Automatic Dimension Selection for a Non-negative Factorization Approach to Clustering Multiple Random Graphs

We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare its performance with two standard clustering algorithms.Comment: This paper has been withdrawn by the author due to a newer version with overlapping content

An Optimal Inventory Model for a Retailer with Price Dependent Demand and Unavailability Supply

Today many retailers face high competition, therefore they have to operate in an efficient way. One aspect of efficiency is inventory. Many research on inventory is conducted intensively to get more realistic inventory model. In this paper, an inventory model was developed by considering pricing. Many retailers try to increase their profit by setting the best price for a single item, especially for some items that have high price-dependent demand. The customer demand depends on the price such household items. In the other side, some retailers face supply problems. Supplier often cannot supply products when the products needed on time. There is delay time between customer demand and products arrive at retailer warehouse. The retailer should determine the optimal price and replenishment time. There are some assumptions are used for the model. The first assumption, the demand is known and has constant elasticity. Second, there is stochastic replenishment period and demand that are not filled are lost sales. The model is developed mathematically and a numerical example is conducted to show how the model works. A sensitivity analysis is accomplished to get some management insight and some interesting result are derived. Keywords: deteriorating inventory model; genetic algorithm; stochastic tim