The optimal layout of football players: A case study for AC Milan

This paper attempts to find the optimal formation of three midfielders and three forward football players on ground, using the classic Quadratic Assignment Problem or Facility Layout problem. Players are treated as “machines”, their positions as locations, and the flow of materials between machines as “flow of passes” and “flow of markings”. Based on detailed statistics from four matches of AC Milan, and formulated the problem as minimum (quick strategy), maximum (slow strategy), and mixed or balanced strategies, a number of various layouts emerged. Compared to the initial formation of players, the efficiency time gains in the unconditioned layouts are between 3 and 6.8%. Also, when the manager claims that his three forwards shouldn’t shift positions with the midfielders, the efficiency gains in these restricted layouts is about 14´´ to 74´´, which is about 1 to 3% of the approximately 40´ effective time spent into passes and markings from both teams.sports; layout; assignment; football players; passes; markings; time;

Facility Planning and Associated Problems: A Survey

In this study, we have classified and reviewed different types of problems which are related to facility planning and layout design for different types of manufacturing processes. The main problems which are related to location of  facilities which also affects the system performance  such as distribution of man, material and machine in a plant or a factory and their optimization technique while using of mathematical models, their solutions and application related to whole problems is presented. For solving this type of problems, intelligent techniques such as expert systems, fuzzy logic and neutral networks have been used. In this paper the recent analysis on facility layout is incorporated and facility layout problem is surveyed. Many intelligent techniques and conventional algorithms for solving FLP are presented. In our discussion different research direction, general remarks and tendencies have been mentioned Keywords—Facility Planning, Material handling Optimization metho

Dynamic Facility Layout for Cellular and Reconfigurable Manufacturing using Dynamic Programming and Multi-Objective Metaheuristics

The facility layout problem is one of the most classical yet influential problems in the planning of production systems. A well-designed layout minimizes the material handling costs (MHC), personnel flow distances, work in process, and improves the performance of these systems in terms of operating costs and time. Because of this importance, facility layout has a rich literature in industrial engineering and operations research. Facility layout problems (FLPs) are generally concerned with positioning a set of facilities to satisfy some criteria or objectives under certain constraints. Traditional FLPs try to put facilities with the high material flow as close as possible to minimize the MHC. In static facility layout problems (SFLP), the product demands and mixes are considered deterministic parameters with constant values. The material flow between facilities is fixed over the planning horizon. However, in today’s market, manufacturing systems are constantly facing changes in product demands and mixes. These changes make it necessary to change the layout from one period to the other to be adapted to the changes. Consequently, there is a need for dynamic approaches of FLP that aim to generate layouts with high adaptation concerning changes in product demand and mix. This thesis focuses on studying the layout problems, with an emphasis on the changing environment of manufacturing systems. Despite the fact that designing layouts within the dynamic environment context is more realistic, the SFLP is observed to have been remained worthy to be analyzed. Hence, a math-heuristic approach is developed to solve an SFLP. To this aim, first, the facilities are grouped into many possible vertical clusters, second, the best combination of the generated clusters to be in the final layout are selected by solving a linear programming model, and finally, the selected clusters are sequenced within the shop floor. Although the presented math-heuristic approach is effective in solving SFLP, applying approaches to cope with the changing manufacturing environment is required. One of the most well-known approaches to deal with the changing manufacturing environment is the dynamic facility layout problem (DFLP). DFLP suits reconfigurable manufacturing systems since their machinery and material handling devices are reconfigurable to encounter the new necessities for the variations of product mix and demand. In DFLP, the planning horizon is divided into some periods. The goal is to find a layout for each period to minimize the total MHC for all periods and the total rearrangement costs between the periods. Dynamic programming (DP) has been known as one of the effective methods to optimize DFLP. In the DP method, all the possible layouts for every single period are generated and given to DP as its state-space. However, by increasing the number of facilities, it is impossible to give all the possible layouts to DP and only a restricted number of layouts should be fed to DP. This leads to ignoring some layouts and losing the optimality; to deal with this difficulty, an improved DP approach is proposed. It uses a hybrid metaheuristic algorithm to select the initial layouts for DP that lead to the best solution of DP for DFLP. The proposed approach includes two phases. In the first phase, a large set of layouts are generated through a heuristic method. In the second phase, a genetic algorithm (GA) is applied to search for the best subset of layouts to be given to DP. DP, improved by starting with the most promising initial layouts, is applied to find the multi-period layout. Finally, a tabu search algorithm is utilized for further improvement of the solution obtained by improved DP. Computational experiments show that improved DP provides more efficient solutions than DP approaches in the literature. The improved DP can efficiently solve DFLP and find the best layout for each period considering both material handling and layout rearrangement costs. However, rearrangement costs may include some unpredictable costs concerning interruption in production or moving of facilities. Therefore, in some cases, managerial decisions tend to avoid any rearrangements. To this aim, a semi-robust approach is developed to optimize an FLP in a cellular manufacturing system (CMS). In this approach, the pick-up/drop-off (P/D) points of the cells are changed to adapt the layout with changes in product demand and mix. This approach suits more a cellular flexible manufacturing system or a conventional system. A multi-objective nonlinear mixed-integer programming model is proposed to simultaneously search for the optimum number of cells, optimum allocation of facilities to cells, optimum intra- and inter-cellular layout design, and the optimum locations of the P/D points of the cells in each period. A modified non-dominated sorting genetic algorithm (MNSGA-II) enhanced by an improved non-dominated sorting strategy and a modified dynamic crowding distance procedure is used to find Pareto-optimal solutions. The computational experiments are carried out to show the effectiveness of the proposed MNSGA-II against other popular metaheuristic algorithms

Prototype solar heating and combined heating and cooling systems

Designs were completed, hardware was received, and hardware was shipped to two sites. A change was made in the heat pump working fluid. Problem investigation of shroud coatings for the collector received emphasis

Overview of Multi-Objective Optimization Approaches in Construction Project Management

The difficulties that are met in construction projects include budget issues, contractual time constraints, complying with sustainability rating systems, meeting local building codes, and achieving the desired quality level, to name but a few. Construction researchers have proposed and construction practitioners have used optimization strategies to meet various objectives over the years. They started out by optimizing one objective at a time (e.g., minimizing construction cost) while disregarding others. Because the objectives of construction projects often conflict with each other, single-objective optimization does not offer practical solutions as optimizing one objective would often adversely affect the other objectives that are not being optimized. They then experimented with multi-objective optimization. The many multi-objective optimization approaches that they used have their own advantages and drawbacks when used in some scenarios with different sets of objectives. In this chapter, a review is presented of 16 multi-objective optimization approaches used in 55 research studies performed in the construction industry and that were published in the period 2012–2016. The discussion highlights the strengths and weaknesses of these approaches when used in different scenarios

Layout Planning with Isles: A Genetic Approach

Plant layout problems involve distributing different resources or departments in a given plant and achieving maximum efficiency for the services or goods being made or offered. To this end, plants are designed to optimize production flow from the first stage (i.e. as raw material) to finish product. However, optimization which is generally expressed either in terms of minimization (for example, of material handling costs) or of maximization (for example, the number of desired adjacencies in a qualitative chart) is not always feasible when real problems or real sizes are being handled. The level of complexity may turn out considerable as the number of parameters, restrictions and other variables considered in the study become larger. This kind of problem has been formulated, from a mathematical view point as a static quadratic assignment problem. However, the number of problems that are usceptible to being solved by optimization methods is very limited. Some alternatives have been called from the field of graph-theory, direct method algorithms, construction algorithms (such as CORELAP), and improvement algorithms (such as CRAFT). In this thesis work, an attempt is made to develop the algorithm for solving layout problem with real-life restriction like aisles, used in factories for the easy transfer of materials from one section to the other, using Genetic Algorithm