Formulation and analysis of some combat-logistics problems

Abstract

Models are developed to study the readiness and subsequent combat performance of an air-interceptor squadron facing sudden attack. These models necessarily link combat with logistics. The models are mainly analytical and not a Monte Carlo simulation, and can be used to indicate the optimal weapon system to be procured and to study the effect of peacetime decisions on combat outcomes. The logistics models use the matrix-geometric approach to study the general multivariate repairman problem, with the possibility of simultaneous component failures. A repairman assignment problem is formulated and solved using a multivariate continuous-time Markov decision process. Surprise scenarios are analyzed and represented explicitly. Air-to-air combat is modelled as a transient multivariate continuous-time discrete-state Markov process. Diffusion theory is used to approximate the solutions. The reason for using diffusions is ease of interpretation and computational economy. A comparison with simulation results shows that diffusion yields good approximations. Improvement to the diffusion approximation is provided by applying "large deviations" procedures.