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...reaching end their functional life either through dumping in landfill sites or through shredding and incineration, are thought to be too polluting and unnecessarily wasteful of precious environmental resources, by failing to retrieve and reuse materials and functional components potentially available in the discarded product. Hence, under the pressure of emerging legislation in most of the developed countries, manufacturers are beginning to set up additional operational networks to retrieve their products upon reaching the end of their life, and if possible, reprocess and reuse the constituent components and materials. This new set of reclaiming, reprocessing and redistribution operations is collectively known as reverse logistics (Fleischmann et al., 1997), and their design and management defines a novel and challenging technical area of production system modeling, analysis and control.
One particular theme that is emerging as a predominant issue in the current reverse logistics related literature is the need for effective modeling, analysis and management of the high levels of uncertainty inherent in the operation of these systems. For instance, three recent survey works (Fleischmann et al., 1997; Lee et al., 2001; Tang et al., 2002) identify the modeling and analysis of the impact of the product and environmental uncertainties underlying the operation of modern reverse logistics systems as one of the major issues to be addressed by the research community. Furthermore, the same works point out that the effective management of these uncertainties is one of the fundamental issues differentiating reverse logistics and remanufacturing-related research from more traditional logistics and manufacturing systems theory.
Motivated by these general remarks, the work presented in this paper undertakes the problem of uncertainty modeling and management in the context of the more specific area of (Optimal) Disassembly Planning (ODP), which constitutes a core problem to be addressed in the operation of any reverse logistics process. A basic characterization of the ODP problem is provided by means of Fig. 1, which has been adapted from Lee et al. (2001). As depicted in Fig. 1, the disassembly of the reclaimed product units into a number of components and subassemblies constitutes a primary step in the entire reverse logistics process. The derived units will be subsequently directed either: (i) for remanufacturing/refurbishing and reuse; or (ii) for extraction and recycling of (some of) their materials; or, finally, (iii) for disposal through dumping or incineration. In this operational context, the ODP problem seeks to determine the level of disassembly of each returned product unit to its constituent elements, and the particular venue of disposition of the retrieved components, so that the total (monetary) value extracted during the process operation is maximized, while at the same time, various technical, legislative, environmental, and any other managerial considerations are observed.
[FIGURE 1 OMITTED]
It can be argued that the ODP problem is one of the most extensively investigated problems in the reverse logistics literature. As already mentioned, three recent and quite comprehensive surveys of the relevant literature are provided in Fleischmann et al. (1997), Lee et al. (2001) and Tang et al. (2002). All the works presented in these surveys address the ODP problem by: (i) first formalizing in a particular representation the dynamics of the disassembly process, as constrained by the relevant technological, environmental and legislative requirements; (ii) subsequently augmenting this representation with a "cost structure" modeling the economic elements involved in the decision-making process; and (iii) finally defining and solving an optimization problem by means of the modeling framework established in steps (i) and (ii). Yet, it is also true, that with the exception of the papers of Looney (1988), Zussman et al. (1994), Geiger and Zussman (1996), Gungor and Gupta (1998), Salomonski and Zussman (1999), Meacham et al. (1999), Zussman and Zhou (2000), Lambert (2002) and Erdos et al. (2001), all the remaining existing works on the ODP problem assume a totally deterministic model for the underlying process dynamics and the applying cost structure. Furthermore, among the works that recognize the potential stochasticity of these problem elements, many of them (e.g., Gungor and Gupta (1998), Meacham et al. (1999), Zussman and Zhou (2000), Lambert (2002), and Erdos et al. (2001)) deal with this issue only as an afterthought, through: (i) a sensitivity analysis of a solution developed according to a deterministic optimization model; and/or (ii) an on-line heuristical adjustment of the derived solution, in case that there exists significant deviation of the actual implementation from the normative model. On the other hand, the papers of Looney (1988), Zussman et al. (1994), and Geiger and Zussman (1996), recognize the need to explicitly address the involved uncertainty during the determination of the optimal policy, but they resort to problem representations that presume the a priori availability of some (quite sophisticated) model that provides a complete quantitative characterization of this uncertainty; only the work of Salomonski and Zussman (1999) recognizes the potential unavailability of the information necessary to develop such a priori fully quantified models and the resulting need to derive this information in real-time.
The defining positions of our work, which are in agreement with the positions taken in Salomonski and Zussman (1999), and also with an emerging consensus in the broader community, are that: (i) understanding the impact of the involved uncertainty and accounting for it during the development of optimized disassembly plans, is important for the effective optimization of the overall process performance; furthermore, (ii) any assumption regarding the a priori availability of a fully quantified model characterizing problem elements such as the statistical distributions and/or indices modeling the randomness in the cost data and the probability distributions determining the classification of the various components and subassemblies to different quality classes, is rather unrealistic, since (much of) the information necessary to develop such a model can be provided only through observation of the process itself. These two positions further suggest that any attempt towards developing an optimizing solution to the ODP problem, which is the focus of this work, must involve some algorithmic components that will allow the decision-making process to: (i) accumulate its past experience to a pertinently defined set of data structures; and, at the same time, (ii) exploit the "knowledge" captured in these data sets towards improving the overall system performance. In broader systems theory, algorithms with the aforementioned capabilities are known as "learning" algorithms (Mitchell, 1997). Hence, the main topic and the intended contribution of this paper is the design of effective and computationally efficient learning algorithms for the ODP problem. More specifically, we focus on a particular class of learning algorithms known as "reinforcement learning" in the relevant literature (Sutton and Barto, 2000). We believe that these algorithms are most appropriate for the ODP problem due to: (i) their strong affinity to the dynamic programming framework (Bertsekas and Tsitsiklis, 1996), which, as will be shown in the next section, is the natural representation of the problem under consideration; and (ii) their computational simplicity and implementation flexibility, two properties which render them compatible with the conditions prevailing in the involved facilities. In addition, reinforcement learning algorithms have been extensively studied recently, and currently, there is a significant body of analytical results characterizing their convergence and dynamics.
With this basic positioning of the presented results, the rest of the paper is organized as follows. The next section provides an analytical characterization of the ODP problem that not only reveals the underlying problem structure but also the nature and impact of the aforementioned uncertainties on the derived solutions. Subsequently, Section 3 establishes that reinforcement learning provides an effective and computationally efficient method for generating optimized disassembly plans in the face of the aforementioned process uncertainties. Section 4 considers the implementation of the proposed algorithms in the remanufacturing facility, providing a number of observations and suggestions that can potentially expedite the learning process and facilitate the integration of these algorithms into the overall operational context. Finally, Section 5 concludes the paper and highlights directions for future work. Throughout the paper, a case study adapted from Krikke et al. (1998) is used to exemplify and elucidate the primary concepts and methods introduced in this work.
2. An analytical formulation of the ODP problem
2.1. A Petri-net-based modeling framework
As was pointed out in the discussion of the introductory section, any analytical characterization of the ODP problem must be based on a formal representation of the disassembly process that will be able to express explicitly, yet compactly, all the feasible (1) disassembly sequences and their associated economics. Presently, the two most widely adopted representations for the...
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