Parallel algorithm for solving integer linear programs

Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for solving ILPs. We discuss a serial algorithm using a breadth-first branch-and-bound search to check the feasible solution space, and then extend it into a parallel algorithm using a client-server model. In the parallel mode, the search may not be truly breadth-first, depending on the solution time for each node in the solution tree. Our search takes advantage of pruning, often resulting in super-linear improvements in solution time. Finally, we present results from sample ILPs, describe a few modifications to enhance the algorithm and improve solution time, and offer suggestions for future work.

Farmer land allocation for maize, groundnut and cotton production in Chipata District, Eastern Province, Zambia

Small-scale farmers in the Chipata District of Zambia rely on their farm fields to grow maize and groundnuts for food security. Cotton production and surplus food security crops are used to generate income to provide for their families. With increasing population pressure, available land has decreased and farmers struggle to provide the necessary food requirements and income to meet their family’s needs. The purpose of the study was to determine how a farmer can best allocate his land to produce maize, groundnuts and cotton when constrained by labor and capital resources to generate the highest potential for food security and financial gains. Data from the 2008-2009 growing season was compiled and analyzed using a linear programming model. The study determined that farmers make the most profit by allocating all additional land and resources to cotton after meeting their minimum food security requirements. The study suggests growing cotton is a beneficial practice for small-scale subsistence farmers to generate income when restricted by limited resources.