A Multi-product, Dynamic, Nonstationary Inventory Problem


Book Description

The paper is concerned with a multi-product dynamic nonstationary inventory problem in which the system is reviewed at the beginning of each of a sequence of periods of equal length. The model has the following features. There is a general demand process with no stationarity or independence assumptions, partial or complete backlogging of unfilled demand, a fixed nonnegative delivery lag (which may be positive only under complete backlogging), a nonstationary linear ordering cost, a nonstationary holding and shortage cost function, discounting of future costs, and nonstationary restrictions like budget and storage limitations. The objective is to choose an ordering policy that minimizes the expected discounted costs over an infinite time horizon. Conditions are given that ensure that the base stock ordering policy is optimal and that the base stock levels in each period are easy to calculate. (Author).







Optimal Policy in a Dynamic, Single Product, Nonstationary Inventory Model with Several Demand Classes


Book Description

A multiperiod single product nonstationary inventory problem is studied in which the system is reviewed at the beginning of each of a sequence of periods of equal length. The model has the following features. There are several classes of demand for the product in each period. The demands in different periods are independent but not necessarily identically distributed. The cost structure is nonstationary with the ordering cost being proportional to the amount ordered. Conditions are given that ensure that the base stock ordering policy is optimal and that the base stock levels in each period are easy to calculate. The results are based on earlier work of the author and on properties of stochastically ordered distributions that are developed in the paper. The case of a linear holding cost and a linear storage cost is studied in detail. (Author).










Handbook of Newsvendor Problems


Book Description

As a fundamental problem in stochastic inventory control, the newsvendor problem has been studied since the 18th century in the economic literature, and has been widely used to analyze supply chains in fashion and seasonal product industries. Since the 1950s, the newsvendor problem has been extensively studied in operations research and extended to model a variety of real-life problems. The simplest and most elementary version of the newsvendor problem is an optimal stocking problem in which a newsvendor needs to decide how many newspapers to order for future demand, where the future demand is uncertain and follows a stationary distribution. Research in this area has greatly increased over the last few years, and now the Handbook of Newsvendor Problems: Models, Extensions and Applications captures the state of the art. The handbook consists of two sections -- Models and Extensions, and Applications. Each section includes many interesting works in the respective domain. Section I presents papers on topics like the multi-product newsvendor problems; the newsvendor problem with law invariant coherent measures of risk; a Copula approach to inventory pooling problems with newsvendor products; repeated newsvendor games with transshipments; cooperative newsvendor games; an economic interpretation for the price-setting newsvendor problem; newsvendor models with alternative risk preferences within expected utility theory and prospect theory frameworks; and newsvendor problems with VaR and CVaR consideration. Section II presents papers on such topics as a two-period newsvendor problem for closed-loop supply chain analysis; the remanufacturing newsvendor problem; inventory centralization in a newsvendor setting when shortage costs differ; production planning on an unreliable machine for multiple items; analysis of the newsvendor problem under carbon emissions policies; optimal decisions of the manufacturer and distributor in a fresh product supply chain involving long distance transportation; a newsvendor perspective on profit target setting for multiple divisions; and a portfolio approach to multi-product newsvendor problem with budget constraint. This well-balanced handbook presents a wealth of theoretical results from different perspectives. With contributions from many of the leading researchers in the field, the Handbook of Newsvendor Problems: Models, Extensions and Applications is a timely addition to the literature and consolidates all the new and exciting works related to the newsvendor problem into one high quality source.







Perishable Inventory Systems


Book Description

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.




Mathematics of the Decision Sciences


Book Description