مدل انتخاب ماشین آلات برنامه ریزی انتگرال خطی مخلوط برای سیستم های چندزمینه ای

An integrated program, called MULTIPREDIO, was developed at University of Guanajuato and University Polytechnic of Valencia using mixed integer linear programming linked to several databases contained in spreadsheets to select agricultural machinery for a multifarm system. The program selects the machinery set for each farm, which corresponds to the lowest annual mechanisation cost of the multifarm system through time. The input information consists of variable and fixed costs for 12 yr from the multifarm, the schedule of operations and the different combinations of equipment and the area of each farm. The program works under the environment of the worksheet and the user does not require knowledge of linear programming to understand the input and output of the model program. The program is capable of calculating the number of working days required for each tractor–implement at each farm in the different periods, and also allows to study the effect of changing values on fixed and variable costs through time. A case in Guanajuato, Mexico, for five farms cultivating wheat and sorghum is used to demonstrate the model application because the mechanisation costs are reduced during the passage of time (at the present value), thus affecting the optimum solution in such a way that alternative solutions are found through time. The optimum solution of the machinery park selected for the first year is not the same as that selected through other years. For the studied case three optimal solutions were found, one of them for years 1–5, another one for years 6–8 and the last one for years 9–12. In case of machinery, the optimal solution is below the quantity of tractors available on the five farms.

One of the main problems of the agricultural mechanisation is investing wisely in farm equipment and making good use of them. Indeed, in any country, suitable machinery management is a very common problem, and there have been a number of research studies to optimise those factors involved in the selection of agricultural machinery. The multifarm use of agricultural machinery was introduced to realise the benefits of high capacity but expensive machines that could not be used economically on individual farms. This multifarm use of machinery reduces mechanisation costs considerably. Multifarm use of machinery also allows farmers to apply the most advanced technology and environmentally friendly production techniques in their operations. However, these groups of machinery must be used efficiently because it is possible to have overlapped periods of operation. The program presented in this paper has the following features. (1) It uses a spreadsheet environment, which facilitates changes in any variable. (2) The program can handle different field capacities for each farm. (3) The user requires no knowledge of mixed integer linear programming. (4) The solution time is relatively low, between 1 and 2 min. The main objective of this paper is to present the program for making decisions on investing in machinery utilised in a multifarm system, assigning the correct machine at the correct time to each farm.

The mixed integer linear program (MILP) developed in the Polytechnic University of Valencia for selection of agricultural machinery to minimise mechanisation costs was adapted to be applied in a multifarm system. (2) The addition of restrictions that involve each farm permits consideration of aspects that could not be included in the original program, as are the different effective field capacities in each farm depending upon the average size of the plot and its location with respect to the machinery warehouse. (3) The MILP model developed operates under the environment of a spread sheet which is linked to the databases which contain information for the calculation through 12 yr of the fixed and variable costs of mechanised labour, and the calculation of the field coefficients of each tractor–implement combination in each one of the farms. (4) The developed program is flexible since changes can be introduced easily through the databases, as are acquisition prices of machinery and their characteristics, hand labour costs, fuel prices, size and shape of farms and interest rates. These changes allow to perform sensitivity analysis on technical and economical parameters. The mechanisation costs, as was expected, are reduced during the pass of time (at present value), which affects the optimum solution in such a way that alternative solutions are found through time. The optimum solution of the machinery park selected for the first year is not the same as that selected through for other years. For the studied case three optimal solutions were found, although the mechanisation cost for each solution is similar. (5) The program is capable of calculating the number of working days required for each tractor–implement at each farm in different periods. With this information the manager can easily schedule the machinery according to the needs of the multifarm system. (6) The number of tractors, which are dedicated to the sorghum production and wheat, indicates that the optimal solution is below the quantity of tractors currently available to the ejidos.