Open AccessJournal Article
An approximation algorithm for a facility location problem with stochastic demands
A.F. Bumb,J.C.W. van Ommeren +1 more
TL;DR: In this paper, the authors proposed an approximation algorithm for a facility location problem with stochastic demands, where the problem is where to locate the facilities and how to assign the demand points to facilities at minimal cost per reorder period.
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Abstract: In this article we propose, for any $\epsilon>0$, a $2(1+\epsilon)$-approximation algorithm for a facility location problem with stochastic demands. This problem can be described as follows. There are a number of locations, where facilities may be opened and a number of demand points, where requests for items arise at random. The requests are sent to open facilities. At the open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. After constant times, the inventory is replenished to a fixed order up to level. The time interval between consecutive replenishments is called a reorder period. The problem is where to locate the facilities and how to assign the demand points to facilities at minimal cost per reorder period such that the above mentioned quality of service is insured. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs (opening costs) of the facilities and the investment in inventory (inventory costs).
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Citations
Location-inventory problem in supply chains: a modeling review
TL;DR: A review of the existing literature of location-inventory problems can be found in this article, where a mathematical model is presented for a basic LIP, which can be further developed to incorporate additional features for use in real-world scenarios.
118
•Journal Article
Approximation algorithms for facility location problems with discrete subadditive cost functions
TL;DR: In this paper, the authors presented a 2-approximation algorithm for facility location with subadditive costs, which implies the existence of a 2(1+επσon,1) approximation algorithm.
References
Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation
Kamal Jain,Vijay V. Vazirani +1 more
TL;DR: A new extension of the primal-dual schema and the use of Lagrangian relaxation to derive approximation algorithms for the metric uncapacitated facility location problem and the metric k-median problem achieving guarantees of 3 and 6 respectively.
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Greedy strikes back: improved facility location algorithms
Sudipto Guha,Samir Khuller +1 more
- 01 Jan 1998
TL;DR: It is shown that a simple greedy heuristic combined with the algorithm by Shmoys, Tardos, and Aardal, can be used to obtain an approximation guarantee of 2.408, and a lower bound of 1.463 is proved on the best possible approximation ratio.
750
Regenerative Stochastic Processes
TL;DR: In this article, a wide class of stochastic processes, called regenerative, is defined, and it is shown that under general conditions the instantaneous probability distribution of such a process tends with time to a unique limiting distribution, whatever the initial conditions.
716
Approximation algorithms for facility location problems (extended abstract)
David B. Shmoys,Éva Tardos,Karen Aardal +2 more
- 04 May 1997
TL;DR: A polynomial-time algorithm is given that finds a solution of cost within a factor of 3.16 of the optimal for the uncapacitated facility location, which is the first constant performance guarantee known for this problem.
The uncapacitated facility location problem
Gérard Cornuéjols,George L. Nemhauser,Lairemce A Wolsey +2 more
- 01 Jan 1990
TL;DR: The capacitated facility location problem as discussed by the authors is an economic problem of great practical importance, where the goal is to choose the location of facilities such as industrial plants or warehouses, in order to minimize the cost (or maximize the profit) of satisfying the demand for some commodity.
596