Optimization of The Best Line-up in Football using Binary Integer Programming Model

2020 ◽  
Vol 1 (3) ◽  
pp. 114-122
Author(s):  
Mahrudinda . ◽  
Sudrajat Supian ◽  
Subiyanto . ◽  
Diah Chaerani
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Binary Integer Programming ◽  
Optimum Result ◽  
Premier League ◽  
Maximum Value ◽  
Football Team ◽  
Selection Of Variables ◽  
English Premier League ◽  
Selection Of

This paper aims to find the formation with the best line-up of the Liverpool FC football team in the English Premier League in the 2020/2021 season. Researchers used binary integer programming (BIP) modeling to determine optimum solutions. The data used for this optimization is the rating value of the players recorded in the performance data from the previous matches. The optimum result of this problem is the selection of variables that are valued at 1, namely {x_1, x_4, x_6, x_8, x_21, x_28, x_34, x_37, and x_39} for formations 4-3-3 with a maximum value of 82.47, and variables {x_1, x_6, x_7, x_8, x_11, x_14, x_16, x_29, x_31, x_32, andx_42} for 4-2-3-1 formations with a maximum value of 80.04. The 4-3-3 formation is more effective because it has a higher maximum rating than the 4-2-3-1 formation.  4-3-3 formation is an attacking formation with a higher intensity of attack and faster than  4-2-3-1 formation that tends to defend moderately.

scholarly journals Optimization of The Best Line-up in Football using Binary Integer Programming Model

2020 ◽  
Vol 1 (3) ◽  
pp. 114-122
Author(s):  
Mahrudinda Mahrudinda ◽  
Sudrajat Supian ◽  
Subiyanto Subiyanto ◽  
Diah Chaerani
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Binary Integer Programming ◽  
Optimum Result ◽  
Premier League ◽  
Maximum Value ◽  
Football Team ◽  
Selection Of Variables ◽  
English Premier League ◽  
Selection Of

This paper aims to find the formation with the best line-up of the Liverpool FC football team in the English Premier League in the 2020/2021 season. Researchers used binary integer programming (BIP) modeling to determine optimum solutions. The data used for this optimization is the rating value of the players recorded in the performance data from the previous matches. The optimum result of this problem is the selection of variables that are valued at 1, namely {𝑥1,𝑥4,𝑥6,𝑥8,𝑥11,𝑥18,𝑥21,𝑥28,𝑥34,𝑥37,dan 𝑥39 } for formations 4-3-3 with a maximum value of 82.47, and variables {𝑥1,𝑥6,𝑥7,𝑥8,𝑥11,𝑥14,𝑥16,𝑥29,𝑥31,𝑥32, dan 𝑥42 } for 4-2-3-1 formations with a maximum value of 80.04. The 4-3-3 formation is more effective because it has a higher maximum rating than the 4-2-3-1 formation. 4-3-3 formation is an attacking formation with a higher intensity of attack and faster than 4-2-3-1 formation that tends to defend moderately.

scholarly journals Reshuffle minimisation to improve storage yard operations efficiency

2021 ◽  
Vol 15 ◽  
pp. 174830262199401
Author(s):  
Hammed Bisira ◽  
Abdellah Salhi
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Heuristic Approach ◽  
Container Terminals ◽  
Exact Method ◽  
Computational Results ◽  
Binary Integer Programming ◽  
Integer Programming Model ◽  
Compatibility Test ◽  
Storage Area

There are many ways to measure the efficiency of the storage area management in container terminals. These include minimising the need for container reshuffle especially at the yard level. In this paper, we consider the container reshuffle problem for stacking and retrieving containers. The problem was represented as a binary integer programming model and solved exactly. However, the exact method was not able to return results for large instances. We therefore considered a heuristic approach. A number of heuristics were implemented and compared on static and dynamic reshuffle problems including four new heuristics introduced here. Since heuristics are known to be instance dependent, we proposed a compatibility test to evaluate how well they work when combined to solve a reshuffle problem. Computational results of our methods on realistic instances are reported to be competitive and satisfactory.

A multi-objective approach to design strategic supply chains and develop responsiveness- efficiency frontiers

2018 ◽  
Vol 29 (1) ◽  
pp. 365-386 ◽  
Author(s):  
Raed AlHusain ◽  
Reza Khorramshahgol
Keyword(s):  
Supply Chain ◽  
Integer Programming ◽  
Programming Model ◽  
Efficient Frontier ◽  
Decision Makers ◽  
Binary Integer Programming ◽  
Content Type ◽  
Strategic Fit ◽  
Cost Efficient ◽  
Alternative Solutions

Purpose The purpose of this paper is twofold. Initially, a multi-objective binary integer programming model is proposed for designing an appropriate supply chain that takes into consideration both responsiveness and efficiency. Then, a responsiveness-cost efficient frontier is generated for the supply chain design that can help organizations find the right balance between responsiveness and efficiency, and hence achieve a strategic fit between organizational strategy and supply chain capabilities. Design/methodology/approach The proposed SC design model used both cross-functional and logistical SC drivers to build a binary integer programming model. To this end, various alternative solutions that correspond to different SC design portfolios were generated and a responsiveness-cost efficient frontier was constructed. Findings Various alternative solutions that correspond to different SC designs were generated and a responsiveness-cost efficient frontier was constructed to help the decision makers to design SC portfolios to achieve a strategic fit between organizational strategy and SC capabilities. Practical implications The proposed methodology enables the decision makers to incorporate both qualitative and quantitative judgements in SC design. The methodology is easy to use and it can be readily implemented by a software. Originality/value The proposed methodology allows for subjective value judgements of the decision makers to be considered in SC design and the efficiency-responsiveness frontier generated by the methodology provides a trade-off to be used when choosing between speed and cost efficiency in SC design.

Case

2013 ◽  
Vol 4 (4) ◽  
pp. 57-74
Author(s):  
Durai Sundaramoorthi
Keyword(s):  
Operations Research ◽  
Real Life ◽  
Point System ◽  
Brand Name ◽  
User Friendliness ◽  
Binary Integer Programming ◽  
Undergraduate Level ◽  
Premier League ◽  
Science Operations ◽  
Selection Of

Cricket is a bat-and-ball team sport, played by two teams with eleven players on each side. Recently, a new format of cricket called ‘Twenty20’ (T20) was introduced, which has increased the excitement, fan following, and business opportunities in cricket. In 2008, Indian Premier League (IPL) was created with eight city-based franchises. Two more franchises were added in 2010. The focus of this case is on the selection of the playing eleven for the team Kolkata Knight Riders (KKR), the most valued brand name among IPL franchises. Thirty five players were on the KKR team roster in the first two editions of the IPL. Unlike many other sports, the playing eleven cannot be changed in a cricket game once the game starts. The case aims to strengthen students’ ability to mathematically formulate a real life “yes-or-no” type decision. Binary Integer Programming (BIP) is a suitable choice for modeling “yes-or-no” type decisions. The case, if provided with International Cricket Council (ICC) rankings data and in-house point system, will be appropriate for an undergraduate level management science/operations research class. The same case will be suitable at graduate level, if students are expected to gather ICC rankings data and build in-house point system. There are competing constraints that would lead to discussions about infeasibility. The case also points out the importance of interpretation of the solution and user friendliness of the model from an end user’s perspective.

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