سیاست های موجودی و قیمت گذاری بهینه برای محصولات اجاره شده با قابلیت تولید دوباره

In this paper we consider a company which leases new products and also sells remanufactured versions of the new product that become available at the end of their lease periods. When the amount of end-of-lease items in stock is not sufficient to meet the demand for remanufactured products, the firm may purchase additional cores from a third-party supplier. We develop a dynamic programming formulation for determining the optimal price of remanufactured products, and optimal payment structure for the leased products. Our objective is to maximize the discounted system-wide profit over a finite horizon. The profit function consists of revenues that are obtained from remanufactured product sales and leasing, remanufacturing and manufacturing costs, inventory holding and shortage costs. We consider a consumer choice based demand model for mapping a potential customer into one of the product segments (a remanufactured product customer or a customer for a leased product with a particular lease period) for a given price/lease payment vector. We explore several properties of the discounted profit function and provide insight on the behavior of pricing and inventory policies. We also investigate the effect of key product characteristics such as deterioration in age, cost of shortage in remanufacturable product inventory, and key market characteristics such as relative willingness-to-pay for buying a remanufactured product and relative willingness-to-pay for leasing a new product on optimal pricing policies through a computational study.

Remanufacturing (in the context of our paper) is the process of bringing a used product to an as-good-as-new condition by inspecting its components and performing repairing, replacing, restoring operations as necessary. A product is considered remanufactured if its primary components come from a used product. Recently, remanufacturing has been receiving growing attention for various reasons such as consumer awareness, environmental concerns, economical benefit, and legislative pressure. Remanufactured products include photocopiers, computers, telecommunication equipment, cellular phones, automotive parts, office furniture, and tires. One of the major issues faced by the firms involved in remanufacturing is taking back used products before the end of their useful life so that some revenue can be generated by remanufacturing or reusing them. Another concern is the uncertainty in the quantity, timing and quality of returned products. At this point, leasing turns out to be a viable strategy that helps to better manage the return process. Leasing is a widely used business strategy in United States. According to the U.S. Equipment Leasing and Finance Association (http://www.elfaonline.org/), in 2005 U.S. leasing organizations financed $248 billion of a total of $800 billion in business equipment investments. Leasing helps a firm in getting a consistent flow of used products for remanufacturing, which in fact reduces the uncertainty in the quantity and timing for returns. Furthermore, it has a positive impact on better forecasting the quality of returns at the end of their lease time because of the periodic maintenance activities performed by the firm. As a consequence, leasing allows firms to control the quality, quantity and timing of product returns, which is a primary concern of many remanufacturing initiatives. Besides the benefits of leasing for the manufacturer, consumers also have advantages when they lease a product instead of buying them. As such, they pay for the service provided by the product rather than for the product itself. Note that only a portion of the product's price is paid, which corresponds to the proportion “used up” during the lease period. Moreover, leasing products like computers makes it easier for customers to sooner upgrade to the newest technology. Certainly, product characteristics affect the viability of a lease. For example, nondurable products are not suitable for leasing since little value remains at the end of the lease period to be captured, so that no product recovery becomes possible except recycling that is considered to be the least desirable recovery form. In this paper, we consider a firm leasing one type of a new product, and selling remanufactured versions of this products. Hence, we assume that the product is durable and remanufacturable. Our main objective is to determine in a multi-period setting the best prices so as the profit of the firm is maximized. Customers in the market are assumed to be heterogeneous in their willingness-to-pay and they perceive the value of remanufactured products less than the new products. Customers are assumed to be grouped in different segments where each segment corresponds to customers who are interested in a certain lease period. Customer preference in each segment is modeled using a maximum utility type approach in which customers make their choice of leasing a new product, buying a remanufactured product, or buying nothing based on the utility they derive from each choice. Leased products return at the end of the lease agreement. This implies that at the beginning of each period we exactly know how many cores will be returned. Therefore, the supply of used products depends on past lease volumes of new products. If returned products in stock are not sufficient to meet demand for remanufactured products in any period, the manufacturer may obtain extra used products from a third-party core supplier. In our inquiry, we attempt to answer the following questions: (1) What are the optimal prices in each period? (2) How do the factors such as deterioration in age and cost of acquiring used remanufacturable products from the third-party core supplier influence the optimal price in each period? (3) How does customers’ perception of remanufactured products with respect to new products affect the optimal pricing strategy? We make three contributions in this paper: (i) we present a decision making framework for products that are leased to customers and that can be remanufactured upon their return, (ii) we develop a dynamic programming formulation for determining the optimal prices for the leased and remanufactured products along with optimal quantities to lease and to remanufacture, (iii) we present a computational study that provides managerial insight on the factors affecting these pricing and quantity decisions. The remainder of the paper is organized as follows: Section 2 includes a literature review about leasing, and pricing-oriented papers within the context of remanufacturing. Problem description and model formulation are given in Section 3. Section 4 includes the solution procedure. Experimental results are presented in Section 5. We conclude in Section 6.

The aim of this paper is to determine the optimal pricing strategy in a multi-period setting for a profit-maximizing firm leasing new, durable, and remanufacturable products as well as selling remanufactured products to a customer base that has a lower willingness-to-pay for the remanufactured product. If available used products are not enough to meet the demand for remanufactured products, the manufacturer acquires the remaining from the third-party core supplier with an extra cost. We formulate a profit maximizing model using the notion of consumer surplus. The resulting problem is solved by a variant of Nelder–Mead simplex search method. Numerical experiments are performed for the single-period problem with respect to the different problem parameters such as relative willingness-to-pay for remanufactured products, relative willingness-to-pay for leasing new products, depreciation rate of the product over the lease period, and cost of supplying used products from the third-party core supplier. In the multi-period setting, we investigate the interdependence of new and remanufactured products. Recall that a decrease in the demand for new products in a particular period results in a decrease in the availability of used products in the succeeding periods. In this framework, we observe that the manufacturer may choose to produce some new products only for the future value that they generate through their sales as remanufactured products. If there is no available stock of used cores at the beginning of the time horizon, and consumers have higher willingness-to-pay for leasing a new product compared to buying a remanufactured product, the manufacturer does not produce remanufactured products in the first period due to the extra cost of supplying used items from the third-party core supplier. However, in the subsequent periods, the manufacturer starts the period with the opportunity to recover used cores that become available from previous leases. Therefore, it favors remanufacturing in the rest of the time horizon. As a future work, it can be interesting to extend this model by considering different unit remanufacturing costs for different lease durations. This requires keeping track of the specific lease duration of the returning products separately in the state space of the model. Another research direction is to consider different demand models, possibly incorporating demand variability. Finally, we assume that the manufacturer holds a monopoly in the markets for new and remanufactured products. To capture the impact of competition in the remanufactured product market, the model can be extended by considering an industry in which the manufacturer holds a monopoly in the new product market and independent remanufacturers compete on the remanufactured product market. Since we assume new products are only leased, and return at the end of the lease period, the selling option of new products can be added to our scenario by considering that they can be collected by independent remanufacturers.