An Integrated Optimizing-Simulator for the Military Airlift Problem

There have been two primary modeling and algorithmic strategies for problems in military logistics: simulation, offering tremendous modeling flexibility, and optimization, which offers the intelligence of math programming. Each offers significant theoretical and practical advantages. In this paper, we use the framework of approximate dynamic programming which produces a form of “optimizingsimulator” which offers a spectrum of models and algorithms which are differentiated only by the information content of the decision function. We claim that there are four information classes, allowing us to construct decision functions with increasing degrees of sophistication and realism as the information content of a decision is increased. Using the context of the military airlift problem, we illustrate the succession of models, and demonstrate that we can achieve improved performance as more information is used. The military airlift problem, faced by the analysis group at the Air Mobility Command (AMC), deals with effectively routing a fleet of aircraft to deliver loads of people and goods (troops, equipment, food and other forms of freight) from different origins to different destinations as quickly as possible under a variety of constraints. In the parlance of military operations, “loads” (or “demands”) are referred to as “requirements.” Cargo aircraft come in a variety of sizes, and it is not unusual for a single requirement to need multiple aircraft. If the requirement includes people, the aircraft has to be configured with passenger seats. There are two major classes of models that have been used to solve the military airlift (and closely related sealift) problem: optimization models (Morton et al. (1996), Rosenthal et al. (1997), Baker et al. (2002)), and simulation models, such as MASS (Mobility Analysis Support System) and AMOS, which are heavily used within the AMC. The analysis group at AMC has preferred AMOS because it offers tremendous flexibility, as well as the ability to handle uncertainty. However, simulation models require that the user specify a series of rules to obtain realistic behaviors. Optimization models, on the other hand, avoid the need to specify various decision rules, but they sharply limit the ability to represent complex operational rules, as well as the ability to incorporate uncertainty. There have been several efforts to incorporate uncertainty using stochastic programming (see, for example, Goggins (1995) and Morton et al. (2002)). However, these have generally been limited to very small problems, and do not improve the ability of optimization models to handle complex operational details. Stochastic programming models appear to be best suited to robust design problems rather than operational problems. One of the biggest weaknesses of simulation models is actually also a strength. Simulation models such as AMOS require that decisions (for example, which aircraft should cover a load of freight) be made using rule-based logic. For problems in transportation and logistics, designing rules that determine which aircraft should cover a load can get extremely complex (in the case of AMOS, the rules are fairly simplistic, and as a result can produce odd results). However, the rules are easy to understand and modify. By contrast, optimization models require that the behavior of a model be governed by various costs and penalties (for example, to govern the tradeoff between flying distance versus using the best type of cargo aircraft for a particular load). Optimization models have been widely studied in the transportation science community (see Crainic & Laporte (1997) for an excellent survey; other examples include Cordeau et al. (1998),