The single-period inventory model, known as the newsboy or Christmas tree problem, is extended for several cost expressions and optimal decision rules for these variations are derived. A two-echelon single-period inventory model is developed and optimal decision rules are found. Conclusions and suggested extensions for the newsboy problem and of the two-echelon inventory model are discussed. (Author).
This book has a dual purpose?serving as an advanced textbook designed to prepare doctoral students to do research on the mathematical foundations of inventory theory, and as a reference work for those already engaged in such research. All chapters conclude with exercises that either solidify or extend the concepts introduced.
This dissertation focuses on issues associated with the value of information in models of sequential decision making under uncertainty. All of these issues are motivated by inventory management problems. First, we study the effect of the accuracy of inventory counts on system performance when using a zero-memory controller in an inventory system that is modeled as a partially observed Markov decision process (POMDP). We derive conditions for which improving the accuracy of inventory counts will either (i) improve system performance, (ii) degrade system performance or (iii) will not affect system performance. With a computational study, we determine the range of profitability impacts that result from inaccurate inventory counts when using reasonable zero-memory control policies. Second, we assess the value of demand observation quality in an inventory system with Markovian demand and lost sales. Again, the POMDP serves as a problem model, and we develop computationally tractable suboptimal algorithms to enable the computation of effective lower bounds on system profitability when demand observations are noise-corrupted. We then extend our results toconsider the effects that product substitution has on system performance. We show that systems with low demand variability, high holding cost levels, and high levels of substitution benefit more from demand bservability than systems with high demand variability, low holding cost levels, and low levels of substitution. Third, to enhance our understanding of sequential inventory control with substitutable products, we analyze a two-item inventory problem with known deterministic primary demand, but stochastic one-way substitution. We model this problem as a MDP and show that a decision rule that minimizes the single period cost function, when applied at every decision epoch over the infinite horizon, is an optimal policy for the infinite horizon problem. A definition of increased substitutability is presented, and it is shown that increased substitutability never increases optimal expected total discounted cost.
Decision Criteria and Optimal Inventory Processes provides a theoretical and practical introduction to decision criteria and inventory processes. Inventory theory is presented by focusing on the analysis and processes underlying decision criteria. Included are many state-of-the-art criterion models as background material. These models are extended to the authors' newly developed fuzzy criterion models which constitute a general framework for the study of stochastic inventory models with special focus on the real world inventory theoretic reservoir operations problems. The applications of fuzzy criterion dynamic programming models are illustrated by reservoir operations including the integrated network of reservoir operation and the open inventory network problems. An interesting feature of this book is the special attention it pays to the analysis of some theoretical and applied aspects of fuzzy criteria and dynamic fuzzy criterion models, thus opening up a new way of injecting the much-needed type of non-cost, intuitive, and easy-to-use methods into multi-stage inventory processes. This is accomplished by constructing and optimizing the fuzzy criterion models developed for inventory processes. Practitioners in operations research, management science, and engineering will find numerous new ideas and strategies for modeling real world multi- stage inventory problems, and researchers and applied mathematicians will find this work a stimulating and useful reference.
This study addresses a general class of decision situations whose solutions are directly applicable to inventory acquisitions and or disposals. Although optimal solutions are well known when subsequent costs are linear to the amount of surplus or shortage, the perhaps more realistic case of non-linear costs has not been extensively studied. The results of this study suggest the optimal solutions i.e., acquisition quantity or supply for both conditions of risk and uncertainty about demand when the associated cost function is non- linear, i.e., quadratic. For conditions of risk optimal solutions are found which will yield minimum expected costs for the two-piece cost function where surplus and shortage costs are quadratic. This is done for both discrete and continuous demand variable. When future need for the item is unknown and only the maximum value can be estimated, optimal solutions are obtained for goals of minimaxing cost, minimaxing regret, and the Laplace criteria using a uniform probability distribution. It is shown that these different approaches to determining acquisition quantities under conditions of uncertainty lead, for this general class of decision problems, to the same optimal result. Hopefully, this information will aid in the decision process while making affordability assessments of new acquisitions.
Use of information is basic to economic theory in two ways. As a basis for optimization, it is central to all normative hypotheses used in eco nomics, but in decision-making situations it has stochastic and evolution ary aspects that are more dynamic and hence more fundamental. This book provides an illustrative survey of the use of information in econom ics and other decision sciences. Since this area is one of the most active fields of research in modern times, it is not possible to be definitive on all aspects of the issues involved. However questions that appear to be most important in this author's view are emphasized in many cases, without drawing any definite conclusions. It is hoped that these questions would provoke new interest for those beginning researchers in the field who are currently most active. Various classifications of information structures and their relevance for optimal decision-making in a stochastic environment are analyzed in some detail. Specifically the following areas are illustrated in its analytic aspects: 1. Stochastic optimization in linear economic models, 2. Stochastic models in dynamic economics with problems of time-inc- sistency, causality and estimation, 3. Optimal output-inventory decisions in stochastic markets, 4. Minimax policies in portfolio theory, 5. Methods of stochastic control and differential games, and 6. Adaptive information structures in decision models in economics and the theory of economic policy.
Minimum expected-cost solutions to the single-period inventory problem (the Newsboy problem) have been well known for many years, for risk cases where the distribution of demand is known. Also well known are minimax cost and Laplace solutions for the uncertainty case where only the range of demand is known. This study explores the use of order-statistic-based quantile estimators as decision procedures while data gathers during the early decision periods. Simulation, using a variety of demand distributions and unit-cost values, provides recommendations on which period to leave the minimax procedure for a suggested data-based decision rule which will be asymtotic to the optimal risk procedure. (Author).
The International Conference on Production Research has a good tradition: The fIrst Conference was held in Birmingham 1971 with 61 participants. With respect to the decision that the Conference should be held every second year, by this time the Conference has been held in the following countries: Birmingham (1971, UK), Copenhagen (1973, Denmark), Amhurst (1975, USA), Tokyo (1977, Japan), Amsterdam (1979, The Netherlands), Novi Sad (1981, Yugoslavia), Windsor (1983, Canada), Stuttgart (1985, Germany), and the next Conference will take place in Cincinnatti (1987, USA). The number of submitted abstracts and papers was continuously increas ing such that the Programme Committee of this actual 8th Conference on Production Research has been forced to introduce a further refereeing procedure. Each submitted abstract was presented to at least two referees. This resulted not only in a reduction of the number of presented full papers and poster contributions but, as the Programme Committee and the Editiors hope, it led also to a considerable increase in the scientifIc quality of this 8th International Conference on Production Research. The preceeding conference in Windsor, Canada, was dedicated to the topic: Production Research as a Means of Productivity Improvement. We don't believe that this statement has become untrue in the meanwhile.
