Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget

In stochastic simulation, input uncertainty (IU) is caused by the error in estimating the input distributions using finite real-world data. When it comes to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the failure of many existing selection procedures. In this paper, we study R&S under IU by allowing the possibility of acquiring additional data. Two classical R&S formulations are extended to account for IU: (i) for fixed confidence, we consider when data arrive sequentially so that IU can be reduced over time; (ii) for fixed budget, a joint budget is assumed to be available for both collecting input data and running simulations. New procedures are proposed for each formulation using the frameworks of Sequential Elimination and Optimal Computing Budget Allocation, with theoretical guarantees provided accordingly (e.g., upper bound on the expected running time and finite-sample bound on the probability of false selection). Numerical results demonstrate the effectiveness of our procedures through a multi-stage production-inventory problem

A Survey on Monochromatic Connections of Graphs

The concept of monochromatic connection of graphs was introduced by Caro and Yuster in 2011. Recently, a lot of results have been published about it. In this survey, we attempt to bring together all the results that dealt with it. We begin with an introduction, and then classify the results into the following categories: monochromatic connection coloring of edge-version, monochromatic connection coloring of vertex-version, monochromatic index, monochromatic connection coloring of total-version.Comment: 26 pages, 3 figure