ON APPLICABILITY OF OPTIMAL CONTROL THEORY TO ADAPTIVE SUPPLY CHAIN PLANNING AND SCHEDULING

Decisions in supply chain planning and control are interconnected and depend on tackling uncertainties and dynamics. From this perspective, control theory (CT) is an interesting research avenue for the supply chain management (SCM). In this paper, the applicability of optimal CT to SCM is investigated. Our analysis is based on the fundamentals of control and systems theory and experimental modeling. The paper describes important issues and perspectives that delineate dynamics in supply chains, identifies and systemizes different streams in application of CT to production, logistics, and SCM in the period from 1960 to 2011. It derives some classifications, performs a critical analysis, and discusses further researches. Some drawbacks and missing links in the literature are pointed out. Several crucial application areas of control theory to SCM are discussed. Subsequently, optimal program control, challenges and advantages of its application in the SCM are addressed. It is shown how optimal program control can be applied to adaptive supply chain planning. In addition, it is concluded that with the help of CT, robustness, adaptability, and resilience of supply chains can be investigated in their consistency with operations planning and execution control within a conceptually and mathematically integrated framework. However, although SCs resemble control systems, they have some peculiarities which do not allow a direct application of CT methods. In this setting, further development of interdisciplinary approaches to supply chain optimization is argued. An extended co-operation between control and supply chain experts may have the potential to introduce more realism to the dynamic planning and models and improve real-time supply chain control policies.

[1]  Stephen M. Disney,et al.  The impact of information enrichment on the Bullwhip effect in supply chains: A control engineering perspective , 2004, Eur. J. Oper. Res..

[2]  Ignacio E. Grossmann,et al.  Dynamic modeling and classical control theory for supply chain management , 2000 .

[3]  José Miguel Laínez,et al.  Capturing dynamics in integrated supply chain management , 2008, Comput. Chem. Eng..

[4]  Alexandre Dolgui,et al.  A continuous model for supply planning of assembly systems with stochastic component procurement times , 2009 .

[5]  Prakash L. Abad,et al.  Multi-product multi-market model for co-ordination of marketing and production decisions , 1989 .

[6]  M. Stevenson,et al.  Flexibility from a supply chain perspective: definition and review , 2007 .

[7]  Alexandre Dolgui,et al.  Pricing strategies and models , 2010, Annu. Rev. Control..

[8]  Jayashankar M. Swaminathan,et al.  Modeling Supply Chain Dynamics: A Multiagent Approach , 1998 .

[9]  Christos D. Tarantilis,et al.  Dynamic modeling and control of supply chain systems: A review , 2008, Comput. Oper. Res..

[10]  S. Axsäter,et al.  Installation vs. echelon stock policies for multilevel inventory control , 1993 .

[11]  Jennifer Blackhurst,et al.  The Severity of Supply Chain Disruptions: Design Characteristics and Mitigation Capabilities , 2007, Decis. Sci..

[12]  Denis Royston Towill,et al.  A discrete transfer function model to determine the dynamic stability of a vendor managed inventory supply chain , 2002 .

[13]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[14]  Jerry C. Wei,et al.  Responding to schedule changes in build‐to‐order supply chains , 2005 .

[15]  Konstantin Kogan,et al.  Scheduling: Control-Based Theory and Polynomial-Time Algorithms , 2000 .

[16]  Bhaba R. Sarker,et al.  Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers , 2009, Eur. J. Oper. Res..

[17]  Marc Goetschalckx,et al.  Strategic production-distribution models: A critical review with emphasis on global supply chain models , 1997 .

[18]  Sean P. Willems,et al.  Optimizing the Supply Chain Configuration for New Products , 2005, Manag. Sci..

[19]  Sushil Verma,et al.  SIMULTANEOUS BATCHING AND SCHEDULING FOR CHEMICAL PROCESSING WITH EARLINESS AND TARDINESS PENALTIES , 2009 .

[20]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[21]  Alain Martel,et al.  The design of robust value-creating supply chain networks , 2010, Eur. J. Oper. Res..

[22]  Chandra Lalwani,et al.  Controllable, observable and stable state space representations of a generalized order-up-to policy , 2006 .

[23]  Suresh P. Sethi,et al.  Optimal Ordering Policies for Inventory Problems with Dynamic Information Delays , 2009 .

[24]  Boris V. Sokolov,et al.  Dynamic supply chain scheduling , 2012, J. Sched..

[25]  Vaidyanathan Jayaraman,et al.  Supply chain management in a sustainable environment , 2007 .

[26]  Knut Sydsæter,et al.  Optimal control theory with economic applications , 1987 .

[27]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[28]  Daniel E. Rivera,et al.  A process control approach to tactical inventory management in production-inventory systems , 2010 .

[29]  Michael Pinedo,et al.  Planning and Scheduling in Supply Chains: An Overview of Issues in Practice , 2004 .

[30]  V. G Boltyanskii,et al.  Optimal Control of Discrete Systems , 1979 .

[31]  Konstantin Kogan,et al.  A supply chain under limited-time promotion: The effect of customer sensitivity , 2008, Eur. J. Oper. Res..

[32]  Suresh P. Sethi,et al.  A Survey of the Maximum Principles for Optimal Control Problems with State Constraints , 1995, SIAM Rev..

[33]  Terry P. Harrison.  Principles for the Strategic Design of Supply Chains , 2004 .

[34]  Alexandre Dolgui,et al.  Generalized newsboy model to compute the optimal planned lead times in assembly systems , 2002 .

[35]  I. Chen,et al.  Understanding supply chain management: critical research and a theoretical framework , 2004 .

[36]  Daniel Tabak,et al.  Optimal control by mathematical programming , 1971 .

[37]  C. C. Holt,et al.  Planning Production, Inventories, and Work Force. , 1962 .

[38]  Yuri Levin,et al.  Risk in Revenue Management and Dynamic Pricing , 2008, Oper. Res..

[39]  Konstantin Kogan,et al.  Maximum principle-based methods for production scheduling with partially sequence-dependent setups , 1997 .

[40]  Joakim Wikner,et al.  Inventory trigger control policies developed in terms of control theory , 1996 .

[41]  V. Daniel R. Guide,et al.  OR FORUM - The Evolution of Closed-Loop Supply Chain Research , 2009, Oper. Res..

[42]  Karl G. Kempf,et al.  A MODEL PREDICTIVE CONTROL FRAMEWORK FOR ROBUST MANAGEMENT OF MULTI-PRODUCT, MULTI-ECHELON DEMAND NETWORKS , 2002 .

[43]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[44]  Josefa Mula,et al.  Mathematical programming models for supply chain production and transport planning , 2010, Eur. J. Oper. Res..

[45]  Sven Axsäter,et al.  Control theory concepts in production and inventory control , 1985 .

[46]  Carlos F. Daganzo,et al.  On the Stability of Supply Chains , 2002, Oper. Res..

[47]  Felix T.S. Chan,et al.  Framework for flexibility in dynamic supply chain management , 2008 .

[48]  Yasuhiko Takahara,et al.  General Systems Theory: Mathematical Foundations , 1975 .

[49]  Yi-Kuei Lin,et al.  A simple algorithm for reliability evaluation of a stochastic-flow network with node failure , 2001, Comput. Oper. Res..

[50]  Kevin B. Hendricks,et al.  Association Between Supply Chain Glitches and Operating Performance , 2005, Manag. Sci..

[51]  Jean-Marie Proth.  Scheduling: New trends in industrial environment , 2006 .

[52]  C. Hwang,et al.  Optimum Production Planning by the Maximum Principle , 1967 .

[53]  Xiuli He,et al.  Cooperative Advertising and Pricing in a Dynamic Stochastic Supply Chain: Feedback Stackelberg Strategies , 2009 .

[54]  Yanfeng Ouyang,et al.  The effect of information sharing on supply chain stability and the bullwhip effect , 2007, Eur. J. Oper. Res..

[55]  C. Gaimon.  Simultaneous and dynamic price, production, inventory and capacity decisions , 1988 .

[56]  Chris N. Potts,et al.  Supply chain scheduling: Batching and delivery , 2003, Oper. Res..

[57]  R. Lamming,et al.  Supply management: is it a discipline? , 2006 .

[58]  Yanfeng Ouyang,et al.  The bullwhip effect in supply chain networks , 2010, Eur. J. Oper. Res..

[59]  Dmitry Ivanov,et al.  An entropy-based approach to simultaneous analysis of supply chain structural complexity and adaptation potential , 2011 .

[60]  M. Ortega,et al.  Control theory applications to the production–inventory problem: a review , 2004 .

[61]  Hermann Kühnle,et al.  A system of models contribution to production network (PN) theory , 2007, J. Intell. Manuf..

[62]  Boris V. Sokolov,et al.  A multi-structural framework for adaptive supply chain planning and operations control with structure dynamics considerations , 2010, Eur. J. Oper. Res..

[63]  Dmitry Ivanov,et al.  Adaptive Supply Chain Management , 2009 .

[64]  Young-Jun Son,et al.  Hierarchical supply chain planning architecture for integrated analysis of stability and performance , 2007, Int. J. Simul. Process. Model..

[65]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[66]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[67]  G. Thompson,et al.  Optimal Control Theory: Applications to Management Science and Economics , 2000 .

[68]  David Simchi-Levi,et al.  Handbook of Quantitative Supply Chain Analysis , 2004 .

[69]  S. Chopra,et al.  Supply Chain Management: Strategy, Planning & Operation , 2007 .

[70]  Ulrich W. Thonemann,et al.  Production , Manufacturing and Logistics Analyzing the effect of the inventory policy on order and inventory variability with linear control theory , 2006 .

[71]  Boris V. Sokolov,et al.  Intelligent planning and control of manufacturing supply chains in virtual enterprises , 2007, Int. J. Manuf. Technol. Manag..

[72]  Axel Klar,et al.  Optimal control for continuous supply network models , 2006, Networks Heterog. Media.

[73]  Donald D. Eisenstein,et al.  Self-organizing logistics systems , 2010, Annu. Rev. Control..

[74]  Richard Bellman,et al.  Adaptive Control Processes: A Guided Tour , 1961, The Mathematical Gazette.

[75]  Panos Kouvelis,et al.  Supply Chain Management Research and Production and Operations Management: Review, Trends, and Opportunities , 2006 .

[76]  Stanley B. Gershwin,et al.  An algorithm for the computer control of a flexible manufacturing system , 1983 .

[77]  Hau L. Lee.  The triple-A supply chain. , 2004, Harvard business review.

[78]  John L. Casti,et al.  Connectivity, Complexity, and Catastrophe in Large-Scale Systems , 1980 .

[79]  Dmitry Ivanov,et al.  Rfid-Based Adaptive Feedbacks between Supply Chain Scheduling and Execution Control , 2011 .

[80]  Nilay Shah,et al.  Logistical network design with robustness and complexity considerations , 2007 .

[81]  Alexandre Dolgui,et al.  Optimal supply planning in MRP environments for assembly systems with random component procurement times , 2008 .

[82]  George L. Vairaktarakis,et al.  Integrated Scheduling of Production and Distribution Operations , 2005, Manag. Sci..

[83]  Dragoslav D. Šiljak,et al.  Decentralized control of complex systems , 2012 .

[84]  A. Dolgui,et al.  A model for supply planning under lead time uncertainty , 2002 .

[85]  Nicholas G. Hall,et al.  Capacity Allocation and Scheduling in Supply Chains , 2010, Oper. Res..

[86]  Alexandre Dolgui,et al.  Supply planning under uncertainties in MRP environments: A state of the art , 2007, Annu. Rev. Control..

[87]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .

[88]  Hau L. Lee,et al.  Unlocking the Value of RFID , 2007 .

[89]  Mohamed Mohamed Naim,et al.  Smoothing Supply Chain Dynamics , 1991 .

[90]  Alexandre Dolgui,et al.  On the performance of binomial and beta-binomial models of demand forecasting for multiple slow-moving inventory items , 2008, Comput. Oper. Res..

[91]  Denis Royston Towill,et al.  Further insights into “The stability of supply chains” , 2015 .

[92]  Jean-Marie Proth,et al.  Scheduling in supply chain environment , 2007, Eur. J. Oper. Res..

[93]  Karl G. Kempf,et al.  Model predictive control strategies for supply chain management in semiconductor manufacturing , 2007 .

[94]  L. T. Fan,et al.  The Discrete Maximum Principle: A Study of Multistage Systems Optimization , 1964 .

[95]  Zhi-Long Chen,et al.  Integrated Production and Outbound Distribution Scheduling: Review and Extensions , 2010, Oper. Res..

[96]  S. Disney,et al.  On the equivalence of control theoretic, differential, and difference equation approaches to modeling supply chains , 2006 .

[97]  Dov Pekelman,et al.  Simultaneous Price-Production Decisions , 1974, Oper. Res..

[98]  Dmitry Ivanov,et al.  DIMA—A research methodology for comprehensive multi-disciplinary modeling of production and logistics networks , 2009 .

[99]  B. Heimann,et al.  Fleming, W. H./Rishel, R. W., Deterministic and Stochastic Optimal Control. New York‐Heidelberg‐Berlin. Springer‐Verlag. 1975. XIII, 222 S, DM 60,60 , 1979 .

[100]  Dmitry Ivanov,et al.  An adaptive framework for aligning (re)planning decisions on supply chain strategy, design, tactics, and operations , 2010 .

[101]  Boris V. Sokolov,et al.  Integrated supply chain planning based on a combined application of operations research and optimal control , 2011, Central Eur. J. Oper. Res..

[102]  Germaine H. Saad,et al.  Managing Disruption Risks in Supply Chains , 2005 .

[103]  Anton V. Eremeev,et al.  Genetic algorithms for a supply management problem: MIP-recombination vs greedy decoder , 2009, Eur. J. Oper. Res..

[104]  Nilay Shah,et al.  Process industry supply chains: Advances and challenges , 2005, Comput. Chem. Eng..

[105]  Donald E. Kirk,et al.  Optimal Control Theory , 1970 .

[106]  R. Hartl,et al.  Optimal pricing and production in an inventory model , 1985 .

[107]  C. E. Riddalls,et al.  The stability of supply chains , 2002 .

[108]  Alexandre Dolgui,et al.  Decomposition approach for a problem of lot-sizing and sequencing under uncertainties , 2005, Int. J. Comput. Integr. Manuf..

[109]  Neale R. Smith,et al.  Supply chain dynamics: analysis of inventory vs. order oscillations trade-off , 2006 .

[110]  Zdzislaw Bubnicki,et al.  Modern Control Theory , 2005 .

[111]  James H. Bookbinder,et al.  An integrated inventory-transportation system with modified periodic policy for multiple products , 1999, Eur. J. Oper. Res..

[112]  Paul van Beek,et al.  Value chain management for commodities: a case study from the chemical industry , 2009, OR Spectr..