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Warranty inventory optimization for Hitachi Global Storage Technologies, Inc.

Article Excerpt
Warranty inventory management is a challenge that many companies must confront. Customers return allegedly defective units to a company for replacement or credit. The company can then economically recover the unit through either a testing or remanufacturing process; it can use recovered units to fulfill future warranty requests. The company also has the option of purchasing a new product from the production line. In high-volume situations, warranty inventory management involves many complexities such as stochastic demand rates, probabilistic requests for credit instead of replacement, probabilistic repairs, multiple sources of supply, and tight customer-service constraints. Companies may also have to consider the complexities that a batch remanufacturing process causes.

In this paper, we formulate several related models of such warranty inventory systems. In these models, we study a periodic, single-location, inventory system that is dedicated to warranty returns. We find near-optimal policies for each system using well-developed heuristics. The models include the following complexities: random warranty claims, random requests for replacement or credit, three sources of supply (testing, remanufacturing, and new product), random flows of returned products into testing and remanufacturing, random yields from testing and remanufacturing, different lead times for each resupply process, remanufacturing lead time variability, and random batching of remanufacturing. The results of the models provide near-optimal inventory-control policies in this complex environment and demonstrate the payoffs that result from reducing production lead times and batching in remanufacturing.

Hitachi GST has gained a great deal from this modeling process. In addition to the direct benefit from the model's calculations, additional sensitivity analyses have shed light on the quantitative importance of various factors, including demand volatility, the percentage of credit requests, the percentage of units successfully remanufactured, and batching effects in remanufacturing.

Key words: inventory; applications; stochastic; closed-loop supply chains; warranty returns; periodic; single location; heuristics.

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Warranty inventory management is a challenge that many of today's companies must confront. Warranties are contracts that companies and customers enter into on the purchase of a product. They are intended to protect the customer from manufacturing or material defects in the product. A warranty return usually involves a customer returning an allegedly defective unit to the company; the company then provides a replacement unit or monetary credit to that customer. Warranties are usually limited in nature (i.e., they cover only certain types of defects over a set length of time); therefore, the pool of items sold that are under warranty does not expand indefinitely over a product's life.

Warranties usually follow the life cycle of a product. The first part of the life cycle is a ramp-up phase--the product is introduced and sales increase. Warranty returns increase because some products fail and customers return them to the company. Next, the product experiences a steady state when the number of units under warranty and returned for service remains roughly constant but with considerable variability. Finally, the cycle ends with a ramp-down (or end-of-life) period--the product is discontinued and all of the warranties subsequently expire. The ramp-down period of the warranty cycle occurs later than the product end-of-life period because the company is required to provide warranty service during the life of the warranty contract--even after a product has been discontinued. In this paper, we focus on the steady-state portion of the warranty life cycle.

To provide acceptable customer service to customers who return products that are under warranty, a company must hold inventory of the product to protect against the variability involved in returns. Companies often manage this inventory through the purchase of new products from a manufacturer and through the remanufacturing of returned units. (Remanufactured products are acceptable and are the norm in warranty returns. Customers often assume that if they receive a remanufactured unit, it is the same unit that they returned; however, this is often not the case because remanufacturing lead times can be longer than the promised lead time for warranty claims.) In high-volume situations, this process involves many complex interactions, such as probabilistic repairs, high demand rates, multiple sources of supply, and strict customer-service constraints.

The exact problem that we study in this paper involves a single-location, periodic-review inventory system that is dedicated to warranty returns. A company sells new units to customers; if a unit fails, the customer returns it to the company for warranty service. The customer has the choice of either a monetary credit or a replacement unit. When a customer returns a product to a company, that company may test it for defects; if there are none, it returns the product to inventory. Otherwise, the company may attempt to remanufacture the product. If successful, it returns the product to inventory. The company's goal is to minimize inventory levels while maintaining a specified customer-service level.

This paper is organized as follows. In the Literature Review section, we discuss the literature pertaining to inventory systems with repairs as well as other related topics. In the Project Collaboration: Current Warranty Planning Process section, we describe the project collaboration with Hitachi Global Storage Technologies (Hitachi GST), warranty as a strategic initiative, challenges at Hitachi, and its current planning process for warranty inventory. The Model Framework section describes several related models for this problem. The Numerical Examples section contains several examples showing sensitivity analysis. The Hitachi GST's Model Use section describes Hitachi GST's experimentation with the model and additional sensitivity analyses and discusses how the model has been also used as an educational tool. We end the paper with a Conclusions section. In addition, we include four models for this problem in the appendix.

Literature Review

The literature pertaining to inventory systems with repairs is wide in its scope. Schrady (1967) developed one of the earliest models by adapting the economic order quantity (EOQ) model to a system with deterministic demand and repairs. Allen and D'Esopo (1968) extended Schrady's model by incorporating stochastic demand. The authors consider a continuous-review model utilizing an (s, S) policy. They assume that units fail according to a Poisson distribution and that returned units are repairable at a fixed rate and a fixed lead time. Richards (1976) further generalizes Allen and D'Esopo's (1968) model by incorporating stochastic lead times for repairs. Simpson (1978) examines a periodic-review system by solving a dynamic program that incorporates random returns, random demand, and zero lead time for purchased and repaired units. This results in a repair-up-to level, a purchase-up-to level, and a scrap-down-to level. All of these classic works focus on a single source of repaired items and the fulfillment of customer (end-user) demands. They do not focus specifically on warranty demands.

Sherbrooke (1968) wrote the seminal paper introducing the Multi-Echelon Technique for Recoverable Item Control (METRIC) methodology. METRIC minimized back orders in a high-cost, multiechelon environment by incorporating marginal-cost analysis. Muckstadt (1973) developed the MOD-METRIC methodology, an extension of the METRIC system incorporating multi-indenture systems. Both of these classic papers assumed independent and identically distributed (i.i.d.) lead times, and Wang et al. (2000) studied the impact of various lead times at different depot locations. Both Sherbrooke and Muckstadt (1973) (and their successors) focused on slow-moving, low-demand items such as repairable airplane components. However, consumer and industrial product warranty returns often have a significant demand rate; thus, most of the methodologies used in this stream of research cannot be utilized when studying warranty returns.

The model we study incorporates three different product sources--testing, remanufacturing, and new production. To our knowledge, this type of system is unique in the repair inventory literature. However, traditional inventory management literature does incorporate multiple sources of supply in some models. For example, Veeraraghavan and Scheller-Wolf (2003) develop a near-optimal solution to a periodic-review inventory system where there are two different supply sources with arbitrarily different but constant lead times. Whittmore and Saunders (1977) found the optimal solution to this problem to be a complex, state-dependent solution (non-base stock) to a dynamic program with a potentially enormous state space. Veeraraghavan and Scheller-Wolf (2003) develop a dual base-stock policy--one for the regular mode and one for the expedited mode--that is within one to two percent of the optimal solution. Meanwhile, Feng et al. (2006) consider N different but consecutive lead times from different suppliers (this can be extended to nonconsecutive lead times by simply charging the same amount for nonexistent lead times as you would for the next-shortest lead time). By counterexample, the authors show that a base-stock policy is not always optimal. They also employ a clever inventory-position vector, where [IP.sub.k] represents the on-hand minus backorder plus onorder inventory that is due to arrive within k periods. However, Feng et al. (2006) do not find the optimal policy for the general problem of multiple suppliers with various constant lead times. DeCroix and Zipkin (2005) study a manufacturing system with various subassemblies that are produced at various echelons of the system. This system is subject to random...

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