Optimization and Mathematical Programming to Design and Planning Issues in Cellular Manufacturing Systems under Uncertain Situations

Introduction

During the past few decades, there have been various types of optimization techniques and mathematical programming approaches for cellular manufacturing systems under different random situations. In a cell manufacturing, once work cells and scheduling of parts in each cell are determined, it may be possible that cycle time in a specific cell be more than the other cells which creates a bottleneck in a manufacturing system. In this way, there are two different approaches in order to decrease cycle time in bottleneck cell: duplicating bottleneck machines or outsourcing exceptional parts which are known as group scheduling (GS) in the literature. Selecting each approach to balance cycle times among all cells can lead to variations in machines layout characteristics by changes in type and number of machines. Finally, formations of cells are also changed according to the changes in scheduling decisions. Thus, scheduling problem is one of the operational issues which must be addressed in design stage concurrently in an integrated problem so that the best performance of cells would be achieved. It is noted that scheduling problem includes many tactical parameters with random and uncertain characteristics. In addition, uncertainty or fluctuations in input parameters leads to fluctuations in scheduling decisions which could reduce the effects of cell formation decisions. Figure 1 indicates transmission of uncertainty from tactical parameters to the CMS problem.

Figure 1.

Illustration of uncertainty transmission to the CMS decision

Thus, in order to intensify effectiveness of the solution, integrated problem in uncertain conditions must be studied so that final solution will be robust and immune against the fluctuations in input parameters.

In the concerned problem, uncertain parameters can be listed as follows:

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  Demand,

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  Processing time,

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  Routings or machine-part matrix,

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  Machines' availability,

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  Failure rate of machines,

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  Capacities,

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  Lead times,

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  Set-up considerations,

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  Market aspects,

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  …,

where the impact of each factor is discussed in the following sections.

Problem Background

Group technology (GT) is a management theory that aims to group products with similar processes or manufacturing characteristics, or both. Cellular manufacturing system (CMS) is a manufacturing concept to group products into part families based on their similarities is manufacturing processing. Machines are also grouped into machine cells based on the parts which are supposed to be manufactured by these machines. CMS framework is a important application of group technology (GT) philosophy. The basic purpose of CM is to identify machine cells and part families concurrently, and to assign part families to machine cells in order to minimize the intercellular and intracellular costs of parts. Some real-world limitations in CF are:

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  Available capacity of machines must not be exceeded,

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  Safety and technological necessities must be met,

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  The number of machines in a cell and the number of cells have not be exceeded an upper bound,

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  Intercellular and intracellular costs of handling material between machines must be minimized,

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  Machines must be utilized in effect (Heragu, 1997).