مدل کنترل موجودی با در نظر گرفتن بازسازی و چرخه عمر محصول

This paper investigates inventory control policies in a manufacturing/remanufacturing system during the product life cycle, which consists of four phases: introduction, growth, maturity, and decline. Both demand rate and return rate of products are random variables with normal distribution; the mean of the distribution varies according to the time in the product life cycle. Closed-form formulas of optimal production lot size, reorder point, and safety stock in each phase of the product life cycle are derived. A numerical example is presented with sensitivity analysis. The result shows that different inventory control policies should be adopted in different phases of the product life cycle. It is also found that the optimal production lot size and reorder point are not sensitive to the phase length and the demand changing rate.

For the past few decades, electronic companies have faced two major pressures: short product life cycle and environmental sustainability. First, technology advances have shortened the life cycles for many products. Product demand may increase rapidly at first and then decrease a few months later due to the emergence of new products. Inventory management under a short product life cycle is not easy. Many problems such as large safety stock, high obsolescence costs, and high forecasting errors will arise. It is necessary to consider the constantly varying demand and its uncertainty when making inventory control policy. In addition, due to the short product life cycle and the emergence of new products, an outdated product may be returned even if it is still in good condition. For example, a customer may buy a new mobile phone to replace his/her old mobile phone just because he/she likes the new one, although the old mobile phone is still in good condition. Second, due to environmental and ecological responsibility, enterprises are trying to reuse, remanufacture, and recycle the used products in order to reduce the negative impact on environment. Companies in many countries are required to conform to the Waste of Electric and Electronic Equipment (WEEE) directives (Rahimifard and Clegg, 2007). Environmental sustainability and green supply chain management have received increasing attention since the 1990s (Seuring and Müller, 2008). Several international journals have published special issues about sustainable/green supply chain management in recent years (Piplani et al., 2007, Rahimifard and Clegg, 2007, Jayaram et al., 2007 and Seuring et al., 2008; see also Srivastava, 2007 and Seuring and Müller, 2008). The pressures of a short product life cycle and environmental sustainability make remanufacturing a reasonable choice. Remanufacturing is an industrial process, whereby used/broken products are restored to useful life. Remanufacturing is also an important part of sustainable supply chain and reverse logistics. The motives for product remanufacturing include legislation, increased profitability, ethical responsibility, secured spare part supply, and brand protection. Reasons for returning used products include end-of-life returns, end-of-use returns, commercial returns, and reusable components (Östlin et al., 2008). After remanufacturing, the returned products, along with the new products, comprise the serviceable inventory and satisfy customer demand. Inventory control in such remanufacturing systems becomes complicated. In many cases, used products are assumed to be collected and remanufactured to a good-as-new state, such as car batteries, printer cartridges, one-time use cameras, and some electronic components. Customers cannot distinguish ‘new’ (i.e. manufactured) products from repaired products (i.e. remanufactured), or they consider these two products as interchangeable. For example, about 90% of Kodak one-time use cameras (OTUCs) are produced from recycled camera bodies, and about 90% (by weight) of a used Kodak (2005) OTUC body is directly reused in the manufacture of new cameras (Mukhopadhyay and Ma, 2009). The purpose of this paper is to investigate the effects of the product life cycle on inventory control in a manufacturing/remanufacturing system and to determine the optimal production lot size, reorder point, and safety stock during each phase of the product life cycle. The product life cycle is divided into following phases: introduction (phase 1), growth (phase 2), maturity (phase 3), and decline (phases 4 and 5). Both demand rate and return rate of products are random variables with normal distribution; the mean of the distribution varies according to the time in the product life cycle. Before introducing our model, we present a brief literature review. van der Laan et al., 1996a and van der Laan et al., 1996b consider several inventory control strategies with remanufacturing and disposal. Product demands and returns are assumed to be independent Poisson processes; push and pull strategies are considered in the inventory model (van der Laan and Salomon, 1997, van der Laan et al., 1999a and van der Laan and Teunter, 2006) to coordinate production, remanufacturing, and disposal operations. Lead time effects are further investigated in a similar remanufacturing system to improve system performance (van der Laan et al., 1999b, Kiesmüller, 2003a and Kiesmüller, 2003b). Recently, Mukhopadhyay and Ma (2009) review joint procurement and production decisions in remanufacturing under quality and demand uncertainty. Three different cases are presented, and the optimal procurement and the production quantity for the firm are determined. All the above articles have an assumption that the demand rate and return rate are independent. In contrast, Kiesmüller and van der Laan (2001) develop an inventory model in which the random returns depend explicitly on the demand stream. They assume a constant probability that an item is returned. Dobos (2003) considers inventory strategies for a reverse logistics system in which demand is a known continuous function in a given planning horizon and the return rate of used items is also a given function of time; there is a constant delay between these two functions. To take stochastic demand rate and return rate into consideration, most relevant articles assume that demand rate and return rate follow specific distributions with fixed parameters, which are consistent through the product life cycle. However, Östlin et al. (2009) have developed strategies to balance supply and demand for remanufactured products during the product life cycle, but they do not present a clear inventory control policy. As previously mentioned, the product life cycle is shorter than before, especially in the electronics industry. Product demand may increase rapidly at first and then decrease a few months later. In addition, the product may be returned even if it is still in good condition. Therefore, the product life cycle influences not only long-term strategies but also operational activities. If the product life cycle is not considered in inventory control, then product shortage or overstocking is more likely to occur. Reiner et al. (2009) point out that when the life cycle structure is not considered in the demand model, forecasting errors may become uncomfortably high, leading to large safety inventories and a substantial risk of high obsolescence costs. To our knowledge, very few articles consider product life cycle, inventory control, and remanufacturing simultaneously. Ahiska and King (2010) use a discrete-time Markov decision process to find the optimal inventory policy (i.e. the manufacturing and the remanufacturing strategy that have the smallest cost) in each life cycle stage. Unlike in our paper, the same inventory policy is adopted within a stage, because the mean demand and the mean return are both assumed to be constant within each stage. Also, the length of a stage is considered to be long enough so that the problem can be treated as a set of infinite-horizon problems. Chung and Wee (2011) also develop an integrated production inventory model with short life cycles to consider green product design and remanufacturing with re-usage concept. An optimal replenishment policy is derived. The result of the analysis shows that the re-manufacturability and the component life cycle of product design are interrelated. They have shown that new technology evolution, remanufacturing ratios, and system's holding costs are critical factors affecting decision making in a green supply chain inventory control system. The rest of this paper is organized as follows. Section 2 presents the assumptions and notations. Section 3 explains the mathematical modeling. Section 4 provides numerical examples and sensitivity analysis. The paper concludes in Section 5.

This paper analyzes the relationship between the demand rate and the return rate in a manufacturing/remanufacturing system during each phase of the product life cycle. The major contribution of the paper is that the closed-form formulas of optimal production lot size, reorder point, and safety stock in each phase of the product life cycle are successfully derived. The numerical example shows the practicability of our model and indicates that different inventory control policies should be adopted in different phases of the product life cycle. In phase 1, the EOQ model with safety stock is enough. The production lot size should increase with production activities in phase 2 and decrease in phases 3 and 4. There is no need to manufacture new products in phase 5, during which some returned products are discarded to reduce unnecessary remanufacturing and holding costs. Phase 5 only requires maintaining inventory at a decreasing level to ensure the necessary fill rate. In addition, the results of sensitivity analysis show that the inventory control policy is not sensitive to the phase length and the demand changing rate. When applying the proposed inventory control policy to a real case, it is particularly suitable for the products with very short life cycle, such as in the mobile phone industry. The demand for these products changes quickly, but traditional inventory models typically assume that demand is stationary. Therefore, traditional inventory models cannot consider the change in demand even in a certain stage of the product life cycle. Our model, however, can provide a detailed inventory control policy within a stage, which may have a dramatically changing demand. Several assumptions in this paper can be relaxed for future research. Customers may consider remanufactured and manufactured products as two different ones. Other distribution can be adopted for demand and return rate. Nonlinear mean demand and return rate functions also deserve investigation.