Linear Programming and Mixed Integer Programming in Management of Seedling Transportation

Abstract

In this paper, the applicability of linear programming (LP) in management of seedling transportation was compared to that of mixed integer programming (MIP). In the LP model, presented in an earlier paper, a linear objective function was used as a surrogate for the actual objective function, which is intrinsically nonlinear. In the LP model, transportation costs were determined per seedling, whereas in the MIP model they were based on vehicle loads. When the number of transported seedlings within a certain period decreased, for instance, due to planting through the growth period, the computational accuracy of the LP model was clearly lower than that of the MIP model. Despite that, differences in allocation of orders between these two models were small. Thus, in the actual business situation of Finnish nursery companies, standard LP seems to be an adequate tool for management of seedling transportation. From the standpoint of cost-efficient seedling business, planting through the growth period increased optimal transportation costs markedly. In addition to the seedling business, these results can be utilized in other types of business dealing with analogous transportation problems.