Related papers: Approximation algorithms for Capacitated Facility …
We consider a natural extension to the metric uncapacitated Facility Location Problem (FLP) in which requests ask for different commodities out of a finite set $S$ of commodities. Ravi and Sinha (SODA'04) introduced the model as the…
In this paper, we focus on a class of constrained nonlinear optimization problems (NLP), where some of its equality constraints define a closed embedded submanifold $\mathcal{M}$ in $\mathbb{R}^n$. Although NLP can be solved directly by…
We consider the robust single-source capacitated facility location problem with uncertainty in customer demands. A cardinality-constrained uncertainty set is assumed for the robust problem. To solve it efficiently, we propose an…
With growing emphasis on e-commerce marketplace platforms where we have a central platform mediating between the seller and the buyer, it becomes important to keep a check on the availability and profitability of the central store. A store…
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
In this paper, we study the hard uniform capacitated $k$- median problem using local search heuristic. Obtaining a constant factor approximation for the \ckm problem is open. All the existing solutions giving constant-factor approximation,…
We study LP-rounding approximation algorithms for metric uncapacitated facility-location problems. We first give a new analysis for the algorithm of Chudak and Shmoys, which differs from the analysis of Byrka and Aardal in that now we do…
We introduce a problem that is a common generalization of the uncapacitated facility location and minimum latency (ML) problems, where facilities need to be opened to serve clients and also need to be sequentially activated before they can…
In the capacitated $k$-median (\CKM) problem, we are given a set $F$ of facilities, each facility $i \in F$ with a capacity $u_i$, a set $C$ of clients, a metric $d$ over $F \cup C$ and an integer $k$. The goal is to open $k$ facilities in…
The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. In this problem, we are given a depot and a set of customers, each with a demand, embedded in a metric space. The…
In this note, we consider the capacitated facility location problem when the transportation costs of the instance satisfy the Monge property. We show that a straightforward dynamic program finds the optimal solution when the demands are…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
We study the extended version of the non-uniform, capacitated facility location problem with multiple fulfilment channels between the facilities and clients, each with their own channel capacities and service cost. Though the problem has…
The facility location problem (FLP) is a classical combinatorial optimization challenge aimed at strategically laying out facilities to maximize their accessibility. In this paper, we propose a reinforcement learning method tailored to…
Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location…
Clustering with capacity constraints is a fundamental problem that attracted significant attention throughout the years. In this paper, we give the first FPT constant-factor approximation algorithm for the problem of clustering points in a…
The Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In…
The Capacitated Sum of Radii problem involves partitioning a set of points $P$, where each point $p\in P$ has capacity $U_p$, into $k$ clusters that minimize the sum of cluster radii, such that the number of points in the cluster centered…
Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing…
The Maximal Covering Location Problem (MCLP) is a classical location problem where a company maximizes the demand covered by placing a given number of facilities, and each demand node is covered if the closest facility is within a…