Purpose – This paper discusses the animal diet problem in grey environment which is adapted to the real situations. In particular, a new approach to solve these problems using is proposed. Design/methodology/approach- With the objective to produce the least cost diet, in the traditional model for optimizing diet problem, the price of foods, the nutrients requirements and the necessity of foods requirement have been considered grey interval numbers. Grey linear programming approach has been employed to solve the grey diet problem. Grey linear programming with flexibility in selection of the coefficients can be more effective for the diet problems. In this research, only the positioned method has been used. The grey diet model is solved by GAMS software based on the positioned method. Findings- The main contribution of this work is introducing new model in the practical case that case that is diet problem under a kind of uncertainty and furthermore proposing a novel method to solve the formulated problem. In this way, using a grey model and applying all restrictions, the least cost for one kilogram of total mixed ration was 6893 to 10163 Rials, and at this level cow, nutrient requirement was met. Based on the numerical examination, which was done on the real case, the achieved results have showed that the uncertainty of foods requirement and nutrients requirements had slight effect on the animal budget diet. Originality/value – This problem must be viewed from another perspective because of the uncertainty regarding the amount of nutrients per unit of foods and the diversity of animals’ daily needs to receive them. In particular, a new method to optimize the fully mixed diet of lactating cows in early lactation that are readily available in the northeast of Iran in uncertainty environment has been proposed.
