This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf (1994).Economics, Equilibrium Pricing; MIP models of markets, MIP Applications
A single-channel magnetic induction system operating at 10 MHz has been constructed. The system consists of an excitation coil and a sensing coil, between which different objects can be scanned. The eddy currents induced in the object cause perturbations in the sensed magnetic field, which are measured with a phase-sensitive detector with backing off of the signal to improve sensitivity. Scans were obtained for saline solutions with conductivities ranging from 0.001 to 6 Sm-1, encompassing the range for biological tissues. The imaginary part of the perturbation in the sensed magnetic field was found to be proportional to saline conductivity, consistent with theoretical prediction, and had a constant of proportionality of -1.2% per Sm-1. A filtered back-projection algorithm was used to generate tomographic images from the scans.
This report discusses the design of computational experiments to test heuristic methods and provides reporting guidelines for such experimentation. The goal is to promote thoughtful, well-planned, and extensive testing of heuristics, full disclosure of experimental conditions, and integrity in and reproducibility of the reported results. 1
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