INTEGRATED MODELS IN PRODUCTION PLANNING, INVENTORY, QUALITY, AND MAINTENANCE

INTEGRATED MODELS IN PRODUCTION PLANNING, INVENTORY, QUALITY, AND MAINTENANCE

Edited by M. A. RAHIM University of New Brunswick

MOHAMED BEN-DAYA King Fahd University of Petroleum & Minerals

~ . . , Springer Science+Business Media, LLC

Library of Congress Cataloging-in-Publication

Integrated models in production planning, inventory, quality, and maintenance / edited by M.A. Rahim, Mohamed Ben-Daya.

p. cm. Includes bibliographical references and index. ISBN 978-1-4613-5652-3 ISBN 978-1-4615-1635-4 (eBook) DOI 10.1007/978-1-4615-1635-4 1. Production planning. 2. Inventory control. 3. Production scheduling. 1. Rahim, M.

A. II. Ben-Daya, M. (Mohamed)

TS176 .155142001 658.5--dc21

Copyright © 2001 Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 1 st edition 2001

2001029405

AlI rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photo­copying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC.

Printed on acid-free paper.

Contents

List of Figures

List of Tables

Preface

Acknowlegments

Contributing Authors

Part I INTRODUCTION

1

xi

xiii

xvii

xxi

xxiii

Integrated Production, Quality & Maintenance Mod- 3 els: An Overview

M. Ben-Daya and M.A. Rahim 1. Introduction 3 2. Preliminaries 4 3. Production and Quality 6 4. Production and Maintenance 9 5. Maintenance and Quality 13 6. Joint Models for Maintenance, Production and Quality 15 7. Integrated Models for Multi-Stage Systems 15 8. Other Integrated Models 16 9. Conclusion and Directions for Future Research 18

Part II PRODUCTION AND MAINTENANACE

2 Computation Algorithms of Cost-Effective EMQ Poli- 31

des with PM H. Okamura, T. Dohi, and S. Osaki

1. Introduction 31

VI INTEGRATED MODELS IN PRODUCTION PLANNING

3

2. 3. 4. 5. 6. 7.

Model description Poisson Process Demand Diffusion Approximation Phase Approximation Numerical Illustrations Conclusion

35 38 43 49 55 60

Optimal Control Policy for a General EM Q Model 67 with Random Machine Failure

V. Makis and X. Jiang 1. Introduction 67 2. Problem Formulation 69 3. Optimal Inspection Schedule for One Production Cycle 71 4. Optimal Lot Sizing and Replacement Policy 73 5. Computational Algorithm and Numerical Example 76

4 A Production/Inventory Policy for an Unreliable Machine 79 Hyo-Seong Lee and Mandyam M. Srinivasan

1. Introduction 80 2. The Model 83 3. Properties of the cost function 86 4. Numerical examples 90 5. Conclusions 92

5 Integrating Maintenance, Lot Sizing and Production 95

Planning for a Single Machine Multi-Product System Suresh K. Goyal and Yasemin Kahyaoglu

1. Introduction 95 2. Assumptions 96 3. Notation 96 4. Numerical Example 100

6 Optimal Models of Preventive Maintenance and Re- 105

placement Policies Eli Shemesh, Abraham Mehrez and Gad Rabinowitz

1. Introduction 105 2. The Model Parameters and Notation 109 3. General Problem Solution of the Optimal Maintenance Strat-

egy 111 4. Stochastic Machine Replace- ment in Finite Horizon 115 5. Numerical Examples 117 6. Conclusions and Applications for Future Research 122

Contents Vll

Part III PRODUCTION/INVENTORY AND QUALITY

7 An Integrated Economic Model for Inventory and 129

Statistical Process Control Enrique Del Castillo and Isabel T. Salcedo

1. Introduction 130 2. The Semi-Markov model 131 3. Economic Optimization Model 136

8 A Generalized Integrated Economic Model for Inven- 145

tory and Quality Control Problems Hiroshi Ohta, Aritoshi Kimura and M. Abdur Rahim

1. Introduction 146 2. Notations and Assumptions 149 3. General Model 151 4. Examples 155 5. Concluding Remarks 158

9 Optimal Inventory Ordering Policies for Quality-Dependent 161

Markets M. Hariga and M. N. Azaiez

1. Introduction 161 2. Model Formulation 164 3. Selecting among alternative arrangements 169 4. Integrated inventory-pricing model 172 5. Conclusion 179

10 Manufacturing System Modeling and Control 185 E. K. Boukas and Z. K. Liu

1. Introduction 185 2. Basic Production Model 187 3. Controlled Piecewise-Deterministic Processes and Numerical

Technique 190 4. Manufacturing System with Deteriorating Terms 195 5. Production System with Quality Control 202 6. Production and Marketing Control 216 7. Concluding Remarks 225

11 A Single Period Inventory Model to Account for De- 231

mand Surprises Dogman Serel and Herbert Moskowitz

1. Introduction 231 2. Model Assumptions 233 3. The Optimal Order Quantity 234 4. Numerical Example 237 5. Sensitivity Analysis 238 6. Summary and Extensions 238

viii INTEGRATED MODELS IN PRODUCTION PLANNING

Part IV QUALITY AND MAINTENANCE

12 Improving and Maintaining Process Profitability 245 Elart von Collani and Gudrun Kiesmiiller

1. The Production Process 246 2. The Control Model 254 3. Process Monitoring 257 4. Process Profitability 259 5. Monitoring and Maintenance Policy 261 6. Normally Distributed Quality Characteristic 262 7. Numerical Example 272 8. Conclusions 273

13 A Simple Model for the Effect of Manufacturing Pro- 277

cess Quality on Product Reliability Michael Tortorella

1. Introduction 277 2. How Does Manufacturing Process Quality Affect Product Re-

liability? 279 3. An Illustration 282 4. Conclusions and Related Questions 285

Part V WARRANTY, MANUFACTURING AND QUALITY

14 Warranty and Manufacturing 289 K.F. Lyons and D.N.P. Murthy

1. Introduction 289 2. Product Warranty: An Overview 291 3. Warranty as an Integrative Element in Manufacturing 292 4. Warranty Management System 294 5. Models and Data Management 305 6. Conclusion 319

15 Warranty and Quality 325 D.N.P. Murthy and I. Djamaludin

1. Introduction 325 2. Product Warranty 327 3. Quality 332 4. Warranty and Quality: Review of Models 341 5. Conclusion and Topics for Future Research 355

Part VI QUALITY

16 SPC-based Diagnosis of Processes with Multiple Con- 363

current Dysfunctional Steps John R. English, Mohammed Alsein, and Michael H. Cole

17

1. 2. 3. 4. 5.

Introduction and motivation Related Literature SPC approach to process diagnosis Results of comparisons between MDS and SDS Conclusions

Contents IX

364 364 365 368 380

Stepwise-Programmed Regulation of Manufacturing 383 Quality

John J. Liu 1. Introduction 383 2. Dispersal Quality Regulation 385 3. Singular Characteristics of DQR 389 4. Singular Dispersal Solutions of DQR 393 5. Optimal Quality Regulation Strategy 395 6. Conclusions 396

18 Simultaneous Monitoring Of Mean And Variance through 399

Optimally Designed SPRT Charts Felipe Pachano-Azuaje and Tapas K. Das

1. Introduction 400 2. Joint SPRT Control Charts for Mean and Variance 405 3. Development of Economic Models 410 4. Numerical Results 423 5. Conclusions 436

Index 441

List of Figures

2.1 Configuration of the EMQ model with PM. 37 2.2 Configuration of the EMQ model with PM using the

virtual stock level. 37 4.1 The Production/Inventory System Where N = 2. 85 4.2 Au and Av for an increasing function, h(t), with v > u. 88 5.1 Production and maintenance schedule for Alterna-

tive 1 101 5.2 Production and maintenance schedule for Alterna-

tive 2 103 6.1 Optimal machine replacement sequences under de-

terministic cases of t3. 119 6.2 Probability of machine's use over time, under Geo-

metric PDF with p=O.07 120 6.3 Deterministic NPV for TL1 and TL2 versus ma-

chine life-cycle. 121 6.4 Deterministic NPV versus the introduction time of

a TL3 machine. 121 7.1 Transitions between two consecutive samples. 133 7.2 A typical inventory graph, showing the average in-

ventory slope. 135 8.1 Quality and inventory control cycle 156 10.1 maintenance rates w1(x, 2), w~(x, 2) . 203 10.2 Value function v(x, i) versus x. 214 10.3 Production rate u(x, i) versus x. 215 10.4 maintenance rates w~(x, 2), w~(x, 2) . 215 14.1 Interactions between warranty related issues (from

Murthy and Blischke (1994». 293

xii INTEGRATED MODELS IN PRODUCTION PLANNING

14.2 Warranty Management System Modules 14.3 Characterisation of the Total Warranty Cost 14.4 D&E Module 14.5 Flow of Activities in the D&E Module 14.6 Production Module

295 296 297 297 299

14.7 Flow of Activities in the Production Module 300 14.8 Marketing Module 302 14.9 Flow of Activities in the Marketing Module 303 14.10 Post Sale Servicing Module 305 14.11 Flow of Activities in the Post-Sale Servicing Module 306 14.12 Failure Model Hierarchy 308 14.13 Database Management System (adapted from Beynon-

Davies and Hutchings (1993)) 318 16.1 M Step Process characterized by N Process Variables. 367 16.2 Interaction plot of number of process variables vs. p. 372

16.3 Interaction plot of number of process variables vs. p value. 374 16.4 Interaction plot of Steps vs. Shifts. 375 16.5 Interaction plot of Steps vs. Number of Process

variables (Var). 375 16.6 Interaction plot of Var vs. value of p. 378

16.7 Interaction plot of Shifts vs. value of p. 379

16.8 Interaction plot of Steps vs. value of p. 379

16.9 Interaction plot of Steps vs. Shift. 380 17.1 Stepwise-programmed regulation 387 17.2 Dispersal singular paths and characteristics 392 18.1 A sequential probability ratio test chart for the mean

(as in (18.11)). 408 18.2 A sequential probability ratio test chart for the variance. 411 18.3 Two sample cases of joint SPRT from (18.64) and (18.65).421 18.4 Decision Limits in Mean Charts for Operational and

Reference Designs. 425

List of Tables

2.1 The PM policy under IFR failure distribution (p = 0.1, a = 2.0). 56

2.2 The PM policy under IFR failure distribution (p = 0.9, a = 2.0). 56

2.3 The PM policy under DFR failure distribution (p = 0.1, a = 0.5). 56

2.4 The optimal EMQ and PM policies and their asso-ciated cost effectiveness. 57

2.5 Comparison between the optimal PM policies based on cost effectiveness (CE) and expected cost per unit time in the steady-state (CU). 57

2.6 The PM policy based on diffusion approximation (p = 0.1). 58

2.7 The PM policy based on diffusion approximation (p = 0.5). 58

2.8 The PM policy based on diffusion approximation (p = 0.9). 58

2.9 The PM policy based on phase approximation (p = 0.1). 59 2.10 The PM policy based on phase approximation (p = 0.5). 59

2.11 The PM policy based on phase approximation (p = 0.9). 59

2.12 The comparison between optimal EMQ policies with PM based on the simulation. 61

4.1 Optimal policy for Example 1 90 4.2 Optimal policy for Example 2 91

4.3 Optimal policy for Example 3 92 5.1 Parameters for the example problem. 100

xiv INTEGRATED MODELS IN PRODUCTION PLANNING

5.2 Production and maintenance schedule in tabular for­mat for the solution to Alternative 1 with mainte-nance time of 60 hrs/cycle. 101

5.3 Determination of Ki(T) values. 102

5.4 Production and maintenance schedule in tabular for­mat for solution to Alternative 2 with maintenance time of 60 hrs/cycle. 102

6.1 Raw Data for the Three-Machine Types. 118 8.1 Fraction defectives and quality cost per unit time,

where po= 0.0231 and Do = 85.0 (<5 = o,~ = 1). 156 8.2 Near-optimal designs obtained using the Simulated

9.1 9.2

9.3

Annealing Method. 157 Effect of the defective rate on the optimal ordering policy 170

Effect of the defective rate on selecting the appro-priate policy 173 Effect of the defective rate on the integrated ordering-pricing policy 177

9.4 Effect of the defective rate on the performance of the approximate solution 180

10.1 Data 202

10.2 example data 213 11.1 Sensitivity to A and T J..Lo = 100, J..Ll = 180, J..L2 = 60,

a5 = 400, ar = 900, a~ = 200, L = 1. 239 11.2 Effect of Demand Distribution Parameters J..Lo =

J..L2 = 100, a5 = a~ = 400, A = L = 1, T = 2 240

13.1 Example 284 16.1 Rule-based Expert Systems for Process Diagnosis. 365 16.2 Model-based Systems for Process Diagnosis. 366 16.3 Process Scenarios. 369 16.4 Data Sets. 370

16.5 Data Set #1 ANOVA. 371

16.6 Data Set #2 ANOVA. 373 16.7 Data Set #3 ANOVA. 376 16.8 Data Set #4 ANOVA. 377 18.1 Glossary of Symbols. 18.2 Glossary of Symbols.

406 413

18.3 Process Conditions. 414 18.4 Input parameters used for numerical study. 426

18.5 Comparison of the Reference and the Operational Designs. 428

List of Tables xv

18.6 Comparison of Pure Economic and Economic Sta-tistical Models 431

18.7 Comparison of EMV-SPRT and Costa's Designs 433 18.8 Comparison ofEMV-SPRT and Non-Economic SPRT

Designs 434 18.9 Sensitivity Analysis 437

Preface

Production planning, inventory management, quality control, and maintenance policy are important components of a manufacturing sys­tem. Effective integration of these four components will give an industry a competitive edge in the market place.

This book provides in one volume the latest developments in inte­grated production, quality, and maintenance models. Prominent re­searchers who are actively engaged in the area have contributed chapters covering a wide range of topics. We hope that this book will serve as a useful and informative introduction to these fields and foster further research and development in these fast growing areas.

This volume is divided into six parts and contains eighteen chapters. Each chapter has been subject to review by at least two experts.

In Part I, Ben-Daya and Rahim provide an overview of the literature dealing with integrated models for production, quality, and maintenance. Directions for future research are outlined.

Part II contains six chapters (chapters 2 to 6) dealing with integrated models for production and maintenance. In chapter 2, Okamura, Dohi, and Osaki develop computational algorithms to determine optimal poli­cies that consider both Economic Manufacturing Quantity (EMQ) and Preventive Maintenance(PM) time for demand that occurs in accordance with a homogeneous Poisson process and for the general case with re­newal process demand. Makis and Jiang present, in chapter 3, a general EMQ model with joint production /maintenance /quality control. They investigate the problem of determining jointly the optimal lot sizing, preventive maintenance, and inspection policy which minimizes the ex­pected average cost per unit time. In chapter 4, Lee and Srinivasan consider the economic lot-sizing problem for an unreliable production facility. A simple approach for determining a practical operating policy regarding the scheduling of maintenance work and lot sizing of several

xviii INTEGRATED MODELS IN PRODUCTION PLANNING

products produced on a single machine is presented in chapter 5 by Goyal and Kahyaoglu. In chapter 6, Shemesh, Mehrez, and Rabinowitz solve a family of problems related to machine replacement and preventive main­tenance that consider the possibility of skipping available technology in order to be ready for the next technological breakthrough.

Part III deals with integrated production/inventory and quality mod­els in chapters 7-11. In chapter 7, Del Castillo and Salcedo present an optimization model for the design of a Shewhart X-bar chart, taking into account both inventory and statistical process control considerations. A generalized economic model for the joint determination of production quantity, an inspection schedule, and the economic design of the X-bar and R control charts are developed in chapter 8 by Ohta, Kimura, and Rahim. An integrated inventory quality problem is presented by Hariga and Azaiez in chapter 9. They investigate the single-period inventory problem when the lot received may contain defective items where good and poor-quality items are sold in primary and secondary markets. The analysis extends to investigate pricing policies in the different markets and their impact on the order size and the expected profit. In chapter 10, Boukas and Liu extend the continuous flow model of a stochastic manufacturing system to include deteriorating items, quality, and mar­keting control, where production quality varies with the change of the system mode. The last chapter of Part III, chapter 11 by Serel and Moskowitz, deals with an extension of the traditional newsboy problem that takes into account random demand surprises.

Part IV focuses on quality and maintenance integrated models and contains two chapters. In the first one, chapter 12, Collani and Kiesmiiller deal with an integrated approach which enables an objective-oriented joint design of monitoring and maintenance policies. The aim is to min­imize disturbances and inappropriate process adjustments which may lead to lower profitability of a production process. The second, chapter 13 by Tortorella, introduces a framework for studying the quantitative relationship between reliability and the quality of post-design product realization processes.

Part V deals with warranty, manufacturing, and quality and contains two chapters. Chapter 14 by Lyons and Murthy is a consideration of warranty and manufacturing. The authors develop a warranty manage­ment system that can assist in decision making at different stages and discusses the elements of the system and the management of informa­tion. In chapter 15, Murthy and Djamaludin deal with the link between warranty servicing cost, design quality, manufacturing quality, and ser­vice quality. The authors also review the literature linking warranty and quality

PREFACE xix

Part VI addresses issues related to quality and contains three chap­ters (chapters 16-18). In chapter 16, English, Alsein, and Cole develop a statistical process control approach to process diagnosis for scenar­ios in which multiple sub-processes can be concurrently dysfunctional. The Multiple Concurrent Dysfunctional Steps approach integrates ex­isting SPC knowledge into the field of process diagnosis. In chapter 17, Liu develops models for the stepwise-programmed regulation of qual­ity. In particular, a dispersal quality regulation model using the dis­crete approximation of Subbotin is developed. The last chapter of Part VI, chapter 18 by Pachano-Azuaje and Das, deals with simultaneous monitoring of mean and variance through optimally designed Sequential Probability Ratio Tests charts. This type of control charts possess four essential properties that a control chart must have namely, applicability, high sensitivity for detecting shifts, cost-optimality and the capability of jointly controlling all the important parameters that characterize a process. Although the chapters in Part VI do not deal with integrated models, they present novel ideas for addressing quality control problems.

The production of quality goods depends upon machine tools, and the performance of machine tools depends upon maintenance policy. Clearly, the reliability of operating equipment is an important issue. Warranties are particularly important to both buyers and sellers. Product quality and production quantity are equally important to them. A book which expresses these simple facts is overdue, and it is anticipated that the findings of the research that is outlined in this edited volume will prove very useful to end users and future researchers.

THE EDITORS

Acknowledgments

The Editors would like to acknowledge the contributing authors for their valuable submissions. This book would not have been possible without their participation and cooperation. Each chapter has gone through several stages of review. We would like to express our grati­tude to all the reviewers whose comments and suggestions have led to substantial improvements in the quality of the text.

We are indebted to Gary Folven, Publishing Editor ORjMS areas at Kluwer, for his interest in this book and his. full cooperation and assistance since the initiation of the project. During the review process of the proposal conducted by the publisher, four anonymous experts made many valuable and insightful comments. We would like to acknowledge their contributions.

The editorial assistance of Janet Gamache throughout the project has been greatly appreciated. It takes a lot of skill and patience to do the word processing, text conversion, proofreading, and typesetting neces­sary for the production of a text such as this. Special thanks go to Kian Keong Lam and Agnes Wong for retrieving the electronic versions of the manuscripts in various formats from the contributors, for converting the manuscripts to MS Word format for editing purposes, and for preparing the final version of the edited manuscripts to be converted into LaTex format. We would like to thank Shaikh Arifusalam for his support in converting Word manuscripts to LaTex and preparing the index. The assistance of Atique Siddiqui and Mohammed EI-Hassen in proofreading the converted manuscripts and formatting references is highly appreci­ated.

This project has been funded by the Faculty of Administration, Uni­versity of New Brunswick through the Faculty Development Fund, and by the King Fahd University of Petroleum and Minerals under project number SEjPIQMj217. These supports are greatly appreciated. The financial assistance of the Natural Science and Engineering Research Council (NSERC) of Canada in support of this collaborative research project is gratefully acknowledged.

Last but certainly not least, we wish to thank our families for their pa­tience and encouragement. The preparation of this book has, on several occasions, required sacrifices on their part.

Contributing Authors

Mohammed Alsein Transplace.com Lowell AR, USA

M. N. Azaiez Industrial Engineering Program, King Saud University, Saudi Arabia

M. Ben-Daya Dept. of Systems Engineering, King Fahd University, Saudi Arabia

E. K. Boukas Mechanical Engineering Department, Ecole Poly technique de Montreal, Canada

E. Del Castillo Dept. of Industrial & Manufacturing Eng. The Pennsylvania State University, USA

M. H. Cole Department of Industrial Engineering University of Arkansas, USA

E. von Collani Institut fur Angewandte Mathematik und Statistik, Wiirzburg, Germany

T. K. Das Dept. of Industrial & Managt. Sys. Eng. University of South Florida, USA

I. Djamaludin Dept. of Mechanical Engineering The Univ. of Queensland, Australia

T. Dohi Dept of Industrial & Systems Eng. Hiroshima University, Japan

John R. English Department of Industrial Engineering University of Arkansas, USA

Suresh K. Goyal Dept. of Decision Sciences and MIS Concordia University, Canada

M. Hariga Industrial Engineering Program, King Saud University, Saudi Arabia

X. Jiang Dept. of Mech. and Industrial Eng. University of Toronto, Canada

Y. Kahyaoglu Department of Management Bogazici University, Turkey

XXIV INTEGRATED MODELS IN PRODUCTION PLANNING

Gudrun Kiesmiiller Eindhoven University of Technology, Eindhoven, The Netherlands

Aritoshi Kimura Dept. of Management Systems Eng. Kinki University, Japan

Hyo-Seong Lee Dept. of Industrial Engineering Kyung-Hee University, Korea

John J. Liu School of Business Administration Univ. of Wisconsin-Milwaukee, USA

Z. K. Liu Mechanical Engineering Department, Ecole Poly technique de Montreal, Canada

K.F. Lyons Dept. of Mechanical Engineering The University of Queensland, Australia

V. Makis Dept. of Mech. and Industrial Eng. University of Toronto, Canada

A. Mehrez Dept. of Industrial Eng. & Management, Ben Gurion Univ. of The Negev, Isreal

H. Moskowitz Krannert Graduate School of Management Purdue University, USA

D.N.P. Murthy Dept. of Mechanical Engineering The University of Queensland, Australia

Hiroshi Ohta Dept. of Industrial Engineering Osaka Prefecture University, Japan

H. Okamura Dept of Industrial & Systems Eng. Hiroshima University, Japan

S. Osaki Dept of Industrial & Systems Eng. Hiroshima University, Japan

F. Pachano-Azuaje Dept. of Industrial & Managt. Sys. Eng. University of South Florida, USA

G. Rabinowitz Dept. of Industrial Eng. & Management, Ben Gurion Univ. of The Negev, Isreal

M. Abdur Rahim Faculty of Administration University of New Brunswick, Canada

I. T. Salcedo Dept. of Industrial & Manufacturing Eng. The Pennsylvania State University, USA

D. Serel Krannert Graduate School of Management Purdue University, USA

E. Shemesh Dept. of Industrial Eng. & Management, Ben Gurion Univ. of The Negev, Isreal

M. M. Srinivasan College of Business Administration, The University of Tennessee, USA

Michael Tortorella Bell Laboratories

Lucent Techn., Holmdel, USA