A compact linear programming formulation of the maximum concurrent flow problem

Networks ◽  
2014 ◽  
Vol 65 (1) ◽  
pp. 68-87 ◽  
Author(s):  
Yuanyuan Dong ◽  
Eli V. Olinick ◽  
T. Jason Kratz ◽  
David W. Matula
Keyword(s):  
Linear Programming ◽  
Flow Problem ◽  
Programming Formulation ◽  
Concurrent Flow ◽  
Linear Programming Formulation ◽  
Maximum Concurrent Flow

Efficient algorithms for the maximum concurrent flow problem

Networks ◽  
2014 ◽  
Vol 65 (1) ◽  
pp. 56-67 ◽  
Author(s):  
Pierre-Olivier Bauguion ◽  
Walid Ben-Ameur ◽  
Eric Gourdin
Keyword(s):  
Flow Problem ◽  
Efficient Algorithms ◽  
Concurrent Flow ◽  
Maximum Concurrent Flow

scholarly journals Multi-Agent Path Finding with Deadlines

2018 ◽  
Author(s):  
Hang Ma ◽  
Glenn Wagner ◽  
Ariel Felner ◽  
Jiaoyang Li ◽  
T. K. Satish Kumar ◽  
...  
Keyword(s):  
Flow Problem ◽  
Search Algorithms ◽  
The Other ◽  
Path Finding ◽  
Combinatorial Search ◽  
Programming Formulation ◽  
Commodity Flow ◽  
Linear Programming Formulation ◽  
Multi Agent ◽  
Integer Linear Programming Formulation

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.

scholarly journals Tournaments as Feedback Arc Sets

10.37236/1214 ◽  
1995 ◽  
Vol 2 (1) ◽  
Author(s):  
Garth Isaak
Keyword(s):  
Linear Programming ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Minimum Size ◽  
Programming Formulation ◽  
Binary Expansion ◽  
Feedback Arc Set ◽  
Disjoint Cycles ◽  
Linear Programming Formulation ◽  
Integer Linear Programming Formulation

We examine the size $s(n)$ of a smallest tournament having the arcs of an acyclic tournament on $n$ vertices as a minimum feedback arc set. Using an integer linear programming formulation we obtain lower bounds $s(n) \geq 3n - 2 - \lfloor \log_2 n \rfloor$ or $s(n) \geq 3n - 1 - \lfloor \log_2 n \rfloor$, depending on the binary expansion of $n$. When $n = 2^k - 2^t$ we show that the bounds are tight with $s(n) = 3n - 2 - \lfloor \log_2 n \rfloor$. One view of this problem is that if the 'teams' in a tournament are ranked to minimize inconsistencies there is some tournament with $s(n)$ 'teams' in which $n$ are ranked wrong. We will also pose some questions about conditions on feedback arc sets, motivated by our proofs, which ensure equality between the maximum number of arc disjoint cycles and the minimum size of a feedback arc set in a tournament.

Preemptive scheduling with transportation delays between machines

2020 ◽  
Vol 15 (3) ◽  
pp. 829-847
Author(s):  
Ryma Zineb Badaoui ◽  
Mourad Boudhar ◽  
Mohammed Dahane
Keyword(s):  
Linear Programming ◽  
Neighborhood Search ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Programming Formulation ◽  
Content Type ◽  
Decision Variables ◽  
Linear Programming Formulation ◽  
Local Search Strategy ◽  
Two Stages

Purpose This paper studies the preemptive scheduling problem of independent jobs on identical machines. The purpose of this paper is to minimize the makespan under the imposed constraints, namely, the ones that relate the transportation delays which are required to transport a preempted job from one machine to another. This study considers the case when the transportation delays are variable. Design/methodology/approach The contribution is twofold. First, this study proposes a new linear programming formulation in real and binary decision variables. Then, this study proposes and implements a solution strategy, which consists of two stages. The goal of the first stage is to obtain the best machines order using a local search strategy. For the second stage, the objective is to determine the best possible sequence of jobs. To solve the preemptive scheduling problem with transportation delays, this study proposes a heuristic and two metaheuristics (simulated annealing and variable neighborhood search), each with two modes of evaluation. Findings Computational experiments are presented and discussed on randomly generated instances. Practical implications The study has implications in various industrial environments when the preemption of jobs is allowed. Originality/value This study proposes a new linear programming formulation for the problem with variable transportation delays as well as a corresponding heuristic and metaheuristics.

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