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

Tim Nonner, Maxim Sviridenko
2013 Lecture Notes in Computer Science  
We give an efficient polynomial-time approximation scheme (EPTAS) for the Joint Replenishment Problem (JRP) with stationary demand.  ...  Moreover, using a similar technique, we give a PTAS for the capacitated JRP with non-stationary demand but constant size capacities. tno@zurich.ibm.com M.I.Sviridenko@warwick.ac.uk,  ...  approximation scheme for the Joint Replenishment Problem with stationary demand.Proof.  ... 
doi:10.1007/978-3-642-36694-9_27 fatcat:cod45jo3afhhlg6c7rtexf7muq

A genetic algorithm for joint replenishment based on the exact inventory cost

Sung-Pil Hong, Yong-Hyuk Kim
2009 Computers & Operations Research  
An improvement of Silver's algorithm for the joint replenishment problem.  ...  To cope with this, we devise an unbiased estimator of the exact cost which is computable in time polynomial of the problem input size and 1/ , where is a pre-specified relative error of estimation.  ...  An algorithm A is called a fully polynomial time randomized approximation scheme (FPRAS) [17] for counting ( ) if A outputs Y, satisfying the following condition in time polynomial in the encoding length  ... 
doi:10.1016/j.cor.2007.08.006 fatcat:a3e76ues5jerjlyoiqcnmxl6cy

The Continuous Joint Replenishment Problem is Strongly NP-Hard [article]

Alexander Tuisov, Liron Yedidsion
2020 arXiv   pre-print
The Continuous Periodic Joint Replenishment Problem (CPJRP) has been one of the core and most studied problems in supply chain management for the last half a century.  ...  Although the CPJRP has one of the tighter constant approximation ratio of 1.02, a polynomial optimal solution to it was never found.  ...  In addition, an efficient polynomial time approximation scheme (EPTAS) for JRP with finite time horizon and stationary demand was presented by Nonner and Sviridenko (2013) .  ... 
arXiv:2006.05310v1 fatcat:i5excap355g4hpnfkdxdwrmsem

Joint Energy Replenishment and Operation Scheduling in Wireless Rechargeable Sensor Networks

Yuanchao Shu, Kang G. Shin, Jiming Chen, Youxian Sun
2017 IEEE Transactions on Industrial Informatics  
We then devise an f -approximate scheduling mechanism by transforming the classical minimum set cover problem, and develop an optimal energy-replenish strategy based on the energy consumption of nodes  ...  To fill this void, we propose a joint energy replenishment and scheduling mechanism so as to maximize the network lifetime while making strict sensing guarantees in the WRSN.  ...  His current research focuses on QoS-sensitive computing and networks as well as on embedded real-time and cyber-physical systems.  ... 
doi:10.1109/tii.2016.2586028 fatcat:gfkbwoto4ja3za5ueapm4q3roy

The Periodic Joint Replenishment Problem is Strongly NP-Hard [article]

Tamar Cohen, Liron Yedidsion
2015 arXiv   pre-print
In this paper we study the long-standing open question regarding the computational complexity of one of the core problems in supply chains management, the periodic joint replenishment problem.  ...  This problem has received a lot of attention over the years and many heuristic and approximation algorithms were suggested.  ...  Acknowledgement 1 We thank Professor Retsef Levi for challenging us to solve the long-lasting question of the complexity of the PJRP.  ... 
arXiv:1511.02454v1 fatcat:4zehaaxmvnbyfcp6z3tdxknupm

Approximation algorithms for the joint replenishment problem with deadlines

Marcin Bienkowski, Jarosław Byrka, Marek Chrobak, Neil Dobbs, Tomasz Nowicki, Maxim Sviridenko, Grzegorz Świrszcz, Neal E. Young
2014 Journal of Scheduling  
The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods from a supplier to retailers.  ...  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.  ...  We would like to thank Lukasz Jeż, Jiří Sgall, and Grzegorz Stachowiak for stimulating discussions and useful comments.  ... 
doi:10.1007/s10951-014-0392-y fatcat:uc5n6tj4dvaj5gtcwfemtbl36i

The submodular joint replenishment problem

Maurice Cheung, Adam N. Elmachtoub, Retsef Levi, David B. Shmoys
2015 Mathematical programming  
For this general problem, we show that a greedy approach provides an approximation guarantee that is logarithmic in the number of demands.  ...  Every time an order of item types is placed, there is an associated joint setup cost depending on the subset of item types ordered.  ...  Acknowledgements We thank the refereeing team for their numerous insightful comments that significantly improved the quality and exposition of the paper.  ... 
doi:10.1007/s10107-015-0920-3 fatcat:gjtmzwdpl5c6hfnjszac63tgz4

Basic Performance Limits and Tradeoffs in Energy Harvesting Sensor Nodes with Finite Data and Energy Storage [article]

Rahul Srivastava, Can Emre Koksal
2012 arXiv   pre-print
Based on the insights developed, we address the problem of energy management for energy-replenishing nodes with finite battery and finite data buffer capacities.  ...  We provide a simple localized energy management scheme that achieves a performance close to that with an unlimited energy source, and at the same time keeps the probability of complete battery discharge  ...  Here K is the data buffer size. In addition, this scheme achieves an exponential decay with M for the battery discharge probability and a polynomial decay with K for the data loss probability.  ... 
arXiv:1009.0569v3 fatcat:cpep7ff7jbfinmt32fyikg3ppq

A comparative study of modeling and solution approaches for the coordinated lot-size problem with dynamic demand

Li-Lian Gao, Nezih Altay, E. Powell Robinson
2008 Mathematical and computer modelling  
This research consolidates the various modeling and algorithmic approaches reported in the literature for the coordinated replenishment problem with deterministic dynamic demand.  ...  efficiency of the algorithmic approaches when used to find heuristic and optimal solutions.  ...  On an average, Xpress-MP solves the shortest path formulation of the joint lot-size problem 40 times faster than P1.  ... 
doi:10.1016/j.mcm.2007.02.035 fatcat:abppx7df2be5hlgaylj2ovtaca

Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System

Yalçin Akçay, Susan H. Xu
2004 Management science  
T his paper considers a multicomponent, multiproduct periodic-review assemble-to-order (ATO) system that uses an independent base-stock policy for inventory replenishment.  ...  The system quotes a prespecified response time window for each product and receives a reward if the demand for that product is filled within its response time window.  ...  The component allocation problem in an ATO environment has not been well studied in the literature.  ... 
doi:10.1287/mnsc.1030.0167 fatcat:5qbxzbyeangh7hcgx5m5ihpdge

Multistage Lot Sizing Problems via Randomized Rounding

Chung-Piaw Teo, Dimitris Bertsimas
2001 Operations Research  
For the joint replenishment problem under a fixed base period model, we construct a 95.8% approximation algorithm to the (possibly dynamic) optimal lot sizing policy.  ...  We use this new technique to extend several results for the capacitated lot sizing problems to the case with submodular ordering cost.  ...  REPLENISHMENT PROBLEMS In this section, we focus on an improved approximation algorithm for the joint replenishment problem under the fixed base period model.  ... 
doi:10.1287/opre.49.4.599.11222 fatcat:xrjebivr4vdqzfrwi5x4kbomaa

Approximation Algorithms for the Joint Replenishment Problem with Deadlines [chapter]

Marcin Bienkowski, Jaroslaw Byrka, Marek Chrobak, Neil Dobbs, Tomasz Nowicki, Maxim Sviridenko, Grzegorz Świrszcz, Neal E. Young
2013 Lecture Notes in Computer Science  
The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods over time from a supplier to retailers.  ...  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.  ...  We would like to thank Lukasz Jeż, Jiří Sgall, and Grzegorz Stachowiak for stimulating discussions and useful comments.  ... 
doi:10.1007/978-3-642-39206-1_12 fatcat:ojwlvgkuh5h2nky6kj5r6ltntq

Optimization Theory, Methods, and Applications in Engineering 2013

Jung-Fa Tsai, John Gunnar Carlsson, Dongdong Ge, Yi-Chung Hu, Jianming Shi
2014 Mathematical Problems in Engineering  
Acknowledgments The guest editors would like to thank the authors for their contributions and the referees for their time and energy in reviewing the manuscripts.  ...  "An efficient approximate algorithm for disjoint QoS routing" by Z.  ...  Ho investigates the joint replenishment problem (JRP) involving multiple items where economies exist for replenishing several items simultaneously.  ... 
doi:10.1155/2014/319418 fatcat:tf6a2rxluncahe4i2djlw7t2vm

Cross-Layer Resource Allocation in Energy-Harvesting Sensor Networks [chapter]

Zhoujia Mao, C. Emre Koksal, Ness B. Shroff
2014 Rechargeable Sensor Networks: Technology, Theory, and Application  
Moreover, we define f n,m to be the fractional outgoing traffic of node n that passes through a parent node m and z n,m ( f ) to be the fractional outgoing traffic of node n that passes through an ancestor  ...  m, where f is the vector of f n,m , ∀n, m.  ...  In Theorem 7, V is a finite tunable approximation parameter that controls the efficiency of the algorithm.  ... 
doi:10.1142/9789814525466_0003 fatcat:xj7eh6s7ofgz3prc4dydaieeti

Optimal Cruiser-Drone Traffic Enforcement Under Energy Limitation

Ariel Rosenfeld, Oleg Maksimov, Sarit Kraus
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
We propose a binary integer linear program for determining the optimal rendezvous cruiser-drone enforcement policy which guarantees that all drones are replenished on time and minimizes the likelihood  ...  In the real world, drones are fundamentally limited by their battery/fuel capacity and have to be replenished during long operations.  ...  Acknowledgments The research has been supported in part by the Ministry of Science and Technology, Israel and the Japan Science and Technology Agency (JST), Japan.  ... 
doi:10.24963/ijcai.2018/535 dblp:conf/ijcai/RosenfeldMK18 fatcat:42e67wrqozf65nvdbdxhgapucy
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