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An effective planning of lot sizes is a key strategy to efficiently manage a combined manufacturing/remanufacturing system in the presence of substantial setup costs. Due to its complex interdependencies, optimal policies and solutions have not been identified so far, but several heuristic approaches have been analyzed in recent contributions. The main heuristic shortcuts are forcing equally sized lot sizes over the planning horizon as well as imposing a specific cycle structure, i.e., a sequence of manufacturing batches is followed by a sequence of remanufacturing batches. We are instead proposing a flexibly structured heuristic that allows for differently sized remanufacturing batches. We show in a comprehensive numerical study that our approach outperforms other existing approaches in more than half of all instances by up to 17%.

In recent years, the idea of incorporating backward flows into traditionally forward-oriented supply chains has received increasing attention in theory and industry. When managed efficiently, this extension promises new opportunities to create profits from the recovery of products, components, and materials. Interestingly, firms cannot only create value from properly functioning product returns but also when a broken product is returned. Thierry et al. [22] name five options to handle the recovery of broken product returns ranging from simple repair to recycling. Among these options, remanufacturing product returns is especially interesting as it attempts to bring product returns to an as-good-as-new quality standard. By doing so, remanufacturing firms provide their customers a cheap alternative to expensive new products while being environmentally friendly at the same time. Remanufacturing a product commences in general with the disassembly of the product which is followed by a thorough inspection of all components obtained. All recoverable components are then mechanically remanufactured. Combined with new components, these remanufactured parts are assembled into the final remanufactured product. Remanufacturing activities can be found in a large variety of industries (see, e.g., [2], for an overview). To give an example, remanufacturing car related components is a practical source of revenues for automotive companies. In 2008, Volkswagen remanufactured, for instance, 3.83 million components (mainly engines and transmissions) and generated with these activities a revenue of around 600 million € (see [23]). In his seminal work, Guide [8] describes the complicating characteristics of remanufacturing in industry and elaborates a number of possible research questions that require further attention. Due to the complexity of an industrial remanufacturing system, all research questions can only be formulated to focus on a small part of the entire system. One important stream of research focuses on strategic network design perspectives (see, e.g., [7], [3] and [18]). Another important line of research analyses how remanufacturing and manufacturing operations have to be properly balanced to satisfy customer demand. In this context, one of the important research questions is the optimal timing and sizing of remanufacturing operations. A lot sizing problem results when substantial setup costs prevail to initiate a (re)manufacturing process. Depending on the characteristics of the demand and return flows, several classes of lot sizing problems (static vs. dynamic and/or deterministic vs. stochastic) can be identified. For the dynamic problem, refer to Teunter et al. [21], Schulz [17], Zhou et al. [24], and Li et al. [10] for more details. An analysis of static and stochastic return flows is provided by Mitra [14]. The first author to analyze the static and deterministic problem setting is Schrady [15]. He proposes to split the infinite planning horizon into identical cycles that are repeated continuously. Each cycle contains a single manufacturing batch that is followed by R equal remanufacturing batches. Henceforth, we will refer to this cyclical structure as the (R ,1)-policy. By minimizing the total cost (including a setup and a holding cost term), the (R ,1)-policy allows to find a first solution to this problem. Teunter [19] presents a different policy structure to define a cycle, the so-called (1, M )-policy. In contrast to Schrady's idea, only a single remanufacturing batch is issued per cycle that is succeeded by M equal manufacturing batches before the next identical cycle commences. Konstantaras and Skouri [9] derive sufficient conditions to determine which class of policy, (R,1)(R,1) or (1,M)(1,M), is optimal for a specific problem instance. Next to formulating the (1, M )-policy, Teunter names two options to further improve the solution. At first, he proposes that a more general (R ,M )-policy could reduce the total cost per time unit. This idea has been elaborated by Choi et al. [4] who define such a policy structure. They prove that there is only one cost minimizing sequence of equally sized batches in a cycle for any given (R ,M ) combination. Moreover, they present an algorithmic procedure to determine the minimum total cost for this policy structure. In comparison to the underlying approach of this contribution, however, they do not allow for variable remanufacturing lot sizes over time. We show that the performance can be considerably increased if this restriction is lifted. Choi et al. [4] procedure has been facilitated later by Liu et al. [11] using a slightly different experimental design as testing environment, however, both contributions derive similar results. The best solution of the (R,1)(R,1) and (1,M)(1,M) policies is only seldom improved by using the (R,M)-policy (in about 0.2% of all instances examined). Moreover, the actual improvement is also small (always less than 0.5%). The second possible improvement option mentioned by Teunter [19] is to allow for scheduling differently sized (re)manufacturing batches in a cycle. This idea has been analyzed at first by Minner and Lindner [12] who show with a Lagrange-multiplier approach that initiating equal remanufacturing batches in a cycle does not have to be optimal. Yet, these authors do not evaluate the actual benefit of scheduling differently sized remanufacturing batches. Feng and Viswanathan [5] contribute to the discussion by considering an (R,M) type policy with differently sized remanufacturing batches. As in our approach, a sequence of manufacturing batches is followed by one remanufacturing batch in each subcycle. However, for facilitating the solution finding process, they allow for only two classes of subcycles. In contrast, our approach is more flexible by not limiting the number of classes to two. Thus, we are pushing the idea of the subcycle approach even further and allow for a flexible sequence of manufacturing/remanufacturing batches while the size of the remanufacturing batch may vary for every single setup. While Feng and Viswanathan [5] conclude that the total costs can only be slightly decreased with two subcycle classes, we find that introducing an even more flexible structure of manufacturing/remanufacturing sequences can decrease costs substantially by up to 17.5% when allowing for differently sized remanufacturing batches compared to the best (R,M)-policy with equally sized (re)manufacturing batches. The main objective of this contribution is to comprehensively analyze the benefits of scheduling differently sized (re)manufacturing batches within a flexible cycle structure. We will show that different batch sizes can reduce the total cost substantially for a large number of problem instances. The remainder of this work is organized as follows. Section 2 introduces the basic modeling assumptions and outlines the solution finding process of the above-mentioned policy structures. In Section 3, we introduce our flexibly structured (R,M)flex(R,M)flex heuristic which we extensively test in a numerical study with the experimental design of Choi et al. [4]. The results of this study can be found in Section 4. Finally, Section 5 presents a short summary and an outlook on future research opportunities

Efficient planning of remanufacturing is critical in closed-loop supply chains facing substantial setup costs for (re)manufacturing. The present work, therefore, aims at improving the cost efficiency of preexisting heuristics. We review the existing approaches and find that all heuristics are somewhat limited in either the flexibility regarding the batch sizes as well as the cycle structure. The only exception is reported by Feng and Viswanathan [5] who are assuming a sub-cycle structure in which the sequences as well as sizes of batches might vary between two subcycles. While Feng and Viswanathan [5] report that “the reduction obtained in the cost is quite marginal”, we find that substantial cost improvements can be achieved by not limiting the number of subcycle classes. Our flexibly structured (R,M)flex(R,M)flex-policy (see Section 3) builds upon the SAIL algorithm as proposed by Choi et al. [4] that provides the optimal batch sequence for the case of equal remanufacturing and equal manufacturing batches. We extend the approach by dividing the sequence of manufacturing and remanufacturing batches into subcycles, and propose a heuristic to define the size of the remanufacturing batch within the subcycle. We performed an extensive numerical study based on Choi et al. [4] factorial design and find that 54.4% of all instances can be improved by applying the (R,M)flex(R,M)flex approach with a mean improvement of around 2% and a maximum improvement of 17.55%. A detailed analysis reveals that our approach performs particularly well in situations when the holding cost rates for returned items are high. We conclude that our approach can substantially improve performance in those industrial settings. This contribution provides an interesting approach for extending the considered problem setting in future contributions. As there are a number of possible extensions (like finite production and recovery rates, a disposal option, etc.), the improvements for introducing differently sized remanufacturing batches in these settings can be analyzed as well. Another interesting task to follow in future would be to analyze optimization approaches as presented in Schulz [16] in order to determine the optimal solution and policy structures. However, due to limited computational power this is hardly possible nowadays. Finally, to model a more realistic remanufacturing system, a multitude of different subprocesses (disassembly, rework, manufacturing, reassembly) should be considered as well as a large number of components that need to be (re)manufactured.