A concurrent solution for intra-cell flow path layouts and I/O point locations of cells in a cellular manufacturing system

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Abstract

In this paper, we study the I/O (Input/Output) point location problem and the intra-cell flow path layout problem of cells in a cellular manufacturing system. Traditional approaches have often solved these two problems as separate problems, despite they are mutually affected. As a result, the results obtained by traditional approaches may not be as desirable as expected. In this study, we propose a layout procedure that can solve these two problems concurrently, so that the sum of the inter-cell flow distance and the intra-cell flow distance can be minimized. We assume cells have been arranged along a straight-line inter-cell flow path. Furthermore, the machines’ positions on each cell’s intra-cell flow path have been determined, but the intra-cell flow path of each cell has not been placed on the shop floor yet. We also assume the configuration of intra-cell flow paths is serpentine. The proposed layout procedure classifies the flow distance incurred by inter-cell flow into five types and minimizes them with different solution procedures containing various linear programming models. The proposed layout procedure has four phases. At the first phase, we find each cell’s input and output points on the inter-cell flow path by considering only the inter-cell flow distance. At the second phase, we find the input and outpoint points on each cell’s intra-cell flow path by considering only the intra-cell flow distance. At the third phase, we use the points found in the previous two phases as references to help us correctly orient and arrange each cell’s intra-cell flow path on the shop floor. Finally, at the fourth phase, we find the accurate the input points and output points on each cell’s intra-cell flow path and the inter-cell flow path by simultaneously considering the inter-cell and the intra-cell flow distance. We use an example to illustrate the proposed layout procedure. The results of the example show that the proposed layout procedure can effectively find each cell’s I/O point locations and intra-cell flow path layout by considering both intra-cell and inter-cell flow distance at the same time.

Research highlights

► We study the I/O point location problem and the intra-cell flow-path layout problem of cells. ► Traditional approaches often solve them separately despite they are mutually affected. ► Solutions obtained by traditional approaches are often not as desirable as expected. ► We solve them simultaneously to minimize the sum of inter-cell and intra-cell flow distance. ► This simultaneous approach indeed can effectively and efficiently find good-quality solutions.

Introduction

The problem environment of this paper is a cellular manufacturing system, in which parts follow predetermined flow paths to move around. The flow distance of a cellular manufacturing system is incurred by two types of flow – inter-cell and intra-cell. The amount of inter-cell and intra-cell flow of each cell is determined by the cell formation design. And, the flow distance of these two types of flow is determined by the system’s various layout designs, e.g. the layout of cells, the layout of inter-cell flow path, the layout of machines in each cell, the layout of intra-cell flow path connecting machines within each cell, and the location of each cell’s I/O (Input/Output) points. In this study, we focus on two layout problems – the intra-cell flow path layout problem within each cell and the problem of locating each cell’s I/O points. Traditional approaches often treat these two problems as separate problems and solve them individually and independently. However, as one will see, these two problems are mutually affected, thus solving them individually and independently may not result in best solutions. This can be realized from the example in Fig. 1. Let us assume M has been determined as the best I/O point for the cell in Fig. 1a. However, if one rearranges the cell’s intra-cell flow path (without changing the positions of machines on the intra-cell flow path) to generate a new intra-cell layout as shown in Fig. 1b, then M may no longer be the best I/O point for the cell. Compared with the cell in Fig. 1a, the cell in Fig. 1b needs a longer flow path segment to connect the intra-cell flow path with the inter-cell flow path at M. A longer flow path segment implies a greater intra-cell flow distance for the cell in Fig. 1b. When the inter-cell flow occurs, it incurs more than inter-cell flow distance. For example, as is shown in Fig. 2, in order for a part P (at a machine N in a cell 1) to visit another machine R in another cell 2, five types of flow distance will be incurred.

  • Type-A flow distance: Type-A flow distance is the distance from P’s current position, N, to the point, M, at which P leaves the intra-cell flow path of Cell 1.

  • Type-B flow distance: Type-B flow distance is the distance from the point, M, to the point, I, at which P enters the inter-cell flow path.

  • Type-C flow distance: Type-C flow distance is the distance from the point, I, to the point J, at which P leaves the inter-cell flow path.

  • Type-D flow distance: Type-D flow distance is the distance from the point, J, to the point, K, at which P enters the intra-cell flow path of Cell 2.

  • Type-E flow distance: Type-E flow distance is the distance from the point, K, to the point at which machine R resides.

From the above explanation, one should be able to understand the mutual effects between the intra-cell flow path layout problem of a cell and its I/O points locating problem. Therefore, in order to find a layout that can minimize the total flow distance (including the intra-cell and inter-cell flow distance), developing a layout procedure that can consider the effects between these two problems and solve them together is imperative.

Section snippets

Literature review

Various problems need to be solved when designing a multiple-cell manufacturing system. According to Jajodia, Minis, Harhalakis, and Proth (1992), the design problem of a cellular manufacturing system involves three problems: grouping production equipment into cells, allocation of cells to the area within the shop floor (i.e. the layout of cells), and layout of the machines within each cell. The first problem is also known as the ‘cell formation problem’. Many clustering algorithms have been

Problem definition

The assumptions of our problems are explained as follows:

  • 1.

    The flow between machines and between cells is known.

  • 2.

    Cells have been arranged into two rows along a straight-line inter-cell flow path. The configuration of each cell’s intra-cell flow path is serpentine.

  • 3.

    The machine content of each cell is known. For each cell, the relative positions of its machines on the intra-cell flow path have been determined, and its intra-cell flow path of each cell is linear. Furthermore, since the relative

The proposed layout procedure

The proposed layout procedure has four phases. The following briefly explains their tasks. An example is provided in Fig. 6 to illustrate the tasks of these phases.

  • Phase I: The problem of this phase is to find each cell’s input point and output point on the inter-cell flow path by minimizing the Type-C flow distance.

  • Phase II: At this phase, for each cell, we find the input point at which parts enter its intra-cell flow path by minimizing the Type-E flow distance, and the output point at which

An example

In this section, an example is given to illustrate the proposed layout procedure. The layout of Fig. 19 shows that the example has four cells. Table 1 gives each cell’s length, width, BSD and MSD. As was explained in Section 3, we assume each cell’s machines have been arranged along its linear intra-cell flow path. Table 2 gives the positions of each cell’s machines on its intra-cell flow path. In this example, all LP models are solved by ILOG CPLEX 7.1 (2001).

Summary and discussion

In this paper, we propose a layout procedure that cannot only locate each cell’s I/O points, but also determine the layout of each cell’s intra-cell flow path for a cellular manufacturing system with a straight line inter-cell flow path. Traditional approaches often treat these two problems as separate problems and solve them individually and independently. In this study, we first show these two problems can mutually affect each and demonstrate the importance of solving them as one problem. In

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