A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions

We consider the problem of optimally allocating the seats on a single flight leg to the demands from multiple fare classes that arrive sequentially. It is well-known that the optimal policy for this problem is characterized by a set of protection levels. In this paper, we develop a new stochastic approximation method to compute the optimal protection levels under the assumption that the demand distributions are not known and we only have access to the samples from the demand distributions. The novel aspect of our method is that it works with the nonsmooth version of the problem where the capacity can only be allocated in integer quantities. We show that the sequence of protection levels generated by our method converges to a set of optimal protection levels with probability one. We discuss applications to the case where the demand information is censored by the seat availability. Computational experiments indicate that our method is especially advantageous when the total expected demand exceeds the capacity by a significant margin and we do not have good a priori estimates of the optimal protection levels.     

A Comparative Study of Receptor-Targeted Magnetosome and HSA-Coated Iron Oxide Nanoparticles as MRI Contrast-Enhancing Agent in Animal Cancer Model

Magnetosomes are specialized organelles arranged in intracellular chains in magnetotactic bacteria. The superparamagnetic property of these magnetite crystals provides potential applications as contrast-enhancing agents for magnetic resonance imaging. In this study, we compared two different nanoparticles that are bacterial magnetosome and HSA-coated iron oxide nanoparticles for targeting breast cancer. Both magnetosomes and HSA-coated iron oxide nanoparticles were chemically conjugated to fluorescent-labeled anti-EGFR antibodies. Antibody-conjugated nanoparticles were able to bind the MDA-MB-231 cell line, as assessed by flow cytometry. To compare the cytotoxic effect of nanoparticles, MTT assay was used, and according to the results, HSA-coated iron oxide nanoparticles were less cytotoxic to breast cancer cells than magnetosomes. Magnetosomes were bound with higher rate to breast cancer cells than HSA-coated iron oxide nanoparticles. While 250 μg/ml of magnetosomes was bound 92 ± 0.2%, 250 μg/ml of HSA-coated iron oxide nanoparticles was bound with a rate of 65 ± 5%. In vivo efficiencies of these nanoparticles on breast cancer generated in nude mice were assessed by MRI imaging. Anti-EGFR-modified nanoparticles provide higher resolution images than unmodified nanoparticles. Also, magnetosome with anti-EGFR produced darker image of the tumor tissue in T2-weighted MRI than HSA-coated iron oxide nanoparticles with anti-EGFR. In vivo MR imaging in a mouse breast cancer model shows effective intratumoral distribution of both nanoparticles in the tumor tissue. However, magnetosome demonstrated higher distribution than HSA-coated iron oxide nanoparticles according to fluorescence microscopy evaluation. According to the results of in vitro and in vivo study results, magnetosomes are promising for targeting and therapy applications of the breast cancer cells.