Optimization of Sea and Air Transportation

In recent years, sea and air transport is becoming a big trend. However, papers concerning sea and air transport can hardly be seen for mathematical formulation and its analysis. In this paper, we make mathematical formulation of the case single supply site and single demand site with multiple delivery dates/different delivery quantities as of a fundamental one. Under certain constraints, minimum cost is pursued. Objective function is expanded from considering transportation cost to considering transportation cost and warehouse stock fee where reduced cost is taken into consideration according to the shortened days to the delivery due date. Simple numerical example is examined. Next, expansion is executed as for the case single supply site and multiple demand sites. Formulation expansion is executed as for the case multiple supply sites and single demand site. By formulating sea and air transport problem, it can be handled clearly and smoothly. Various solving method should be examined hereafter.