A Competitive Analysis of Online Knapsack Problems with Unit Density

Ma, Will; Simchi‐Levi, David; Zhao, Jinglong

doi:10.2139/ssrn.3423199

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…We refer to Borodin and El-Yaniv [3] and to Hentenryck and Bent [4] for a comprehensive description of online algorithms and competitive analyses, to Albers [5] for a survey on online algorithms, and to Jaillet and Wagner [6] for a survey of online vehicle routing problems. Recent contributions have been presented by Chen et al [7] for an online machine minimization problem; Ma et al [8] for online knapsack problems; Ber ǵe et al [9] for the online k-Canadian traveller problem; Li et al [10,11], Yu and Jacobson [12], Shamsaei et al [13], and Jiang et al [14] for online scheduling problems; Akbari et al [15] for a post-disaster road restoration problem; Zhang et al [16] for the management of online orders in modern crowdsourced truck logistics platforms; Shiri et al [17] for ambulance routing in disaster response with partial or no information on victim conditions; Fujii et al [18] for the Secretary problem with predictions; Arnosti et al [19] for static threshold policies in the prophet Secretary problem; Salem et al [20] for Secretary problems with biased evaluations using partial ordinal information; Shiri et al [21] for the ambulance routing problem on a road network; and Chen et al [22] for a review of online integrated production and distribution scheduling. Finally, for an extensive overview of the most recent contributions on online algorithms, we refer the work by to Höhne et al [23][24][25] and Amouzandeh et al [26].…”

Section: Alg(i) Opt(i)mentioning

confidence: 99%

Competitive Analysis of Algorithms for an Online Distribution Problem

Barba,

Bertazzi,

Golden

2024

Algorithms

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We study an online distribution problem in which a producer has to send a load from an origin to a destination. At each time period before the deadline, they ask for transportation price quotes and have to decide to either accept or not accept the minimum offered price. If this price is not accepted, they have to pay a penalty cost, which may be the cost to ask for new quotes, the penalty cost for a late delivery, or the inventory cost to store the load for a certain duration. The aim is to minimize the sum of the transportation and the penalty costs. This problem has interesting real-world applications, given that transportation quotes can be obtained from professional websites nowadays. We show that the classical online algorithm used to solve the well-known Secretary problem is not able to provide, on average, effective solutions to our problem, given the trade-off between the transportation and the penalty costs. Therefore, we design two classes of online algorithms. The first class is based on a given time of acceptance, while the second is based on a given threshold price. We formally prove the competitive ratio of each algorithm, i.e., the worst-case performance of the online algorithm with respect to the optimal solution of the offline problem, in which all transportation prices are known at the beginning, rather than being revealed over time. The computational results show the algorithms’ performance on average and in the worst-case scenario when the transportation prices are generated on the basis of given probability distributions.

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Section: Alg(i) Opt(i)mentioning

confidence: 99%

Competitive Analysis of Algorithms for an Online Distribution Problem

Barba,

Bertazzi,

Golden

2024

Algorithms

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“…Obvious applications of the KP include determining what cargo to load into a plane or truck to transport. Other applications come from finance, we may imagine an investor with limited funds who is seeking to build a portfolio, or apply the framework to warehouse storage for retailers [Ma et al, 2019].…”

Section: Knapsackmentioning

confidence: 99%

OR-Gym: A Reinforcement Learning Library for Operations Research Problems

Hubbs,

Perez,

Sarwar

et al. 2020

Preprint

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Reinforcement learning (RL) has been widely applied to game-playing and surpassed the best human-level performance in many domains, yet there are few use-cases in industrial or commercial settings. We introduce OR-Gym, an open-source library for developing reinforcement learning algorithms to address operations research problems. In this paper, we apply reinforcement learning to the knapsack, multi-dimensional bin packing, multi-echelon supply chain, and multi-period asset allocation model problems, as well as benchmark the RL solutions against MILP and heuristic models. These problems are used in logistics, finance, engineering, and are common in many business operation settings. We develop environments based on prototypical models in the literature and implement various optimization and heuristic models in order to benchmark the RL results. By re-framing a series of classic optimization problems as RL tasks, we seek to provide a new tool for the operations research community, while also opening those in the RL community to many of the problems and challenges in the OR field.

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“…一个后续工作 (参见文献 [79]) 研究了一个单约束条件的背包问题并发展了相应的自适应算法. [80][81][82]) 研究了以竞争比率作为表现评估的问题并提出了可达到常数竞争比率的算法. Jiang 等 [83] 提出了一个自适应阈值策略并得到 O( √ n) 的遗憾.…”

Section: 秘书问题 (Secretary Problem)unclassified

Modern optimization theory and applications

Deng¹,

Jian-jun²,

Ge³

et al. 2020

Sci. Sin.-Math.

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线性规划问题可以说是目前优化领域中最重要且已经被大量研究过的一类问题. 本节将回顾 3 个线性规划相关主题的最新进展: (i) 线性规划算法; (ii) 线性规划和 Markov 决策过程; (iii) 在线线性规划. 本节主要介绍 (i) 和 (ii) 两个领域近期一些比较重要和有趣的发现. (iii) 将在下一节讨论, 希望这些讨论能激发科研工作者在这些领域进行新的研究.

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A Competitive Analysis of Online Knapsack Problems with Unit Density

Cited by 4 publications

References 31 publications

Competitive Analysis of Algorithms for an Online Distribution Problem

Competitive Analysis of Algorithms for an Online Distribution Problem

OR-Gym: A Reinforcement Learning Library for Operations Research Problems

Modern optimization theory and applications

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