Dynamic Control of Quality in Production-Inventory Systems

by Yao, David D.; Zheng, Shaohui

• ISBN13: 9780387954912
• ISBN10: 0387954910
• Format: Hardcover
• Copyright: 2002-09-01
• Publisher: Springer Verlag

Summary

This book aims to address the coordination of quality control with other aspects of a firm's production system and supply chain, specifically, the coordination between the inspection-repair of finished products and their follow-up services, between inspection and process revision, between production and inspection under capacity constraints, between replenishment and rework quantities, and between supply and substitution decisions. To address these issues, the authors have in recent years developed a set of dynamic approaches based on Markov decision programming and using stochastic comparison techniques, including those based on notions of stochastic convexity and submodularity. The focal question driving their studies is this: under what conditions and for what systems does a certain class of policies become optimal in the sense of striking the best coordination among several competing or even conflicting aspects in the production-inventory system? Particular emphasis has been put on the class of policies that have simple, threshold structures -- simple enough to facilitate implementation, but sophisticated enough to be optimal. Written in a self-contained and well-motivated manner, the book offers a timely and useful text or reference to researchers and practitioners in operations research and management, industrial and quality engineering, systems and control, applied mathematics and statistics, and related fields.

Table of Contents

Acknowledgments	v
Introduction	1	(4)
Theme and Methodologies	2	(1)
Relations to Other Approaches	2	(2)
Organization and Overview	4	(1)
Stochastic Monotonicity, Convexity, and Submodularity	5	(14)
Stochastic and Likelihood-Ratio Orderings	5	(2)
Stochastic Convexity	7	(4)
Stochastic Submodularity	11	(3)
Markov Chain Applications	14	(2)
Notes	16	(3)
Quality Control for Products with Warranty	19	(18)
Warranty Cost Functions	20	(3)
K-Submodularity	23	(3)
Conditional Distribution for Defectives	26	(1)
Optimal Policy	27	(4)
The Individual Warranty Model	31	(3)
Examples and Extensions	34	(1)
Notes	35	(2)
Process Control in Batch Production	37	(28)
Machine Revision	38	(4)
MDP Formulation	42	(3)
MDP Essentials	42	(2)
The MDP Problem	44	(1)
Discounted-Cost Model	45	(11)
Optimality Equations	45	(2)
Structural Properties	47	(4)
Optimal Policies	51	(5)
Average-Cost Model	56	(1)
A Special Case: No Inspection Cost	57	(5)
Notes	62	(3)
Coordinated Production-Inspection in a Tandem System	65	(24)
A Two-Stage Tandem Queue	66	(6)
Problem Statement	66	(1)
The SMDP Formulation	67	(5)
Stationary Optimal Policies	72	(7)
Structure of the Optimal Policy	79	(7)
Notes	86	(3)
Sequential Inspection Under Capacity Constraints	89	(20)
Capacity Constraints	90	(3)
Optimality of the Threshold Policy	93	(7)
Further Characterization of the Optimal Policy	100	(4)
An Application in Semiconductor Manufacturing	104	(2)
Notes	106	(3)
Coordination of Interstage Inspections	109	(30)
Two-Stage Quality Control	110	(2)
Analysis of Stage 1	112	(4)
Optimal Policy at Stage 2	116	(9)
Priority Structure	116	(4)
Threshold Structure	120	(5)
A Special Case: Constant Defective Rates	125	(2)
Optimal Policy at Stage 1	127	(5)
General Cost Functions	132	(4)
Notes	136	(3)
Optimal Inspection in an Assembly System	139	(20)
A Two-Component Assembly Model	140	(3)
Dynamic Programming Formulation	143	(2)
One Component with a Constant Defective Rate	145	(9)
A Heuristic Policy	154	(2)
Notes	156	(3)
Coordinated Replenishment and Rework with Unreliable Supply Sources	159	(30)
The Inspection/Rework Model	160	(2)
Properties of the Cost Function	162	(4)
Optimal Solution to the Inspection Problem	166	(5)
Optimal Replenishment Quantities	171	(6)
Optimal Replenishment over an Infinite Horizon	177	(7)
A Random Yield Model with Multiple Sources	184	(3)
Notes	187	(2)
Inventory Control with Substitution	189	(18)
Model Description	189	(2)
The Optimal Substitution Policy	191	(3)
Formulation of the Replenishment Decision	194	(3)
Concavity and Submodularity	197	(3)
The Optimal Order Quantities	200	(2)
Upper and Lower Bounds	202	(2)
Notes	204	(3)
References	207	(9)
Index	216