مشکل تعیین اندازه دسته تولید اقتصادی با بازسازی و جایگزینی یک طرفه
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|22758||2010||7 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : International Journal of Production Economics, Volume 124, Issue 2, April 2010, Pages 482–488
We investigate a lot-sizing problem with different demand streams for new and remanufactured items, in which the demand for remanufactured items can be also satisfied by new products, but not vice versa. We provide a mathematical model for the problem and demonstrate it is NP-hard, even under particular cost structures. We also show the key role that remanufacturing plays in the problem resolution. With the aim of finding a near optimal solution of the problem, we develop and evaluate a Tabu-Search-based procedure. The numerical experiment carried out confirms the success of the procedure for different cases.
The economic lot-sizing problem with remanufacturing and final disposal options (ELSR) refers to the problem of finding the quantities to produce, remanufacture, and dispose in each period over the planning horizon such that all demand requirements of a single item are satisfied on time, minimizing the sum of all the involved costs. The main difference with the traditional economic lot-sizing problem (ELSP) is that the demand can be also satisfied by recovering used items returned to the origin. Governmental and social pressures as well as economic opportunities have motivated many firms to become involved with the return of used products for recovery (Gungor and Gupta, 1999; Guide, 2000; Fleischmann, 2001; Brito et al., 2002). Remanufacturing can be defined as the recovery of returned products, after which the products are as good as new (Gungor and Gupta, 1999; Hormozi, 2003). Remanufacturing tasks often involve disassembly, cleaning, testing, part replacement or repairing, and reassembling operations. Products that are remanufactured include automotive parts, engines, tires, aviation equipment, cameras, medical instruments, furniture, toner cartridges, copiers, computers, and telecommunications equipment. However, possible downgrading in the remanufactured products may cause that they are offered at an inferior market price than the new ones, i.e. they are not identical from the consumer's viewpoint. Then, it makes sense to assume different demand segments for remanufactured and new items. Industrial applications where segmented market for manufactured and remanufactured occurs include photocopiers, tires and personal computers (Ayres et al., 1997; Ferrer, 1977; Maslennikova and Foley, 2000; Inderfurth, 2004). Since the demand requirements must be fulfilled on time, the case where the available returned items in a certain period are not sufficient to meet the demand requirements for remanufactured products must be considered. To address this problem, a manufacturer's market strategy is to allow substitution of remanufactured products by new ones, possibly maintaining the selling price of the remanufactured products in order to avoid losing potential customers (Bayindir et al., 2007; Inderfurth, 2004). Thus, we can consider the substitution necessary rather than desirable. On the other hand, as we will see further in a numeric example of Section 3.1, allowing substitution can result in cost savings, even when the returns are sufficient to fulfill the requirements of remanufactured products in any period and the remanufacturing costs are favorable. As it is noted by Inderfurth (2004), when manufacturing and remanufacturing processes are sharing common manufacturer resources and/or the different markets are interconnected by substitution, it is necessary to coordinate manufacturing and remanufacturing decisions. In this paper we investigate the economic lot-sizing problem with products returns under the circumstances described above, i.e. two independent demand streams for remanufactured and new items, respectively, and where the substitution for the remanufactured items is allowed. We refer to this problem as the Economic Lot-Sizing Problem with Remanufacturing and Final Disposal options and one-way Substitution (ELSR-S). We provide a mathematical model for the problem and show it is NP-hard, even under stationary cost parameters. We also show that in order to optimally solve the ELSR-S, we can focus on the remanufacturing activity. Considering this last result, we suggest a Tabu-Search-based procedure for solving the ELSR-S, exploiting the key role that the remanufacturing plays in the problem resolution and employing the divide and conquer principle in order to obtain the plans for the different activities. The procedure can be considered as an extension of that presented in Piñeyro and Viera (2009) for the traditional ELSR, i.e. when substitution is not allowed. To the best of our knowledge, this is the first time that a metaheuristic, and in particular the Tabu Search, is used for solving this kind of problem. The remainder of this paper is organized as follows. Section 2 is devoted to the literature review. In Section 3 we provide the problem definition and the respective mathematical model. We also show the relevance that remanufacturing plays in the ELSR-S resolution and certain effects of the substitution in its determination. In Section 4 we present the Tabu Search procedure suggested for solving the ELSR-S. The computational analysis is provided in Section 5. Finally, Section 6 is devoted to our conclusions and several directions for future research.
نتیجه گیری انگلیسی
In this paper we investigate the economic lot-sizing problem with product returns and one-way substitution (ELSR-S). We provide a mathematical model for the problem and show the key role that remanufacturing plays in the ELSR-S resolution. As in the traditional ELSR, we show that optimally solving the ELSR-S reduces to finding a remanufacturing plan of perfect-cost. However, this is not a simple task, because the problem is NP-hard (it can be considered as an extension of the ELSR). Unlike the ELSR, when substitution is allowed, maximizing the total remanufacturing quantity cannot be the most suitable option. Considering these last results together, we suggest a Tabu-Search-based procedure for solving the ELSR-S, extending that of Piñeyro and Viera (2009) for the ELSR. The procedure explores different remanufacturing plans, guided by the rule of maximizing the useful remanufacturing quantity for each period fixed as positive remanufacturing-period. After the remanufacturing plan is determined, the corresponding optimal production and final disposal plans are obtained by means of the Wagner–Whitin algorithm. The experiment conducted shows that the suggested procedure will be cost-effective for a wide-range of problem instances. We note that the optimal solution was found for nearly one third of tested cases and for most cases the gap with the optimal solution was less than 1%. We conclude that maximizing the useful remanufacturing quantity rather than maximizing the total remanufacturing quantity seems to be the best option when substitution is allowed. However, how to identify the periods with positive remanufacturing is not even clear. Despite the low running-time obtained for the procedure, we note that for larger problems, it could be necessary to replace the Wagner and Whitin algorithm for any of the new faster algorithm of O(T log T) time developed by Federgruen and Tzur (1991), Wagelmans et al. (1992) or Aggarwal and Park (1993). From a theoretical point of view, a detailed analysis about the structural properties of the ELSR-S optimal solutions must be done. In this sense, further analysis on the problem of obtaining the perfect-cost remanufacturing plan seems an important goal. Other possible direction is to extend the analysis of Yang et al. (2005) on the extreme-point optimal solutions of the minimum concave-cost network flow formulation for the ELSR in order to include substitution. Also the analysis of stability regions as in Konstantaras and Papachristos (2007) for the case of constant parameters and large returns available in the first period should be extended in order to cover more general situations as discussed in this paper.