Spelling suggestions: "subject:"facility dplayout 3dproblem"" "subject:"facility dplayout 23problem""
1 
A Semidefinite Programming Model for the Facility Layout ProblemAdams, Elspeth January 2010 (has links)
The continuous facility layout problem consists of arranging a set of facilities so that no pair overlaps and the total sum of the pairwise connection costs (proportional to the centertocenter rectilinear distance) is minimized. This thesis presents a completely mixed integer semidefinite programming (MISDP) model for the continuous facility layout problem.
To begin we describe the problem in detail; discuss the conditions required for a feasible layout; and define quaternary variables. These variables are the basis of the MISDP model. We prove that the model is an exact formulation and a distinction is made between the constraints that semidefinite programming (SDP) optimization software can solve and those that must be relaxed. The latter are called exactness constraints and three possible exactness constraints are shown to be equivalent.
The main contribution of this thesis is the theoretical development of a MISDP model that is based on quaternary, as oppose to binary, variables; nevertheless preliminary computational results will be presented for problems with 5 to 20 facilities. The optimal solution is found for problems with 5 and 6 facilities, confirming the validity of the model; and the potential of the model is revealed as a new upper bound is found for an 11facility problem.

2 
A Semidefinite Programming Model for the Facility Layout ProblemAdams, Elspeth January 2010 (has links)
The continuous facility layout problem consists of arranging a set of facilities so that no pair overlaps and the total sum of the pairwise connection costs (proportional to the centertocenter rectilinear distance) is minimized. This thesis presents a completely mixed integer semidefinite programming (MISDP) model for the continuous facility layout problem.
To begin we describe the problem in detail; discuss the conditions required for a feasible layout; and define quaternary variables. These variables are the basis of the MISDP model. We prove that the model is an exact formulation and a distinction is made between the constraints that semidefinite programming (SDP) optimization software can solve and those that must be relaxed. The latter are called exactness constraints and three possible exactness constraints are shown to be equivalent.
The main contribution of this thesis is the theoretical development of a MISDP model that is based on quaternary, as oppose to binary, variables; nevertheless preliminary computational results will be presented for problems with 5 to 20 facilities. The optimal solution is found for problems with 5 and 6 facilities, confirming the validity of the model; and the potential of the model is revealed as a new upper bound is found for an 11facility problem.

3 
Optimización multiobjetivo de la distribución en planta de procesos industriales. Estudio de objetivosMontalva Subirats, José Miguel 08 July 2011 (has links)
En el proceso de diseño e las construcciones industriales, es de vital importancia conocer cual es la ubicación óptima de las diferentes áras de trabajo que conforman un proceso de fabricación, así como de las instalaciones y servicios auxiliares. El problema de distribución en planta (Facilities Layout Problem, FLP) integra a todas las actividades industriales y se ha convertido desde los años 60 en uno de los problemas clásicos de optimización combinatoria, en el que trabajan multiutd de investigadores a nivel internacional. Hasta los años 90, el enfoque que se realizaba del problema era básicamente un enfoque monobjetivo, en el que se primaba fundamentalmente la minimización del coste de transporte de material o personas entre las diferentes áreas productivas o de servicios. Para ello se han venido empleando diferentes técnicas de optimización heurística, que persiguen minimizar el tiempo de cálculo y facilitar la búsqueda de mínimos, aunque sean locales, pues el espacio de soluciones es tan grande, que es difícil garantizar la existencia de un mínimo global del problema.
No obstante, el criterio de coste no es el único que se debe considerar en este tipo de planteamientos, pues existen otra serie de indicadores que son de vital importancia, para garantizar que la solución propuesta tiene un nivel de desarrollo tecnológico con la aparición de equipos y programas informáticos más desarrollados, han prosperado las aproximaciones multiobjetivos al problema de distribución en planta.
Entre los objetivos principales del presente trabajo se encuentran; la realización de un estado del arte de los indicadores que se han empleado en la bibliografía para la resolución en planta, obteniendo un conjunto de indicadores independientes y suficientes que puedan ser empleados en la obtención de distribuciones en planta óptimas. Se investigará si es necesario definir algún nuevo indicador que cubra los objetivos fundamentales de la distribución en planta establecidos por distintos autores.
Una vez seleccionados los indicadores se propone una técnica de optimización
multiobjetivo basada en un algoritmo de recocido simulado (Simulated Annealing). Finalmente se presentan los resultados de los experimentos realizados, empleando la
técnica de optimización multiobjetivo propuesta, sobre un problema ampliamente utilizado
en la bibliografía, el propuesto por Armour y Buffa de 20 actividades. Se obtienen las
fronteras de Pareto para diferentes bicriterios, introduciendo puntos que completan las
existentes hasta la actualidad, estudiando la posibilidad de extender la optimización a 3
indicadores. / Montalva Subirats, JM. (2011). Optimización multiobjetivo de la distribución en planta de procesos industriales. Estudio de objetivos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11147 / Palancia

4 
A SequencePair and Mixed Integer Programming Based Methodology for the Facility Layout ProblemLiu, Qi 01 December 2004 (has links)
The facility layout problem (FLP) is one of the most important and challenging problems in both the operations research and industrial engineering research domains. In FLP research, the continuousrepresentationbased FLP can consider all possible allrectangular department solutions. Given this flexibility, this representation has become the representation ofchoice in FLP research. Much of this research is based on a methodology of mixed integer programming (MIP) models. However, these MIPFLP models can only solve problems with a limited number of departments to optimality due to a large number of binary variables used in the models to prevent departments from overlapping. Our research centers around the sequencepair representation, a concept that originated in the Very Large Scale Integration (VLSI) design literature. We show that an exhaustive search of the sequencepair solution space will result in finding the optimal layout of the MIPFLP and that every sequencepair solution is binaryfeasible in the MIPFLP. Based on this fact, we propose a methodology that combines the sequencepair and MIPFLP model to efficiently solve large continuousrepresentationbased FLPs. Our heuristic approach searches the sequencepair solution space and then use the sequencepair representation to simplify and solve the MIPFLP model. Based on this methodology, we systematically study the different aspects of the FLP throughout this dissertation.
As the first contribution of this dissertation, we present a genetic algorithm based heuristic, SEQUENCE, that combines the sequencepair representation and the most recent MIPFLP model to solve the allrectangulardepartment continuousrepresentationbased FLP. Numerical experiments based on different sized test problems from both the literature and industrial applications are provided and the solutions are compared with both the optimal solutions and the solutions from other heuristics to show the effectiveness and efficiency of our heuristic. For eleven data sets from the literature, we provide solutions better than those previously found.
For the FLP with fixed departments, many sequencepairs become infeasible with respect to the fixed department location and dimension restrictions. As our second contribution, to address this difficulty, we present a repair operator to filter the infeasible sequencepairs with respect to the fixed departments. This repair operator is integrated into SEQUENCE to solve the FLP with fixed departments more efficiently. The effectiveness of combining SEQUENCE and the repair operator for solving the FLP with fixed departments is illustrated through a series of numerical experiments where the SEQUENCE solutions are compared with other heuristics' solutions.
The third contribution of this dissertation is to formulate and solve the FLP with an existing aisle structure (FLPAL). In many industrial layout designs, the existing aisle structure must be taken into account. However, there is very little research that has been conducted in this area. We extend our research to further address the FLPAL. We first present an MIP model for the FLPAL (MIPFLPAL) and run numerical experiments to test the performance of the MIPFLPAL. These experiments illustrate that the MIPFLPAL can only solve very limited sized FLPAL problems. Therefore, we present a genetic algorithm based heuristic, SEQUENCEAL, to combine the sequencepair representation and MIPFLPAL to solve largersized FLPAL problems. Different sized data sets are solved by SEQUENCEAL and the solutions are compared with both the optimal solutions and other heuristics' solutions to show the effectiveness of SEQUENCEAL.
The fourth contribution of this dissertation is to formulate and solve the FLP with nonrectangularshaped departments. Most FLP research focuses on layout design with all rectangularshaped departments, while in industry there are many FLP applications with nonrectangularshaped departments. We extend our research to solve the FLP with nonrectangularshaped departments. We first formulate the FLP with nonrectangularshaped departments (FLPNR) to a MIP model (MIPFLPNR), where each nonrectangular department is partitioned into rectangularshaped subdepartments and the subdepartments from the same department are connected according to the department's orientation. The effect of different factors on the performance of the MIPFLPNR is explored through a series of numerical tests, which also shows that MIPFLPNR can only solve limitedsized FLPNR problems. To solve largersized FLPNR problems, we present a genetic algorithm based heuristic, SEQUENCENR, along with two repair operators based on the mathematical properties of the MIPFLPNR to solve the largersized FLPNR. A series of numerical tests are conducted on SEQUENCENR to compare the SEQUENCENR solutions with both the optimal solutions and another heuristic's solutions to illustrate the effectiveness of SEQUENCENR.
As the first systematic research study on a methodology that combines the sequencepair representation and the MIPbased FLP, this dissertation addresses different types of continuousrepresentation based facility layout design problems: from block layout design with and without fixed departments to relayout design with an existing aisle structure, and from layout design with allrectangularshaped departments to layout design with arbitrary nonrectangularshaped departments. For each type of layout design problem, numerical experiments are conducted to illustrate the effectiveness of our specifically designed family of sequencepair and MIPbased heuristics. As a result, better solutions than those previously found are provided for some widely used data sets from the literature and some new datasets based on both the literature and industrial applications are proposed for the first time. Furthermore, future research that continues to combine the sequencepair representation and the MIPFLP model to solve the FLP is also discussed, indicating the richness of this research domain. / Ph. D.

5 
CuttingPlane Separation Strategies for Semidefinite Programming Models to Solve SingleRow Facility Layout ProblemsYen, Ginger January 2008 (has links)
The singlerow facility layout problem (SRFLP) is concerned with finding the optimal linear placement of n departments with different lengths in a straight line. It is typically achieved by minimizing the cost associated with the interactions between the departments. The semidefinite programming (SDP) relaxation model that incorporates cutting planes proposed recently by Anjos, Kennings, and Vannelli (AKV) was considered a breakthrough in the field. This thesis presents a new SDP model AKV' and compares the two relaxations. The AKV' is largely based on the previous model, but it reduces the number of linear constraints from O(n³) to O(n²). Therefore, it reduces the computing time at the expense of a slightly weaker lower bound. However, AKV' is observed to pay off as the instance size increases. By examining the gap for both the AKV and AKV' relaxations, we notice that both relaxations generate very small gaps at the root node, which demonstrates the effectiveness of the relaxations.
Six different strategies are presented to separate the cutting planes for the mediumsized SRFLP. In combination with the two SDP relaxations, we compare the six strategies using three instances of different characteristics. An overall best strategy is deduced from the computational results, but the best choice of relaxations and the best number of cuts added at each iteration changes depending on the characteristics of the instances. Two new cutting plane strategies are proposed for large instances. This allows the solution to optimality of new instances with 36 departments, which is higher than previously published results in literature. We also briefly point out how the computing time can vary greatly between different sets of data of the same size due to the characteristics of the department lengths.

6 
CuttingPlane Separation Strategies for Semidefinite Programming Models to Solve SingleRow Facility Layout ProblemsYen, Ginger January 2008 (has links)
The singlerow facility layout problem (SRFLP) is concerned with finding the optimal linear placement of n departments with different lengths in a straight line. It is typically achieved by minimizing the cost associated with the interactions between the departments. The semidefinite programming (SDP) relaxation model that incorporates cutting planes proposed recently by Anjos, Kennings, and Vannelli (AKV) was considered a breakthrough in the field. This thesis presents a new SDP model AKV' and compares the two relaxations. The AKV' is largely based on the previous model, but it reduces the number of linear constraints from O(n³) to O(n²). Therefore, it reduces the computing time at the expense of a slightly weaker lower bound. However, AKV' is observed to pay off as the instance size increases. By examining the gap for both the AKV and AKV' relaxations, we notice that both relaxations generate very small gaps at the root node, which demonstrates the effectiveness of the relaxations.
Six different strategies are presented to separate the cutting planes for the mediumsized SRFLP. In combination with the two SDP relaxations, we compare the six strategies using three instances of different characteristics. An overall best strategy is deduced from the computational results, but the best choice of relaxations and the best number of cuts added at each iteration changes depending on the characteristics of the instances. Two new cutting plane strategies are proposed for large instances. This allows the solution to optimality of new instances with 36 departments, which is higher than previously published results in literature. We also briefly point out how the computing time can vary greatly between different sets of data of the same size due to the characteristics of the department lengths.

7 
Material Flow Cost Versus Congestion In Dynamic Distributed Facility Layout ProblemOzen, Aykut 01 July 2008 (has links) (PDF)
In this thesis, we study both dynamic and distributed facility layout problems, where the demand for product mix changes over time. We propose a new simulated annealing algorithm, SALAB, for the dynamic facility layout problem. Four variants of SALAB find the best known solution for 20 of the 48 benchmark problems from the literature, improving upon the best known solutions of 18 problems. We modify SALAB to obtain DSALAB, solving the dynamic distributed facility layout problem with the objective of minimizing relocation cost and total (full and empty) travel cost of the material handling system. We simulate DSALAB solutions of randomly generated problems to study the tradeoff between total cost and congestion in the system. Our experimental results indicate that distributing the department duplicates throughout the facility reduces the total cost with diminishing returns and causes increasing congestion. Therefore, distribution beyond a certain level is not justified.

8 
Models and Algorithms for Some Combinatorial Optimization Problems: University Course Timetabling, Facility Layout and Integrated ProductionDistribution SchedulingWang, Yuqiang 24 August 2007 (has links)
In this dissertation, we address three different combinatorial optimization problems (COPs), each of which has specific reallife applications. Owning to their specific nature, these problems are different from those discussed in the literature. For each of these problems, we present a mathematical programming formulation, analyze the problem to determine its useful, inherent structural properties, and develop an efficient methodology for its solution by exploiting these properties.
The first problem that we address is the course timetabling problem encountered at Virginia Tech. The course timetabling problem for a university is a difficult problem and has been studied by many researchers over the years. As a result, a plethora of models and approaches have been reported in the literature. However, most of these studies have focused on applications pertaining to course scheduling for a single or at most few departments of a university. The sheer size of the universitywide timetabling problem that we address, involving thousands of courses to be scheduled in hundreds of classrooms in each semester, makes it a challenging problem. We employ an appropriate decomposition technique that relies on some inherent structural properties of the problem both during the modeling and algorithmic development phases. We show the superiority of the schedules generated by our methodology over those that are currently being used. Also, our methodology requires only a reasonable amount of computational time in solving this largesize problem.
A facility layout problem involving arbitraryshaped departments is the second problem that we investigate in this dissertation. We designate this problem as the arbitraryshaped facility layout problem (ASFLP). The ASFLP deals with arranging a given set of departments (facilities, workstations, machines) within the confines of a given floor space, in order to optimize a desired metric, which invariably relates to the material handling cost. The topic of facility planning has been addressed rather extensively in the literature. However, a major limitation of most of the work reported in the literature is that they assume the shape of a department to be a rectangle (or even a square). The approach that relies on approximating an arbitraryshaped department by a rectangle might result in an unattractive solution. The key research questions for the ASFLP are: (1) how to accurately model the arbitraryshaped departments, and (2) how to effectively and efficiently determine the desired layout. We present a mixedinteger programming model that maintains the arbitrary shapes of the departments. We use a metaheuristic to solve the largesize instances of the ASFLP in a reasonable amount of time.
The third problem that we investigate is a supply chain scheduling problem. This problem involves two stages of a supply chain, specifically, a manufacturer and one or more customers. The key issue is to achieve an appropriate coordination between the production and distribution functions of the manufacturer so as to minimize the sum of the shipping and job tardiness costs. We, first, address a single customer problem, and then, extend our analysis to the case of multiple customers. For the singlecustomer problem, we present a polynomialtime algorithm to solve it to optimality. For the multiplecustomer problem, we prove that this problem is NPhard and solve it by appropriately decomposing it into subproblems, one of which is solvable in polynomial time. We propose a branchandboundbased methodology for this problem that exploits its structural properties. Results of an extensive computational experimentation are presented that show the following: (1) our algorithms are efficient to use and effective to implement; and (2) significant benefits accrue as a result of integrating the production and distribution functions. / Ph. D.

9 
Semidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout ProblemsFraticelli, Barbara M. P. 26 April 2001 (has links)
This dissertation develops efficient solution techniques for general and problemspecific applications within nonconvex optimization, exploiting the constructs of the ReformulationLinearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex optimization through the use of a new class of RLT cuts, called semidefinite cuts. While these cuts are valid for any general problem for which RLT is applicable, we demonstrate their effectiveness in optimizing a nonconvex quadratic objective function over a simplex. Computational results indicate that on average, the semidefinite cuts have reduced the number of nodes in the branchandbound tree by a factor of 37.6, while decreasing solution time by a factor of 3.4. The semidefinite cuts have also led to a significant reduction in the optimality gap at termination, in some cases producing optimal solutions for problems that could not be solved using RLT alone.
We then narrow our focus to the class of mixedinteger programming (MIP) problems, and develop a modification of Benders' decomposition method using concepts from RLT and liftandproject cuts. This method is particularly motivated by the class of twostage stochastic programs with integer recourse. The key idea is to design an RLT or liftandproject cutting plane scheme for solving the subproblems where the cuts generated have righthand sides that are functions of the firststage variables. An illustrative example is provided to elucidate the proposed approach. The focus is on developing a first comprehensive finitely convergent extension of Benders' methodology for problems having 01 mixedinteger subproblems.
We next address a specific challenging MIP application known as the facility layout problem, and we significantly improve its formulation through outerlinearization techniques and concepts from disjunctive programming. The enhancements produce a substantial increase in the accuracy of the layout produced, while at the same time, providing a dramatic reduction in computational effort. Overall, the maximum error in department size was reduced from about 6% to nearly zero, while solution time decreased by a factor of 110. Previously unsolved test problems from the literature that had defied even approximate solution methods have been solved to exact optimality using our proposed approach. / Ph. D.

10 
A new framework considering uncertainty for facility layout problemOheba, Jamal Bashir January 2012 (has links)
In today’s dynamic environment, where product demands are highly volatile and unstable, the ability to design and operate manufacturing facilities that are robust with respect to uncertainty and variability is becoming increasingly important to the success of any manufacturing firm in order to operate effectively in such an environment. Hence manufacturing facilities must be able to exhibit high levels of robustness and stability in order to deal with changing market demands. In general, Facility Layout Problem (FLP) is concerned with the allocation of the departments or machines in a facility with an objective to minimize the total material handling cost (MHC) of moving the required materials between pairs of departments. Most FLP approaches assume the flow between departments is deterministic, certain and constant over the entire time planning horizon. Changes in product demand and product mix in a dynamic environment invalidate these assumptions. Therefore there is a need for stochastic FLP approaches that aim to assess the impact of uncertainty and accommodate any possible changes in future product demands.This research focuses on stochastic FLP with an objective to present a methodology in the form of a framework that allows the layout designer to incorporate uncertainty in product demands into the design of a facility. In order to accomplish this objective, a measure of impact of this uncertainty is required. Two solution methods for single and multi period stochastic FLPs are presented to quantify the impact of product demand uncertainty to facility layout designs in terms of robustness (MHC) and variability (standard deviation). In the first method, a hybrid (simulation) approach which considers the development of a simulation model and integration of this model with the VIPPLANOPT 2006 algorithm is presented. In the second method, mathematical formulations of analytic robust and stable indices are developed along with the use of VIPPLANOPT for solution procedure. Several case studies are developed along with numerical examples and case studies from the literature are used to demonstrate the proposed methodology and the application of the two methods to address different aspects of stochastic FLP both analytically and via the simulation method. Through experimentation, the proposed framework with solution approaches has proven to be effective in evaluating the robustness and stability of facility layout designs with practical assumptions such as deletion and expansion of departments in a stochastic environment and in applying the analysis results of the analytic and simulation indices to reduce the impact of errors and make better decisions

Page generated in 0.1055 seconds