Optimization Models for Military Aircraft Deployment

摘要

A military aircraft deployment problem from the United States Transportation Command is modeled as a generalized transportation problem with side constraints and solved using a general purpose linear programming package. The model involves the assignment of military units and material to aircraft and the assignment of aircraft to missions in order to appraise the utility and to determine the assets required for preliminary military operation plans. A transformation of this model which aggregates variables relating to the early or late delivery of requirements is also described. A specialized algorithm which separates an instance of the model into subgroups of independent time windows, finding the globally optimal solution by solving independent subproblems, I also explored. Lastly, an integer rounding model is described which converts continuous solutions to integer in order to facilitate implementation of the former models with an existing post-solution processor. Excellent quality solutions are provided for problems involving nine routes, 80 movement requirements distributed across two cargo classes involving 200,000 short tons of freight, and 250 aircraft using four different aircraft types for each of 12 time periods. The problem, which has the potential of having over 10,000 variables, is reduced significantly using variable reduction and the aggregation transformation. The reduced problem required approximately 1,000 variables and 300 constraints and solutions are obtainable in under 14 minutes using the General Algebraic Modeling System (GAMS) on an 80286-based personal computer. Keywords: Linear programming; Air transportation; Transport aircraft. (EDC)