A linear programming formulation of a semi-Markov model to design pig facilities

Housing facilities design represents the main strategic decision in pig farms. This paper introduces a linear programming formulation of a semi-Markov process to approach the facilities design. Thus, the Linear Programming formulation determines the optimum replacement policy and provides the equilibrium distribution of the herd along pig facilities. Then, the calculation of the associated needs of room for each sow facility is derived from sow herd distribution at equilibrium. Results show the flexibility of the model for designing pig facilities and computational advantages in the solving procedure compared to previous proposals. Furthermore, the robustness of the optimal solution is studied by means of sensitivity analysis.