Make-to-Order Integrated Scheduling and Distribution

Azar, Yossi; Epstein, Amir; Jeż, Łukasz; Vardi, Adi

doi:10.1137/1.9781611974331.ch11

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…[13 13]) as an α-HSBT. 6 In the offline version of the metric min-cost perfect matching problem it suffices to consider only sets (rather than multisets) for the input and output instances. The generalization to multisets is necessary for the transition to the online version of the problem.…”

Section: Preliminariesmentioning

confidence: 99%

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Online matching: haste makes waste!

Emek

Kutten

Wattenhofer

2016

Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing

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This paper studies a new online problem, referred to as min-cost perfect matching with delays (MPMD), defined over a finite metric space (i.e., a complete graph with positive edge weights obeying the triangle inequality) M that is known to the algorithm in advance. Requests arrive in a continuous time online fashion at the points of M and should be served by matching them to each other. The algorithm is allowed to delay its request matching commitments, but this does not come for free: the total cost of the algorithm is the sum of metric distances between matched requests plus the sum of times each request waited since it arrived until it was matched. A randomized online MPMD algorithm is presented whose competitive ratio is O(logwhere n is the number of points in M and ∆ is its aspect ratio. The analysis is based on a machinery developed in the context of a new stochastic process that can be viewed as two interleaved Poisson processes; surprisingly, this new process captures precisely the behavior of our algorithm. A related problem in which the algorithm is allowed to clear any unmatched request at a fixed penalty is also addressed. It is suggested that the MPMD problem is merely the tip of the iceberg for a general framework of online problems with delayed service that captures many more natural problems.

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Section: Preliminariesmentioning

confidence: 99%

“…3 3, we show in Sec. 6 6 that the competitive ratio of its natural deterministic counterpart is Ω(n).…”

Section: Introductionmentioning

confidence: 99%

Online matching: haste makes waste!

Emek

Kutten

Wattenhofer

2016

Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing

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“…There are many other problems that use this paradigm: most notably the ski-rental problem and its continuous counterpart, the spin-block problem [29], where a purchase decision can be delayed until renting cost becomes sufficiently large. Such rent-or-buy (wait-or-act) trade-offs are also found in other areas, for example in aggregating messages in computer networks [1,11,21,28,31,39], in aggregating orders in supply-chain management [9,10,14,15,17,18] or in some scheduling variants [6].…”

Section: Related Workmentioning

confidence: 85%

“…)) = |L(T )|. Therefore, applying(6) to the whole tree T yields ws(T ) ≤ (ws(L(T )) + |L(T )|) log 2 (ξ+2) = (2 • |L(T )|) log 2 (ξ+2) = (ξ + 2) • |L(T )| log 2 (ξ+2) . Hence, weight(T ) weight(L(T )) = ws(T ) ws(L(T )) ≤ (ξ + 2) • |L(T )| log 2 (ξ+2) |L(T )| = (ξ + 2) • |L(T )| log 2 (ξ/2+1) ,which concludes the proof.…”

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confidence: 99%

A Match in Time Saves Nine: Deterministic Online Matching with Delays

Bieńkowski

Kraska

Schmidt

2018

Approximation and Online Algorithms

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We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online algorithm is to match them in pairs. In contrast to traditional online matching problems, in MPMD all requests appear online and an algorithm can match any pair of requests, but such decision may be delayed (e.g., to find a better match). The cost is the sum of matching distances and the introduced delays.We present the first deterministic online algorithm for this problem. Its competitive ratio is O(m log 2 5.5 ) = O(m 2.46 ), where 2m is the number of requests. This is polynomial in the number of metric space points if all requests are given at different points. In particular, the bound does not depend on other parameters of the metric, such as its aspect ratio. Unlike previous (randomized) solutions for the MPMD problem, our algorithm does not need to know the metric space in advance. time τ , an online algorithm may decide to match any pair of requests (p i , t i ) and (p j , t j ) that have already arrived (τ ≥ t i and τ ≥ t j ) and have not been matched yet. The cost incurred by such matching edge is dist(p i , p j ) + (τ − t i ) + (τ − t j ), i.e., is the sum of the connection cost and the waiting costs of these two requests.The goal is to eventually match all requests and minimize the total cost. We use a typical yardstick to measure the performance: a competitive ratio [13], defined as the maximum, over all inputs, of the ratios between the cost of an online algorithm and the cost of an optimal offline solution Opt that knows the entire input sequence in advance.

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Joint replenishment meets scheduling

Györgyi

Kis

Tamási

et al. 2022

J Sched

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In this paper, we consider a combination of the joint replenishment problem (JRP) and single-machine scheduling with release dates. There is a single machine and one or more item types. Each job has a release date, a positive processing time, and it requires a subset of items. A job can be started at time t only if all the required item types were replenished between the release date of the job and time point t. The ordering of item types for distinct jobs can be combined. The objective is to minimize the total ordering cost plus a scheduling criterion, such as total weighted completion time or maximum flow time, where the cost of ordering a subset of items simultaneously is the sum of a joint ordering cost, and an additional item ordering cost for each item type in the subset. We provide several complexity results for the offline problem, and competitive analysis for online variants with min–sum and min–max criteria, respectively.

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Make-to-Order Integrated Scheduling and Distribution

Cited by 4 publications

References 16 publications

Online matching: haste makes waste!

Online matching: haste makes waste!

A Match in Time Saves Nine: Deterministic Online Matching with Delays

Joint replenishment meets scheduling

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