在线配送问题算法的竞争力分析

Algorithms Pub Date : 2024-06-03 DOI:10.3390/a17060237
Alessandro Barba, L. Bertazzi, Bruce L. Golden
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引用次数: 0

摘要

我们研究的是一个在线配送问题,在这个问题中,生产者必须将货物从起点运往终点。在截止日期前的每个时间段,他们都会询问运输报价,并决定接受或不接受最低报价。如果不接受该价格,则必须支付惩罚成本,可能是要求新报价的成本、延迟交货的惩罚成本或在一定时间内储存货物的库存成本。我们的目标是最大限度地降低运输成本和惩罚成本之和。这个问题在现实世界中有着有趣的应用,因为现在可以从专业网站上获得运输报价。我们的研究表明,考虑到运输成本和罚款成本之间的权衡,用于解决众所周知的秘书问题的经典在线算法平均而言无法为我们的问题提供有效的解决方案。因此,我们设计了两类在线算法。第一类基于给定的接受时间,第二类基于给定的门槛价格。我们正式证明了每种算法的竞争比率,即在线算法相对于离线问题最优解的最坏情况性能,在离线问题中,所有运输价格在一开始都是已知的,而不是随着时间的推移而揭示的。计算结果显示了根据给定概率分布生成运输价格时,算法的平均性能和最坏情况下的性能。
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Competitive Analysis of Algorithms for an Online Distribution Problem
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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