Double Row Layout Problem Research Articles

A hybrid niching memetic algorithm for multi-modal optimization of double row layout problem

Double row layout problem (DRLP) involves identifying the exact locations of machines participating in a production task on two rows. There are typically multiple layouts with approximately optimal material handling cost for a DRLP. These layouts often exhibit significantly different layout configurations. Identifying multiple global or local optimal layouts can provide layout designers with a wide range of options, which is of great significance for enhancing the maintainability, scalability, and customisability of the facility. However, most existing studies on DRLPs typically focus on designing a single optimal layout. In this paper, we study a multi-modal optimization of double row layout problem (MDRLP). A hybrid approach combing a fast niching memetic algorithm and linear programming (FNMA-LP) is proposed for MDRLP to locate multiple global or local optimal layouts with a similar quality. First, a fast niching memetic algorithm is developed to find a set of approximate optimal machine sequences. Then, LP is employed to optimise the exact locations of machines for each machine sequence. To evaluate the performance of the proposed algorithm, FNMA-LP is compared against three popular multi-modal algorithms and a state-of-the-art single-modal algorithm developed for DRLP. Experiments show that our approach outperforms competing approaches on almost all problem instances.

A mixed-integer programming formulation for optimizing the double row layout problem

The Double Row Layout Problem (DRLP) asks for an arrangement of machines on both sides of a straight line corridor so as to minimize the total cost for transferring materials among machines. The DRLP is NP-Hard and has practical relevance, specially in manufacturing systems design. In this paper, we drastically reduce the time required to solve the problem by constructing a new and effective mixed-integer linear programming (MILP) model of the DRLP. The new model was obtained by reformulating an existing MILP model. This includes tightening some constraints, introducing new variables, implementing constraints to link the new and original variables; and adding valid inequalities and a valid system of equations. To reduce the size of the reformulated model, we eliminate several of the new introduced variables by a substitution using the system of equations. The computational results demonstrate that the proposed model requires considerably smaller computational times compared to the ones in the literature. As a consequence, optimal solutions can now be efficiently found for larger instances of the problem. Previous studies have been able to optimally solve, within reasonable time, instances with size up to 16 machines, while with the new model four instances with 20 machines could be optimally solved.

A Mixed-Integer Programming Formulation for a Simplified Model of the Double Row Layout Problem

The double row layout problem (DRLP) is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is minimized. Since it is vital to save cost and enhance productivity, the DRLP plays an important role in many application fields. Nevertheless, it is very hard to handle the DRLP because of its complex model. In this paper, we consider a new simplified model for the DRLP (SM-DRLP) and provide a mixed integer programming (MIP) formulation for it. The continuous decision variables of the DRLP are divided into two parts: start points of double rows and adjustable clearances between adjacent facilities. The former one is considered in the new simplified model for the DRLP with the purpose of maintaining solution quality, while the latter one is not taken into account with the purpose of reducing computational time. To evaluate its performance, our SM-DRLP is compared with the model of a general DRLP and the model of another simplified DRLP. The experimental results show the efficiency of our proposed model.

Mathematical formulation and a novel two-stage algorithm for double-row layout problem with fixed loading and unloading points

Loading and unloading operations are frequent and important in the production workshop. Thus, this paper proposes a novel double-row layout problem, which involves the location planning of material loading and unloading points of the facility in the layout; It needs to solve the sequence and precise coordinates of facilities with safety clearance to ensure the safety of the layout. Subsequently, a mixed-integer programming model and an improved discrete differential evolution algorithm with linear programming are developed to minimize material handling costs. The algorithm includes four efficient operations in optimization: the annealing mechanism, random strategy, variable neighborhood search strategy, and double-threshold termination mode. Thereafter, compared with the computational results of benchmark cases, the validity of the model and the efficiency of the algorithm are verified. In the basic problem, the calculation results of the algorithm are compared with many algorithms in the literature, and the algorithm still performs well. Finally, the algorithm is applied to solve the reducer workshop and provides a better layout scheme.

An Enhanced Multiobjective Double Row Layout Model considering the Machine Breakdowns.

Machine breakdowns (MB) often occur, resulting in changes in the production layout and the material flow and causing a surge in production cost. Obviously, it is imperative to consider MB in workshop layout. Scholars mainly focus on the double row layout problem in an ideal nonfailure condition while scarcely considering MB mentioned above in the layout field. This paper proposes an enhanced multiobjective double row layout model considering MB (MDRLP-MB) to fill the research gaps. That model adds redundancy to reduce the losses caused by machine failure based on the prediction of breakdowns. In MDRLP-MB, machines with the same machine type have the same size and failure rate. Besides, this paper redefines the biobjectives of material handling costs (MHC) and the utilization ratio based on the feature of MDRLP-MB. To reduce the complexity of the problem, a decision rule is developed to reduce the alternative machine types. Furthermore, it revises the NSGA-II to solve the MDRLP-MB effectively. Results of numerical experiments and application cases show MDRLP-MB can obtain the optimal set of Pareto solutions in the case of increasing different numbers of redundancy considering MB to provide a more refined layout scheme for decision making.

Mathematical formulation and two-phase optimisation methodology for the constrained double-row layout problem

Mathematical formulation and two-phase optimisation methodology for the constrained double-row layout problem

The double row layout problem with safety consideration: a two-stage variable neighborhood search approach

ABSTRACT The double row layout problem (DRLP) concerns on arranging a set of machines with various size on the two parallel rows with the aim to minimize the handling cost of material flow between machines. In some industrial applications, the layout planning requires the decision-makers to consider the safety factor, enforcing them to comply with a minimum distance between machines. Therefore, this study considers the inclusion of a safety factor in the DRLP, and a two-stage variable neighborhood search-sine cosine algorithm is proposed. In the first stage, the improved variable neighborhood search (IVNS) is developed for determining the placement of the machines in both rows. Then, in the second stage, a sine-cosine algorithm (SCA) is presented for adjusting the exact position of machines in the shorter row. The effectiveness and efficiency of the proposed algorithm are demonstrated by extensive computational test with various level of complexity.

A Surrogate Model-Based Hybrid Approach for Stochastic Robust Double Row Layout Problem

The double row layout problem is to arrange a number of machines on both sides of a straight aisle so as to minimize the total material handling cost. Aiming at the random distribution of product demands, we study a stochastic robust double row layout problem (SR-DRLP). A mixed integer programming (MIP) model is established for SR-DRLP. A surrogate model is used to linearize the nonlinear term in the MIP to achieve a mixed integer linear programming model, which can be readily solved by an exact method to yield high-quality solutions (layouts) for small-scale SR-DRLPs. Furthermore, we propose a hybrid approach combining a local search and an exact approach (LS-EA) to solve large-scale SR-DRLPs. Firstly, a local search is designed to optimize the machine sequences on two rows and the clearance from the most left machine on row 1 to the left boundary. Then, the exact location of each machine is further optimized by an exact approach. The LS-EA is applied to six problem instances ranging from 8 to 50 machines. Experimental results show that the surrogate model is effective and LS-EA outperforms the comparison approaches.

A Genetic Algorithm for the Double Row Layout Problem

The double row layout problem (DRLP) is an NP-hard and has many applications in the industry. The problem concerns on arranging the position of machines on the two rows so that the material handling cost is minimized. Although several mathematical programming models and local heuristics have been previously proposed, there is still a requirement to develop an approach that can solve the problem efficiently. Here, a genetic algorithm is proposed, which is aimed to solve the DRLP in a reasonable and applicable time. The performances of the proposed method, both its obtained objective values and computational time, are evaluated by comparing it with the existing mathematical programming model. The results demonstrate that the proposed GA can find relatively high-quality solutions in much shorter time than the mathematical programming model, especially in the problem with large number of machines.

A mixed-integer programming formulation of the double row layout problem based on a linear extension of a partial order

The double row layout problem (DRLP) occurs in automated manufacturing environments, where a material-handling device transports materials among machines arranged in a double-row layout, i.e. a layout in which the machines are located on either side of a straight line corridor. The DRLP is how to minimize the total cost of transporting materials between machines. The problem is NP-Hard and one great challenge nowadays is how to solve problem instances in reasonable computational times. In this paper, we give a new mixed-integer programming model of the DRLP, which is based on a linear extension of a partial order. In addition, we propose a reformulation of this model, which yields stronger results. The new models have the least number of 0–1 variables in comparison with previous models in the literature. Computational experiments demonstrate that the proposed models obtain optimal solutions faster than previously published ones.

A heuristic approach for the double row layout problem

In the double row layout problem, we wish to position n machines on two parallel rows in order to minimize the cost of material flow among machines. The problem is NP-hard and has applications in industry. Here, an algorithm is presented, which works in two phases: (1) applying an improvement heuristic to optimize a random double row layout of a certain type and, then, (2) adjusting the absolute position of each machine in the layout via Linear Programming. Four variants of this two-phase algorithm are proposed and their efficiency is demonstrated by computational tests on several instances from the literature with sizes up to 50 machines.

A mixed integer programming model for a double row layout problem

This paper presents the double row layout problem which determines an arrangement of machines on either side of a central corridor so that the total material moved is minimized when the material handling path is the straight line along the corridor. We propose a mixed integer programming (MIP) model which modifies a recently proposed model in the literature by introducing tighter constraints. For the performance comparison, models in the literature and the new model that we propose are tested to solve 26 well known instances and two additional instances introduced in this paper. Computational results show that the new model performs remarkably well compared with the models in the literature. Specifically, the new model solves larger problems, and the shortest processing time is obtained by the new model for all instances.

MOEA/D With Linear Programming for Double Row Layout Problem With Center-Islands.

Facility layout problems (FLPs) in hospitals are typically to arrange facilities or rooms along both sides of a corridor to minimize some objectives. In a hospital, very often there are center-islands to decrease the flow cost among facilities or rooms. However, these islands have not been considered before. In this article, we propose an FLP with center-islands that involves two parallel rows and center-islands. A mixed-integer program formulation is established for modeling it. A methodology for combining a multiobjective evolutionary algorithm based on decomposition (MOEA/D) and linear program is proposed to solve this problem. MOEA/D optimizes the sequence of facilities on two rows and center-islands while the linear program is embedded into MOEA/D to optimize the exact locations of center-islands. A tabu search with a local search is also integrated into MOEA/D to enhance its search capability. Experiments show that our proposed methodology can effectively solve the problem.

A decomposition-based algorithm for the double row layout problem

The double row layout problem (DRLP) is a common pattern of facility layout problem, which has practical applications in flexible manufacturing systems. The double row layout problem is vital to save transportation cost and enhance productivity. Nevertheless, it is very hard to handle the DRLP because of its characteristic of combination of combinatorial and continuous aspects. In this paper, a decomposition-based algorithm is proposed to solve the DRLP. We decompose the DRLP into two subproblems. In the first subproblem, the adjustable clearances between adjacent facilities are temporarily ignored. A first improvement based local search is applied to optimize the sequences of facilities on double rows. During this process, the facilities of double rows are placed starting at different abscissas rather than starting at the same abscissa for each arrangement. A property of the objective function of the DRLP is used to obtain the optimal difference between two starting abscissas. In the second subproblem, a particle swarm optimization is applied to optimize the adjustable clearances between adjacent facilities under the condition that the sequences of facilities are fixed. Our proposed algorithm is evaluated on 59 test instances and compared with the state-of-the-art methods. The experimental results demonstrate the high competitiveness of our proposed algorithm.

Double-row facility layout with replicate machines and split flows

This paper presents a new variant of the double row layout problem (DRLP) that features types of capacitated machines. This variant dramatically improves the fidelity with which the DRLP represents the complex production alternatives in many production environments, especially in the microcomputer industry. The problem consists of placing different classes of machines, each with multiple replicates, on either side of a central aisle. This is a common type of layout problem observed in many production and service environments. This work extends the DRLP literature by utilizing machine replicates in the layout. Multiple replicates of the same machine allow the product flow to split into multiple branches, each representing a parallel flow line. Flow splitting can improve machine utilization and reduces the number of machines needed. We also introduce machine sharing, which lets different products use the same machine. This eliminates the need for dedicated assignments of products to machines, which is a common assumption in the current literature. The consideration of re-entrant product flow, whereby each product can visit the same machine multiple times, represents another unique aspect of this research. The problem is formulated as a nonlinear mixed integer program. Due to the computational complexity of this problem a hierarchical optimization approach is developed and evaluated on test problems of various sizes. Computational results show that the proposed method produces consistent and high quality solutions across problem sizes.

An improved mixed-integer programming model for the double row layout of facilities

We consider the double row layout problem, which is how to allocate a given number of machines at locations on either side of a corridor so that the total cost to transport materials among these machines is minimized. We propose modifications to a mixed-integer programming model in the literature, obtaining a tighter model. Further, we describe variants of the new model that are even tighter. Computational results show that the new model and its variants perform considerably better than the one in the literature, leading to both fewer enumeration tree nodes and smaller solution times.

A mixed-integer programming formulation for the double row layout of machines in manufacturing systems

The Double Row Layout Problem (DRLP) is the problem of allocating a given set of machines on both sides of a straight line corridor so as to minimise the total cost of transporting materials among machines. The DRLP occurs in several manufacturing plants, particularly in semiconductor manufacturing. While it has a large practical importance, the problem is very difficult to solve to optimality. In this paper, we construct a mixed-integer programming (MIP) formulation of the problem, which favourably compares to a previously published MIP formulation. The new model is found to present similar performance to another published MIP formulation, and it has the advantage of being more intuitive for handling qualitative inputs that may be required in a layout refinement phase.

Bi-objective corridor allocation problem using a permutation-based genetic algorithm hybridized with a local search technique

As a more practical form of the double-row layout problem, the bi-objective corridor allocation problem (bCAP) was introduced, in which a given number of facilities are to be placed on opposite sides of a central corridor so as to minimize both the overall flow cost among the facilities and the length of the corridor. Further, the bCAP seeks the placement of the facilities starting from the same level along the corridor without allowing any gap between two facilities of a row. In the initial proposal, the bCAP was solved as an unconstrained optimization problem using a permutation-based genetic algorithm (pGA). It is observed that the pGA alone is not sufficient to reach to the potential solutions of the complicated bCAP. In this work, incorporating a promising local search technique in the pGA, the hybridized pGA is found outperforming the simple pGA as well as a simulated annealing and tabu search-based approach in a number of instances of sizes 60 and above, in terms of both the best objective values and statistical analysis. Moreover, the hybridized pGA could explore multiple optimal solutions for some of such instances.

Sharing clearances to improve machine layout

This paper considers a double-row layout problem with shared clearances in the context of semiconductor manufacturing. By sharing some clearances, reductions in both layout area and material handling cost of approximately 7–10% are achieved. Along with minimal clearances for separating adjacent machines, clearances that can be shared by adjacent machines are considered. The shared clearances may be located on either or both sides of machines. A mixed integer linear programming formulation of this problem is established, with the objective to minimise both material flow cost and layout area. A hybrid approach combining multi-objective tabu search and heuristic rules is proposed to solve it. Computational results show that the hybrid approach is very effective for this problem and finds machine layouts with reduced areas and handling costs by exploiting shared clearances.

Solving dynamic double row layout problem via combining simulated annealing and mathematical programming

Double row layout problem (DRLP) is to allocate facilities on two rows separated by a straight aisle. Aiming at the dynamic environment of product processing in practice, we propose a dynamic double-row layout problem (DDRLP) where material flows change over time in different processing periods. A mixed-integer programming model is established for this problem. A methodology combining an improved simulated annealing (ISA) with mathematical programming (MP) is proposed to resolve it. Firstly, a mixed coding scheme is designed to represent both of sequence of facilities and their exact locations. Secondly, an improved simulated annealing algorithm is suggested to produce a solution to DDRLP. Finally, MP is used to improve this solution by determining the optimal exact location for each facility. Experiments show that this methodology is able to obtain the optimal solutions for small size problems and outperforms an exact approach (CPLEX) for problems of realistic size.