and will not work in practice. One of the major problems in SBF is the obtaining of the attribute levels {ai} for all ingredients, both meat and non-meat, eligible for use in formulae. The ideal method to obtain these estimates is via a lot-replicated designed mixture model experiment which involves direct measurements on finished product. However, these types of experiment are costly, as they involve testing many individual blends, and have scale-up issues relating to the methods used to simulate preparation and cooking in the laboratory. More economical is to make direct measurements upon individual ingredients or comparisons between ingredients (and not blends of them), but this has issues of generalizability, as methods designed for meats are difficult to apply to non-meat ingredients, and vice versa. So, perforce, the starting point for non-easily measured attributes has historically been educated guesses. This easily applied, but subjective, method works as follows: an arbitrary scale is established, with some ingredient chosen as a standard of comparison, and assigned a value on the scale (e.g., bull meat as 1.0). Other ingredients are subjectively assigned values based upon experience of usage. These subjectively defined attributes, although not optimal, work surprisingly well in practice, if designed intelligently. The attribute levels can be approximately validated by formulating

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Scientific modeling of blended meat products

199

substitution blends, and verifying that the property of interest is not significantly different. If it is, the assigned value can be increased or decreased in the direction of interest, and re-validated. This works fairly well for meats. Non-meat ingredients are then either ignored, or assigned values based upon ingredient supplier estimates of substitutability for meats.

8.3.2 Crude chemistry (proximate analysis) Generally chemistry attributes are conserved, and so follow the form of eq. (8.7) with the shrink-effect adjustment. This includes moisture, fat, protein, ash, salts and carbohydrates, and such derived quantities as ‘USDA Added Water’ defined by regulation in the USA as USDA AW = Moisture − 4 Protein

8.15

when the non-meat protein is less than 1% FW, and USDA AW = Moisture − 4 Meat Protein − 0.04

8.16

when the non-meat protein exceeds 1% FW. The proper ‘shrink-effect’ factor γ for eq. (8.15) is 1.0 and for eq. (8.16) is 0.96. Two of the three constituents – moisture, fat and protein – must be constrained to control product chemistry. (Salts and carbohydrates are typically subject to fixed limits.) In the USA this is accomplished by regulations on fat and ‘USDA Added Water’. Some other countries use moisture and protein. Table 8.1 lists the crude chemistry of a sample set of materials (ingredients).

8.3.3 Compositional groupings (logical relationships) For product identity and regulatory order of predominance labeling, certain logical groupings of materials must be defined. Examples include ‘beef’, ‘pork’, ‘chicken’ and ‘turkey’. Customer requirements may specify limits on mechanically separated or frozen meats. Such logical groups can be implemented by defining an associated attribute, e.g., ‘Beef’, which has values of 1.0 if the material is classified as ‘beef’ on the label, and 0.0 if it is not. Work-in-process composite materials (e.g., preblends) will have fractional values between 0 and 1. Some LCF systems (such as the Least Cost Formulator™ from Least Cost Formulations, Ltd) deal with groups of materials in a simpler manner by assigning individual ‘group letters’ to materials (e.g., ‘B’ for ‘beef’), with a hidden attribute dynamically constructed based upon the associations. Table 8.1 shows the logical relationship among materials as common ‘group’ letters. For example, materials having the common group letter ‘B’ are those qualifying as ‘Beef’ on the label ingredient statement in the USA. Similarly ‘P’ indicates ‘Pork’, ‘C’ indicates ‘Mechanically separated chicken’ and ‘T’ indicates ‘Mechanically separated turkey’.

© Woodhead Publishing Limited, 2011

Table 8.1 Sample material chemical analyses and costs for use in least-cost formulations. ‘Nitrite’ is NaNO2 content. Individual group letters indicate relational associations (see text)

© Woodhead Publishing Limited, 2011

ID

Description

Groups

BF50 BZ50 BF85 BZ85 BF90 BZ90 BFBULL BZCHEEK BZHEAD CFMSM15 CFMSM18 CFMSM22 PF42 PF72 PZCHEEK PFHAM

BF FRSH 50% TRIM BF FROZ 50% TRIM BF FRSH 85% TRIM BF FROZ 85% TRIM BF FRSH 90% TRIM BF FROZ 90% TRIM BF FRSH FC BULL MT BF FROZ CHEEK MT BF FROZ HEAD MT CK FRSH MSM 15% FAT CK FRSH MSM 18% FAT CK FRSH MSM 22% FAT PF FRSH 42% TRIM PK FRSH 72% TRIM PK FROZ CHEEK MT PK FRSH 95% BNLS HAM

B BZ B BZ B BZ B BZ BZ C C C P P PZ P

Moisture (g/g)

Fat (g/g)

Protein (g/g)

0.4034 0.4034 0.6580 0.6580 0.6912 0.6912 0.7080 0.6309 0.6800 0.6812 0.6620 0.6376 0.3581 0.5707 0.6580 0.7430

0.4801 0.4801 0.1491 0.1491 0.1123 0.1123 0.0820 0.1914 0.1226 0.1339 0.1724 0.2063 0.5412 0.2707 0.1631 0.0500

0.1114 0.1114 0.1897 0.1897 0.1886 0.1886 0.2020 0.1716 0.1911 0.1499 0.1324 0.1247 0.0958 0.1528 0.1770 0.1990

Salt (g/g)

0.0200 0.0200 0.0200

Nitrite (g/g)

0.00015 0.00015 0.00015

Carbo (g/g)

Cost ($/lb) 0.4499 0.4499 0.8698 0.8900 0.9298 0.9500 1.0197 0.6998 0.4999 0.2199 0.1899 0.1700 0.3799 0.6398 0.6798 1.1626

© Woodhead Publishing Limited, 2011

PZHEAD1 PZHEAD2 TZMSM20 WATER XISP XSTRCHCM XYEAST YCORN YCSS YCURE YDEXT YERYTH YLACTATE YNITRITE YSALT YSTPP ZFLAV ZMUST ZSPICE

PK FROZ HEAD MT PK FROZ HEAD MT TK FROZ MSM 20% FAT TAP WATER SOY PROTEIN ISOLATE MODIFIED CORN STARCH AUTOLYZED YEAST CORN SYRUP CORN SYRUP SOLIDS DRY CURE (PRAGUE PWD DEXTROSE SODIUM ERYTHORBATE SODIUM LACTATE SODIUM NITRITE SALT SODIUM TRIPOLYPHOS FLAVORINGS MUSTARD FLOUR SPICE

PZ PZ TZ WN XN XN XN N N N N N N N N N N N N

0.5550 0.3622 0.6909 1.0000 0.0600 0.0832 0.0300 0.2000 0.0350

0.2910 0.5244 0.1596

0.1474 0.1100 0.1329

0.0100 0.0005

0.8550 0.0026 0.5100

0.0300 0.9128 0.4500 0.8000 0.9650 0.9375

0.06250

0.0800

0.9200

0.4000 1.00000 1.0000 0.1000 0.0600 0.1000

Note: Copyright © 1991 by Least Cost Formulations, Ltd., reprinted by permission.

0.2500

0.1200 0.3200 0.1200

0.7700 0.3650 0.7700

0.5199 0.3799 0.2299 0.0020 1.4496 0.2900 1.3696 0.1500 0.1800 0.2999 0.2399 2.9992 0.9997 0.8498 0.0500 0.6498 0.8998 0.3099 0.8998

202

Processed meats

8.3.4 Nutritional content Generally, nutrients, such as ‘calories’, ‘fat’, ‘saturated fat’, ‘sugars’, ‘sodium’, etc., are conserved, and are handled the same as the crude chemistry attributes of Section 8.3.2. Exceptions to conservation might be ‘sodium’, which can be increased slightly by brine chilling, and ‘vitamin C’, which is typically depleted severely in cooking. These special effects are usually dealt with most easily by standard post-formulation adjustment in values before constructing nutritional labels. Table 8.2 shows selected nutritional contents of the sample materials.

8.3.5 Functional attributes As of the current time, the functional attributes most commonly controlled in formulation are ‘bind’ (firmness, or gel strength), internal ‘color’ (pigmentation) and ‘WHC’ (water-holding capacity). Of these, the most important to cooked meat product formulation is ‘bind’. As mentioned above, the first approach to controlling ‘bind’ was to individually or collectively control the usage of ‘filler’ (i.e., poor binding) meats in the formula. After some experience with early use of LCF for blended meat products, consultants started providing subjectively-derived attributes for ‘bind’ and ‘color’. (See Anderson and Clifton, 1967, reproduced in Pearson and Tauber, 1974.) Then the pioneering work of Saffle and co-workers (Carpenter and Saffle, 1964; Saffle et al., 1967; Saffle, 1968) provided ‘bind’ attributes based upon oil titration of salt-soluble protein in meat ingredients. This was the first time that designed experiments with an underlying model was used to attempt to measure an attribute across a wide range of materials, and was a key milestone in the birth of SBF. Porteous (1979) repeated the Saffle and coworkers methodology for Canadian cuts of meats. Finally, in LaBudde (1992) and LaBudde and Lanier (1995) the concept was introduced of using mixture models and full-up finished product testing as a means of measuring gel strength effect from material composition and processing variables. LaBudde and Lanier (1995) also showed the high degree of correlation between the Saffle-derived ‘bind’ attribute and the gel strength measurements. With respect to internal ‘color’, generally the values measurement by Saffle and co-workers continue to be used in practice, as they are the only values systematically measured (spectrophotometric measurement of extracted hemochrome) by the same technique across a wide range of meats. In principle, the mixture model method of LaBudde and Lanier (1995) could be used to measure chroma or (L*, a*, b*) or (L*, r*, s*) (see LaBudde and Cusick, 2003) as the source of attribute levels. To date, however, no such experiment on a sufficiently wide range of ingredients to be useful in LCF has been done.

© Woodhead Publishing Limited, 2011

Table 8.2 Selected nutrient contents for the sample materials of Table 8.1. ‘LCFBIND’ and ‘LCFCOLOR’ are smoothed estimates based upon Saffle and co-worker measurements © Woodhead Publishing Limited, 2011

ID

Description

Groups

BF50 BZ50 BF85 BZ85 BF90 BZ90 BFBULL BZCHEEK BZHEAD CFMSM15 CFMSM18 CFMSM22 PF42 PF72 PZCHEEK PFHAM

BF FRSH 50% TRIM BF FROZ 50% TRIM BF FRSH 85% TRIM BF FROZ 85% TRIM BF FRSH 90% TRIM BF FROZ 90% TRIM BF FRSH FC BULL MT BF FROZ CHEEK MT BF FROZ HEAD MT CK FRSH MSM 15% FAT CK FRSH MSM 18% FAT CK FRSH MSM 22% FAT PF FRSH 42% TRIM PK FRSH 72% TRIM PK FROZ CHEEK MT PK FRSH 95% BNLS HAM

B BZ B BZ B BZ B BZ BZ C C C P P PZ P

LCFBIND 15.50 12.40 26.40 21.10 26.20 21.00 30.60 11.10 6.90 24.30 21.50 20.20 11.60 18.60 7.00 24.20

LCFCOLOR 25.0 25.0 42.0 42.0 42.0 42.0 48.0 48.0 29.0 21.8 19.2 18.1 9.6 15.4 29.3 20.0

LCFWHC

LCFMEAT

Collagen (g/g)

0.600 0.500 1.700 1.300 1.700 1.300 2.100 0.600 0.400 1.200 0.950 0.840 0.370 0.950 0.420 1.600

5.6 5.6 8.8 8.8 8.5 8.5 10.1 9.3 6.3 3.4 2.7 2.5 3.6 3.7 6.0 4.2

0.0368 0.0368 0.0379 0.0379 0.0396 0.0396 0.0384 0.1012 0.1395 0.0540 0.0516 0.0499 0.0268 0.0336 0.1274 0.0398

Table 8.2

Continued

© Woodhead Publishing Limited, 2011

ID

Description

Groups

PZHEAD1 PZHEAD2 TZMSM20 WATER XISP XSTRCHCM XYEAST YCORN YCSS YCURE YDEXT YERYTH YLACTATE YNITRITE YSALT YSTPP ZFLAV ZMUST ZSPICE

PK FROZ HEAD MT PK FROZ HEAD MT TK FROZ MSM 20% FAT TAP WATER SOY PROTEIN ISOLATE MODIFIED CORN STARCH AUTOLYZED YEAST CORN SYRUP CORN SYRUP SOLIDS DRY CURE (PRAGUE PWD DEXTROSE SODIUM ERYTHORBATE SODIUM LACTATE SODIUM NITRITE SALT SODIUM TRIPOLYPHOS FLAVORINGS MUSTARD FLOUR SPICE

PZ PZ TZ WN XN XN XN N N N N N N N N N N N N

LCFBIND 5.80 4.30 18.10 100.00 80.00 30.00 6.00 7.00

7.00 2.00 15.00 2.00

LCFCOLOR 15.1 11.2 19.9

LCFWHC 0.280 0.160 0.800 4.500 7.000 1.000 0.300 0.400 0.300

0.300 10.000 0.300 2.000 0.300

LCFMEAT 3.7 3.9 2.9

Collagen (g/g) 0.1017 0.0825 0.0532

Scientific modeling of blended meat products

205

Water-holding capacity (WHC) is primarily of interest in pumped muscle products or fat-reduced sausage products, where a considerable addition of free water is made. The goal is to bind the free water and prevent its separation in the package. As of the current date, the only attribute of this type known to be in use in the meat industry is the subjectively defined one supplied with the Least Cost Formulator™ software system (see the ‘LCFWHC’ attribute in Table 8.3). Table 8.3 lists estimated functional attributes for the example materials.

8.3.6 Physical attributes A number of physical properties meet the requirements of Section 8.2.1 for formulatability. These include density, heat capacity, thermal conductivity and freezing-point depression, among others. Many predictive formulae for physical properties based upon proximate analysis (moisture fat, protein, fiber, other carbohydrates, ash) are collected in Appendix A.11 of Toledo (1991). The density is actually estimated by the inverse of the ‘specific volume’ v which is calculated as the weighted average of the inverse densities of each ingredient: ρ=1/v

8.17

v = x1 / ρ1 + xn / ρn + ... + xn / ρn

8.18

where the {xi} are the weight fractions, as before, and the {ρi} are the individual ingredient densities. Alternatively, as in Toledo (1991), the formulae can be based upon the proximate analysis composition attributes. Thermal conductivity is best estimated using the volume-weighted average of the compositional attribute thermal conductivities. Heat capacity and freezing point depression are based upon mass-weighted averages. Simple averages typically suffice to estimate physical properties within several percent error. For more accurate work, the effects of incorporated air must be included for volume-weighted properties.

8.3.7 Flavor attributes At least two flavor attributes have been measured and modeled across a sufficient group of ingredients to be useful in LCF: ‘sweetness’ (relative to sucrose = 1.0) and ‘heat’ (in Scoville units). The ‘sweetness’ attribute is useful to allow automatic substitutability among sweeteners, particularly when changing them systematically, as a move from dry ingredients to liquid corn syrup. The ‘heat’ attribute might be useful for controlling pepperiness in, e.g., ‘hot Polish-style sausage’, although this is seldom done, as ‘heat’ is considered more the province of spice suppliers.

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Table 8.3

Functional attributes of the sample materials of Table 8.1

© Woodhead Publishing Limited, 2011

ID

Description

Groups

BF50 BZ50 BF85 BZ85 BF90 BZ90 BFBULL BZCHEEK BZHEAD CFMSM15 CFMSM18 CFMSM22 PF42 PF72 PZCHEEK PFHAM PZHEAD1

BF FRSH 50% TRIM BF FROZ 50% TRIM BF FRSH 85% TRIM BF FROZ 85% TRIM BF FRSH 90% TRIM BF FROZ 90% TRIM BF FRSH FC BULL MT BF FROZ CHEEK MT BF FROZ HEAD MT CK FRSH MSM 15% FAT CK FRSH MSM 18% FAT CK FRSH MSM 22% FAT PF FRSH 42% TRIM PK FRSH 72% TRIM PK FROZ CHEEK MT PK FRSH 95% BNLS HAM PK FROZ HEAD MT

B BZ B BZ B BZ B BZ BZ C C C P P PZ P PZ

Calories Cal-fat Fat-sat Cholest (Cal/g) (Cal/g) (g/g) (mg/g) 4.8 4.8 2.1 2.1 1.8 1.8 1.5 2.4 1.9 1.8 2.1 2.4 5.3 3.0 2.2 1.2 3.2

4.3 4.3 1.3 1.3 1.0 1.0 0.7 1.7 1.1 1.2 1.6 1.9 4.9 2.4 1.5 0.5 2.6

0.1986 0.1986 0.0599 0.0599 0.0444 0.0444 0.0318 0.0776 0.0488 0.0462 0.0523 0.0623 0.1958 0.0974 0.0582 0.0177 0.1048

0.85 0.85 0.64 0.64 0.62 0.62 0.60 0.67 0.63 1.02 1.08 1.17 0.60 0.63 0.64 0.65 0.63

Sodium Sugars Vitamin A Iron (mg/g) (g/g) (IU/g) (mg/g) 0.41 0.41 0.58 0.58 0.60 0.60 0.62 0.56 0.60 8.37 8.34 8.30 0.33 0.51 0.58 0.64 0.50

1.05 1.36 1.86 0.11 0.08 0.07 0.06 0.08

0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01

© Woodhead Publishing Limited, 2011

PZHEAD2 TZMSM20 WATER XISP XSTRCHCM XYEAST YCORN YCSS YCURE YDEXT YERYTH YLACTATE YNITRITE YSALT YSTPP ZFLAV ZMUST ZSPICE

PK FROZ HEAD MT TK FROZ MSM 20% FAT TAP WATER SOY PROTEIN ISOLATE MODIFIED CORN STARCH AUTOLYZED YEAST CORN SYRUP CORN SYRUP SOLIDS DRY CURE (PRAGUE PWD DEXTROSE SODIUM ERYTHORBATE SODIUM LACTATE SODIUM NITRITE SALT SODIUM TRIPOLYPHOS FLAVORINGS MUSTARD FLOUR SPICE

PZ TZ WN XN XN XN N N N N N N N N N N N N

5.2 2.0

4.7 1.4

0.1897 0.0531

3.6 3.7 3.8 3.2 3.9

0.1 0.0

0.0042 0.0001

0.61 0.95

0.34 0.48

0.11

0.50 0.09 0.15

0.01 0.02 0.14 0.00 0.19

0.3360 0.4200 389.60

3.7

1.0000 116.00 123.10 333.20 393.40 312.50

3.6 5.0 3.6

2.3

Note: Copyright © 1991 by Least Cost Formulations, Ltd., reprinted by permission.

0.0146

0.05

0.62

0.10

208

Processed meats

8.4 Solving the least-cost formulation–science-based formulation (LCF-SBF) problem The LCF problem to be solved is a combination of the inputs from the raw material attributes and relations, and the requirements of the product specification. The LCF process involves four major steps: problem build; problem solution; problem un-build; and sensitivity analysis. Examples of the LCF process for blended meat products can be found in Selfridge and LaBudde (1982) and LaBudde (1996). 8.4.1 Problem build The first step in building the LCF problem is identifying the variables in the problem. These are the weights of all ingredients allowed for consideration in the formula, whether or not they will have non-zero usage in the final solution. In addition, it is sometimes useful or necessary to consider explicitly ‘non-weight’ variables that are part of the problem, but do not enter into the determination of GW in eq. (8.2). These non-weight variables can be used to manipulate cost and thereby the solution to the problem. After identifying all variables in the problem, the next step is identify all of the constraints associated with the variables and the product specification. Typical constraints include upper and lower bounds on the usage of each variable, a total weight constraint, and constraints related to each product requirement. A total weight constraint is needed to define the meaning of ‘least-cost’. If GW is fixed, the solution will be the least-cost per unit GW formula. For fixed shrink loss, this is also the least-cost per unit FW formula. This is normally the ideal constraint to use, as this then minimizes the cost of product produced. In principle, however, this constraint may be replaced by some other linear functional of the material weights, such as fat (least-fat solution), or some subset of the material weights (e.g., least-cost per unit meat block weight). Each product requirement may generate zero, one or two constraints. Zero constraints are generated if the requirement cannot attain either its lower or upper limit. One constraint is generated if only the lower or upper limit is attainable, but not both, or if it is an equality constraint. Two constraints are needed when both upper and lower limits are attainable and distinct. As an example, suppose we wish to carry out a LCF for a frankfurtertype sausage with ingredient statement reading ‘Pork, Water, Beef, Sodium Lactate, ...’, and the requirements listed under ‘Limits imposed’ in Table 8.4. These requirements can be subdivided into four broad categories: 1. Proximate chemistry (fat = 28.5% FW, salt = 2.5% FW, fat + USDA-AW ≤ 39% FW, nitrite = 150 ppm MW). 2. Fixed special ingredients and flavorings (corn syrup = 2.5% GW, erythorbate = 540 ppm MW, mustard flour = 1% GW, spices = 2% GW).

© Woodhead Publishing Limited, 2011

Table 8.4

Product formulation requirements specification and report for ‘PWBFRANK’ example product

Requirement

Limits imposed Value

Type

Description

© Woodhead Publishing Limited, 2011

A MOISTURE MOISTURE 51.6199 A FAT TOTAL FAT 28.5000 A PROTEIN TOTAL PROTEIN 10.6508 AA USDA-AW 37.5166 + FAT A SALT TOTAL SALT NaCl 2.5000 A NITRITE TOTAL NITRITE NaNO2 150.0000 M YCORN CORN SYRUP 2.5000 M YERYTH SODIUM ERYTHORBATE 540.0001 M YLACTATE SODIUM LACTATE 3.0000 M ZMUST MUSTARD FLOUR 1.0000 M ZSPICE SPICE 2.0000 A LCFBIND LCF BIND INDEX 13.0000 A LCFCOLOR LCF COLOR INDEX 13.0628 AA LCFWHC / MOISTURE 1.2046 A LCFMEAT LCF MEAT FLAVOR 3.2039 A COLLAGEN CALC COLLAGEN 2.5390 GG P 30.1339 >W GG W 0.1000 >B GM B 16.6102 > YLACTATE G Z 0.0000 20 Reqs. Shrink: 8.5000 % GW BW: 2083.63 GW: 3000.00

Lower

Upper

Type

Activity coef.

Penalty cost

Range High

Low

BIG % FW BIG −BIG −BIG 28.5000 28.5000 % FW 28.1472 −0.00027 44.7245 BIG % FW BIG −BIG −BIG 39.0000 % FW 39.0000 0.0000 −BIG 2.5000 2.5000 % FW 2.3477 −0.00125 18.9087 150.0000 150.0000 ∧ MW 4262392 −312539 2.5000 2.5000 % GW 0.00004 22.1130 2.2551 540.0000 540.0000 ∧ MW 450419936 −1125099 3.0000 3.0000 % GW 2.7224 −0.01175 10.8633 1.0000 1.0000 % GW 0.00212 58.3144 0.8874 2.0000 2.0000 % GW 1.8323 −0.00982 18.2870 13.0000 BIG FW 0.03818 17.1986 12.9671 BIG FW BIG −BIG −BIG 1.2000 BIG ABS 76.3865 6.5453 BIG FW BIG −BIG −BIG BIG % FW BIG −BIG −BIG 0.1000 BIG % GW 49.6355 25.4646 0.1000 BIG % GW 0.00084 15.1140 −3.2093 0.1000 BIG % GW 18.1670 0.1000 BIG % GW BIG −BIG −BIG FW: 2745.00 YW: 2745.00 MW: 2083.63 SW: 57.00

210

Processed meats

3. Functional requirements (LCFBIND ≥ 13 FW, LCFWHC:Water ≥ 1.2). 4. Order of predominance and labeling (pork > water, water > beef, beef > sodium lactate). After identifying variables and generating constraints, a mathematical problem of the form Minimize c1 x1 + ... + cn xn

8.19

subject to: a1 1 x1 + ... + a1 n xn ≤ or = or ≥ b1 ...

8.20

am 1 x1 + ... + am n xn ≤ or = or ≥ bm where the {xj} are the (unknown) values of the n variables, and there are m total constraints, each of which is either of the ‘≤’, ‘=’ or ‘≥’ form. The {bi} are fixed (constant) values associated with the constraints, and the {aij} are fixed coefficients of the xj in the inequations. The identification of variables and the parsing of a product specification to generate constraints is typically the most difficult part of the LCF process. 8.4.2 Problem solution The LCF problem given in eqs. (8.19) and (8.20) is a standard one (‘linear programming problem’), amenable to solution by several algorithms, including the famous ‘simplex’ method (see, e.g., Dantzig, 1963). The LCF solution consists of two parts: a logical answer to the question ‘Does a feasible solution to the problem as posed mathematically exist?’ and the {xj} values which either solve the problem, or come closest to doing so. If there is no solution to the problem posed in eqs. (8.19) and (8.20), the problem is called ‘infeasible’. Generally a unique solution is found. 8.4.3 Problem un-build After solving the LCF problem, the problem build must be reversed and the solution put back into the units and references of the original product specification. In complex material management applications, this may also involve decrementing inventory by usage of materials. Reports of the LCF are then generated. Typical examples are shown in Tables 8.4, 8.5 and 8.6. 8.4.4 Sensitivity analysis Most LCF software also has the ability to generate post-solution marginal costs associated with the opportunities of increasing or decreasing material usages (‘cost to use more’ and ‘cost to use less’), and the incremental cost of a unit change in a requirement limit, if that limit is attained (‘penalty cost’).

© Woodhead Publishing Limited, 2011

Table 8.5

Product formulation material usage report for ‘PWBFRANK’ example product

Material name Usage

Percent of GW

Usage range

© Woodhead Publishing Limited, 2011

Description

BF50 PF42 PF72

BF FRSH 50% TRIM PF FRSH 42% TRIM PK FRSH 72% TRIM

588.31 323.83 1171.50

19.6102 10.7942 39.0500

BLOCK WEIGHT (BW): TAP WATER CORN SYRUP DRY CURE (PRAGUE PWD SODIUM ERYTHORBATE SODIUM LACTATE SALT MUSTARD FLOUR SPICE

2083.63

69.4544

591.31 75.00 5.00

19.7102 2.5000 0.1667

638.01 75.00 5.61

335.91 75.00 4.89

0.0020 −0.0181 0.1500 −BIG 0.2999 −210.5374

1.13

0.0375

1.26

1.10

2.9992 −934.0558

90.00 63.94 30.00 60.00

3.0000 2.1312 1.0000 2.0000

90.00 64.04 30.00 60.00

90.00 63.36 30.00 60.00

GROSS WEIGHT (GW): SHRINK LOSS:

3000.00

100.0000

255.00

8.5000

FINISHED WEIGHT(FW):

2745.00

91.5000

YERYTH YLACTATE YSALT ZMUST ZSPICE

BF85 BF90 BFBULL

BF FRSH 85% TRIM BF FRSH 90% TRIM BF FRSH FC BULL MT BZCHEEK BF FROZ CHEEK MT BZHEAD BF FROZ HEAD MT 16 Materials. BW: 2083.63 GW: 3000.00

Use less

588.31 667.72 1373.12

408.51 211.92 734.23

Cost range

ID

WATER YCORN YCURE

Use more

Cost LCF

Use more

0.4499 −BIG 0.3799 0.3772 0.6398 0.4672 0.5458

0.9997 0.0500 0.3099 0.8998

Use less 0.4551 4.3116 0.6420

Penalty cost

Limits on use Lower

Upper

Type

0.0000 0.0000 0.0000

0.0000 BIG 0.0000 BIG 0.0000 BIG

% GW % GW % GW

0.5077 BIG 8.6700

0.0000 0.0000 0.0000

0.0000 BIG 0.0000 BIG 0.0000 BIG

% GW % GW % GW

40.1995

0.0000

0.0000 BIG

% GW

BIG 224.9432 BIG BIG

0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000

BIG BIG BIG BIG

% GW % GW % GW % GW

$1137.25

−BIG −8.8781 −BIG −BIG

0.4370

$1311.01

0.4776

$1311.01

8.5000 % GW

628.31 619.79 226.50

0.8698 0.8571 0.9298 0.8484 1.0197 1.0156

BIG BIG BIG

0.0127 0.0813 0.0041

0.0000 BIG 0.0000 BIG 0.0000 BIG

% GW % GW % GW

389.56

0.6998 0.2741

BIG

0.4257

0.0000 BIG

% GW

332.91 FW: 2745.00 YW: 2745.00

0.4999 0.1119 MW: 2083.63 SW: 57.00

BIG

0.3879

0.0000 BIG

% GW

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Table 8.6

Sample nutritional label report for ‘PWBFRANK’ example

Nutrition Facts Serving Size xxxx (57 g) Servings Per Container xx Amount per Serving Calories 180

Total Fat 16 g Saturated Fat 6 g Trans fat 0.0 g Cholesterol 30 mg Sodium 820 mg Total Carbohydrate 2 g Dietary Fiber 0 g Sugars 1 g Protein 6 g Vitamin A 0% Calcium 0%

Calories from Fat 150 % Daily Value* 25% 31% 10% 34% 1% 0%

Amount per g 3.16174

2.56500

0.28500 0.10739 0.00000 0.52204 14.30129 0.04268 0.00000 0.00918 0.10651

Vitamin C 0% Iron 2%

0.05512 0.10479

0.00351 0.00784

Table 8.5 shows the ‘usage range’ and ‘cost range’ for the example formulation. Material BF50 (fresh beef 50% lean trim) is in the formula at 588.31 lb, based upon its current cost of $0.4499/lb. If that cost were to increase to $0.4551/lb, the usage of BF50 would drop (‘use-less’) to 106.61 lb, ceteris parabis (same limits reached). Material BF85 (fresh beef 85% lean trim) is not used in the formula, based upon its current cost of $0.8698/lb. If that cost were to drop to $0.8571/lb, BF85 would then enter the formula at 653.91 lb (‘use-more’). Table 8.4 illustrates the ‘penalty cost’ of the requirements which have their limits attained. If the 13.0 limit on LCFBIND were to be raised by +1.0 to 14.0, the cost of the formulated product would be raised by $0.03818/ lb. This ‘penalty cost’ will be valid for changes made to this limit which fall in the range (12.9671, 17.1986). When computers were slow and LCF time-consuming, sensitivity analysis was of great importance. Nowadays it is frequently simpler to just adjust assumptions and reformulate.

8.5 Advanced topics There are a number of advanced application issues that are not directly related to SBF, but which must be dealt with in practical applications of LCF as a management tool in meat processing.

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8.5.1 Inventories Frequently meat processors use LCF as a material management tool in production. For this purpose (‘materials requirements planning’ or MRP), it is necessary to maintain a perpetual inventory, coordinate this inventory with that maintained by information services (IS), and include constraints to prevent materials being used beyond that allocated for use. This is generally a complex subject outside the scope of SBF, and may include issues such as lot-based formulation and chemistry and pricing subtleties (see, e.g., Selfridge and LaBudde, 1982).

8.5.2 Multiproduct formulation When determining purchasing or production plans that must incorporate constraints on the usages of scarce materials across multiple products being formulated, the optimum solution will generally be obtained only if all products are combined into a single, large-scale ‘multiproduct’ formulation problem. This multiproduct formulation problem with contain not only constraints associated with particular product requirements, but also inventory and usage requirements across all products, or ‘global’ constraints. The combined problem still has the mathematical form of eqs. (8.19) and (8.20), if variables across all products are included. For a company with many availability restrictions, multiproduct formulation typically results in a 0.5– 1.0% further cost reduction over intelligently sequenced single product formulations on reducing availabilities.

8.5.3 Multicomponent formulation Frequently it is advisable to split the physical flow in production of many meat products into two parts. The first step is a ‘preblend’, which typically consists of meat, water and salts. The second step is a ‘final blend’, where the preblend is combined with a smaller weight of meat, water, salts, spices, sweeteners and other ingredients. The purpose of the preblend is allow a 4–24 hour dwell time for the meat to swell with water and salt to increase subsequent gel strength and water-holding capacity. The time-separated two-step production complicates the phrasing and the solution of the combined product formulation problem. For more information, see LaBudde and Selfridge (1982).

8.5.4 The cost of LCF The name ‘least-cost formulation’ implies that use of LCF will always reduce cost. Although this is true in a narrow sense, it may not be true in an enterprise sense. Manufacturing operations benefit from predictability and consistency in production, and this must be taken into account as well.

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Product blends made with fixed formulae over time will have less chemical and functional attribute consistency owing to uncontrolled variability pass-through from materials (i.e., ‘constant formulae mean varying product’). Fixed formulae thus mean increased giveaway costs and lost opportunities in purchasing, and thus are not, on the average, as economical in material cost as the LCF varying formula solutions would be. But the lower material costs of LCF comes at a cost itself: production must deal with varying formulae for blends. This requires formulation (i.e., engineering) in tandem with production scheduling, and production management is subject to continuing disturbances as formulae change. This degradation of production management results in errors to due miscommunication, misunderstandings, oversights and addition errors. These errors results in decreased production efficiency and increased rework. If the savings from LCF is less than 1% of product cost, the savings may be illusory, owing to the offsets from production inefficiency. In such a situation, the simplicity of the constant formula environment may be preferable, if the resulting finished product variation is tolerable.

8.5.5 Reverse-engineering formulae using LCF and SBF In the USA, for example, the package label disclosure provides a significant quantity of information about the composition of a meat product. The product title and qualifier shows the species and types of meats allowed in the product, and may have a standard of identity in regulations that specifies limits on moisture, fat and protein, and usages of special non-meat ingredients. For example, a product labeled ‘Beef Frank’ in the USA must only skeletal beef as the meat, must have a fat content of less than 30%, the sum of fat plus moisture minus four times protein must not exceed 40%, and there are limits on functional non-meat ingredients. The ingredient statement on the label lists the reverse order of predominance. This places strong constraints on the composition of the product. Finally, the nutritional label places additional restrictions on the relative material usages. In addition to label information, product chemistry, texture and color are measurable in many ways (including sensory panels and testing devices), particularly in comparison to a reference product formulated to known limits. Generally, with the above restrictions on the product formula, it is possible to set up an LCF specification with estimated target limits, formulation the product, and discover an equivalent formula. This process of using LCF for reverse engineering a meat is typically successful in finding a formula that can be used for copying a competitive product in the marketplace. Production of a test batch of two, with subsequent tweaking of formulation limits is usually all that is needed to provide a relatively indistinguishable result. This process of reverse-engineering competitor’s products is a common activity in facilities that bid for contracts to ‘co-pack’ branded products of other companies.

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8.6 Conclusions LCF and SBF models supplied by software vendors have been in widespread and continuous use for nearly 50 years across the meat industry in North America and, to a lesser extent, throughout the world. The models for ‘bind’ and ‘color’ developed by Saffle and coworkers have been validated by vast numbers of production batches. However, despite this pervasive use, the SBF element remains immature and undeveloped. Other than the pioneering work of Saffle and associates in the 1960s, and the presentation by LaBudde and Lanier of the finished product testing of mixture models in the 1990s, little of practical value was done by meat scientists and technologists to improve science-based models of blended meat product properties. The primary reason for this lack of progress is the conspicuous lack of funding available for this type of research, either from government or from industry. Research in the meat industry is driven by regulatory changes (funded by the industry associations) and new function ingredients (funded by ingredient suppliers). A secondary reason why new research is scarce is the difficulty of the studies needed to develop science-based models suitable for use in LCF. Firstly, a large range of meats and ingredients must be included, so that practical formulations can be accomplished. Secondly, meat lots are highly variable, so multiple replications of the experiments are required. Finally, small-scale pilot operations found in university environments have variable product output, sensitive to personnel, equipment and operating conditions. For best results, SBF models should be developed in a controlled, largescale operating process, so that product batch-to-batch uniformity is maximized. The best approach to moving science-based models for formulation forward is to embed academic researchers in a long-term cooperation with a large-scale, well-controlled processing plant. Over a substantial period of time, multiple lots and a wide range of materials can be consistently tested in varying formulae under controlled conditions. Ideally the experiment should involve replication in at least two different plants to provide the most general results. This would obviously require long-term interest on the part of researchers, a substantial budget, and a willingness on the part of plant management to allow outsiders into their process.

8.7 References anderson, hv and clifton, es. (1967). How the small plant can profitably use leastcost sausage formulation. Meat Processing 2: 17. anon. (1970). Linear programming – meat blending. IBM Corporation. carpenter, ja and saffle, rl. (1964). A simple method of estimating the emulsifying capacity of various sausage meats. J Food Sci 29: 774–781.

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charnes, a and cooper, w. (1961). Management Models and Industrial Applications of Linear Programming. Volumes I and II. Wiley, NY. comer, fw and dempster, s. (1981). Functionality of fillers and meat ingredients in comminuted meat products. Can Inst Food Sci Tech J 14: 295–303. cornell, j. (2002). Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data, 3rd ed. Wiley-Interscience, NY. danø, s. (1974). Linear Programming in Industry, 4th ed. Springer-Verlag, NY. dantzig, gb. (1963). Linear Programming and Extensions. Princeton Univ. Press, Princeton, NJ. gordon, a and barbut, s. (1992). Mechanisms of meat batter stabilization: a review. Crit Rev Food Sci & Nutr 32(4): 299–332. hsu, c-k, kolbe e and english, m. (1996). A nonlinear programming technique to develop least cost formulations of surimi products. J Food Proc Eng 20(3): 179–196. labudde, ra. (1991). LaBudde’s Ready Reference. Least Cost Formulations, Ltd., Virginia Beach, VA. labudde, ra. (1992, revised 2006). Review of comminuted and cooked meat product properties from a sol, gel and polymer viewpoint. TR059. Least Cost Formulations, Ltd., Virginia Beach, VA. Available on-line at: http://www.lcfltd.com/downloads/TR059%20review%20properties%20sol%20gel%20polymer.pdf. labudde, ra. (1996). Scientific formulation of low-fat meat products. TR107, Least Cost Formulations, Ltd, Virginia Beach, VA. Available on-line at: http://www. lcfltd.com/downloads/Tr107%20scientific%20formulation%20of%20low-fat%20 meat%20prods.pdf. labudde, ra and cusick, rs. (2003). Color trajectories as visual indication of spoilage in fresh meats. American Meat Science Association, Proc. 56th Annual Reciprocal Meats Conference. Also available as TR195 from Least Cost Formulations, Ltd, Virginia Beach, VA. Available on-line at: http://www.lcfltd.com/downloads/ tr195%20color%20trajectories%20as%20visual%20indication%20of%20 spoilage.pdf. labudde, ra and lanier, tc. (1995). Protein functionality and development of bind values. Amer Meat Sci Assn Recip Meat Conf Proc 48: 59–68. labudde, ra and selfridge, gs. (1982). Preblending. In Romans, JR. et al. (1994). The Meat We Eat, 13th ed. pp. 869–882. Interstate Publishers, Danville, IL. lanier, tc. (1985). Fish proteins in processed meat. Amer Meat Sci Assn Recip Meat Conf Proc 38: 129. lanier, tc and labudde, ra. (1993). Gelation approach to determining bind values for least cost formulation: Phase II studies. Final report to National Live Stock and Meat Board, Chicago, IL. lanier, tc, labudde, ra and carpenter, ja. (1993). Gelation approach to determining bind values for least cost formulation. Final report to National Live Stock and Meat Board, Chicago, IL. pearson, am and tauber, fw. (1984). Processed Meats, 2nd ed. AVI Publishing, Westport, CT. porteous, jd. (1979). Some physico-chemical ‘constants’ of various meats for optimum sausage formulation. Can J Food Sci Technol 12(3): 145–148. pouttu, p and puolanne, e. (2003). A procedure to determine the water-binding capacity of meat trimmings for cooked sausage formulation. Meat Sci 66(2): 329–334. regenstein, jm. (1988). Meat batters: why it is not an emulsion. Amer Meat Sci Assn Recip Meat Conf Proc 41: 40. regenstein, jm. (1989). Are comminuted meat products emulsions or a gel matrix? In Food Proteins, Kinsella, KE and Soucie, WG eds. Amer Oil Chem Soc, Champaign, IL pp. 178–194.

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saffle, rl. (1968). Meat emulsions. Adv Food Res 165: 105–160. saffle, rl, christian, ja, carpenter, ja and zirkle, sb. (1967). Rapid method to determine stability of sausage emulsions and effects of processing temperatures and humidites. Food Tech 21: 100–104. selfridge, gc and labudde, ra. (1982). Least cost formulation. In Romans, JR. et al. (1994). The Meat We Eat, 13th ed. pp. 844–869. Interstate Publishers, Danville, IL. stigler, gj. (1945). The cost of subsistence. J Farm Econ 27(2): 303–314. swift, ce. (1965). The emulsifying properties of meat emulsions. Proc Meat Industry Res Conf, Amer Meat Sci Assn, pp. 78–93. swift, ce. et al. (1961). Comminuted meat emulsions. The capacity of meats for emulsifying fat. Food Technol 15(11): 468. toledo, rt. (1991). Fundamentals of Food Process Engineering, 2nd ed. Van Nostrand Reinhold, NY.

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