A 5/3-Approximation Algorithm for Joint Replenishment with Deadlines

Nonner, Tim; Souza, Alexander

doi:10.1007/978-3-642-02026-1_3

Cited by 13 publications

(10 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The JRP-D is shown NP-hard in the strong sense by Becchetti, et al [6] as claimed by Bienkowski et al [7], and APX-hardness is proved by Nonner and Souza [24], whole also describe an 5/3-approximation algorithm. Bienkowski et al [7] provide an 1.574 approximation algorithm, and new lower bounds for the best possible approximation ratio.…”

Section: Literature Reviewmentioning

confidence: 89%

“…The NP-hardness of JRP-W with linear delay cost functions follows from that of JRP-INV (reverse the time line). This has been sharpened by Nonner and Souza [24] by showing that the problem is still NP-hard even if each item admits only three distinct demands over the time horizon. Buchbinder et al [10] study the online variant of the problem providing a 3-competitive algorithm along with a lower bound of 2.64 for the best possible competitive ratio.…”

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Joint replenishment meets scheduling

Györgyi¹,

Kis²,

Tamási³

et al. 2021

Preprint

View full text Add to dashboard Cite

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. keywords Joint replenishment single machine scheduling complexity polynomial time algorithms online algorithms

show abstract

Section: Literature Reviewmentioning

confidence: 89%

Section: Literature Reviewmentioning

confidence: 99%

Joint replenishment meets scheduling

Györgyi¹,

Kis²,

Tamási³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Nonner and Souza (2009) further showed that this problem is APX-hard when holding costs are nonlinear with respect to time, which is the case for the models we consider. Several heuristics for the non-stationary additive JRP have been proposed with varying degrees of theoretical performance guarantees in Veinott Jr (1969), Zangwill (1969), Kao (1979), Joneja (1990), Federgruen and Tzur (1994), Levi et al (2006), and Stauffer et al (2011).…”

Section: Literature Reviewmentioning

confidence: 84%

The submodular joint replenishment problem

et al. 2015

View full text Add to dashboard Cite

The joint replenishment problem is a fundamental model in supply chain management theory that has applications in inventory management, logistics, and maintenance scheduling. In this problem, there are multiple item types, each having a given time-dependent sequence of demands that need to be satisfied. In order to satisfy demand, orders of the item types must be placed in advance of the due dates for each demand. Every time an order of item types is placed, there is an associated joint setup cost depending on the subset of item types ordered. This ordering cost can be due to machine, transportation, or labor costs, for example. In addition, there is a cost to holding inventory for demand that has yet to be served. The overall goal is to minimize the total ordering costs plus inventory holding costs.In this paper, the cost of an order, also known as a joint setup cost, is a monotonically increasing, submodular function over the item types. For this general problem, we show that a greedy approach provides an approximation guarantee that is logarithmic in the number of demands. Then we consider three special cases of submodular functions which we call the laminar, tree, and cardinality cases, each of which can model real world scenarios that previously have not been captured. For each of these cases, we provide a constant factor

show abstract

“…More recently, Levi et al [11] proposed a 2-approximation algorithm for the JRP and Levi et al [12] improved this result to a 1.8-approximation algorithm for the OWMR problem. Furthermore in the special case of JRP with deadlines, Nonner and Souza [14] have improved this result to a 5/3-approximation using a similar LP-rounding technique.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast with the approximation algorithms presented in [11,12,14], which exploit this formulation via primal-dual and LP-rounding techniques, we develop a combinatorial algorithm, based on a natural decomposition of the problem, that can be implemented to run in O(N T 2 )-time and yields 2-approximation algorithms for both problems under an even more general holding cost structure. The complexity of the algorithm can even be made linear (i.e.…”

Section: Introductionmentioning

confidence: 99%

A simple and fast 2-approximation algorithm for the one-warehouse multi-retailers problem

Stauffer¹,

Massonnet²,

Rapine³

et al. 2011

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

We consider a well-known NP-hard deterministic inventory control problem: the One-Warehouse Multi-Retailer (OWMR) problem. We present a simple combinatorial algorithm to recombine the optimal solutions of the natural single-echelon inventory subproblems into a feasible solution of the OWMR problem. This approach yields a 3approximation. We then show how this algorithm can be improved to a 2-approximation by halving the demands at the warehouse and at the retailers in the subproblems. Both algorithms are purely combinatorial and can be implemented to run in linear time for traditional linear holding costs and quadratic time for more general holding cost structures. We finally show that our technique can be extended to the Joint Replenishment Problem (JRP) with backorders and to the OWMR problem with non-linear holding costs.

show abstract

A 5/3-Approximation Algorithm for Joint Replenishment with Deadlines

Cited by 13 publications

References 13 publications

Joint replenishment meets scheduling

Joint replenishment meets scheduling

The submodular joint replenishment problem

A simple and fast 2-approximation algorithm for the one-warehouse multi-retailers problem

Contact Info

Product

Resources

About