Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> Formulating Livestock Rations and Feeding Stuffs <s> Abstract The livestock ration formulation problem is postulated within the framework of multiple-criteria decision-making techniques. This exercise is motivated by the fact that the ordinary least-cost approach can, and does, generate solutions that either cannot be implemented or supply nutritionally undesirable levels of various nutrients. This originates from using cost as the criterion for selecting the ingredients of the diet. But in fact, diet formulation problems involve several criteria and should, therefore, be solved using techniques designed for modelling such problems. This paper is an attempt at introducing these techniques to agricultural systems modellers and then demonstrating their use in livestock ration formulation. The multiple-criteria decision-making techniques covered include goal programming and its variants such as weighted and lexicographic approaches and multiple-objective programming. <s> BIB001 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> Formulating Livestock Rations and Feeding Stuffs <s> Abstract This paper contends that the conventional linear programming paradigm commonly used for livestock ration formulation suffers from several inherent weaknesses. One such weakness is the mathematical rigidity that must be respected to meet the minimum nutritional requirements specified in the model, thus making the paradigm inflexible and unrealistic under many situations. Goal programming techniques, on the other hand, do not impose such rigid conditions and also allow consideration of several decision criteria. This paper represents a departure from the traditional LP approach by formulating the diet formulation problem as a GP model incorporating penalty functions that make the specification of minimum levels of nutrients more flexible and realistic. <s> BIB002 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> Formulating Livestock Rations and Feeding Stuffs <s> Abstract Farmers frequently have to decide whether to keep or to replace cows that suffer from clinical mastitis. A dynamic programming model was developed to optimize these decisions for individual cows within the herd, using the hierarchic Markov process technique. This technique provides a method to model a wide variety of cows, differing in age, productive performance, reproductive status, and clinical mastitis occurrence. The model presented was able to support decisions related to 63% of all replacements. Results—for Dutch conditions—showed the considerable impact of mastitis on expected income of affected cows. Nevertheless, in most cases, the optimal decision was to keep and to treat rather than to replace the cow. Clinical mastitis occurring in the previous lactation negligibly influence expected income. Clinical mastitis in current lactation, especially in the current month, however, had a significant effect on expected income. Total losses caused by clinical mastitis were US$83/yr per cow. Farm level treatment, which reduced incidence by 25% on a farm with 10 clinical quarter cases per 10,000 cow days, may cost at maximum US$27/yr per cow. <s> BIB003 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> Formulating Livestock Rations and Feeding Stuffs <s> Agway uses chance-constrained programming to formulate commercial feeds for animals. The finished feeds averaged 40 percent greater nutritional consistency and were lower in cost than feeds formulated by traditional linear programming with a margin of safety. Formulating animal feeds by chance-constrained programming saves Agway, Inc. more than $250,000 per year. <s> BIB004 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> Formulating Livestock Rations and Feeding Stuffs <s> Despite many advances in biotechnology being futuristic, in some industries such technological improvements are now becoming generally available for absorption into commercial practice. The new reproductive technologies for bovine animals are such an example. For a regulated industry like agriculture, an ex ante evaluation of the impact of their adoption is the concern of policy makers. This paper describes a modelling strategy devised to assess these impacts, using a sequence of stochastic, financial and linear programming models. A set of individual farm type models were developed and later extended to a national model to simulate the interactions that occur between dairy and beef enterprises and the competition between them for resources on individual farms. Restraints reflecting national policies such as quotas on milk production and industry support through subsidies are built into the model to explore several scenarios. These models are used to assess the impact of new technologies on dairy and beef production nationally and for regions which have been identified by the Ministry of Agriculture, Fisheries and Food. <s> BIB005
In the first successful application of mathematical programming in agriculture,  used LP models to determine the least-cost combination for the feeding-stuffs industry and livestock rations at the farm level that would meet specified nutritional requirements. Since the early 1950s, many farmers and most feed mixers have relied on LP for the optimum design of livestock diets. Analysts have extended the original analytical LP framework in several directions. They use parametric LP to study the effect of price changes in ingredients (coefficients of the objective function) on the optimum mix. By analyzing the dual models, they establish the shadow price of each constraint (nutritional requirement) of the model. Incorporating chance-constraint programming increases the realism of the model when the real content of some ingredients is uncertain. Analysts have extended the approach in this field in various ways, including investigating the relationship between the bulk and cost of the ration and using the technique within a practical environment. Despite its proven success, using LP models to determine optimum animal diets is not without difficulties. Decision makers cannot rely on the cost of the blend as the only relevant criterion, especially in calculating livestock rations at the farm level. Farmers seek economically optimal rations that achieve a compromise among such conflicting objectives as cost, bulkiness of the mix, and nutritional imbalances. These objectives introduce multiple criteria in the traditional LP approach. Analysts have formulated multicriteria models for the optimum design of animal diets within a multiple criteria context (for example, BIB001    . Another problem underlying the traditional LP approach is the overrigid specification of nutritional requirements. Some relaxation of the constraints would not seriously affect the animals' performance. Such relaxation would increase the size of the feasible set, allowing a reduction in the cost of the ration. Some analysts have tackled this problem. Thus, BIB002 have addressed the overrigid specifications of nutritional requirements by incorporating a system of penalty functions into a goal-programming model.  A problem methodologically related to formulating livestock rations is determining fertilizer combinations (Minguez et al. 1988 ). Finally, analysts use dynamic programming and Markov models to address other problems in livestock production, such as optimum replacement or culling policies BIB003  and assessing the adoption of new reproductive technologies BIB005 . Even though LP and parametric LP models are still the most widely used models in the feedingstuffs industry, advanced approaches, such as chanceconstraint programming, have led to important savings in this industry BIB004 ).