Approximate Network Model Research Articles

A novel approach for designing rental vehicle repositioning strategies

An important tactical decision for vehicle rental providers is the design of a repositioning strategy to balance vehicle utilization with customer wait times due to vehicle unavailabilities. To address this problem, this article analyzes alternative repositioning strategies: a no-repositioning strategy, a customer repositioning strategy, and a vehicle repositioning strategy, using queuing network models that are able to handle stochastic demand and vehicle unavailabilities. Optimization models are formulated to determine the repositioning fractions for alternate strategies that minimize the rental provider’s cost by balancing repositioning costs with customer waiting penalty costs. The nonlinear optimization problems are challenging to solve because the objective functions are non-differentiable and the decision variables (such as effective arrival rates and customer repositioning fractions) are interrelated. Therefore, a two-phase sequential solution approach to estimate the repositioning fractions is developed. Phase 1 determines the effective arrival rates by developing an approximate network model, deriving structural results, determining a high-quality solution point, and refining the solution. Phase 2 determines the repositioning fractions by solving a transportation problem. Numerical experiments are used to evaluate the efficacy of the proposed solution approach, to analyze alternate repositioning strategies, and to illustrate how the developed techniques can be adopted to create a better readiness at a depot.

Automated computer-controlled tuning of waveguide filters using adaptive network models

This paper describes a method for computer-controlled tuning of waveguide filters. The tuning algorithm is based on approximate filter network models, which take into account the effects of input/output coupling. Based on measurements of an initial filter design, the approximate network model is then corrected by optimizing the element values such that they minimize the mean square error between the measured and simulated response. The sensitivities of the tuning screws are determined directly from the sensitivities of the element values. Filter tuning is accomplished by gradient optimization of the corrected computer model rather than its physical realization. Only as a final step are the tuning screws of the physical model turned to the position determined by the optimization process.