Multi-row Layout Research Articles

Optimization Model of Autonomous Vehicle Parking Facilities, Developed With the Nondominated Sorting Genetic Algorithm With an Elite Strategy 2 and by Comparing Different Moving Strategies

Fully self-driving cars, or autonomous vehicles (AVs), will have self-parking functions, which will revolutionize and reshape parking facilities in several ways. Automated parking technology could realize high-density and intensive parking space efficiency through multirow layouts and with narrower spaces per vehicle, which would completely change traditional parking facilities. Nonetheless, extra movements and congestion are generated by releasing stuck vehicles inside rows of parking spaces. Profits in parking space efficiency might be reduced by losses extra movements and congestion. This article aims to optimize the multirow and multichannel layout of parking facilities for AVs, balancing maximal space utilization and minimal movements while satisfying a designated parking demand. A new moving strategy, “first storage and shortest moving to outdistance (FSSMD),” is put forward first. Then, the geometric attributes, other movement strategies, demand characteristics, and other design elements of parking facilities are comprehensively quantified to describe the profit and loss of self-parking. An optimization model for the multirow layout of parking spaces is constructed with the dual goals of maximizing the number of berths and minimizing the number of movements. The nondominated sorting genetic algorithm with an elite strategy 2 is designed to solve the optimal model. Finally, the optimal zones and layouts of parking facilities are put forward by numerical experiments, and the sensitivity of different moving strategies is discussed. The results show that the moving strategy based on the FSSMD significantly reduces expected movement times, without decreasing the utilization rate of parking spaces. Although having only one zone enables maximizing the number of parking berths and the utilization rate of parking facilities, such benefits and improvements might be compromised by additional movements. Therefore, the multirow optimal layout with a zoning of 4 and 2 interzone channels should be decided by assessing the paradoxical relationships between the maximal utilization rate and minimal movements.

Strategy to Reduce Floor Area and Flow Distance of Products in Multi-Row Parallel Machine Layout Design Using Cuckoo Search Algorithm

A multi-row parallel machine layout (MRPML) design is the best alternative solution to overcome the downside associated with a single-row machine layout design. Especially, the reduction in the investment cost on machines by eliminating its duplicates is the greatest advantage of a MRPML over the single-row machine layout. This paper addresses the MRPML design strategy to reduce the floor area of the layout along with a reduction in demand-based flow distance of products. The cuckoo search algorithm is used for this purpose. The efficacy of the proposed method is assessed and proved by comparing the solutions to the problems associated with single-row layout design dealt by [Lenin et al. Eur. J. Ind. Eng. 12(2) (2018) 252–275] and multi-row layout design dealt by [Vitayasak and Pongcharoen Exp. Syst. Appl. 98 (2018) 129–152] along with few randomly generated problems. This work provides a better tool to identify the optimal MRPML design to satisfy the objectives of mass production industries.

Robust optimization to design a dynamic cellular manufacturing system integrating group layout and workers assignment

In this paper, a robust optimisation approach is proposed to solve a mathematical model integrating cell formation, group layout and operators assignment decisions under a dynamic situation. The main aim of applying a robust approach is to obtain an optimal design of a cellular manufacturing system that is robust with respect to encountered uncertainties in part demands and processing times. The integrated model incorporates several design attributes including operations sequence, group layout, equal-area facilities multi-rows layout, flexible cell reconfiguration, operators hiring/firing and training, operator available time, limitations of cell size and uncertain processing times and part demands. Two illustrative numerical examples are solved to investigate the validity of the robust model. Regarding the NP-hardness of the proposed model, an efficient simulated annealing algorithm is implemented. Some test problems either generated randomly or taken from the literature are solved and the results are compared with the ones obtained using CPLEX. [Received: 31 May 2019; Accepted: 3 May 2020]

Mathematical optimization approach for facility layout on several rows

The facility layout problem is concerned with finding an arrangement of non-overlapping indivisible departments within a facility so as to minimize the total expected flow cost. In this paper we consider the special case of multi-row layout in which all the departments are to be placed in three or more rows, and our focus is on, for the first time, solutions for large instances. We first propose a new mixed integer linear programming formulation that uses continuous variables to represent the departments’ location in both x and y coordinates, where x represents the position of a department within a row and y represents the row assigned to the department. We prove that this formulation always achieves an optimal solution with integer values of y, but it is limited to solving instances with up to 13 departments. This limitation motivates the application of a two-stage optimization algorithm that combines two mathematical optimization models by taking the output of the first-stage model as the input of the second-stage model. This algorithm is, to the best of our knowledge, the first one in the literature reporting solutions for instances with up to 100 departments.

A Three-Stage Approach to a Multirow Parallel Machine Layout Problem

Facility layout is vital to save operational cost and enhance production efficiency. Multirow layout is a common pattern in practical manufacturing environment. Although parallel machines are frequently implemented in practice to enhance productivity, there lacks any in-depth study on multirow layout problem with parallel machines. In this paper, its mathematical programming formulation is established to minimize material flow cost. A three-stage approach is proposed to solve it. First, a Monte Carlo heuristic is devised to optimize the sequence of machines on multiple rows. Second, a linear program is used to determine the optimal exact location of each machine. Finally, an exchange heuristic is adopted to reassign material flows among parallel machines in different machine groups. An iterative optimization strategy is suggested to execute the three stages repeatedly to improve the solution quality. This approach is applied to a number of problem instances and compared against others. The experimental results show that it is able to effectively solve this new problem and significantly decrease material flow cost. Note to Practitioners —Multirow layout is common in practical manufacturing systems in which parallel machines are often used to improve productivity, shorten production time, and guarantee some flexibility. This paper studies a multirow parallel machine layout problem that involves machine groups, each of which contains parallel machines. Solving it is to locate all machines at multiple parallel rows to minimize material flow cost. It is challenging because one needs to decompose material flows and determine exact locations of machines simultaneously. A three-stage approach is proposed to do so. It is applied to many problem instances. The results demonstrate that it works well for such layout problems with parallel machines.

Multi-Objective Bi-Level Programming for the Energy-Aware Integration of Flexible Job Shop Scheduling and Multi-Row Layout

The flexible job shop scheduling problem (FJSSP) and multi-row workshop layout problem (MRWLP) are two major focuses in sustainable manufacturing processes. There is a close interaction between them since the FJSSP provides the material handling information to guide the optimization of the MRWLP, and the layout scheme affects the effect of the scheduling scheme by the transportation time of jobs. However, in traditional methods, they are regarded as separate tasks performed sequentially, which ignores the interaction. Therefore, developing effective methods to deal with the multi-objective energy-aware integration of the FJSSP and MRWLP (MEIFM) problem in a sustainable manufacturing system is becoming more and more important. Based on the interaction between FJSSP and MRWLP, the MEIFM problem can be formulated as a multi-objective bi-level programming (MOBLP) model. The upper-level model for FJSSP is employed to minimize the makespan and total energy consumption, while the lower-level model for MRWLP is used to minimize the material handling quantity. Because the MEIFM problem is denoted as a mixed integer non-liner programming model, it is difficult to solve it using traditional methods. Thus, this paper proposes an improved multi-objective hierarchical genetic algorithm (IMHGA) to solve this model. Finally, the effectiveness of the method is verified through comparative experiments.

Improved exact approaches for row layout problems with departments of equal length

Facility layout is a well-known operations research problem that arises in various applications. The multi-row layout is a challenging optimization problem where the task is to determine the optimal placement of one-dimensional departments on a given number of rows. This paper is concerned with multi-row facility layout problems in which all the departments have the same length. This is an important special case that includes most multi-row facility layout applications from the literature. We prove two theoretical results about the structure of optimal layouts, namely that only spaces of unit length are necessary to obtain an optimal solution, and that exact expressions exist for the minimum number of such spaces that need to be added so as to preserve at least one global optimal solution. Using these results we propose a binary linear optimization model and a binary semidefinite optimization model for the problem, neither of which uses continuous variables, which has a significant positive computational impact. Our computational experiments show that our specially tailored approaches can handle much larger instances than other exact methods applicable to this important problem class.

Designing parking facilities for autonomous vehicles

Autonomous vehicles will have a major impact on parking facility designs in the future. Compared to regular car-parks that have only two rows of vehicles in each island, future car-parks (for autonomous vehicles) can have multiple rows of vehicles stacked behind each other. Although this multi-row layout reduces parking space, it can cause blockage if a certain vehicle is barricaded by other vehicles and cannot leave the facility. To release barricaded vehicles, the car-park operator has to relocate some of the vehicles to create a clear pathway for the blocked vehicle to exit. The extent of vehicle relocation depends on the layout design of the car-park. To find the optimal car-park layout with minimum relocations, we present a mixed-integer non-linear program that treats each island in the car-park as a queuing system. We solve the problem using Benders decomposition for an exact answer and we present a heuristic algorithm to find a reasonable upper-bound of the mathematical model. We show that autonomous vehicle car-parks can decrease the need for parking space by an average of 62% and a maximum of 87%. This revitalization of space that was previously used for parking can be socially beneficial if car-parks are converted into commercial and residential land-uses.

Single and multi-row layout design for flexible manufacturing systems

In this paper, machines are allocated in horizontal rows along sides of an automated guided vehicle path so that the total cost of material transportation between machines is optimised. The problems of locating machines in single, double and multi-row layouts are addressed. Different layout arrangements as well as random permutations of machines are obtained using a simple construction algorithm, then the search for optimal solution and the best machine arrangements is obtained by implementing both Ant Colony and Simulated Annealing algorithms. Computational test examples show that the proposed method provides the best-known solutions for the single-row and double-row layout problems. Furthermore, experimental results demonstrate that both algorithms provide identical solutions for the single and multi-row layout problems.

A semidefinite optimization-based approach for global optimization of multi-row facility layout

This paper is concerned with the Multi-Row Facility Layout Problem. Given a set of rectangular departments, a fixed number of rows, and weights for each pair of departments, the problem consists of finding an assignment of departments to rows and the positions of the departments in each row so that the total weighted sum of the center-to-center distances between all pairs of departments is minimized. We show how to extend our recent approach for the Space-Free Multi-Row Facility Layout Problem to general Multi-Row Facility Layout as well as some special cases thereof. To the best of our knowledge this is the first global optimization approach for multi-row layout that is applicable beyond the double-row case. A key aspect of our proposed approach is a model for multi-row layout that expresses the problem as a discrete optimization problem, and thus makes it possible to exploit the underlying combinatorial structure. In particular we can explicitly control the number and size of the spaces between departments. We construct a semidefinite relaxation of the discrete optimization formulation and present computational results showing that the proposed approach gives promising results for several variants of multi-row layout problems on a variety of benchmark instances.

An Optimization Method for the Remanufacturing Dynamic Facility Layout Problem with Uncertainties

Remanufacturing is a practice of growing importance due to increasing environmental awareness and regulations. Facility layout design, as the cornerstone of effective facility planning, is concerned about resource localization for a well-coordinated workflow that leads to lower material handling costs and reduced lead times. However, due to stochastic returns of used products/components and their uncontrollable quality conditions, the remanufacturing process exhibits a high level of uncertainty challenging the facility layout design for remanufacturing. This paper undertakes this problem and presents an optimization method for remanufacturing dynamic facility layout with variable process capacities, unequal processing cells, and intercell material handling. A dynamic multirow layout model is presented for layout optimization and a modified simulated annealing heuristic is proposed toward the determination of optimal layout schemes. The approach is demonstrated through a machine tool remanufacturing system.

Integrated cell formation and layout problem considering multi-row machine arrangement and continuous cell layout with aisle distance

Cellular manufacturing is an important application of group technology and the cell formation process is one of the important steps in designing cellular manufacturing system. In recent years, researchers have noticed potential benefits when the layout problem is considered within the cell formation process. Nevertheless, there are not sufficient studies about consideration of real-life features in the cell formation and layout design process. In this paper, a new approach is presented to integrate the cell formation and its layout design. The proposed approach has three important design features not found in other papers. These design features are multi-row intra-cell layout (layout of machines within the cells), continuous inter-cell layout (layout of rectangular shape cells on the planar area), and aisle distance. The objective of the proposed approach is to form machine cells, find the layout of machine cells, and obtain the arrangement of machines within the cells such that the total material handling cost is minimized. In order to have a more accurate layout design, the material handling cost is calculated in terms of the actual position of machines within the cell. Due to the computational complexity of the proposed problem, a heuristic method is proposed to solve medium- and large-scale problems in a reasonable computational time. Three lower bounds are developed for the proposed integrated problem in which the tightest of them is chosen for evaluating the solution of the heuristic method. Finally, numerical examples adopted from the literature are solved to verify the performance of the proposed heuristic method and illustrate the advantages of the proposed integrated approach. The results indicated that the heuristic method is both effective and efficient in solving real-sized problems. The results also demonstrated that the proposed layout approach gives better layout design in comparison with the existing approaches.

Solving a multi-floor layout design model of a dynamic cellular manufacturing system by an efficient genetic algorithm

This paper presents a mixed-integer programming model for a multi-floor layout design of cellular manufacturing systems (CMSs) in a dynamic environment. A novel aspect of this model is to concurrently determine the cell formation (CF) and group layout (GL) as the interrelated decisions involved in the design of a CMS in order to achieve an optimal (or near-optimal) design solution for a multi-floor factory in a multi-period planning horizon. Other design aspects are to design a multi-floor layout to form cells in different floors, a multi-rows layout of equal area facilities in each cell, flexible reconfigurations of cells during successive periods, distance-based material handling cost, and machine depot keeping idle machines. This model incorporates with an extensive coverage of important manufacturing features used in the design of CMSs. The objective is to minimize the total costs of intra-cell, inter-cell, and inter-floor material handling, purchasing machines, machine processing, machine overhead, and machine relocation. Two numerical examples are solved by the CPLEX software to verify the performance of the presented model and illustrate the model features. Since this model belongs to NP-hard class, an efficient genetic algorithm (GA) with a matrix-based chromosome structure is proposed to derive near-optimal solutions. To verify its computational efficiency in comparison to the CPLEX software, several test problems with different sizes and settings are implemented. The efficiency of the proposed GA in terms of the objective function value and computational time is proved by the obtained results.

A genetic algorithm for solving a multi-floor layout design model of a cellular manufacturing system with alternative process routings and flexible configuration

This paper presents a novel integer linear programming model for designing multi-floor layout of cellular manufacturing systems (CMS). Three major and interrelated decisions are involved in the design of a CMS; namely cell formation (CF), group layout (GL), and group scheduling (GS). A novel aspect of this model is concurrently making the CF and GL decisions to achieve an optimal design solution in a multi-floor factory. Other compromising aspects are: multi-floor layout to form cells in different floors is considered, multi-rows layout of equal area facilities in each cell is allowed, cells in flexible shapes are configured, and material handling cost based on the distance between the locations assigned to machines are calculated. Such an integrated CMS model with an extensive coverage of important manufacturing features has not been proposed before and this model incorporates several design features including alternative process routings, operation sequence, processing time, production volume of parts, duplicate machines, machine capacity, new machine purchasing, lot splitting, material flow between machines, intra-cell layout, inter-cell layout, multi-floor layout and flexible configuration. The objective is to minimize the total costs of intra-cell, inter-cell, and inter-floor material handling, new machines purchasing and machine processing. Two numerical examples are solved by the Lingo software to verify the performance of the proposed model and illustrate the model features. Sensitive analysis is also implemented on some model parameters. An improved genetic algorithm (GA) is proposed to derive near-optimal solutions for the integrated model because of its NP hardness. It is then tested using several problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison to a classic simulated annealing algorithm and the Lingo software. The obtained results show the efficiency of proposed GA in terms of objective function value and computational time.

Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing

This paper presents a novel mixed-integer non-linear programming model for the layout design of a dynamic cellular manufacturing system (DCMS). In a dynamic environment, the product mix and part demands are varying during a multi-period planning horizon. As a result, the best cell configuration for one period may not be efficient for successive periods, and thus it necessitates reconfigurations. Three major and interrelated decisions are involved in the design of a CMS; namely cell formation (CF), group layout (GL) and group scheduling (GS). A novel aspect of this model is concurrently making the CF and GL decisions in a dynamic environment. The proposed model integrating the CF and GL decisions can be used by researchers and practitioners to design GL in practical and dynamic cell formation problems. Another compromising aspect of this model is the utilization of multi-rows layout to locate machines in the cells configured with flexible shapes. Such a DCMS model with an extensive coverage of important manufacturing features has not been proposed before and incorporates several design features including alternate process routings, operation sequence, processing time, production volume of parts, purchasing machine, duplicate machines, machine capacity, lot splitting, intra-cell layout, inter-cell layout, multi-rows layout of equal area facilities and flexible reconfiguration. The objective of the integrated model is to minimize the total costs of intra and inter-cell material handling, machine relocation, purchasing new machines, machine overhead and machine processing. Linearization procedures are used to transform the presented non-linear programming model into a linearized formulation. Two numerical examples taken from the literature are solved by the Lingo software using a branch-and-bound method to illustrate the performance of this model. An efficient simulated annealing (SA) algorithm with elaborately designed solution representation and neighborhood generation is extended to solve the proposed model because of its NP-hardness. It is then tested using several problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison with the Lingo software. The obtained results show that the proposed SA is able to find the near-optimal solutions in computational time, approximately 100 times less than Lingo. Also, the computational results show that the proposed model to some extent overcomes common disadvantages in the existing dynamic cell formation models that have not yet considered layout problems.

Designing an intra-cell layout model in dynamic cellular manufacturing systems with unequal-area facilities

This paper presents a novel mixed-integer non-linear programming model for an intra-cell layout (ICL) design for a dynamic cellular manufacturing system (DCMS). In a dynamic environment, the product mix and part demands vary during a multi-period planning horizon. As a result, the best cell configuration and part routings for one period may not be efficient for successive periods, and necessitating reconfiguration. A novel aspect of this model is the concurrent making of the cell formations and ICL decisions in a dynamic environment. Another aspect of this model is the utilization of a multi-row machine layout for machines of unequal-area. The DCMS model presented incorporates several design features including alternative process routings, operation sequencing, processing time, parts production volume, duplicate machines, machine capacity, ICL, multi-row layout of unequal-area facilities, continuous-area cells and machine relocation. The objective of the integrated model is to minimize the total costs of intra and inter-cell material handling, machine relocation, machine overheads and machine processing. The main constraints are part processing requirements, machine availability, maximal and minimal cell size, machine time-capacity and the non-overlapping of facilities. A comprehensive example is solved using Lingo software to verify the performance of the proposed model. Also, the computational results show that to some extent the proposed model overcomes common disadvantages in the existing dynamic cell formation models that have not yet considered layout problems of unequal-area facilities.

Multi-floor layout design of cellular manufacturing systems

This paper presents a novel integer linear programming model for designing multi-floor layout of cellular manufacturing systems. Three major and interrelated decisions are involved in the design of a cellular manufacturing system (CMS); namely cell formation (CF), group layout (GL) and group scheduling (GS). A novel aspect of this model is concurrently making the CF and GL decisions to achieve an optimal design solution. The proposed model integrating the CF and GL decisions can be used by researchers and practitioners to design GL of a CMS in a multi-floor factory. Other compromising aspects are: considering multi-floor layout to form cells in the different floors, considering multi-rows layout of equal area facilities in each cell, configuring cells in flexible shapes, calculating material handling cost based on the distance between the locations assigned to machines. The proposed model incorporates several design features including alternative process routings, operation sequence, processing time, production volume of parts, duplicate machines, machine capacity, purchasing machine, lot splitting, material flow between machines, intra-cell layout, inter-cell layout, multi-floor layout and flexible configuration. The objective is to minimize the total costs of intra-cell, inter-cell and inter-floor material handling, purchasing new machines and machine processing. The main constraints are demand satisfaction, cell size, machine time-capacity, material flow conservation and machine location. Two numerical examples are solved by the Lingo software to verify the performance of the proposed model and illustrate the model features.

DESIGN OF A CONSTRAINED MULTI-ROWS LAYOUT IN PRESENCE OF UNCERTAINTY

This paper deals with a multi-rows layout problem where different machines need to be placed in available locations so as to minimize the material handling costs. The market demands of products are subject to uncertainty. One particularity of this problem is that machines can not be placed to any distance from each other. The proximity between machines belongs to a bounded interval and a preference relation exists on the choice of the possible values. We model the problem using fuzzy sets and propose a technique, which is based on genetic algorithms, to solve the problem. An illustrative example shows the benefits of this approach.

An efficient algorithm for some multirow layout problems

Three multirow layout problems are presented: transistor orientation, contact positioning and symbolic-to-shape translation. It is shown that these multirow problems have a common property, called quantitative dependency. Using this property, an optimization technique which is based on a penalty-delay strategy is presented. It is proved that the penalty-delay strategy assures optimality, and that the optimal solution can be obtained in linear time. The algorithmic approach is based on the observation that optimal layout decisions in any region within a cell or a macro depend only on quantitative measures of the decisions in other regions, rather than on their details. This suggests a departure from the traditional approach of handling the different regions separately and combining them afterward into a single unit, an approach that may degrade the quality of the final layout. Instead, the entire macro can be processed at once, taking into account the mutual quantitative dependency between distinguished regions. >

Experimental analysis of simulated annealing based algorithms for the layout problem

In this paper, results from an experimental analysis involving the 2-way and 3-way exchange algorithms, a modified penalty algorithm, the simulated annealing algorithm and a hybrid simulated annealing algorithm are presented. The hybrid simulated annealing algorithm uses the modified penalty algorithm to generate an initial solution and then improves it using simulated annealing. It is tested on single-row layout problems with facilities of unequal area and multi-row layout problems with facilities of equal area. The algorithm produced solutions better than those previously reported in the literature for two of the larger single-row problems and five multi-row layout problems. For all the other single-row problems and eight of ten multi-row layout test problems, it produced the best known solutions. The hybrid simulated annealing algorithm appears to produce better quality solutions than the simulated annealing and tabu navigation algorithms, but requires more computation time than simulated annealing.