Bowon Kim Optimal Control Applications for Operations Strategy Optimal Control Applications for Operations Strategy Bowon Kim Optimal Control Applications for Operations Strategy 123 Bowon Kim KAIST Business School Seoul Korea (Republic of) ISBN 978-981-10-3598-2 DOI 10.1007/978-981-10-3599-9 ISBN 978-981-10-3599-9 (eBook) Library of Congress Control Number: 2017932003 © Springer Nature Singapore Pte Ltd 2017 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore For My Family Preface This book ‘Optimal Control Applications for Operations Strategy’ is about applications of optimal control theory to operations and supply chain management While teaching masters and Ph.D students at KAIST Business School for the last 20 years, I have found that optimal control theory is a very powerful tool to analyze and understand the fundamental issues in operations strategy One of the most important roles played by optimal control theory is to provide managerial and economic insights, which enable the students to comprehend the dynamic activities and interactions in operations In the literature, however, optimal control theory is not one of the mainstream approaches to study operations management As such, not many reference books on optimal control theory applied to operations are available Like any other research methodology in management, it is obvious that optimal control theory alone is not complete Nevertheless, it is certainly an effective tool to supplement other methodologies in operations, i.e., it plays a very significant role in analyzing the complex dynamics embodied in operations strategy This book could fill the gap in the literature and contribute to complementing other research methodologies for operations and supply chain management It consists of five chapters, which are based on and refined versions of some of the papers I have published for the last 20 years Each chapter starts with an abstract and keywords, followed by the ‘key learning’ box, which succinctly summarizes core lessons the students are expected to learn from the chapter There are exercise problems at the end of the main text in the chapter Detailed proofs and explanations of the theorems in the chapter appear in the appendices I discuss the primary goals and contents for each of the chapters as follows: Chapter ‘Optimal Control Theory and Operations Strategy’ introduces some of the basic concepts in optimal control theory and elaborates on the dynamics of production technology development, an essential part of operations strategy Chapter ‘Value of Coordination in Supply Chain Management’ looks into coordination as the infrastructural dimension of supply chain management, one of the most important subjects in operations strategy, and endeavors to define the value of coordination vii viii Preface Chapter ‘Innovation Competition and Strategy’ discusses innovation and postulates innovation competition as a crucial factor in operations strategy, exploring the conditions under which competing firms collaborate for innovation Chapter ‘Dynamic Coordination for New Product Development’ puts forth that new product development calls for significant supply chain coordination and suggests how to take into account the serviceability when developing a new product Chapter ‘Sustainable Supply Chain Management’ identifies two key players for ensuring sustainability, i.e., the government and consumers, and examines the critical role of consumer awareness in accomplishing the environmental sustainability I would like to thank Mr William Achauer in Springer Singapore for his help during the initial discussion for possible publication of my book Bill helped me complete the proposal review process productively My Ph.D student Jeong Eun Sim assisted me in compiling my papers for the book I appreciate Jeong Eun for her making a diligent effort I also would like to acknowledge my Ph.D students, Sunghak Kim, Taehyung Kim, Hyunjin Kang, Jaeseok Na, and Yeoyoung Cho, for their assiduous working during the proofreading I hope this book can help the students in operations strategy learn how to apply optimal control theory to analyze, understand, and solve actual managerial problems, especially in operations and supply chain management I am confident that it enables the students to develop their own research capability eventually ‘I hear, I know I see, I remember I do, I understand.’—Confucius KAIST, Seoul, Korea January 2017 Bowon Kim Contents 2 6 24 26 28 30 33 34 Value of Coordination in Supply Chain Management Joint Decision-Making in Supply Chain Management 1.1 Decision-Making Structure 1.2 Optimal Control Theory Models 1.3 Analysis of the Model 1.4 Numerical Examples 1.5 Managerial Implications Supply Chain Coordination 2.1 Model Formulation 2.2 Numerical Examples 2.3 Conclusion and Managerial Implications Exercise Problems Appendix Appendix Appendix 3: Discontinuous Control Variable 35 36 36 38 43 47 50 51 53 62 66 67 68 75 78 Optimal Control Theory and Operations Strategy Basics of Optimal Control Theory 1.1 Optimal Control Theory Model 1.2 Maximum Principle Dynamics of Production Technology Development 2.1 Introduction 2.2 Production Technology Development 2.3 Dynamic Optimal Control Model 2.4 Inferences and Implications Exercise Problems Appendix 1: Derivation of Eqs (27)–(29) Appendix 2: Basics of Differential Equations Appendix 3: Current Value Hamiltonian Appendix 4: Bounded Controls ix x Contents 79 80 81 82 83 84 84 94 98 99 99 100 104 107 109 110 111 117 127 Dynamic Coordination for New Product Development Optimal Dynamics of Technology and Price in a Duopoly Market 1.1 A Differential Game Model for Duopoly 1.2 Managerial Implications and Conclusions Supplier–Manufacturer Collaboration on New Product Development 2.1 Model Formulation 2.2 Noncooperative Game 2.3 Cooperative Game 2.4 Conclusion New Product and Warranty Strategy 3.1 The Two-Stage Optimal Control Theory Model 3.2 Numerical Analysis 3.3 Managerial Implications Exercise Problems Appendix Appendix 129 130 131 135 135 136 139 143 145 146 147 157 163 165 166 168 Sustainable Supply Chain Management Role of Government and Consumers in Pollution Reduction 1.1 Optimal Control Theory Model and Analysis Outcomes 1.2 Theorems 1.3 Discussion and Conclusion 175 176 177 179 182 Innovation Competition and Strategy Basics of Dynamic Programming Basics of Differential Games 2.1 Open-Loop Solution 2.2 Feedback Solution Innovation Competition 3.1 A Continuous Dynamic Model 3.2 Numerical Examples 3.3 Managerial Implications and Discussion Firms’ Cooperation and Competition for Innovation 4.1 Competition Versus Collaboration 4.2 A Differential Game Model 4.3 Analysis of the Model 4.4 Numerical Examples and Inferences 4.5 Managerial Implications Exercise Problems Appendix 1: An Example of Differential Games Problem Appendix Appendix Contents Supply Chain Coordination and Consumer Awareness for Pollution Reduction 2.1 Differential Game Models and Analysis Outcome 2.2 Theorems 2.3 Numerical Examples 2.4 Discussion and Conclusion Exercise Problems Appendix Appendix Appendix 3: Literature Review xi 183 184 189 192 196 198 200 202 209 References 213 Index 219 Appendix 207 Plugging the values of K41 and K32 in Table into (48) and utilizing Q1 and Q2 , III yIV LR À yLR [ is equivalent to h iÀ Á 2 cUQ1 a [ elr ỵ dịc2 U bcU f U ỵ edr þ dÞ 2c1 U À c ð49Þ Since cUQ1 is positive, (49) is equivalent to elr ỵ dịcU i À b 2c1 U À c ¼ ~a: a[ h f U ỵ edr ỵ dị 50ị I IV a Therefore, it holds that yIII LR \yLR ¼ yLR , when a [ ~ Similarly, IV vIII LR À vLR ¼ À Á U 1À dK32 À Ul þ K41 2e U ð51Þ Plugging the values of K32 and K41 in Table into (51) and rearranging the IV equation, vIII a LR À vLR [ is equivalent to a [ ~ III I IV Therefore, it holds that vLR [ vLR ¼ vLR , when a [ ~a Furthermore, since D ¼ a À bp2 À cy in Model 3, the long-term demand is III III DIII LR ¼ a À bp2 LR À cyLR ! a1 ỵ 2bc1 ỵ 2bc2 ị 2bc1 U ỵ bc c1 ỵ 2bc1 ỵ 2bc2 ị K32 cK32 ẳab 2b1 ỵ bc1 ỵ bc2 ị 2b1 ỵ bc1 ỵ bc2 ị ẳ 2bc1 U bc c aỵ 21 ỵ bc1 ỵ bc2 ị 21 þ bc1 þ bc2 Þ 2ð1 þ bc1 þ bc2 ị 4belU ỵ bc1 ỵ bc2 ịr þ dÞ À cU a À bc þ 2bc1 U h i : 2 4b1 ỵ bc1 ỵ bc2 ị f U ỵ edr ỵ dị c2 U ð52Þ For the long-term demand to be positive, rearranging Eq (52), 4bcelU ỵ bc1 ỵ bc2 ịr þ dÞÀc2 U ðaÀbc þ 2bc1 U Þ Â a ỵ 2bc1 U bc [ should 2 4b1 ỵ bc1 ỵ bc2 ị f U ỵ edr ỵ dị c U hold which is equivalent to h i i À Áh 2 f U ỵ edr ỵ dị a ỵ 2bc1 U bc f U ỵ edr ỵ dị celU r þ dÞ [ 0: ð53Þ Therefore, after rearranging (53), it is obvious that DIII LR [ holds if and only if elr ỵ dịcU b 2c1 U À c ¼ ~a a[ f U ỵ edr ỵ dị 208 Sustainable Supply Chain Management Proof of Theorem Part @yILR U ẳ h i2 eUlr ỵ dị\0 @f f U ỵ edr ỵ dị 54ị It is obvious that (54) holds because all parameters are positive Similarly, @vILR ¼ h @f flU f U ỵ edr ỵ dị i2 ỵ 2 elU dr ỵ dị ẳh i2 [ 0: 2 f U ỵ edr ỵ dị f U ỵ edr ỵ dị lU 55ị I IV Since yILR ¼ yIV LR and vLR ¼ vLR , it also holds that @yIV LR @f \0, @vIV LR @f [ Part n È Â À 2U ỵ bc2 ị o2 U c1 þ bc2 Þ Àðp1 À cÞ þ 2c1 a À U h i 2 21 ỵ bc2 ị f U ỵ edr ỵ dị ỵ c2 U c1 ẫ cc1 a ỵ 2abc2 ỵ bp1 ịg ỵ 2elU r ỵ dị1 ỵ bc2 ị @yIILR ẳn @f ð56Þ Utilizing the value of K21 in Table 6, @yIILR @f \0 is equivalent to: n 2U ỵ bc2 Þ h i o Á K21 \0 2 21 ỵ bc2 ị f U ỵ edr ỵ dị þ c2 U c1 ð57Þ Note that K21 is assumed to be nonnegative for feasible controls Therefore, (57) holds Similarly, @vIILR 2dU ỵ bc2 ị h i o K21 [ ẳn 2 @f 21 ỵ bc2 ị f U ỵ edr ỵ dị ỵ c2 U c1 ð58Þ Appendix 209 Part @yIII LR ẳn @f 4b1 ỵ bc1 ỵ bc2 ịU h i o 2 4b1 ỵ bc1 ỵ bc2 ị f U ỵ edr ỵ dị c2 U h i 4belU ỵ bc1 ỵ bc2 ịr þ dÞ À cU a À bc þ 2bc1 U Utilizing the value of K32 in Table 6, @yIII LR @f ð59Þ \0 is equivalent to Àn Note that 4b1 ỵ bc1 ỵ bc2 ịU h i o K32 \0 2 4b1 ỵ bc1 ỵ bc2 ị f U ỵ edr ỵ dị c2 U 60ị h i n o 2 4b1 ỵ bc1 ỵ bc2 ị f U ỵ edr ỵ dị c2 U [ since K31 is assumed to be positive Also, K32 is assumed to be nonnegative for feasible controls Therefore, (60) holds Similarly, @vIII 4bd1 ỵ bc1 ỵ bc2 ÞU LR h i o Á K32 [ 0: ¼n 2 @f 4b1 ỵ bc1 ỵ bc2 ị f U ỵ edr ỵ dị c2 U 61ị Appendix 3: Literature Review In environmental economics, a number of studies examined how the regulators could effectively induce pollution reduction through diverse instruments and incentives (Benchekroun and van Long 1998; Chen and Sheu 2009; Jung et al 1996; Krass et al 2013; Li et al 2014; Li 2013) Milliman and Prince (1989) investigated five regulatory regimes such as direct controls, emission subsidies, emission taxes, free marketable permits, and auctions marketable permits, and examined which policy would facilitate firms’ technological change in the pollution control most effectively Jung et al (1996) also evaluated the effectiveness of various regulatory instruments in terms of firms’ incentives to develop and adopt pollution abatement technology Subramanian et al (2007) studied how firms’ pollution reduction strategies would vary under a regulator’s decision on the permits for emissions More recently, in the literature, there have been emerging interests in operational and market factors beyond the regulatory policies in inducing firms’ environmental performance In reviewing studies in environmentally and socially sustainable operations, Tang and Zhou (2012) emphasized that the role of environmentally conscious consumers and cooperation within a supply chain deserves further 210 Sustainable Supply Chain Management investigation Despite the importance of supply chain coordination and consumer’s environmental awareness, however, how the two factors simultaneously affect firm’s environmental performance remains largely unexplored One notable exception is a study of Zhang et al (2015) They examined how consumer’s environmental awareness would influence the order quantity decision and profits in three supply chain scenarios, i.e., a centralized supply chain, a decentralized supply chain, and a decentralized supply chain with a return contract Regarding supply chain coordination, the commonly accepted view is that a cooperative supply chain leads to higher environmental performance and sustainability (Handfield et al 1997; Hollos et al 2012; Simpson 2010) Ni et al (2010) found that socially responsible or environmental performance is the highest in the cooperative supply chain, where the supplier and the manufacturer jointly maximize the supply chain profit, mainly because the double marginalization problem is eliminated Lou et al (2015) also examined three supply chain configurations and found that the cooperative supply chain in which the manufacturer and the retailer act as a single firm and the supply chain coordinated by a revenue sharing contract invest in emission reduction more than the decentralized supply chain Klassen and Vachon (2003) empirically showed that an increased collaboration in the supply chain helps the firms invest more in environmental programs Consumer’s increasing preference for environment-friendly products is another important mechanism to motivate firms to reconsider their environmental strategy Lee (2010) described how consumer’s environmental awareness influenced Esquel, one of the leading suppliers of premium cotton, to improve its environmental sustainability Several studies incorporated environmentally conscious consumers explicitly and analyzed its impact on firms’ decisions and environmental performance (Conrad 2005; Du et al 2015; Ghosh and Shah 2012; Wang et al 2014) Bagnoli and Watts (2003) investigated how firms’ competition for socially responsible or environment-friendly consumers influenced firm’s decisions Yalabik and Fairchild (2011) showed that pressures from environment-conscious consumers and regulators both lead to lower emissions as long as the initial emissions are not severe Also, they found that high environmental competition between firms not only induces lower emissions but also improves the effectiveness of environmental pressures from consumers or regulators Liu et al (2012) also examined the impact of consumer’s environmental awareness and firms’ competition in production or retail on the supply chain Another important issue in modeling the firm’s environmental effort is concerned with what actually generates pollution For instance, is the pollution emission rate proportional to the production rate or production capacity? Examining firm’s effort to reduce pollution, Subramanian et al (2007) put forth two types of pollution reduction, one independent of and the other dependent on the production volume Similarly, Chung et al (2013) specified two sources of manufacturer’s pollution emission, one due to the plant operations, e.g., the size of the capacity, independent of production rate and the other due to and proportional to the production rate There is no shortage of empirical studies, which reported that the plant capacity is related with the firm’s pollution emission rate, e.g., a plant with a larger Appendix 3: Literature Review 211 capacity emits more pollution and thus has lower environmental performance (Grant et al 2002; Gray and Shadbegian 2004; Laplante and Rilstone 1996; Ludwig 2004; Vachon and Klassen 2006) We conjecture that as long as the firm utilizes its capacity sufficiently, the firm’s pollution emission rate is proportional to its plant capacity, which in turn is closely related to its production rate References Agrawal VV, Ferguson M, Toktay LB, Thomas VM (2012) Is leasing greener than selling? 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195 Absorption capacity, 177 Adaptation, 8, After-sales services, 147, 148, 164 Analytical tractability, 55, 100 Apple, 81 Arrow, 6, 7, 53 Attention allocation, 1, 10, 25 Attention allocation patterns, 23 Aware consumer, 184, 188, 191, 194–196 B Balanced decision-making, 35–37, 41–43, 45, 47, 48, 50, 51, 67 Balanced decision-making structure, 42, 49–51 Bargaining power, 36–41, 43, 46, 48, 67, 68 Biased decision-making, 42 Boundary condition, 20, 91, 92 Bounded controls, 34 Brand power, 132 C Capability, 4, 11, 15, 23, 47, 55, 66, 79, 84, 85, 94, 95, 97, 98, 165 Capability-based competition, 98 Carrying capacity, 187 Catastrophic effect of learning prophecy, 6, 25 Causal relationship map, 84 Cause-and-effect relations, 92 Cellular phone, 146, 147 Centralized decision-making structure, 37 Closed-loop equilibrium, 139 Coercive case, 39, 43, 46–50 Coercive decision-making, 67 Coercive decision-making structure, 48 Co-evolution, Collective power of consumers, 183 Collusive, 37, 99, 103–109, 123 Collusive arrangement, 80, 109 Common benefit, 80, 100, 104, 107–109, 127, 128 Common constraints, 82, 187 Common effort, 80, 109 Common infrastructure, 79, 80, 100, 109, 110 Common market, 130 Common state variables, 81 Competitive advantage, 79, 80, 131 Competitive market, 53, 54 Competitive reaction, 93 Competitive supply chain, 183, 184, 190, 191, 193–197 Competitive supply chain coordination, 175, 176, 183, 184, 194–196, 198, 209 Complements, 23, 175, 179, 181, 182 Conditional probability, 136, 138 Consumer awareness, 175, 176, 179, 181–184, 190–197 Consumer-ignorant, 185, 188, 189, 191–197 Consumer’s environmental awareness, 194, 195, 198, 210 Consumer’s sensitivity to pollution, 176 Consumer utility, 177 Contingency strategy, 83 Continuous-time dynamic optimization, Contractual commitment, 52 Control capability, 10, 11, 15 Control variable, 2, 34, 41, 56, 82, 83, 85, 88, 113, 116, 117, 148, 158, 159 Cooperative game, 143 Cooperative supply chain, 183, 184, 188, 189, 191–197, 210 Cooperative supply chain coordination, 175, 176, 183, 184, 194 Coordination, 35, 36, 38, 42, 51, 52, 54, 64–66, 103, 104, 106, 107, 109, 123, 127, 128, 130, 144, 175, 176, 183, 184 Coordination strategy, 65, 165, 175 © Springer Nature Singapore Pte Ltd 2017 B Kim, Optimal Control Applications for Operations Strategy, DOI 10.1007/978-981-10-3599-9 219 220 Costate variables, 13, 15, 19, 20, 43, 139, 140, 143, 144, 157 Creative response, 130 Cumulative distribution function, 85 Current value Hamiltonian, 13, 19, 28, 33, 103, 124 Current value Lagrangian, 13, 19 D Decentralized structure, 37 Decision-making, 2, 35–39, 48, 50, 81, 103, 104, 106, 144, 147, 164 Decision-making entity, 81, 184 Decision-making structure, 35, 36, 38–40, 48, 50 Decision time horizon, 6, 16, 18, 21–23, 25, 37, 43, 49, 62, 82, 88, 89, 97, 130, 149, 150, 172 Decreasing concave, 86 Defect rate, 161, 162, 164 Delivery lead time, 164 Demand sensitivity, 60, 64, 66 Depreciation rate of market reward, 97 Differential equation, 10, 13, 19, 30, 32, 33, 81, 169–171, 200 Differential games, 80–83, 98, 111, 115, 116, 177, 187 Diffusion model, 130 Discounting factor, 33, 56, 89 Discount rate, 86, 87, 100, 165, 178, 186 Diseconomies of scale, 40 Disutility, 176 Double marginalization, 144, 192, 194, 197, 210 Duopoly, 130, 131, 135 Dynamic causal relation map, 93 Dynamic control problem, 12, 18, 91 Dynamic environment, 80 Dynamic evolution of pollution stock, 179, 187 Dynamic optimization, 1, 2, 102 Dynamic path, 5, 9, 84, 135 Dynamic programming, 80, 90 E Early commitment, 49 Effective capacity, 165, 178, 186 Emission of pollutants, 178, 183, 187 End-of-life warranty, 129, 130 Endogenous, 6–9, 11, 15, 17 Endogenous (on-shop) mechanism, 1, 6–8, 15 Entrepreneur, 130 Index Environmental performance, 193, 194, 209–211 Environmental sustainability, 176, 197, 210 Environment-conscious consumers, 210 Environment-friendly products, 210 EOL warranty, 147, 148, 158, 159, 163, 164 Equilibrium sales price, 192 Excludability, Exogenous, 6–11, 16, 17, 68, 165, 198, 199 Exogenous (off-shop) mechanism, 6–9, 16 Expected profit, 92, 93 Experience factor, 86 Exponential random variable, 85 Extraordinary rents, 51, 84 F Factory environment, Feedback Nash equilibrium, 110, 111, 116, 166 Feedback solution, 83, 111 Fidelity, 8, 10 Firm-specific benefit, 79, 99, 100, 104, 106–109 Firm-specificity, 8, 10 Free rider, 99, 101, 104, 106–110 Freezing effect of learning intention, 6, 25 G Game-theoretic approach, 37 Game-theoretic nature, 89 Government penalty, 175–179, 181–183, 196–199 Government regulation, 183 Green supply chain management, 183 H Hamiltonian, 3, 4, 33, 34, 41, 42, 56, 60, 68, 70, 78, 82, 83, 139, 140, 143, 154, 155, 166, 200, 203 Hamilton-Jacobi-Bellman (HJB) equation, 81, 83, 90, 101, 111, 119 Hazard rate, 138 I Ignorant consumer, 183, 184 Imitation process, Implementation cost, 6, 12, 16, 21, 23–25 Increasing concave, 14, 86 Increasing rate of investment, 79 Induced bias hypothesis, Industry-wide collaboration, 101, 105 Industry-wide infrastructure, 99, 109 Infinite horizon autonomous problem, 81 Index In-house, 1, 6, 8, 100, 157 Initial strategy, 82 In-line learning, 6, 8–10 Innovation, 35, 36, 51–57, 59–62, 64–67, 75, 76, 79, 80, 84–89, 92, 93, 95, 97, 98, 110, 130–134, 142, 144, 146, 165 Innovation capability, 55, 62, 66, 80, 165 Innovation competition, 79, 80, 84, 98 Innovation cost, 86–89, 92, 94–96, 110 Innovation cost factor, 84, 92, 98 Innovation cost structure, 84, 93, 95 Innovation effort, 85–88, 92, 93, 95, 97, 110, 141–145, 166 Innovation effort level, 94 Innovation game, 84–87, 93–95, 97, 98, 110 Innovation knowledge, 85, 93, 94 Innovation knowledge stock, 94, 97, 110 Innovation management, 80 Innovation process, 80, 84, 86, 143 Innovation strategy, 84, 93–98 Installed base, 132, 148, 151, 152, 163 Integrating factor, 33 Inter-firm collaboration, 109 Inventory holding cost, 148, 153, 157, 158, 160, 163 Inventory management cost, 151, 157 J Joint decision-making, 42 Joint-profit maximization, 183 K Knowledge, 2, 6–12, 27, 30, 80, 84, 85, 88, 89, 92, 93, 95, 100, 101, 109, 110, 136, 137 Knowledge accumulation, 28, 110, 137, 142, 145 Knowledge tacitness, 11 Knowledge transformation capability, 92 L Lagrangian, 13, 19, 34, 41–43, 68, 70, 78 Learning-by-doing, 98 Learning capability, 23, 84, 86, 94, 95, 97, 98 Learning function, 86 Learning-induced bias, Learning-induced control model, 6, 21 Learning propensity, 6, 21, 25 Learning rate, 21, 22, 24, 55, 62, 86, 88, 95–97 Liability, 149 Linear demand curve, 60 Local search process, Long-term competitiveness, 51 Long-term cumulative pollution, 191 221 Long-term equilibrium, 179, 181, 189, 191, 193, 205 Lump-sum payment, 87 Lump sum payoff, 157 M Managerial attention, 11, 15, 18, 20, 24, 25 Manufacturer-dominating, 38, 39 Marginal effectiveness, 94 Marginal value, 17, 43, 45, 142, 172 Market demand structure, 52, 53, 59, 61, 62 Market potential, 67, 159, 182 Market readiness, 131 Market reward, 79, 84, 87–89, 93–95, 97, 98, 110 Market reward depreciation, 88, 95, 97 Market reward function, 87 Market reward structures, 84, 87, 90, 94, 96–98 Markov perfect Nash equilibrium, 99, 100, 102, 104–106, 127 Markup, 60 Maximum principle, 1–3, 33, 34, 56, 82, 115 Memoryless property, 85 Microprocessor, 146, 147 Monopolistic, 54 Myopic perspective, 50 N Nash equilibrium, 82, 102, 103, 105, 139, 165 Necessary conditions, 3, 26–28, 34, 56, 68, 71, 78, 82, 83, 103, 124, 139, 140, 143, 147, 154, 156, 168, 171, 200, 203 Negative exponential distribution, 136, 138 Network profit, 52 New product development, 39, 40, 47, 80, 129, 130, 135–137, 141 Noncooperative, 130, 139, 145 O Off-shop, 1, 6, 8, 11, 15, 16, 26 Off-shop mechanism, 12, 16, 20, 21 Off-shop technology, 10, 11, 16–18, 20, 21, 24, 25 Oligopolistic, 53, 54 Oligopolistic innovation strategy, 93, 96 Oligopolistic reaction, 93 On-shop, 6, 8, 10, 11, 16, 18, 20–22, 25 On-shop mechanism, 7, 12, 16, 21 On-shop technology, 6, 16, 17, 21, 24, 25 Open-loop Nash equilibrium, 110, 115, 116, 199 Open-loop solution, 82, 83 Opportunism, 99, 109 222 Opportunistic behavior, 79, 99, 100, 105, 106 Opportunity cost, 12, 87 Optimal control theory, 1, 2, 56, 103 Optimization, 2, 56 Optimization models, 30 Organizational competence, 98 P Pareto-improving, 51 Part failure rate, 158 Patent competition, 87 Perfect coordination case, 103 Pharmaceutical industry, 98 Plant capacity, 38, 178, 186, 193, 210 Pollution abatement, 179, 193, 197 Pollution abatement effort, 176, 178, 181, 186, 192–194, 196 Pollution emission rate, 210 Pollution reduction, 175, 176, 182, 183, 192, 197, 209, 210 Pollution stock, 178, 179, 184, 186–189, 191, 192, 196–199 Pontryagin, 13 Potential market size, 130–132, 135, 150, 151, 158, 176, 178, 186, 191, 192, 194, 196, 197 Present value, 16, 87, 92, 110 Price-dependent market demand, 60 Price differential, 130, 132, 133, 135 Price skimming strategy, 157 Probability density function, 85, 88 Problem-solving, Procedural knowledge, Process control, Process innovation, 67 Production capacity, 53, 54, 56, 59 Production knowledge, 7, 8, 11 Production lead time, 151, 163 Production rate, 28, 161, 210 Production technology, 1, 7–12, 15, 26 Product life cycle, 65, 131, 146, 149, 157, 158, 160–164 Profitability factor, 92 Profit sharing, 48, 51, 137 Public goods, 79, 99, 100, 105, 107, 109 Q Quadratic cost function, 86, 185 Quality, 28, 52, 131, 135–137, 141, 144–146, 164 Quality improvement, 136–138, 142, 145 Quality innovation, 165 Index R Rate of parts failure, 150 Relative efficiency, 45, 46, 51 Relative innovation effort, 93 Renewal process, 150 Research and development (R&D), 2, 6, 7, 98 Research-intensive environment, 85 Research-intensive process, 98 Resource allocation dynamics, 24, 43 Resource availability, 41, 55 Resource utilization, 35–37, 44, 46, 51 Returns to scale, 10, 11 S Salvage value, 18, 132, 150, 153, 158, 172 Samsung, 81 Schumpeter, 130 Schumpeterian dynamics, 131 Semi-finished products, 185 Service, 68, 80, 131, 147, 149, 152, 157, 161 Service failure, 163 Shadow prices, 15 Shared decision-making, 41 Single decision-making authority, 103 Single player-dominating, 42, 43, 45–48, 50 Smartphone manufacturing industry, 181, 192 Smartphone market, 81 Spare parts, 129, 130, 146–148, 150–152, 157, 158, 160, 163, 169 Stakeholders, 81, 176 Standardization, 101, 109 Steady-state equilibrium, 99 Subcontracting, 1, Subsidy, 52, 55, 57–59, 61, 62, 65, 66, 75, 77 Substitute relationship, 181 Substitutes, 87, 175, 179, 181, 182 Success probability factor, 92 Sufficient condition, 13, 19, 20, 22, 56, 133, 156, 167 Supplier subsidy, 54, 57, 59–62, 75 Supply chain coordination, 51, 52, 129, 175, 183 Supply chain coordination strategy, 176 Supply chain partnership, 36 Sustainability, 175, 176, 210 Sustainable supplier–manufacturer coordination, 52 Sustainable supply chain management, 175, 176, 183 System capability, 11, 12 System level capability, 10 Index System utility function, 11 T Technical knowledge decay, 10 Technological knowledge, 92, 95, 110 Time gap, 184 Transfer price, 137, 139, 141, 143, 146, 176, 185, 186, 190, 192, 193, 196, 197 Transversality condition, 4, 34, 140, 144, 201 Transferability, 8, 10 Two-stage optimal control theory model, 147, 163 U Utility, 137, 176 223 V Value chain management, 176 Value function, 81, 101, 114, 119 W Warranty, 129, 130, 146–150, 158, 159, 161, 164 Wholesale price, 68, 165, 199 Willingness to pay, 131 Winner-takes-all reward system, 98 Z Zero-sum game, 67 Zone of coordination, 65 .. .Optimal Control Applications for Operations Strategy Bowon Kim Optimal Control Applications for Operations Strategy 123 Bowon Kim KAIST Business School Seoul Korea... East, Singapore 189721, Singapore For My Family Preface This book ? ?Optimal Control Applications for Operations Strategy? ?? is about applications of optimal control theory to operations and supply... become an irreversible force the firm could not deny to follow in the later stage © Springer Nature Singapore Pte Ltd 2017 B Kim, Optimal Control Applications for Operations Strategy, DOI 10.1007/978-981-10-3599-9_1