Inventory Control Under Stochastic Lead Time and Stochastic Demand
Inventory Control Under Stochastic Lead Time and Stochastic Demand

Author: Kenneth R Rand (Jr)

Publisher:

Published: 1965

Total Pages: 109

ISBN-13:

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An attempt is made to investigate the behavior of an inventory system in which lead time, the size of the demand order, and the time between successive demand orders are all random variables with known probability distributions. Since adequate analytical mathematical models are not existant, a computer-based simulation model is used to study the inventory system. An introduction to the inventory problem and a description of inventory systems currently in use are provided. The formulation of the model is described. Results are presented as graphs of stockout time as a function of reorder point.

A Multi-echelon Inventory System with Supplier Selection and Order Allocation Under Stochastic Demand
A Multi-echelon Inventory System with Supplier Selection and Order Allocation Under Stochastic Demand

Author: Cong Guo (Industrial engineer)

Publisher:

Published: 2013

Total Pages: 0

ISBN-13:

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This article addresses the development of an integrated supplier selection and inventory control problems in supply chain management by developing a mathematical model for a multi-echelon system. In particular, a buyer firm that consists of one warehouse and N identical retailers wants to procure a type of product from a group of potential suppliers, which may require different price, ordering cost, lead time and have restriction on minimum and maximum total order size, to satisfy the stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the model. The objective of the model is to select suppliers and to determine the optimal inventory policy that coordinates stock level between each echelon of the system while properly allocating orders among selected suppliers to maximize the expected profit. The model has been solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained by performing some sensitivity analysis.

Inventory Management with Stochastic Lead Times
Inventory Management with Stochastic Lead Times

Author: Kumar Muthuraman

Publisher:

Published: 2013

Total Pages: 34

ISBN-13:

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This article analyzes a continuous time back-ordered inventory system with stochastic demand and stochastic delivery lags for placed orders. This problem in general has an infinite dimensional state space and is hence intractable. We first obtain the set of minimal conditions for reducing such a system's state space to one-dimension and show how this reduction is done. Next, by modeling demand as a diffusion process, we reformulate the inventory control problem as an impulse control problem. We simplify the impulse control problem to a Quasi-Variation Inequality (QVI). Based on the QVI formulation, we obtain the optimality of the (s, S) policy and the limiting distribution of the inventory level. We also obtain the long run average cost of such an inventory system. Finally, we provide a method to solve the QVI formulation. Using a set of computational experiments, we show that significant losses are incurred in approximating a stochastic lead time system with a fixed lead time system, thereby highlighting the need for such stochastic lead time models. We also provide insights into the dependence of this value loss on various problem parameters.

A Solution for the Intractable Inventory Model When Both Demand and Lead Time are Stochastic
A Solution for the Intractable Inventory Model When Both Demand and Lead Time are Stochastic

Author: Terry P. Harrison

Publisher:

Published: 2008

Total Pages: 27

ISBN-13:

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We consider the reorder point, order quantity inventory model where the demand, D, and the lead time, L, are independently and identically distributed (iid) randiom variables. This model is analytically intractable because of order crossover. However, we show how to resolve the intractability by empirical means, for example, by simulation and regression relationships. Using a normal approximation, we show how to obtain regression equations for the optimal cost and the optimal policy parameters (here the order quantity and the safety stock factor) in terms of the problem parameters (ordering cost per order, holding cost per unit per unit time, shortage cost per unit, the standard deviation of demand, and the standard deviation of lead time).

(S, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times
(S, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

Author: Richard Ehrhardt

Publisher:

Published: 1980

Total Pages: 29

ISBN-13:

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A stochastic lead time inventory model is analyzed under the assumptions that (1) replenishment orders do not cross in time and (2) the lead time distribution for a given order is independent of the number and sizes of outstanding orders. This study corrects errors in the existing literature on the finite-horizon version of the model and yields an intuitively appealing dynamic program that is nearly identical to one that would apply in a transformed model with all lead times fixed at zero. Hence, many results that have been derived for fixed lead time models generalized easily. Conditions for the optimality of (s, S) policies are established for both finite and infinite planning horizons. The infinite-horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s, S) policies. (Author).

Foundations of Stochastic Inventory Theory
Foundations of Stochastic Inventory Theory

Author: Evan L. Porteus

Publisher: Stanford University Press

Published: 2002

Total Pages: 330

ISBN-13: 9780804743990

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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.

Supply Chain Disruptions
Supply Chain Disruptions

Author: Haresh Gurnani

Publisher: Springer Science & Business Media

Published: 2011-09-28

Total Pages: 339

ISBN-13: 0857297783

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One of the most critical issues facing supply chain managers in today’s globalized and highly uncertain business environments is how to deal proactively with disruptions that might affect the complicated supply networks characterizing modern enterprises. Supply Chain Disruptions: Theory and Practice of Managing Risk presents a state-of the-art perspective on this particular issue. Supply Chain Disruptions: Theory and Practice of Managing Risk demonstrates that effective management of supply disruptions necessitates both strategic and tactical measures – the former involving optimal design of supply networks; the latter involving inventory, finance and demand management. It shows that managers ought to use all available levers at their disposal throughout the supply network – like sourcing and pricing strategies, providing financial subsidies, encouraging information sharing and incentive alignment between supply chain partners – in order to tackle supply disruptions. The editors combine up-to-date academic research with the latest operational risk management practices used in industry to demonstrate how theoreticians and practitioners can learn from each other. As well as providing a wealth of knowledge for students and professors who are interested in pursuing research or teaching courses in the rapidly growing area of supply chain risk management, Supply Chain Disruptions: Theory and Practice of Managing Risk also acts as a ready reference for practitioners who are interested in understanding the theoretical underpinnings of effective supply disruption management techniques.