The Multi-shop Ski Rental Problem

We consider the {\em multi-shop ski rental} problem. This problem generalizes the classic ski rental problem to a multi-shop setting, in which each shop has different prices for renting and purchasing a pair of skis, and a \emph{consumer} has to make decisions on when and where to buy. We are interested in the {\em optimal online (competitive-ratio minimizing) mixed strategy} from the consumer's perspective. For our problem in its basic form, we obtain exciting closed-form solutions and a linear time algorithm for computing them. We further demonstrate the generality of our approach by investigating three extensions of our basic problem, namely ones that consider costs incurred by entering a shop or switching to another shop. Our solutions to these problems suggest that the consumer must assign positive probability in \emph{exactly one} shop at any buying time. Our results apply to many real-world applications, ranging from cost management in \texttt{IaaS} cloud to scheduling in distributed computing

On Optimal Consistency-Robustness Trade-Off for Learning-Augmented Multi-Option Ski Rental

The learning-augmented multi-option ski rental problem generalizes the classical ski rental problem in two ways: the algorithm is provided with a prediction on the number of days we can ski, and the ski rental options now come with a variety of rental periods and prices to choose from, unlike the classical two-option setting. Subsequent to the initial study of the multi-option ski rental problem (without learning augmentation) due to Zhang, Poon, and Xu, significant progress has been made for this problem recently in particular. The problem is very well understood when we relinquish one of the two generalizations -- for the learning-augmented classical ski rental problem, algorithms giving best-possible trade-off between consistency and robustness exist; for the multi-option ski rental problem without learning augmentation, deterministic/randomized algorithms giving the best-possible competitiveness have been found. However, in presence of both generalizations, there remained a huge gap between the algorithmic and impossibility results. In fact, for randomized algorithms, we did not have any nontrivial lower bounds on the consistency-robustness trade-off before. This paper bridges this gap for both deterministic and randomized algorithms. For deterministic algorithms, we present a best-possible algorithm that completely matches the known lower bound. For randomized algorithms, we show the first nontrivial lower bound on the consistency-robustness trade-off, and also present an improved randomized algorithm. Our algorithm matches our lower bound on robustness within a factor of e/2 when the consistency is at most 1.086.Comment: 16 pages, 2 figure

Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis

In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.Comment: 23 pages, 1 figur

Spartan Daily, October 16, 1981

Volume 77, Issue 32https://scholarworks.sjsu.edu/spartandaily/6808/thumbnail.jp

Spartan Daily, December 5, 1962

Volume 50, Issue 50https://scholarworks.sjsu.edu/spartandaily/4371/thumbnail.jp

Montana Kaimin, November 18, 2020

Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/10769/thumbnail.jp

Lake Powell

The purpose of the “Lake Powell’ case is to help students of Strategic Management learn the process of strategic management. This case can provide an opportunity for the students to learn strategy formulation and implementation along with some of the current issues such as “cooking the books”. Some sections of the Lake Powell case are real life situations, but all of the numbers and most of operations information are fictitious. Four experienced and knowledgeable men started Lake Powell Company with many opportunities and strength. However the company has lost money in the last five years. Students analyze, formulate and write an implementation of a strategy to save this company. Students then try to answer the following questions. What should be the proposed plan to Richmond for the Marina in order to have an effective, efficient, and profitable operation? How would it be funded? However the instructor will look at other scenarios and ask the students to figure out the four partner’s real goal

Housing church and community space : the St. Andrew's Place redevelopment project

Report : 39 leaves : ill