No description available.

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The design and optimisation of inventory replenishment systems has already been exhaustively studied by the operational research community. Many classical mathematical methods and simulation techniques have been developed and introduced in the literature. However, what can be observed is the fact that in a real case scenario the lead-time, deterioration of goods and demand for product are likely to be time-varying and uncertain, which traditionally have not necessarily been reflected in the model formulations. Therefore, in response to the dynamical nature of inventory systems, the potential of algorithms based on control theory to reduce the undesirable influences of system uncertainties on inventory level stability, have been investigated /proposed. Consequently, the mapping of the inventory problem into the control theory domain, for cost-benefit inventory trade-off achievement has been realised. Although, the application of control theory in inventory optimisation appears to be beneficial, there are certain reasons why the approach has gained yet little attention among the operational research community. One reason is that it cannot be adopted easily by researchers who are unfamiliar with control theory and another is due to a communication gap which exists between the control theory and operational research communities. Prompted by these observations, the thesis presents a novel, systematic mathematical approach for finding the optimal order quantities. The proposed approach has been mathematically demonstrated to be equivalent in study-sate to model-based predictive control, which is one of the more well-established productive control techniques with industrial application today. The mathematically reduced approach attempts to bridge the identified gap to fulfil the lacking dual perceptions of both communities. It enables the straightforward benefits afforded by predictive control without the necessity to become familiarised with principles of control theory. The method is shown to be applicable for both perishable and non-perishable inventory. Although the novel technique was inspired by MPC and noticing the MPC patterns in the mathematical description, the resulting proposal is no longer MPC. It is in fact a minimum variance approach, or dear beat controller, with an incorporated Smith predictor. Therefore using the adjective ‘predictive’ in the title of the thesis refers to both, the inspiration of MPC and the predictive nature of the minimum variance controller to accommodate lead time, being incorporated within an inherent Smith predictor. The developed approach is considered to be transferable to other applications, where similar model formulations may be applicable.

Call number: LD2668 .T4 1963 D55 / Master of Science

LD2668 .T4 1966 A988 / Master of Science

This dissertation contains a number of varied, yet closely related, results that are relevant to the construction of mathematical and statistical models of inventory systems. Its primary focus is on the sensitivity of some specific inventory models to errors in certain modeling assumptions. Motivation for this research is provided through the development of analytical expressions that show that the deterministic economic order quantity can be quite sensitive to errors in the forecast of the demand rate whenever the lead time is non-zero. Similar results are provided for the stochastic case by means of a carefully designed experiment that shows that the specific form or "shape" of the distribution chosen to represent the stochastic behavior of the lead time demand can have a significant impact on a minimum cost (Q,R) policy. Together, these results refute the "conventional wisdom" that inventory models are generally insensitive to errors in model specification or parameter estimation. Considerable attention is also given to the postulation of a "robust" model for the lead time demand distribution (LTDD). This discussion culminates with the introduction of a new probability distribution, based on a hyperbolic cosine transformation of normal random variables, that appears to be well-suited for modeling the LTDD. Furthermore, it is concluded that the two- and three-parameter versions of the lognormal and inverse Gaussian distributions can also be considered as viable candidates to model the LTDD in a wide variety of inventory systems. A number of new algorithms for computing optimal (Q,R) policies are also introduced. These significantly reduce both the amount and complexity of computation required by the standard iterative method. Two additional sets of analytical results are chronicled in this work. The first allows the LTDD to be characterized (by its first four moments) on the basis of information about the distributions of the lead time and demand rate. The second expresses the linear loss functions (LLF's) for a number of probability distributions whose LLF's are not readily available in the inventory control literature. Complete and intuitive proofs of these results are included.

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This research is directed towards the minimization of the total cost of the single-item, single-source, deterministic inventory system in the face or multiple constraints. The Lagrangian multiplier technique is used for optimization. Two models, the general model and the special model, with multiple constraints are studied. For the special model the solution becomes indeterminate and/or incompatible whenever more than one constraint is active and the trial and error method is suggested for this situation. For the general model, the constraints are classified into two basic groups of incompatible constraints. Also, other possible groups of incompatible constraints are listed. A sample solution for one group, out of many possible groups, of compatible constraints is presented. Illustrative examples are given. / Master of Science

Finally, we study a multi-period, risk-averse inventory model. The objective is to maximize the expected pay-offs. The risk-averse behavior is modeled as to penalize the decision maker if a target-profit level is not satisfied for each financial reporting cycle. We recognize that the operational period is usually faster than the financial reporting cycle. Therefore, the financial reporting cycle can be considered as an integer times of the operational periods. We study this model under both accrual-basis accounting principle and cash-basis accounting principle. We prove that the optimal inventory policy is a state-dependent base-stock policy under the accrual-basis accounting method. We then show that the structure of an optimal policy is a complicated one for the cash-basis accounting method. / In this thesis we study three supply chain models which address downside risk from a different angle. We start with a commitment-option supply contract in a Conditional Value-at-Risk (CVaR) framework. We show that a CVaR trade-off analysis with advanced reservation can be carried out efficiently. Moreover, our study indicates how the corresponding contract decisions differ from decisions for optimizing an expected value. / Key words. Downside Risk Measure; CVaR; Risk; Loss-Averse; Dynamic Programming. / Owing to the growing globalization in economy and the advances in commerce, research in supply chain management has attracted large number of researchers in the last two decades. Yet standard treatments of supply chain models are mainly confined for the optimization of expected values with little reflection on risk considerations. Even for those that consider a risk measure in the objective function, there are quite few literatures employing downside risk measure. The downside risk measure takes into account only the part of the distribution that is below a critical value. Thus it indicates a safety-first strategy for decision maker. / The thesis is organized in five chapters. In Chapter 1, we provide the background and research motivation for considering downside risk measures in supply chain models. In Chapter 2, we study the pay-to-delay supply contracts with a Conditional Value-at-Risk (CVaR) framework. In Chapter 3, we study the loss-averse newsvendor problem. In Chapter 4, we extend the loss-averse model to a multi-period setting. We conclude the thesis in Chapter 5 with discussions for future research. / Then, we employ a loss-aversion utility function to characterize newsvendor's decision-making behavior. We find that when there is no shortage cost, the loss-averse newsvendor consistently orders less than a risk-neutral newsvendor. Further, we discover that the loss-averse newsvendor orders a constant quantity when the reference target is sufficiently large. We discuss the importance of initial inventory to achieve the target profit level. When the target is a decision variable, the newsvendor always sets the target no higher or no lower. / Ma, Lijun. / "October 2007." / Adviser: Houmin Yan. / Source: Dissertation Abstracts International, Volume: 69-08, Section: B, page: 5003. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 140-154). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.