Integration of control theory and scheduling methods for supply chain management

Abstract In this paper, we propose to use distributed model predictive control for supply chain optimization. In particular, we focus on inventory management in supply chains. We use cooperative model predictive control, in which each agent makes their local decisions by optimizing the overall supply chain objective. Motivated by recent results in Stewart, Wright, and Rawlings (2011) , we develop a new cooperative MPC algorithm that is applicable to any stabilizable system, and in particular to supply chain models. We illustrate cooperative MPC for a two node supply chain example and compare its performance and properties with other classical distributed operating policies.

[1]  Arthur Richards,et al.  Robust distributed model predictive control with cooperation , 2007, 2007 European Control Conference (ECC).

[2]  James B. Rawlings,et al.  Postface to “ Model Predictive Control : Theory and Design ” , 2012 .

[3]  Xiang Li,et al.  Robust supply chain performance via Model Predictive Control , 2009, Comput. Chem. Eng..

[4]  Awi Federgruen,et al.  Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model , 1984, Oper. Res..

[5]  Peter M. Verderame,et al.  Planning and Scheduling under Uncertainty: A Review Across Multiple Sectors , 2010 .

[6]  Christos T. Maravelias,et al.  Integration of production planning and scheduling: Overview, challenges and opportunities , 2009, Comput. Chem. Eng..

[7]  Benita M. Beamon,et al.  A multi-objective approach to simultaneous strategic and operational planning in supply chain design , 2000 .

[8]  Marianthi G. Ierapetritou,et al.  Reactive scheduling using parametric programming , 2008 .

[9]  Stephen F. Smith,et al.  Reactive Scheduling Systems , 1995 .

[10]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[11]  Frank Allgöwer,et al.  Cooperative control of dynamically decoupled systems via distributed model predictive control , 2012 .

[12]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[13]  Christos T. Maravelias,et al.  General framework and modeling approach classification for chemical production scheduling , 2012 .

[14]  Gérard P. Cachon Supply Chain Coordination with Contracts , 2003, Supply Chain Management.

[15]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[16]  R. Sargent,et al.  A general algorithm for short-term scheduling of batch operations */I , 1993 .

[17]  Frank Allgöwer,et al.  Assessment and Future Directions of Nonlinear Model Predictive Control , 2007 .

[18]  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 .

[19]  Eduardo F. Camacho,et al.  Distributed model predictive control based on a cooperative game , 2011 .

[20]  Christos T. Maravelias,et al.  A General Framework for Process Scheduling , 2011 .

[21]  Christos T. Maravelias,et al.  A state-space model for chemical production scheduling , 2012, Comput. Chem. Eng..

[22]  Marianthi G. Ierapetritou,et al.  Process scheduling under uncertainty: Review and challenges , 2008, Comput. Chem. Eng..

[23]  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..

[24]  Jing-Sheng Song,et al.  Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand , 2001, Oper. Res..

[25]  Sebastian Engell,et al.  Modeling and solving real-time scheduling problems by stochastic integer programming , 2004, Comput. Chem. Eng..

[26]  Hartmut Stadtler,et al.  Supply chain management and advanced planning--basics, overview and challenges , 2005, Eur. J. Oper. Res..

[27]  Jing-Sheng Song,et al.  Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains , 2001, Manag. Sci..

[28]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

[29]  Christian A. Ullrich Introduction to Supply Chain Management , 2014 .

[30]  Frank Y. Chen,et al.  Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information.: The Impact of Forecasting, Lead Times, and Information. , 2000 .

[31]  Marianthi G. Ierapetritou,et al.  Rolling horizon based planning and scheduling integration with production capacity consideration , 2010 .

[32]  Eduardo F. Camacho,et al.  Distributed MPC: a supply chain case study , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[33]  Benita M. Beamon,et al.  Measuring supply chain performance , 1999 .

[34]  Nicoleta S. Tipi,et al.  Modelling the dynamics of supply chains , 2000, Int. J. Syst. Sci..

[35]  Anders Rantzer,et al.  Distributed Model Predictive Control with suboptimality and stability guarantees , 2010, 49th IEEE Conference on Decision and Control (CDC).

[36]  W. P. M. H. Heemels,et al.  Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions , 2009, Autom..

[37]  Denis Royston Towill,et al.  Dynamic analysis of an inventory and order based production control system , 1982 .

[38]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[39]  Vineet Padmanabhan,et al.  Comments on "Information Distortion in a Supply Chain: The Bullwhip Effect" , 1997, Manag. Sci..

[40]  K.G. Kempf,et al.  Control-oriented approaches to supply chain management in semiconductor manufacturing , 2004, Proceedings of the 2004 American Control Conference.

[41]  Panagiotis D. Christofides,et al.  Sequential and Iterative Architectures for Distributed Model Predictive Control of Nonlinear Process Systems , 2010 .

[42]  Stephen M. Disney,et al.  Measuring and avoiding the bullwhip effect: A control theoretic approach , 2003, Eur. J. Oper. Res..

[43]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[44]  A. S. White Management of inventory using control theory , 1999 .

[45]  John F. Forbes,et al.  Price-driven coordination method for solving plant-wide MPC problems , 2007 .

[46]  U. Rothblum,et al.  Inducing coordination in supply chains through linear reward schemes , 2006 .

[47]  D. Schmeidler The Nucleolus of a Characteristic Function Game , 1969 .

[48]  Nilay Shah Process industry supply chains: Advances and challenges , 2004 .

[49]  Ignacio E. Grossmann,et al.  Dynamic Modeling and Decentralized Control of Supply Chains , 2001 .

[50]  Young-Jun Son,et al.  INFORMATION SYNCHRONIZATION EFFECTS ON THE STABILITY OF COLLABORATIVE SUPPLY CHAIN Jayendran Venkateswaran , 2005 .

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

[52]  Efstratios N. Pistikopoulos,et al.  A bilevel programming framework for enterprise-wide process networks under uncertainty , 2004, Comput. Chem. Eng..

[53]  Ton Backx,et al.  TOWARDS INTENTIONAL DYNAMICS IN SUPPLY CHAIN CONSCIOUS PROCESS OPERATIONS , 1998 .

[54]  Sven Axsäter,et al.  A framework for decentralized multi-echelon inventory control , 2001 .

[55]  Stephen J. Wright,et al.  Inherently robust suboptimal nonlinear MPC: Theory and application , 2011, IEEE Conference on Decision and Control and European Control Conference.

[56]  Martin W. P. Savelsbergh,et al.  Integer-Programming Software Systems , 2005, Ann. Oper. Res..

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

[58]  Christos I. Papanagnou,et al.  Supply-chain modelling and control under proportional inventory-replenishment policies , 2008, Int. J. Syst. Sci..

[59]  B. Beamon Supply chain design and analysis:: Models and methods , 1998 .

[60]  D. Iglehart Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem , 1963 .

[61]  Bart De Schutter,et al.  Accelerated gradient methods and dual decomposition in distributed model predictive control , 2013, Autom..

[62]  Eduardo F. Camacho,et al.  Model predictive control techniques for hybrid systems , 2010, Annu. Rev. Control..

[63]  Hau L. Lee,et al.  Optimal Policies and Approximations for a Serial Multiechelon Inventory System with Time-Correlated Demand , 2003, Oper. Res..

[64]  E. L. Nichols,et al.  Introduction to Supply Chain Management , 1998 .

[65]  Jeremy F. Shapiro,et al.  Challenges of strategic supply chain planning and modeling , 2004, Comput. Chem. Eng..

[66]  Gabriela P. Henning,et al.  Computers and Chemical Engineering , 2022 .

[67]  Ravindra D. Gudi,et al.  A Multilevel, Control-Theoretic Framework for Integration of Planning, Scheduling, and Rescheduling , 2005 .

[68]  Y. Arkun,et al.  Optimization of Operations in Supply Chain Systems Using Hybrid Systems Approach and Model Predictive Control , 2006 .

[69]  Panos Seferlis,et al.  A two-layered optimisation-based control strategy for multi-echelon supply chain networks , 2004, Comput. Chem. Eng..

[70]  A. Richards,et al.  A decentralized algorithm for robust constrained model predictive control , 2004, Proceedings of the 2004 American Control Conference.

[71]  D. Simchi-Levi,et al.  The impact of exponential smoothing forecasts on the bullwhip effect , 2000 .

[72]  John J. Bartholdi,et al.  Using Shapley Value to Allocate Savings in A Supply Chain , 2005 .

[73]  Stephen J. Wright,et al.  Conditions under which suboptimal nonlinear MPC is inherently robust , 2011, Syst. Control. Lett..

[74]  C. L. Hamblin You and I , 1972 .

[75]  Stephen J. Wright,et al.  Cooperative distributed model predictive control , 2010, Syst. Control. Lett..

[76]  Stephen J. Wright,et al.  Hierarchical cooperative distributed model predictive control , 2010, Proceedings of the 2010 American Control Conference.

[77]  Bart De Schutter,et al.  A distributed version of Han's method for DMPC using local communications only , 2009 .

[78]  Panos J. Antsaklis,et al.  Linear Systems , 1997 .

[79]  M. Parlar,et al.  Game Theoretic Applications in Supply Chain Management: A Review , 2005 .

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

[81]  Alberto Bemporad,et al.  Model predictive control of hybrid systems with applications to supply chain management , 2005 .

[82]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[83]  K. Sari Exploring the benefits of vendor managed inventory , 2007 .

[84]  David Shan-Hill Wong,et al.  Controller design and reduction of bullwhip for a model supply chain system using z-transform analysis , 2004 .

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

[86]  Wolfgang Marquardt,et al.  Sensitivity-based coordination in distributed model predictive control , 2011 .

[87]  C. Floudas,et al.  Production Scheduling of a Large-Scale Industrial Batch Plant. II. Reactive Scheduling , 2006 .

[88]  Johan A. K. Suykens,et al.  Application of the proximal center decomposition method to distributed model predictive control , 2008, 2008 47th IEEE Conference on Decision and Control.

[89]  C. Pantelides,et al.  Design of Multi-echelon Supply Chain Networks under Demand Uncertainty , 2001 .

[90]  Ion Necoara,et al.  Parallel and distributed optimization methods for estimation and control in networks , 2011, 1302.3103.

[91]  Paul H. Zipkin,et al.  Foundations of Inventory Management , 2000 .

[92]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[93]  Wolfgang Marquardt,et al.  Integration of Model Predictive Control and Optimization of Processes: Enabling Technology for Market Driven Process Operation , 2000 .

[94]  Martin Guay,et al.  Coordination of Distributed Model Predictive Controllers for Constrained Dynamic Processes* *This work is supported by Natural Sciences and Engineering Research Council of Canada (NSERC) and Alberta Ingenuity. , 2009 .

[95]  Chandra Lalwani,et al.  Observable and controllable state space representations of a generalized Order-Up-To policy , 2003 .

[96]  I. Y. Kim,et al.  Adaptive weighted-sum method for bi-objective optimization: Pareto front generation , 2005 .

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

[98]  Ou Tang,et al.  An Overview of Input-Output Analysis Applied to Production-Inventory Systems , 2000 .

[99]  K. Binmore Dynamic Noncooperative Game Theory (Tamer Baser and Geert Jan Olsder) , 1984 .

[100]  James B. Rawlings,et al.  Coordinating multiple optimization-based controllers: New opportunities and challenges , 2008 .

[101]  Ignacio E. Grossmann,et al.  Enterprise‐wide optimization: A new frontier in process systems engineering , 2005 .

[102]  A. Barbosa‐Póvoa,et al.  Reactive Scheduling Framework for a Multiproduct Pipeline with Inventory Management , 2007 .

[103]  W. P. M. H. Heemels,et al.  Lyapunov Functions, Stability and Input-to-State Stability Subtleties for Discrete-Time Discontinuous Systems , 2009, IEEE Transactions on Automatic Control.

[104]  Mohammed M. Naim,et al.  The System Simplification Approach in Understanding the Dynamic Behaviour of a Manufacturing Supply Chain , 1992 .

[105]  Stephen J. Wright,et al.  Cooperative distributed model predictive control for nonlinear systems , 2011 .

[106]  Srinivasan Raghunathan,et al.  Impact of demand correlation on the value of and incentives for information sharing in a supply chain , 2003, Eur. J. Oper. Res..

[107]  R. Sargent,et al.  A general algorithm for short-term scheduling of batch operations—II. Computational issues , 1993 .

[108]  Mahesh Nagarajan,et al.  Game-Theoretic Analysis of Cooperation Among Supply Chain Agents: Review and Extensions , 2008, Eur. J. Oper. Res..

[109]  Petru-Daniel Morosan,et al.  A distributed MPC strategy based on Benders' decomposition applied to multi-source multi-zone temperature regulation , 2011 .

[110]  B. D. Sivazlian,et al.  Dynamic analysis of multi-echelon supply systems , 1978 .

[111]  Özalp Özer,et al.  A new algorithm and a new heuristic for serial supply systems , 2005, Oper. Res. Lett..

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

[113]  Karl G. Kempf,et al.  A Model Predictive Control framework for robust management of multi-product, multi-echelon demand networks , 2003, Annu. Rev. Control..

[114]  Jaime Cerdá,et al.  Dynamic scheduling in multiproduct batch plants , 2003, Comput. Chem. Eng..

[115]  M. D. Doan,et al.  A dual decomposition-based optimization method with guaranteed primal feasibility for hierarchical MPC problems , 2011 .

[116]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[117]  Mato Baotic,et al.  Hybrid Systems Modeling and Control , 2003, Eur. J. Control.

[118]  Lars Grüne,et al.  Analysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems , 2009, SIAM J. Control. Optim..

[119]  Qinan Wang,et al.  Coordination mechanisms of supply chain systems , 2007, Eur. J. Oper. Res..

[120]  Awi Federgruen,et al.  An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion , 1986, Math. Oper. Res..

[121]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[122]  Jr. Arthur F. Veinott On the Opimality of $( {s,S} )$ Inventory Policies: New Conditions and a New Proof , 1966 .

[123]  Christodoulos A. Floudas,et al.  Operational planning framework for multisite production and distribution networks , 2009, Comput. Chem. Eng..

[124]  Gintaras V. Reklaitis,et al.  A framework for schedule evaluation with processing uncertainty , 1999 .

[125]  Suresh P. Sethi,et al.  Optimality of (s, S) Policies in Inventory Models with Markovian Demand , 1995, Oper. Res..

[126]  Jay H. Lee,et al.  Model predictive control: past, present and future , 1999 .

[127]  Brahim Chaib-draa,et al.  Information Sharing as a Coordination Mechanism for Reducing the Bullwhip Effect in a Supply Chain , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[128]  Alain Bensoussan,et al.  Optimality of an (s, S) Policy with Compound Poisson and Diffusion Demands: A Quasi-Variational Inequalities Approach , 2009, SIAM J. Control. Optim..

[129]  Sven Axsäter,et al.  Inventory Control, 2nd edition , 2006 .

[130]  Francesco Borrelli,et al.  A distributed predictive control approach to building temperature regulation , 2011, Proceedings of the 2011 American Control Conference.

[131]  Jing-Sheng Song,et al.  Inventory Control in a Fluctuating Demand Environment , 1993, Oper. Res..

[132]  Sridhar Seshadri,et al.  Policy mechanisms for supply chain coordination , 2000, IIE Transactions.

[133]  David Angeli,et al.  Economic optimization using model predictive control with a terminal cost , 2011, Annu. Rev. Control..

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

[135]  Ignacio E. Grossmann,et al.  A strategy for the integration of production planning and reactive scheduling in the optimization of a hydrogen supply network , 2003, Comput. Chem. Eng..

[136]  Christos T. Maravelias,et al.  Modeling methods and a branch and cut algorithm for pharmaceutical clinical trial planning using stochastic programming , 2010, Eur. J. Oper. Res..

[137]  Lazaros G. Papageorgiou,et al.  Supply chain optimisation for the process industries: Advances and opportunities , 2009, Comput. Chem. Eng..

[138]  Christos T. Maravelias,et al.  A projection‐based method for production planning of multiproduct facilities , 2009 .

[139]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[140]  C. V. Rao,et al.  Steady states and constraints in model predictive control , 1999 .

[141]  A. Federgruen Chapter 3 Centralized planning models for multi-echelon inventory systems under uncertainty , 1993, Logistics of Production and Inventory.

[142]  Marianthi G. Ierapetritou,et al.  A New Approach for Efficient Rescheduling of Multiproduct Batch Plants , 2000 .

[143]  Ignacio E. Grossmann,et al.  A model predictive control strategy for supply chain optimization , 2003, Comput. Chem. Eng..

[144]  S. Hohmann The Bullwhip Effect in Supply Chains , 2014 .

[145]  Gérard P. Cachon,et al.  Game Theory in Supply Chain Analysis , 2004 .

[146]  L. Puigjaner,et al.  Incorporating on-line scheduling strategies in integrated batch production control , 1995 .

[147]  Karl Henrik Johansson,et al.  Distributed Model Predictive Consensus , 2006 .

[148]  James B. Rawlings,et al.  Model Predictive Control , 2012 .

[149]  Maria Teresa Moreira Rodrigues,et al.  Reactive scheduling approach for multipurpose chemical batch plants , 1996 .

[150]  Mahmut Parlar,et al.  Allocation of Cost Savings in a Three-Level Supply Chain with Demand Information Sharing: A Cooperative-Game Approach , 2009, Oper. Res..

[151]  William B. Dunbar,et al.  Distributed Model Predictive Control for Dynamic Supply Chain Management , 2005 .

[152]  Moritz Diehl,et al.  A Lyapunov Function for Economic Optimizing Model Predictive Control , 2011, IEEE Transactions on Automatic Control.

[153]  Awi Federgruen,et al.  An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion , 1986, Math. Oper. Res..

[154]  Joseph F. Pekny,et al.  A model predictive framework for planning and scheduling problems: a case study of consumer goods supply chain , 2000 .

[155]  Aswin N. Venkat Distributed Model Predictive Control: Theory and Applications , 2006 .

[156]  Panagiotis D. Christofides,et al.  Distributed model predictive control: A tutorial review and future research directions , 2013, Comput. Chem. Eng..

[157]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[158]  Marios C. Angelides,et al.  System dynamics modelling in supply chain management: research review , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[159]  Georgia Perakis,et al.  The Price of Anarchy in Supply Chains: Quantifying the Efficiency of Price-Only Contracts , 2007, Manag. Sci..

[160]  Herbert E. Scarf,et al.  Optimal Policies for a Multi-Echelon Inventory Problem , 1960, Manag. Sci..

[161]  C. Maravelias,et al.  An attainable region approach for production planning of multiproduct processes , 2007 .

[162]  Ignacio E. Grossmann,et al.  A Class of stochastic programs with decision dependent uncertainty , 2006, Math. Program..

[163]  Paul H. Zipkin,et al.  Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain , 1999 .

[164]  Riccardo Scattolini,et al.  Architectures for distributed and hierarchical Model Predictive Control - A review , 2009 .

[165]  Jaime Cerdá,et al.  State-of-the-art review of optimization methods for short-term scheduling of batch processes , 2006, Comput. Chem. Eng..

[166]  David B. Shmoys,et al.  Approximation Algorithms for Capacitated Stochastic Inventory Control Models , 2008, Oper. Res..

[167]  David Angeli,et al.  On Average Performance and Stability of Economic Model Predictive Control , 2012, IEEE Transactions on Automatic Control.

[168]  Eduardo F. Camacho,et al.  Distributed model predictive control based on agent negotiation , 2011 .

[169]  Arkadi Nemirovski,et al.  Robust optimization – methodology and applications , 2002, Math. Program..

[170]  P. Trodden,et al.  Robust distributed model predictive control using tubes , 2006, 2006 American Control Conference.

[171]  Christos T. Maravelias,et al.  A stochastic programming approach for clinical trial planning in new drug development , 2008, Comput. Chem. Eng..

[172]  Kanya Tanaka,et al.  Decentralized model predictive control via dual decomposition , 2008, 2008 47th IEEE Conference on Decision and Control.

[173]  Nikolaos V. Sahinidis,et al.  Optimization under uncertainty: state-of-the-art and opportunities , 2004, Comput. Chem. Eng..

[174]  D. Mayne,et al.  Approximation of the minimal robustly positively invariant set for discrete-time LTI systems with persistent state disturbances , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).