Home | Business News | Browse by Publication | I | Interfaces

Optimal control of an inventory with simultaneous obsolescence.

Article Excerpt
We consider the problem of determining the optimal ordering and reordering policy for an inventory in which the entire stock will simultaneously become obsolete at some (typically random) future time. Many manufacturing, publishing, distribution, and high-tech businesses face the challenge of maintaining inventories that do not age in the conventional sense; instead, they suddenly become obsolete and lose most or all of their value. These circumstances render traditional inventory analysis unsuitable for balancing reordering costs with the costs of overstocking. We study a continuous-review and stochastic-demand obsolescence inventory model, and calculate its optimal control policy. We gear our solution technique to problems that involve large inventories and small holding costs.

Key words: stochastic modeling; optimization; inventory management.

**********

Many publishers, manufacturing and high-tech companies, and information service providers face the challenge of managing inventory that has the potential to suddenly become obsolete. Examples range from military-aircraft spare parts (Hadley and Whitin 1963) to high-tech products with limited life cycles (David et al. 1997), and even Swiss watches and breast implants (Joglekar and Lee 1993).

In the literature, most obsolescence inventory models feature periodic review, e.g., Hadley and Whitin (1963), Brown et al. (1964), Barankin and Denny (1965), Pierskalla (1969), and Song and Lau (2004). Models with continuous review include Masters (1991), Joglekar and Lee (1993), David and Mehrez (1995), and David et al. (1997). Most obsolescence inventory models feature stochastic demand; however, by assuming a deterministic demand, they simplify the analysis considerably so that they can derive explicit results that are otherwise intractable. In particular, David et al. (1997) characterize optimal policies in a continuous-review obsolescence inventory model with deterministic demand. Their solution is appropriate in applications in which the stochastic component of the demand is not significant.

Jeppesen, recognized as the world's leading integrated aviation information provider, maintains and distributes navigational charts to airline pilots worldwide. Changes in navigational information such as radio-frequency changes, approach-minimum changes, airspace restructuring, etc., require Jeppesen to revise its current charts, making the stock in inventory outdated and obsolete. Because Jeppesen must fill requests for navigational charts immediately, it must review its inventory continuously. The demand for charts is quite unpredictable in the short term; therefore, the techniques that David et al. (1997) describe do not apply to the Jeppesen navigational-chart inventory problem. OR literature has not yet properly addressed the continuous-review and stochastic-demand obsolescence inventory problem, which is the proper model for Jeppesen.

Our mathematical contribution is a numerically tractable solution for the optimal control policy of a continuous-review and stochastic-demand obsolescence inventory problem. Using state-of-the-art algorithms from Numerical Recipes in C (Press et al. 2002), we wrote a program to calculate the optimal control policies that we describe in this paper. This code, which is in production at Jeppesen, is used to generate (and maintain) optimal control policies for all of the large and complex charts in its library. The implementation has resulted in significant savings in inventory costs.

In the Jeppesen Enroute Charts and Legacy Inventory Planning at Jeppesen sections, we describe the Jeppesen navigational charts that make up the inventories that are subject to obsolescence and Jeppesen's legacy inventory planning. In the Optimal Control Policies for Enroute Charts and Numerical Results sections, we present numerical data that illustrate the kinds of optimal control policies that arise in real-world problems, such as Jeppesen navigational-chart inventories. The resulting policies are quite different from the simple cases that we study in the Two Special Cases section. Finally, in Implementation at Jeppesen, we discuss implementation of optimal control policies at Jeppesen.

Appendix 1 comprises three sections. In The Model section, we describe our continuous-review and stochastic-demand obsolescence inventory model. In the Two Special Cases section, we present two important special cases of the model that can be (approximately) solved without using the full power of our general solution. In the Numerical Calculation of the Optimal Control Policy section, we present our general solution.

Jeppesen Enroute Charts

Jeppesen, whose customers include business, general, and commercial pilots, is recognized as the world's foremost provider of integrated aviation information solutions. Its portfolio of products and services includes flight information, flight-operations services, international trip-planning services,...

View this article FREE - Now for a Limited Time, try Goliath Business News
Free for 3 Days!