Linear programming in disassembly/clustering sequence generation
Introduction
Disassembly processes are studied for a number of reasons. Originally, these studies strongly focused on repair and maintenance applications. Presently, the growing emphasis on sustainable production has strongly stimulated the study on disassembly. This has shifted the emphasis towards topics related to recovery of parts and materials from discarded products. Product stewardship enforces manufacturers to product responsibility during the complete product lifecycle, inclusive the waste phase. Discarded products should be taken back by the producer and, subsequently, processed in a way that is both environmentally sound and economically feasible.
Disassembly does not automatically mean reverse assembly. From a technical point of view, in many cases the disassembly process needs less precision, e.g. when it is principally aimed at materials recycling. Moreover, more uncertainty in quality exists. Besides that, the supply will often be a mix of related, but different products. This makes that in general analysis of disassembly processes should not be on the same level of accuracy as is required for the assembly process. E.g. geometrical considerations are usually of reduced importance. Contrary to assembly operations, the disassembly process should not always be carried out completely. A reasonable trade-off between economic and environmental benefit, that determines the disassembly depth, should be made. Frequently, complete disassembly is also infeasible from a technical point of view.
A number of papers deals with the disassembly process within the framework of the extended recovery process that includes further processes such as: recollection, disassembly, dismantling, clustering, shredding, mechanical separation, upgrading and reuse [1], [2], [3], [4]. In the models that are described in these papers, the description of the disassembly process has been largely simplified.
Many other authors restrict themselves to the actual disassembly process. Parameters of this process, such as the revenue of materials, are externally defined, so the mechanisms that determine the values of these parameters are beyond the systems boundary, see, e.g. [5]. One of the tasks of studying disassembly processes is the generation of a set of near optimal disassembly sequences. This usually involves the appropriate order of the separate actions and the required disassembly depth, to arrive at a maximum net revenue, combined with fulfilling definite environmental constraints. This has been investigated by a multitude of authors. A brief survey of this work is included in Ref. [6]. Solution methods include: graphical methods, empirical methods, fuzzy methods e.g. simulated annealing [7], search algorithms and mathematical programming. The first proposal for application of mathematical programming is worked out in Ref. [8]. Here, linear programming is applied to some assembly and disassembly problems. The method is derived via Petri net representation. Unfortunately, this approach has never been noticed and worked out by other authors. In Ref. [9], the application of a modification of the travelling salesman problem is investigated. In Ref. [6] a graphical method on the generation of optimal disassembly sequences has been presented. The present paper describes an algorithm that is derived from this method. It is an extension of the idea that has been worked out in Ref. [8]. The algorithm is based on straightforward linear programming which can also be used for large systems. It is shown that this algorithm not only supports divergent operations such as disassembly, but is also appropriate to a combination of divergent and convergent processes. An example is the disassembly/clustering problem, where a sorting process next to disassembly is incorporated. This means that, subsequent to disassembly, parts consisting of similar materials are put together in the same container, according to market prices of the different categories of materials, in order to obtain maximum net revenue.
Section snippets
Selective disassembly
Selective disassembly is the nondestructive, reversible, dismantling of complex products into less complex subassemblies or single parts. It is carried out for a multitude of reasons, including:
- 1.
maintenance and repair,
- 2.
availability of subassemblies as service parts or for assembly in new products,
- 3.
removal of parts prior to set free other, desired parts,
- 4.
availability of parts aimed at material reuse,
- 5.
increasing purity of materials by removal of contaminants,
- 6.
complying regulations that prescribe
Model description
The system boundaries of the disassembly model that is described here, are determined by the point where the complete discarded product is available, and the point where the desired materials fractions are stored for sale. The only process that is modelled here is the disassembly process, i.e. a sequence of processes consisting of one step, in which one parent subassembly falls apart into two child subassemblies. A child subassembly might be a single part. From an economic point of view, such a
Cases on disassembly
As an illustration of the method described in the previous section, the optimal disassembly sequence of a 10-parts ball-point pen has been determined. Its assembly drawing, that has been taken from Ref. [6], is presented in Fig. 3.
It can be expressed both by a list of disassembly operations and the disassembly graph of Fig. 1. Single parts are not indicated in the diagram. The optimal disassembly sequence, calculated by the model, is depicted by a tree of bold lines. The results of this
Clustering problem
Selective disassembly is aimed at minimisation of economic, environmental and/or energetic costs. This is realised by proper selection of the disassembly process as has been elaborated in the preceding section. Selective disassembly transforms the discarded product into a number of parts and materials such that regulation is complied with and the net revenues of the resulting parts and materials are maximum. This involves, however, only one process in the chain of processes that is required for
Combined model
The disassembly/clustering problem is modelled with the disassembly model as a starting point. A typical clustering operation is illustrated in Fig. 7.
This figure shows a combination E of subassemblies or parts, that can be obtained by merging A and B or C and D. For instance, if E is a mixture of parts 1 through 5, it can be obtained by merging subassembly 1/3 and subassembly 4,5. It can also be obtained by merging 1,2 and 3/5. Subsequently, E might be combined with C, or with D, resulting in
Cases on disassembly/clustering
The modelling method has been applied to simple and more complex products. To that purpose the earlier described disassembly models of the ballpoint pen and the radio have been extended with a clustering part. As an example, a disassembly graph of the assembly of Fig. 6 is presented in Fig. 8. The node equations read:Disassembly section: node A/C: x1+x2≤1 node A,B: x3≤x1 node A,C: x4≤x2 node B: x5≤x2+x3 node C: x5≤x1+x4
Clustering section:
Table 3 contains the data that are used in the calculation.
Assuming these data, the solution 1,3,5
Conclusions
A new approach for generation of optimal disassembly sequences, based on LP techniques, has been presented and validated, using some configurations from literature. The method is applicable to a broader class of problems than the approach of Kanehara et al. [8], because their approach is restricted to determination of the optimal task sequence from a given initial state up to a defined final state, with inclusion of action costs only. The method described in this paper does not need the
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