Table 1.
Feed formulation technique and various models used from 1980 to 2020.
| Year | Livestock | Application/Objective | Reference | |
| 1980 | Beef | A beef cattle ration formulation technique that satisfies the nutrient standards. | [52] | |
| Lactating cow/growing cattle | Existence of variability in the nutrient requirements of individual animals and errors in feed intake prediction. | [53] | ||
| Mature dairy cows | The integration of current biological knowledge into mathematical models that can be used both as a framework for defining research priorities and for making decisions on dairy cattle feeding. | [54] | ||
| Unspecified | The introduction of multiple-criteria decision-making techniques to agricultural systems modelers and the demonstration of their use in livestock ration formulation. |
[48] | ||
| 1985 | Broilers Chick | Least-cost optimizer. This model calculates the dietary nutrients dynamically for the entire growth period. | [55] | |
| Laying hens | To simultaneously determine both the optimum economic dose and nutrient density of feed for laying hens. | [56] | ||
| 1990 | Unspecified | The development of a ration formulation program. | [50] | |
| Turkey | Predicting the values of the flock performance indicators of significant economic importance, body weight and feed consumption. |
[57] | ||
| Dairy cow | A method for relaxing the right-hand sides of a least-cost ration. | [58] | ||
| Dairy cow | Minimize cost and maximize the amounts of stored feeds in the diet. | [59] | ||
| Dairy cow | The relaxation of over-rigid specifications of nutrient requirements for livestock rations. |
[37] | ||
| Not specified. | To formulate two non-linear optimization problems as an iterative sequence of LP problems. | [60] | ||
| Dairy cattle | Treats the fuzziness of the right-hand side of constraint functions in nutrient requirement. It also combines both relaxation and improvement in trade-offs considered. | [61] | ||
| Dairy cow | The determination of a realistic optimal replacement strategy. | [62] | ||
| 1995 | Dairy cow | An estimate of the cost of feeding a cow was studied, and the identification of alternative lower-cost forage practices with the potential to replace feeding hay. | [63] | |
| 2000 | Broiler grower ration | To minimize nutrient variance and ration cost. | [38] | |
| Broiler | Identification of optimal feed mix that maximizes profit margin. | [64] | ||
| 2005 | Pig | Determination of the optimal composition for an animal diet that will provide the best result for the animal. | [5] | |
| Dairy cows | To operationalize a programming method that can be used on a farm in deciding the optimum diet formulation and minimization of nutrient loading. | [65] | ||
| Sheep, dairy cow, and buffalo | Three models were developed for maximizing animal weight gain in sheep, cow milk yield, and buffalo weight gain. | [66] | ||
| Pig | An optimization method based on the traditional least-cost method that reduces feed cost and total phosphorus. | [67] | ||
| Beef | Optimization of feed formulation with least-cost ration while ensuring a lesser risk of worsening its nutritional value. | [68] | ||
| Unspecified | This method confronts the cost of the ration and meets nutrient requirements while enhancing the feed formulation process. | [69] | ||
| Dairy cow | By applying a penalty function and merging two models, a more efficient ratio was formulated in terms of economic and nutritional values. | [70] | ||
| Pig | A 3-step approach is used to formulate a nutritionally and economically balanced ration that meets organic farming conditions. | [70] | ||
| Beef | Preparation of a user-friendly tool for optimal ration formulation via the combination of mathematical programming techniques. | [70] | ||
| Unspecified | Determination of optimal livestock feed blend. | [71] | ||
| Beef | In the determination of economically and environmentally optimal rations using various feed resources. | [72] | ||
| Dairy cow | A linear fuzzy model was used instead of linear programming models, reducing feed cost to about eight percent. | [73] | ||
| Poultry | The application of a linear programming approach for higher productivity level. | [74] | ||
| Unspecified animal | The development of a feed formula to optimize maximum weight gain. | [75] | ||
| Cattle | The cost minimization of ration and maximization of the value of nutrients at different weight stages. | [30] | ||
| 2010 | Fish feed | The development of an optimized feed formulation model to enhance productivity. |
[76] | |
| 2020 | Broiler | To optimize energy density and bird performance. | [77] | |
| Dairy cow | To develop the optimal feed mix for dairy cows at different stages of livestock. | [78] | ||
| Livestock | The determination of the optimal livestock feed mix. |
[78] | ||
| Broiler | To minimize the total production cost of the diet ration and make it affordable for the average farmer. |
[36] | ||
| Sheep, cattle, and rabbit | High priority materials are selected by the decision-makers to solve the mixture problem and cost minimization and optimization was also achieved in the study. | [79] | ||
| Unspecified animal. | Feed formulation technique to produce an optimal solution that is both economical and high energy yield. | [31] | ||
| Broiler | Feed ration formulation to find the optimal quantities of Moringa Oleifera | [80] | ||
| Poultry | Development of an optimal solution that is both economical and brings out the best energy yield. | [79] | ||
| Poultry | The development of a generic decision support system for feed formulation optimization. | [79] | ||
| Beef Cattle | Identifying a least-cost ratio that captures the volatility of feedstuff prices. | [6] | ||
| Dairy cattle during pregnancy | The use of a real-coded genetic algorithm (RGA) to find least-cost feedstuffs without any nutrient deficiency. | [81] | ||
| Animal diet | The evaluation of optimal values for feed components to achieve minimum cost and maximum shelf life. |
[82] | ||
| Animal diet | To obtain an optimized animal ration at minimum costs and better shelf life. | [82] | ||
| Poultry | To find the minimum cost of feeding, considering many factors (the purpose of breeding, poultry type, growth stage, nutritional requirements, and available feedstuffs). | [83] | ||
| Broiler | The development of a tool for broiler diet formation designed to target and reduce specific environmental impact categories in the UK and US. | [84] | ||
| Pig | An algorithm was developed to formulate diets that minimize the feed cost per kg live weight gain (least-cost) for the grower/finisher phase in each tax scenario. | [85] | ||
| Dairy Cow | The development of algorithms for formulating an optimal feed mix with minimal cost and maximum shelf life at distinct stages of livestock. | [30] | ||
| Shrimp | To formulate the most appropriate combination of ingredients for shrimp to tackle the feed mix problem by leveraging genetic algorithms. | [86] | ||
| Broiler | To access the nutritional and economic benefits of using a multi-stage linear programming model as an optimization model in broiler feed formulation. | [84] | ||
| Swine | Studied the economic and environmental concerns (cost and phosphorus content) involved with introducing distiller’s dried grains with soluble to swine feed rations, which minimized cost and reduced the phosphorus content. | [87] | ||
| Sheep, cattle, and rabbit | The use of a model that specifies the type of material and the amount of the material to be selected. | [88] | ||
| Non-pregnant dairy buffaloes | Optimization of the total mixed ration cost where the vital requirements for the feed are met with no deficiency in nutrients. | [89] | ||
| Dairy and beef cattle | An evolutionary algorithm minimizes feed cost and deviation from the specified requirements. | [28] | ||
| 2020 | Poultry | The use of linear programming technique in the minimization of cost in a small-scale poultry farm. | [83] | |
| Poultry | In the determination of economically and environmentally optimal rations using various feed resources. | [90] | ||
| Legend | ||||
| Methods/Models | ||||
| Linear programming algorithm | ||||
| Multi-goal programming | ||||
| Multi-objective optimization algorithm | ||||
| Mixed-integer programming | ||||
| Simulation | ||||
| Combination spreadsheet | ||||
| Non-linear programming | ||||
| Multi-criteria decision model | ||||
| Stochastic programming | ||||
| Goal programming | ||||
| Least-cost feed formulation method | ||||
| Linear fuzzy model | ||||
| proximal bundle approach | ||||
| Real-coded genetic algorithm | ||||
| Java Programming | ||||
| Evolutionary algorithm | ||||
| Multi-stage linear programming | ||||