We study two stochastic inventory systems. The first part deals with an (s, S) system system, and the second part with an ( R, T) system. In a (s, S) system, the inventory position of a product is reviewed regularly (every T periods), and, if it is found to be below a threshold s, an order is placed to bring the item's inventory position to the level S. In a (R, T) system, an order is placed every T periods to bring the inventory up to the base stock R; it is a special case of an (s, S) system, with s set at minus infinity.
A perishable item is one that has constant utility up until an expiration date (which may be known or uncertain), at which point the utility drops to zero. This includes many types of packaged foods such as milk, cheese, processed meats, and canned goods. It also includes virtually all pharmaceuticals and photographic film, as well as whole blood supplies. This book is the first devoted solely to perishable inventory systems. The book’s ten chapters first cover the preliminaries of periodic review versus continuous review and look at a one-period newsvendor perishable inventory model. The author moves to the basic multiperiod dynamic model, and then considers the extensions of random lifetime, inclusion of a set-up cost, and multiproduct models of perishables. A chapter on continuous review models looks at one-for-one policies, models with zero lead time, optimal policies with positive lead time, and an alternative approach. Additional chapters present material on approximate order policies, inventory depletion management, and deterministic models, including the basic EOQ model with perishability and the dynamic deterministic model with perishability. Finally, chapters explore decaying inventories, queues with impatient customers, and blood bank inventory control. Anyone researching perishable inventory systems will find much to work with here. Practitioners and consultants will also now have a single well-referenced source of up-to-date information to work with.
We present a periodic review inventory model with multiple delivery modes. We generalize the notion of the base-stock policy for inventory systems with multiple delivery modes. While base-stock policies are optimal for one or two consecutive delivery modes, it is not so otherwise. For multiple consecutive delivery modes, we show that only the fastest two modes have optimal base stocks, and provide simple counterexamples to show that the remaining ones do not in general. We investigate why the base-stock policy is not optimal through detailed analyses of two numerical examples.
The focus of the work is twofold. First, it provides an introduction into fundamental structural and behavioral aspects of periodic review inventory systems. Second, it includes a comprehensive study on analytical and optimization aspects of a specific class of those systems. For the latter purpose, general solution methods for problems of inventory management in discrete time are described and developed along with highly specialized methods to solve very specific problems related to the model variants examined. The work is thus addressed to students and practitioners who seek a deeper understanding of managing inventories in discrete time as well as to software developers who require implementation aids on specific problems of inventory management.
We consider a setting in which inventory plays both promotional and service roles; that is, higher inventories not only improve service levels but also stimulate demand by serving as a promotional tool (e.g., as the result of advertising effect by the enhanced product visibility). Specifically, we study the periodic-review inventory systems in which the demand in each period is uncertain but increases with the inventory level. We investigate the multiperiod model with normal and expediting orders in each period, that is, any shortage will be met through emergency replenishment. Such a model takes the lost sales model as a special case. For the cases without and with fixed order costs, the optimal inventory replenishment policy is shown to be of the base-stock type and of the (s, S) type, respectively.
We analyze a periodic-review base-stock inventory system where outstanding orders can be expedited. Most inventory models assume that lead times are exogenously given, i.e., that orders arrive after a lead time that cannot be controlled by the inventory manager. However, in many situations inventory managers have the option to expedite open orders. We incorporate the expediting option into a periodic-review base-stock inventory model and solve the model optimally. We prove several structural properties of the model and show how the optimal solution can be computed efficiently. We numerically analyze the sensitivity of the inventory system with respect to the key parameters and quantify the benefit of order expediting using data from the service division of a global equipment manufacturer.
