scholarly journals Knights Exchange Puzzle—Teaching the Efficiency of Modeling

2020 ◽  
Author(s):  
Mehdi Iranpoor
Keyword(s):  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Minimum Cost ◽  
Network Flow Problem ◽  
Binary Programming ◽  
Combinatorial Optimization Problems ◽  
Minimum Cost Network Flow ◽  
Binary Formulation

Puzzles and games enhance the quality of teaching by creating an enjoyable, interactive, and playful atmosphere. The knight exchange is a famous, very old, and amusing game on the chessboard. This puzzle was used by the author to teach modeling in a mathematical programming course designed for graduate students. The aim was to teach the students the efficiency of the models. Accordingly, first, a binary programming formulation was developed. This formulation was, however, found to be inefficient, and tremendous time (i.e., more than four hours) and a large amount of processing memory were needed to solve the puzzle. The puzzle was subsequently formulated as a minimum cost network flow problem. The latter formulation outperformed the general binary formulation by solving the puzzle in less than a minute. The network formulation could also save the required processing memory. The results could help students to learn the value of modeling combinatorial optimization problems as network flows.

scholarly journals Minimum cost network flows: Problems, algorithms, and software

2013 ◽  
Vol 23 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Angelo Sifaleras
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Network Flows ◽  
Minimum Cost ◽  
Network Flow Problem ◽  
Software Packages ◽  
Wide Range ◽  
Solution Methods ◽  
Minimum Cost Network Flow ◽  
Algorithmic Approaches

We present a wide range of problems concerning minimum cost network flows, and give an overview of the classic linear single-commodity Minimum Cost Network Flow Problem (MCNFP) and some other closely related problems, either tractable or intractable. We also discuss state-of-the-art algorithmic approaches and recent advances in the solution methods for the MCNFP. Finally, optimization software packages for the MCNFP are presented.

scholarly journals A crowdsourced dynamic repositioning strategy for public bike sharing systems

2022 ◽  
Vol 12 (1) ◽  
pp. 31
Author(s):  
I-Lin Wang ◽  
Chen-Tai Hou
Keyword(s):  
Network Flow ◽  
Flow Model ◽  
Demand Forecasting ◽  
Minimum Cost ◽  
Real World Data ◽  
Time Space ◽  
Time Period ◽  
Bike Sharing ◽  
Minimum Cost Network Flow

<p style='text-indent:20px;'>Public bike sharing systems have become the most popular shared economy application in transportation. The convenience of this system depends on the availability of bikes and empty racks. One of the major challenges in operating a bike sharing system is the repositioning of bikes between rental sites to maintain sufficient bike inventory in each station at all times. Most systems hire trucks to conduct dynamic repositioning of bikes among rental sites. We have analyzed a commonly used repositioning scheme and have demonstrated its ineffectiveness. To realize a higher quality of service, we proposed a crowdsourced dynamic repositioning strategy: first, we analyzed the historical rental data via the random forest algorithm and identified important factors for demand forecasting. Second, considering 30-minute periods, we calculated the optimal bike inventory via integer programming for each rental site in each time period with a sufficient crowd for repositioning bikes. Then, we proposed a minimum cost network flow model in a time-space network for calculating the optimal voluntary rider flows for each period based on the current bike inventory, which is adjusted according to the forecasted demands. The results of computational experiments on real-world data demonstrate that our crowdsourced repositioning strategy may reduce unmet rental demands by more than 30% during rush hours compared to conventional trucks.</p>

An exterior simplex type algorithm for the Minimum Cost Network Flow Problem

2009 ◽  
Vol 36 (4) ◽  
pp. 1176-1190 ◽  
Author(s):  
Konstantinos Paparrizos ◽  
Nikolaos Samaras ◽  
Angelo Sifaleras
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Minimum Cost ◽  
Network Flow Problem ◽  
Type Algorithm ◽  
Minimum Cost Network Flow
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