Approximating the Joint Replenishment Problem With Deadlines

Nonner, Tim; Souza, Alexander

doi:10.1142/s1793830909000130

Cited by 14 publications

(24 citation statements)

References 14 publications

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“…(They considered an equivalent problem of packet aggregation with deadlines on two-level trees.) Nonner and Souza [NS09] then showed that JRP-D is APX-hard, even if each retailer issues only three demands. Levi, Roundy and Shmoys [LRS06] gave a 2-approximation algorithm based on a primal-dual scheme.…”

Section: I} a Solution (Also Called A Schedule) Is A Set Of Ordementioning

confidence: 99%

“…Levi, Roundy and Shmoys [LRS06] gave a 2-approximation algorithm based on a primal-dual scheme. Using randomized rounding, Levi et al [LRSS08,LS06] (building on [LRS05]) improved the approximation ratio to 1.8; Nonner and Souza [NS09] reduced it further to 5/3. These results use a natural linear-program (LP) relaxation, which we use too.…”

Section: I} a Solution (Also Called A Schedule) Is A Set Of Ordementioning

confidence: 99%

“…Let p be a probability distribution on [0, 1]. As we are about to show, the approximation ratio of algorithm Round p (defined below) and the integrality gap of the LP are at most 1/Z(p), where Z(p) is defined by the following so-called tally game (following [NS09] …”

Section: Upper Bound Of 1574mentioning

confidence: 99%

“…Note that the distribution p that chooses The main ideas underlying Round p and its analysis are from [NS09]; the presentation here (Section 2.1) addresses some technical subtleties. Subsequent sections (with a minor exception) use Lemma 1 as a black box; they can be read independently of the proof in Section 2.1.…”

Section: Upper Bound Of 1574mentioning

confidence: 99%

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Approximation Algorithms for the Joint Replenishment Problem with Deadlines

Bieńkowski

Byrka

Chrobák

et al. 2013

Automata, Languages, and Programming

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The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supplychain management, concerned with optimizing the flow of goods from a supplier to retailers. Over time, in response to demands at the retailers, the supplier ships orders, via a warehouse, to the retailers. The objective is to schedule these orders to minimize the sum of ordering costs and retailers' waiting costs.We study the approximability of JRP-D, the version of JRP with deadlines, where instead of waiting costs the retailers impose strict deadlines. We study the integrality gap of the standard linear-program (LP) relaxation, giving a lower bound of 1.207, a stronger, computerassisted lower bound of 1.245, as well as an upper bound and approximation ratio of 1.574. The best previous upper bound and approximation ratio was 1.667; no lower bound was previously published. For the special case when all demand periods are of equal length we give an upper bound of 1.5, a lower bound of 1.2, and show APX-hardness.

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Section: I} a Solution (Also Called A Schedule) Is A Set Of Ordementioning

confidence: 99%

Section: I} a Solution (Also Called A Schedule) Is A Set Of Ordementioning

confidence: 99%

Section: Upper Bound Of 1574mentioning

confidence: 99%

Section: Upper Bound Of 1574mentioning

confidence: 99%

See 2 more Smart Citations

Approximation Algorithms for the Joint Replenishment Problem with Deadlines

Bieńkowski

Byrka

Chrobák

et al. 2013

Automata, Languages, and Programming

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“…Constraints 13,14,16,17,19,7 are the same as in the LP for Uncapacitated SIRPFL. Constraint 15 requires that the number of trips to v on day s must be at least the total demand at v that were served from day s scaled by the capacity limit.…”

Section: B Capacitated Splittable Sirpflmentioning

confidence: 99%

Inventory Routing Problem with Facility Location

Jiao

Ravi

2019

Lecture Notes in Computer Science

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0000−0001−9583−0784] and R. Ravi 1[0000−0001−7603−1207]Abstract. We study problems that integrate depot location decisions along with the inventory routing problem of serving clients from these depots over time balancing the costs of routing vehicles from the depots with the holding costs of demand delivered before they are due. Since the inventory routing problem is already complex, we study the version that assumes that the daily vehicle routes are direct connections from the depot thus forming stars as solutions, and call this problem the Star Inventory Routing Problem with Facility Location (SIRPFL). As a stepping stone to solving SIRPFL, we first study the Inventory Access Problem (IAP), which is the single depot, single client special case of IRP. The Uncapacitated IAP is known to have a polynomial time dynamic program. We provide an NP-hardness reduction for Capacitated IAP where each demand cannot be split among different trips. We give a 3-approximation for the case when demands can be split and a 6-approximation for the unsplittable case. For Uncapacitated SIRPFL, we provide a 12-approximation by rounding an LP relaxation. Combining the ideas from Capacitated IAP and Uncapacitated SIRPFL, we obtain a 24-approximation for Capacitated Splittable SIRPFL and a 48approximation for the most general version, the Capacitated Unsplittable SIRPFL.

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An Efficient Polynomial-Time Approximation Scheme for the Joint Replenishment Problem

Nonner

Sviridenko

2013

Integer Programming and Combinatorial Optimization

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Approximating the Joint Replenishment Problem With Deadlines

Cited by 14 publications

References 14 publications

Approximation Algorithms for the Joint Replenishment Problem with Deadlines

Approximation Algorithms for the Joint Replenishment Problem with Deadlines

Inventory Routing Problem with Facility Location

An Efficient Polynomial-Time Approximation Scheme for the Joint Replenishment Problem

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