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

2013
*
Lecture Notes in Computer Science
*

We give

doi:10.1007/978-3-642-36694-9_27
fatcat:cod45jo3afhhlg6c7rtexf7muq
*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. ...##
###
A genetic algorithm for joint replenishment based on the exact inventory cost

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 ...

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

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) . ...

##
###
Joint Energy Replenishment and Operation Scheduling in Wireless Rechargeable Sensor Networks

2017
*
IEEE Transactions on Industrial Informatics
*

We then devise

doi:10.1109/tii.2016.2586028
fatcat:gfkbwoto4ja3za5ueapm4q3roy
*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. ...##
###
The Periodic Joint Replenishment Problem is Strongly NP-Hard
[article]

2015
*
arXiv
*
pre-print

In this paper we study

arXiv:1511.02454v1
fatcat:4zehaaxmvnbyfcp6z3tdxknupm
*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. ...##
###
Approximation algorithms for the joint replenishment problem with deadlines

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. ...

##
###
The submodular joint replenishment problem

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. ...

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

2012
*
arXiv
*
pre-print

Based on

arXiv:1009.0569v3
fatcat:cpep7ff7jbfinmt32fyikg3ppq
*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. ...##
###
A comparative study of modeling and solution approaches for the coordinated lot-size problem with dynamic demand

2008
*
Mathematical and computer modelling
*

This research consolidates

doi:10.1016/j.mcm.2007.02.035
fatcat:abppx7df2be5hlgaylj2ovtaca
*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. ...##
###
Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System

2004
*
Management science
*

T his paper considers a multicomponent, multiproduct periodic-review assemble-to-order (ATO) system that uses

doi:10.1287/mnsc.1030.0167
fatcat:5qbxzbyeangh7hcgx5m5ihpdge
*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. ...##
###
Multistage Lot Sizing Problems via Randomized Rounding

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. ...

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

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. ...

##
###
Optimization Theory, Methods, and Applications in Engineering 2013

2014
*
Mathematical Problems in Engineering
*

Acknowledgments

doi:10.1155/2014/319418
fatcat:tf6a2rxluncahe4i2djlw7t2vm
*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. ...##
###
Cross-Layer Resource Allocation in Energy-Harvesting Sensor Networks
[chapter]

2014
*
Rechargeable Sensor Networks: Technology, Theory, and Application
*

Moreover, we define f n,m to be

doi:10.1142/9789814525466_0003
fatcat:xj7eh6s7ofgz3prc4dydaieeti
*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. ...##
###
Optimal Cruiser-Drone Traffic Enforcement Under Energy Limitation

2018
*
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
*

We propose a binary integer linear program

doi:10.24963/ijcai.2018/535
dblp:conf/ijcai/RosenfeldMK18
fatcat:42e67wrqozf65nvdbdxhgapucy
*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. ...
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