Dynamic modeling and control of supply chain systems: A review.

*(English)*Zbl 1146.90353Summary: Supply chains are complicated dynamical systems triggered by customer demands. Proper selection of equipment, machinery, buildings and transportation fleets is a key component for the success of such systems. However, efficiency of supply chains mostly depends on management decisions, which are often based on intuition and experience. Due to the increasing complexity of supply chain systems (which is the result of changes in customer preferences, the globalization of the economy and the stringy competition among companies), these decisions are often far from optimum. Another factor that causes difficulties in decision making is that different stages in supply chains are often supervised by different groups of people with different managing philosophies. From the early 1950s it became evident that a rigorous framework for analyzing the dynamics of supply chains and taking proper decisions could improve substantially the performance of the systems. Due to the resemblance of supply chains to engineering dynamical systems, control theory has provided a solid background for building such a framework. During the last half century many mathematical tools emerging from the control literature have been applied to the supply chain management problem. These tools vary from classical transfer function analysis to highly sophisticated control methodologies, such as model predictive control (MPC) and neuro-dynamic programming. The aim of this paper is to provide a review of this effort. The reader will find representative references of many alternative control philosophies and identify the advantages, weaknesses and complexities of each one. The bottom line of this review is that a joint co-operation between control experts and supply chain managers has the potential to introduce more realism to the dynamical models and develop improved supply chain management policies.

##### MSC:

90B10 | Deterministic network models in operations research |

##### Keywords:

supply chain management; control; dynamic modeling; review; dynamic programming; model predictive control##### Software:

DYNAMO
PDF
BibTeX
XML
Cite

\textit{H. Sarimveis} et al., Comput. Oper. Res. 35, No. 11, 3530--3561 (2008; Zbl 1146.90353)

Full Text:
DOI

##### References:

[1] | Beamon, B.M., Supply chain design and analysis: models and methods, International journal of production economics, 55, 281-294, (1998) · Zbl 0951.90521 |

[2] | Lee, H.L.; Padmanabhan, V.; Whang, S., The bullwhip effect in supply chains, Sloan management review, 38, 3, 93-102, (1997) |

[3] | Miragliotta, G., Layers and mechanismsa new taxonomy for the bullwhip effect, International journal of production economics, 104, 2, 365-381, (2006) |

[4] | Geary, S.; Disney, S.M.; Towill, D.R., On bullwhip in supply chains—historical review, present practice and expected future impact, International journal of production economics, 101, 2-18, (2006) |

[5] | Riddalls, C.E.; Bennett, S.; Tipi, N.S., Modelling the dynamics of supply chains, International journal of systems science, 31, 8, 969-976, (2000) · Zbl 1080.93603 |

[6] | Axsäter, S., Control theory concepts in production and inventory control, International journal of systems science, 16, 2, 161-169, (1985) · Zbl 0557.90043 |

[7] | Edghill, J.S.; Towill, D.R., The use of systems dynamics in manufacturing systems, Transactions of the institute of measurement and control, 11, 4, 208-216, (1989) |

[8] | Ortega, M.; Lin, L., Control theory applications to the production – inventory problem: a review, International journal of production research, 42, 2303-2322, (2004) · Zbl 1060.90011 |

[9] | Bertsekas, D.P., Dynamic programming and optimal control, (2000), Athena Scientific Belmont, MA |

[10] | Bellman, R.E., Dynamic programming, (1957), Princeton University Press New Jersey, NJ |

[11] | Camacho, E.F.; Bordons, C., Model predictive control, (1999), Springer London · Zbl 1080.93001 |

[12] | Zhou, K.; Doyle, J.C.; Glover, K., Robust and optimal control, (1995), Prentice Hall New Jersey, NJ |

[13] | Bertsekas, D.P.; Tsitsiklis, J.N., Neuro-dynamic programming, (1996), Athena Scientific Belmont, MA · Zbl 0924.68163 |

[14] | Simon, H.A., On the application of servomechanism theory in the study of production control, Econometrica, 20, 247-268, (1952) · Zbl 0046.37804 |

[15] | Vassian, J.H., Application of discrete variable servo theory to inventory control, Operations research, 3, 272-282, (1955) |

[16] | Forrester, J.W., Industrial dynamics: a major breakthrough for decision makers, Harvard business review, 36, 37-66, (1958) |

[17] | Forrester, J.W., Industrial dynamics, (1961), MIT Press Cambridge, MA |

[18] | Barlas, Y.; Yasarcan, H., Goal setting, evaluation, learning and revision: a dynamic modeling approach, Evaluation and program planning, 29, 79-87, (2006) |

[19] | Sterman, J.D., Business dynamics: systems thinking and modeling for a complex world, (2000), McGraw-Hill New York, NY |

[20] | Ansof, H.I.; Slevin, D.P., An appreciation of industrial dynamics, Management science, 14, 91-106, (1968) |

[21] | Towill, D.R., Dynamic analysis of an inventory and order based production control system, International journal of production research, 20, 671-687, (1982) |

[22] | Coyle, R.G., Management system dynamics, (1977), Wiley London · Zbl 0874.90126 |

[23] | Lalwani, C.S.; Disney, S.M.; Towill, D.R., Controllable, observable and stable state space representations of a generalized order-up-to policy, International journal of production dynamics, 101, 172-184, (2006) |

[24] | Wikner, J.; Naim, M.M.; Towill, D.R., The system simplification approach in understanding the dynamic behaviour of a manufacturing supply chain, Journal of systems engineering, 2, 167-178, (1992) |

[25] | Wikner, J., Continuous-time dynamic modeling of variable lead times, International journal of production research, 41, 2787-2798, (2003) · Zbl 1052.90514 |

[26] | Burbidge JL. Automated production control with a simulation capability. In: Proceedings of IFIP conference WG 5-7, Copenhagen, 1984. p. 1-14. |

[27] | Towill, D.R., Industrial dynamics modeling of supply chains, Logistics information management, 9, 43-56, (1996) |

[28] | Towill, D.R.; McCullen, P., The impact of agile manufacturing programme on supply chain dynamics, International journal of logistics management, 10, 1, 83-96, (1999) |

[29] | Disney, S.M.; Towill, D.R., On the bullwhip and inventory variance produced by an ordering policy, Omega, 31, 157-167, (2003) |

[30] | Chen, F.; Drezner, Z.; Ryan, J.K.; Simchi-Levi, D., Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, lead times, and information, Management science, 46, 436-443, (2000) · Zbl 1231.90019 |

[31] | Agrell, P.J.; Wikner, J., An MCDM framework for dynamic systems, International journal of production economics, 45, 279-292, (1996) |

[32] | Edghill, J.E.; Towill, D.R., Assessing manufacturing system performance: frequency response revisited, Engineering costs and production economics, 19, 319-326, (1990) |

[33] | John, S.; Naim, M.M.; Towill, D.R., Dynamic analysis of a WIP compensated decision support system, International journal of manufacturing system design, 1, 283-297, (1994) |

[34] | Disney, S.M.; Naim, M.M.; Towill, D.R., Genetic algorithm optimization of a class of inventory control systems, International journal of production economics, 68, 259-278, (2000) |

[35] | Deziel, D.P.; Elion, S., A linear production – inventory control rule, The production engineer, 43, 93-104, (1967) |

[36] | Riddalls, C.E.; Bennett, S., The stability of supply chains, International journal of production research, 40, 459-475, (2002) · Zbl 1060.91500 |

[37] | Bellman, R.; Cooke, K.L., Differential-difference equations, (1963), Academic Press New York, NY · Zbl 0118.08201 |

[38] | Warburton, R.D.H.; Disney, S.M.; Towill, D.R.; Hodgson, J.P.E., Further insights into “the stability of supply chains”, International journal of production research, 42, 639-648, (2004) · Zbl 1176.90061 |

[39] | Zhou, L.; Naim, M.M.; Tang, O.; Towill, D.R., Dynamic performance of a hybrid inventory system with a kanban policy in remanufacturing process, Omega, 34, 585-598, (2006) |

[40] | Lai, C.L.; Lee, W.B.; Ip, W.H., A study of system dynamics in just-in-time logistics, Journal of materials processing technology, 138, 265-269, (2003) |

[41] | Dejonckheere, J.; Disney, S.M.; Lambrecht, M.R.; Towill, D.R., Measuring and avoiding the bullwhip effect: a control theoretic approach, European journal of operational research, 147, 567-590, (2003) · Zbl 1026.90030 |

[42] | Lee, H.L.; Padmanabhan, V.; Whang, S., Information distortion in a supply chain: the bullwhip effect, Management science, 43, 546-558, (1997) · Zbl 0888.90047 |

[43] | Dejonckheere, J.; Disney, S.M.; Lambrecht, M.R.; Towill, D.R., The impact of information enrichment on the bullwhip effect in supply chains: a control engineering perspective, European journal of operational research, 153, 727-750, (2004) · Zbl 1099.90503 |

[44] | Lalwani, C.S.; Disney, S.M.; Towill, D.R., Controllable, observable and state space representations of a generalized order-up-to policy, International journal of production economics, 101, 172-184, (2006) |

[45] | Franklin, G.F.; Powell, J.D.; Workman, M., Digital control of dynamic systems, (1998), Addison-Wesley Menlo Park, CA |

[46] | Disney, S.M.; Towill, D.R., Eliminating inventory drift in supply chains, International journal of production economics, 93-94, 331-344, (2005) |

[47] | White, A.S., Management of inventory using control theory, International journal of technology management, 17, 847-860, (1999) |

[48] | Towill, D.R.; Evans, G.N.; Cheema, P., Analysis and design of an adaptive minimum reasonable inventory control system, Production planning & control, 8, 545-557, (1997) |

[49] | Evans, G.N.; Naim, M.M.; Towill, D.R., Application of a simulation methodology to the redesign of a logistical control system, International journal of production economics, 56-57, 157-168, (1998) |

[50] | Dejonckheere, J.; Disney, S.M.; Lambrecht, M.R.; Towill, D.R., Transfer function analysis of forecasting induced bullwhip in supply chains, International journal of production economics, 78, 133-144, (2002) |

[51] | Grubbström, R.W.; Wikner, J., Inventory trigger policies developed in terms of control theory, International journal of production economics, 45, 397-406, (1996) |

[52] | Wiendahl, H.P.; Breithaupt, J.W., Automatic production control applying control theory, International journal of production economics, 63, 33-46, (2000) |

[53] | Grubbström, R.W., A net present value approach to safety stocks in planned production, International journal of production economics, 56-57, 213-229, (1998) |

[54] | Grubbström, R.W.; Molinder, A., Safety production plans in MRP-systems using transform methodology, International journal of production economics, 46-47, 297-309, (1996) |

[55] | Lancaster, K., Mathematical economics, (1968), Macmillan New York, NY · Zbl 0181.46302 |

[56] | Grubbström, R.W.; Orvin, P., Intertemporal generalization of the relationship between material requirements planning and input – output analysis, International journal of production economics, 26, 311-318, (1992) |

[57] | Grubbström, R.W.; Wang, Z., A stochastic model of multi-level/multi-stage capacity constrained production – inventory systems, International journal of production economics, 81-82, 483-494, (2003) |

[58] | Grubbström, R.W.; Huynh, T.T.T., Multi-level, multi-stage capacity constrained production – inventory systems in discrete-time with non-zero lead times using MRP theory, International journal of production economics, 101, 53-62, (2006) |

[59] | Grubbström, R.W.; Tang, O., An overview of input – output analysis applied to production – inventory systems, Economic systems research, 12, 3-25, (2000) |

[60] | Popplewell, K.; Bonney, M.C., The application of discrete linear control theory to the analysis and simulation of multi-product, multi-level production control systems, International journal of production research, 25, 45-56, (1987) |

[61] | Wikner, J., Dynamic analysis of a production – inventory model, Kynernetes, 34, 803-823, (2003) |

[62] | Burns, J.F.; Sivazlian, B.D., Dynamic analysis of multi-echelon supply systems, Computers and industrial engineering, 2, 181-193, (1978) |

[63] | Wikner, J.; Towill, D.R.; Naim, M., Smoothing supply chain dynamics, International journal of production economics, 22, 231-248, (1991) |

[64] | Disney, S.M.; Towill, D.R., A discrete transfer function model to determine the dynamic stability of a vendor managed inventory supply chain, International journal of production research, 40, 179-204, (2002) · Zbl 1175.90138 |

[65] | Perea, E.; Grossmann, I.; Ydstie, E.; Tahmassebi, T., Dynamic modeling and classical control theory for supply chain management, Computers and chemical engineering, 24, 1143-1149, (2000) |

[66] | Perea-López, E.; Grossmann, I.; Ydstie, E.; Tahmassebi, T., Dynamic modeling and decentralized control of supply chains, Industrial engineering chemistry research, 40, 3369-3383, (2001) |

[67] | Lin, P.H.; Wong, D.S.H.; Jang, S.S.; Shieh, S.S.; Chu, J.Z., Controller design and reduction of bullwhip for a model supply chain system using z-transform analysis, Journal of process control, 14, 487-499, (2004) |

[68] | Arrow, K.J.; Karlin, S.; Scarf, H., Studies in the mathematical theory of inventory and production, (1958), Stanford University Press Stanford, CA · Zbl 0079.36003 |

[69] | Clark, A.; Scarf, H., Optimal policies for a multi-echelon inventory problem, Management science, 6, 475-490, (1960) |

[70] | Scarf, H., The optimality of \((s, S)\) policies for the dynamic inventory problem, () · Zbl 0203.22102 |

[71] | Iglehart, D., Optimality of \((s, S)\) policies in the infinite horizon dynamic inventory problem, Management science, 9, 259-267, (1963) |

[72] | Hausman, W.H.; Peterson, R., Multiproduct production scheduling for style goods with limited capacity, forecast revisions and terminal delivery, Management science, 18, 370-383, (1972) · Zbl 0246.90016 |

[73] | Federgruen, A.; Zipkin, P., Computational issues in an infinite-horizon, multi-echelon inventory model, Operations research, 32, 818-836, (1984) · Zbl 0546.90026 |

[74] | Iglehart, D.; Karlin, S., Optimal policy for dynamic inventory process with nonstationary stochastic demands, (), [Chapter 8] · Zbl 0121.15002 |

[75] | Song, J.S.; Zipkin, P., Inventory control in a fluctuating demand environment, Operations research, 43, 351-370, (1993) · Zbl 0798.90035 |

[76] | Sethi, S.P.; Cheng, F., Optimality of \((s, S)\) policies in inventory models with Markovian demand, Operations research, 45, 931-939, (1997) · Zbl 0895.90079 |

[77] | Beyer, D.; Sethi, S., Average cost optimality in inventory models with Markovian demands, Journal optimization theory applications, 92, 497-526, (1997) · Zbl 0873.90021 |

[78] | Bensoussan, A.; Liu, R.H.; Sethi, S.P., Optimality of an \((s, S)\) policy with compound Poisson and diffusion demands: a QVI approach, SIAM journal on control and optimization, 44, 1650-1676, (2006) · Zbl 1151.90304 |

[79] | Dong, L.; Lee, H.L., Optimal policies and approximations for a serial multiechelon inventory system with time-correlated demand, Operations research, 51, 969-980, (2003) · Zbl 1165.90312 |

[80] | Heath, D.C.; Jackson, P.L., Modeling the evolution of demand forecasts with application to safety stock analysis in production/distribution systems, IEE transactions, 26, 17-30, (1994) |

[81] | Graves, S.C.; Kletter, D.B.; Hetzel, W.B., A dynamic model for requirements planning with application to supply chain optimization, Operations research, 46, S35-S49, (1998) · Zbl 0987.90005 |

[82] | Gallego, G.; Ozer, O., Integrating replenishment decisions with advance order information, Management science, 47, 1344-1360, (2001) · Zbl 1232.90047 |

[83] | Gallego, G.; Ozer, O., Optimal replenishment policies for multiechelon inventory problems under advance demand information, Manufacturing & service operations management, 5, 157-175, (2003) |

[84] | Ozer, O.; Wei, W., Inventory control with limited capacity and advance demand information, Operations research, 52, 988-1000, (2004) · Zbl 1165.90332 |

[85] | Sethi, S.P.; Yan, H.; Zhang, H., Peeling layers of an onion: a periodic review inventory model with multiple delivery modes and forecast updates, Journal of optimization theory and applications, 108, 253-281, (2001) · Zbl 1033.90005 |

[86] | Bensoussan, A.; Crouhy, M.; Proth, J.M., Mathematical theory of production planning, (1983), North-Holland New York, NY · Zbl 0564.90010 |

[87] | Sethi, S.P.; Yan, H.; Zhang, H., Inventory models with fixed costs multiple delivery modes, and forecast updates, Operations research, 51, 321-328, (2003) · Zbl 1163.90348 |

[88] | Feng, Q.; Gallego, G.; Sethi, S.P.; Yan, H.; Zhang, H., Periodic-review inventory model with three consecutive delivery modes and forecast updates, Journal of optimization theory and applications, 124, 137-155, (2005) · Zbl 1059.90008 |

[89] | Simchi-Levi, D.; Zhao, Y., The value of information sharing in a two-stage supply chain with production capacity constraints, Naval research logistics, 50, 888-916, (2003) · Zbl 1055.90030 |

[90] | Olsder, G.J.; Suri, R., Time optimal part-routing in a manufacturing system with failure prone machines, (), 722-727 |

[91] | Rishel, R., Dynamic programming and minimum principles for systems with jump Markov disturbances, SIAM journal on control, 13, 338-371, (1975) · Zbl 0304.93025 |

[92] | Rishel, R., Control of systems with jump Markov disturbances, IEEE transactions on automatic control, 20, 241-244, (1975) · Zbl 0305.93059 |

[93] | Davis, M.H.A., Markov models and optimization, (1993), Chapman & Hall London · Zbl 0780.60002 |

[94] | Akella, R.; Kumar, P.R., Optimal control of production rate in a failure-prone manufacturing system, IEEE transactions on automatic control, 31, 116-126, (1986) · Zbl 0579.90047 |

[95] | Bielecki, T.; Kumar, P.R., Optimality of zero-inventory policies fro unreliable manufacturing systems, Operations research, 36, 353-362, (1988) · Zbl 0652.90054 |

[96] | Kimemia, J.G.; Gershwin, S.B., An algorithm for the computer control production in flexible manufacturing systems, IIE transactions, 15, 353-362, (1983) |

[97] | Sethi, S.P.; Soner, H.M.; Zhang, Q.; Jiang, J., Turnpike sets and their analysis in stochastic production planning problems, Mathematics of operations research, 17, 932-950, (1992) · Zbl 0770.90030 |

[98] | Fleming, W.H.; Soner, H.M., Controlled Markov processes and viscosity solutions, (1993), Springer New York · Zbl 0773.60070 |

[99] | Presman, E.; Sethi, S.P.; Zhang, Q., Optimal feedback production planning in a stochastic N-machine flowshop, Automatica, 31, 1325-1332, (1995) · Zbl 0834.90068 |

[100] | Presman, E.; Sethi, S.P.; Suo, W., Optimal feedback production planning in a stochastic N-machine flowshop with limited buffers, Automatica, 33, 1899-1903, (1997) · Zbl 0889.90080 |

[101] | Sethi, S.P.; Zhou, X.Y., Optimal feedback controls in deterministic dynamic two-machine flowshops, Operations research letters, 19, 225-235, (1996) · Zbl 0874.90107 |

[102] | Gharbi, A.; Kenne, J.P., Optimal production control problem in stochastic multiple-product multiple-machine manufacturing systems, IEE transactions, 35, 941-952, (2003) |

[103] | Boukas, E.K.; Haurie, A., Manufacturing flow control and preventive maintenance: a stochastic control approach, IEEE transactions on automatic control, 35, 1024-1031, (1990) · Zbl 0718.90036 |

[104] | Kushner, H.J.; Dupuis, P.G., Numerical methods for stochastic control problems in continuous time, (1992), Springer New York, NY · Zbl 0754.65068 |

[105] | Boukas, E.K.; Yang, H., Optimal control of manufacturing flow control and preventive maintenance, IEEE transactions on automatic control, 41, 881-885, (1996) · Zbl 0855.90065 |

[106] | Boukas, E.K.; Kenne, J.P.; Zhu, Q., Age dependent hedging point policies in manufacturing systems, Proceedings of the American control conference, 3, 2178-2179, (1995) |

[107] | Kenne, J.P.; Gharbi, A.; Boukas, E.K., Control policy simulation based on machine age in a failure prone one-machine, one-product manufacturing system, International journal of production research, 35, 1431-1445, (1997) · Zbl 0942.90517 |

[108] | Kenne, J.P.; Gharbi, A., Experimental design in production and maintenance control of a single machine, single product manufacturing system, International journal of production research, 37, 621-637, (1999) · Zbl 0943.90560 |

[109] | Kenne, J.P.; Gharbi, A., Production planning problem in manufacturing systems with general failure and repair time distributions, Production planning and control, 11, 581-588, (2000) |

[110] | Sethi, S.P.; Zhang, Q., Hierarchical production and setup scheduling in stochastic manufacturing systems, IEEE transactions on automatic control, 40, 924-930, (1995) · Zbl 0830.90068 |

[111] | Yan, H.; Zhang, Q., A numerical method in optimal production and set-up scheduling of stochastic manufacturing systems, IEEE transactions on automatic control, 42, 1452-1455, (1997) · Zbl 0892.90094 |

[112] | Boukas, E.K.; Kenne, J.P., Maintenance and production control of manufacturing systems with setups, Lectures in applied mathematics, 33, 55-70, (1997) · Zbl 0886.90077 |

[113] | Liberopoulos, G.; Caramanis, M., Numerical investigation of optimal policies for production flow control and set-up scheduling: lessons from two-part-type failure-prone fmss, International journal of production research, 35, 2109-2133, (1997) · Zbl 0945.90586 |

[114] | Bai, S.X.; Elhafsi, M., Scheduling an unreliable manufacturing system with non-resumamble set-ups, Computers & industrial engineering, 32, 909-925, (1997) |

[115] | Gharbi, A.; Kenne, J.P.; Hajji, A., Operational level-based policies in production rate control of unreliable manufacturing systems with set-ups, International journal of production research, 44, 545-567, (2006) · Zbl 1095.90028 |

[116] | Feng, Y.; Yan, H., Optimal production control in a discrete manufacturing system with unreliable machines and random demands, IEEE transactions on automatic control, 35, 2280-2296, (2000) · Zbl 0982.90020 |

[117] | Song, D.P.; Sun, Y.X., Optimal service control of a serial production line with unreliable workstations and random demand, Automatica, 34, 1047-1060, (1998) · Zbl 0965.90017 |

[118] | Boukas, E.K.; Liu, Z.K., Manufacturing systems with random breakdowns and deteriorating items, Automatica, 37, 401-408, (2001) · Zbl 0964.90014 |

[119] | Sharifnia, A., Production control of manufacturing system with multiple machine state, IEEE transactions on automatic control, 33, 620-625, (1988) · Zbl 0647.90040 |

[120] | Liberopoulos, G.; Hu, J.Q., On the ordering of optimal hedging points in a class of manufacturing flow control models, IEEE transactions on automatic control, 40, 282-286, (1995) · Zbl 0821.90062 |

[121] | Perkins, J.R.; Srikant, R., Hedging policies for failure-prone manufacturing systems: optimality of JIT and bounds on buffer levels, IEEE transactions on automatic control, 43, 953-957, (1998) · Zbl 0949.90033 |

[122] | Sethi, S.P.; Suo, W.; Taksar, M.I.; Zhang, Q., Optimal production planning in a stochastic manufacturing system with long-run average cost, Journal of optimization theory and applications, 92, 161-188, (1997) · Zbl 0886.90084 |

[123] | Sethi, S.P.; Suo, W.; Taksar, M.; Yan, H., Optimal production planning in a multi product stochastic manufacturing system with long-run average cost, Journal of discrete event dynamic systems: theory and applications, 8, 37-54, (1998) · Zbl 0907.90179 |

[124] | Sethi, S.P.; Zhang, H., Average-cost optimal policies for an unreliable flexible multiproduct machine, International journal of flexible manufacturing systems, 11, 147-157, (1999) |

[125] | Lehoczky, J.; Sethi, S.; Soner, H.M.; Taskar, M., An asymptotic analysis of hierarchical control of manufacturing systems under uncertainty, Mathematics of operations research, 16, 596-608, (1991) · Zbl 0742.90037 |

[126] | Kenne, J.P.; Boukas, E.K., Hierarchical control of production and maintenance rates in manufacturing systems, Journal of quality in maintenance engineering, 9, 66-82, (2003) · Zbl 1048.90088 |

[127] | Sethi, S.P.; Zhang, Q., Hierarchical decision making in stochastic manufacturing systems, (1994), Birkhauser Boston, Cambridge, MA · Zbl 0923.90002 |

[128] | Sethi, S.P.; Yan, H.; Zhang, H.; Zhang, Q., Optimal and hierarchical controls in dynamic stochastic manufacturing systems: a survey, Manufacturing & service operations management, 4, 133-170, (2002) |

[129] | Samaratunga, C.; Sethi, S.P.; Zhou, X.Y., Computational evaluation of hierarchical production control policies for stochastic manufacturing systems, Operations research, 45, 258-274, (1997) · Zbl 0890.90087 |

[130] | Keerthi, S.S.; Gilbert, E.G., Optimal, infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations, Journal of optimization theory and application, 57, 265-293, (1998) · Zbl 0622.93044 |

[131] | Morari, M.; Lee, J.H., Model predictive control: past, present, and future, Computers and chemical engineering, 23, 667-682, (1999) |

[132] | Mayne, D.Q.; Rawlings, J.B.; Rao, C.V.; Scokaert, P.O.M., Constrained model predictive control: stability and optimality, Automatica, 36, 789-814, (2000) · Zbl 0949.93003 |

[133] | Modigliani, F.; Hohn, F.E., Production planning over time and the nature of the expectation and planning horizon, Econometrica, 23, 46-66, (1955) · Zbl 0064.39504 |

[134] | Charnes, A.; Cooper, W.W.; Mellon, B., A model for optimizing production by reference to cost surrogates, Econometrica, 23, 307-323, (1955) · Zbl 0064.39601 |

[135] | Johnson, S.M., Sequential production planning over time at minimum cost, Management science, 3, 435-437, (1957) · Zbl 0995.90530 |

[136] | Wagner, H.M.; Whitin, T.M., Dynamic version of the economic lot size model, Management science, 5, 89-96, (1958) · Zbl 0977.90500 |

[137] | Sethi, S.P.; Sorger, G., A theory of rolling horizon decision making, Annals of operations research, 29, 387-416, (1991) · Zbl 0732.93084 |

[138] | Chand, S.; Hsu, V.N.; Sethi, S., Forecast, solution, and rolling horizons in operations management problems: a classified bibliography, Manufacturing and service operations management, 4, 25-43, (2002) |

[139] | Kapsiotis, G.; Tzafestas, S., Decision making for inventory/production planning using model-based predictive control, (), 551-556 |

[140] | Tzafestas, S.; Kapsiotis, G.; Kyriannakis, E., Model-based predictive control for generalized production planning problems, Computers in industry, 34, 201-210, (1997) |

[141] | Perea Lopez, E.; Ydstie, B.E.; Grossmann, I., A model predictive control strategy for supply chain management, Computers & chemical engineering, 27, 1201-1218, (2003) |

[142] | Seferlis, P.; Giannelos, N.F., A two-layered optimization-based control strategy for multi-echelon supply chain networks, Computers & chemical engineering, 28, 799-809, (2004) |

[143] | Braun, M.W.; Rivera, D.E.; Flores, M.E.; Carlyle, W.M.; Kempf, K.G., A model predictive control framework for robust management of multi-product, multi-echelon demand networks, Annual reviews in control, 27, 229-245, (2003) |

[144] | Braun, M.W.; Rivera, D.E.; Carlyle, W.M.; Kempf, K.G., Application of model predictive control to robust management of multiechelon demand networks in semiconductor manufacturing, Simulation, 79, 139-156, (2003) |

[145] | Wang, W.; Rivera, D.E.; Kempf, K.G.; Smith, K.D., A model predictive control strategy for supply chain management in semiconductor manufacturing under uncertainty, (), 4577-4582 |

[146] | Wang, W.; Rivera, D.E.; Kempf, K.G., A novel model predictive control algorithm for supply chain management in semiconductor manufacturing, (), 208-213 |

[147] | Dunbar WB, Desa S. Distributed model predictive control for dynamic supply chain management. In: Proceedings of the international workshop on assessment and future directions of NMPC, Freudenstadt-Lauterbad, Germany, August, 2005. |

[148] | Dunbar, W.B.; Murray, R.M., Distributed receding horizon control with application to multi-vehicle formation stabilization, Automatica, 42, 549-558, (2006) · Zbl 1103.93031 |

[149] | Lin, P.H.; Jang, S.S.; Wong, D.S.H., Predictive control of a decentralized supply chain unit, Industrial engineering chemistry research, 44, 9120-9128, (2005) |

[150] | Yildirim, I.; Tan, B.; Karaesmen, F., A multiperiod stochastic production planning and sourcing problem with service level constraints, OR spektrum, 27, 471-489, (2005) · Zbl 1124.90317 |

[151] | Birge, J.R.; Louveaux, F., Introduction to stochastic programming. Springer series in operations research, (1997), Springer New York |

[152] | Bitran, G.R.; Haas, E.A.; Matsuo, H., Production planning of style goods with high setup costs and forecast revisions, Operations research, 34, 226-236, (1986) · Zbl 0606.90059 |

[153] | Zhou, K.; Doyle, J.; Glover, K., Robust and optimal control, (1995), Prentice-Hall Upper Saddle River, NJ |

[154] | Basar, T.; Bernhard, P., H-infinity optimal control and related minimax design problems: a dynamic game approach, (1995), Birkhäuser Boston, MA |

[155] | Dullerud, G.E.; Paganini, F., A course in robust control theory: a convex approach, (2000), Springer New York, NY · Zbl 0939.93001 |

[156] | Blanchini, F.; Rinaldi, F.; Ukovich, W., A network design problem for a distribution system with uncertain demands, SIAM journal on optimization, 7, 560-578, (1997) · Zbl 0878.90055 |

[157] | Blanchini, F.; Rinaldi, F.; Ukovich, W., Least inventory control of multistorage systems with non-stochastic unknown inputs, IEEE transactions on robotics and automation, 13, 633-645, (1997) |

[158] | Blanchini, F.; Pesenti, R.; Rinaldi, F.; Ukovich, W., Feedback control of production-distribution systems with unknown demand and delays, IEEE transactions on robotics and automation, 16, 313-317, (2000) |

[159] | Bertsekas, D.P.; Rhodes, I.B., On the minimax reachability of target sets and target tubes, Automatica, 7, 233-247, (1971) · Zbl 0215.21801 |

[160] | Bertsekas, D.P., Infinite-time reachability of state-space regions by using feedback control, IEEE transactions on automatic control, 17, 604-613, (1972) · Zbl 0264.93011 |

[161] | Blanchini, F.; Miani, S.; Ukovich, W., Control of production-distribution systems with unknown inputs and system failures, IEEE transactions on automatic control, 45, 1072-1081, (2000) · Zbl 0988.90013 |

[162] | Blanchini, F.; Miani, S.; Pesenti, R.; Rinaldi, F., Stabilization of multi-inventory systems with uncertain demand and setups, IEEE transactions on robotics and automation, 19, 103-116, (2003) |

[163] | Blanchini, F.; Miani, S.; Rinaldi, F., Guaranteed cost control for multi-inventory systems with uncertain demand, Automatica, 40, 213-223, (2004) · Zbl 1039.90002 |

[164] | Boukas, E.K.; Yang, H.; Zhang, Q., Minimax production planning in failure-prone manufacturing systems, Journal of optimization theory and applications, 82, 269-286, (1995) · Zbl 0839.90055 |

[165] | Boukas, K.E.; Shi, P.; Andijani, A., Robust inventory-production control problem with stochastic demand, Optimal control applications and methods, 20, 1-20, (1999) |

[166] | Boukas, E.K.; Shi, P.; Agarwal, R.K., An application of robust control technique to manufacturing systems with uncertain processing time, Optimal control applications and methods, 21, 257-268, (2000) · Zbl 1070.90513 |

[167] | Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004 |

[168] | Nesterov, Y.; Nemirovski, A., Interior point polynomial time algorithms, (1994), SIAM Philadelphia, PA · Zbl 0824.90112 |

[169] | Boukas, E.K.; Rodrigues, L., () |

[170] | Liberzon, D.; Morse, A.S., Basic problems in stability and design of switched systems, Control systems magazine, 19, 5, 59-70, (1999) · Zbl 1384.93064 |

[171] | Laumanns, M.; Lefeber, E., Robust optimal control of material flows in demand-driven supply networks, Physica A, 363, 24-31, (2006) |

[172] | Bemporad, A.; Borrelli, F.; Morari, M., Min – max control of constrained uncertain discrete-time linear systems, IEEE transactions on automatic control, 48, 1600-1606, (2003) · Zbl 1364.93181 |

[173] | Sutton, R.S.; Barto, A.G., Reinforcement learning, (1998), MIT Press Cambridge, MA |

[174] | Tesauro, G.J.; Gammon, T.D., A self-teaching backgammon program, achieves master-level play, Neural computation, 6, 215-219, (1998) |

[175] | Bertsekas, D.P.; Tsitsiklis, J.N., Neuro-dynamic programming, (1996), Athena Scientific Belmont, MA · Zbl 0924.68163 |

[176] | Van Roy, B.; Bertsekas, D.P.; Lee, Y.; Tsitsiklis, J.N., A neuro-dynamic programming approach to retailer inventory management. technical report, laboratory for information and decision systems, (1998), Massachusetts Institute of Technology Cambridge, MA |

[177] | Patrinos P, Sarimveis H. An RBF based neuro-dynamic approach for the control of stochastic dynamic systems. In: Proceedings of the 16th IFAC world congress, Prague, Czech Republic, 2005. |

[178] | Nedic, A.; Bertsekas, D.P., Least squares policy evaluation algorithms with linear function approximation, Discrete event dynamic systems: theory and applications, 13, 79-110, (2003) · Zbl 1030.93061 |

[179] | Powell, W.B.; Van Roy, B., Approximate dynamic programming for high dimensional resource allocation problems, () |

[180] | Powell WB, George A, Bouzaiene-Ayari B, Simao H. Approximate dynamic programming for high dimensional resource allocation problems. In: Proceedings of the IJCNN, Montreal, August 2005. |

[181] | Topaloglu, H.; Powell, W.B., Dynamic programming approximations for stochastic, time-staged integer multicommodity flow problems, Informs journal on computing, 18, 31-42, (2006) · Zbl 1241.90172 |

[182] | Kushner, H.J.; Yin, G.G., Stochastic approximation algorithms and applications, (1997), Springer New York · Zbl 0914.60006 |

[183] | Powell, W.B.; Ruszczynski, A.; Topaloglu, H., Learning algorithms for separable approximations of stochastic optimization problems, Mathematics of operations research, 29, 814-836, (2004) · Zbl 1082.90079 |

[184] | Powell WB. Approximate dynamic programming for operations research. Available for download at \(\langle\)http://www.castlelab.princeton.edu/Papers.html⟩; 2006. |

[185] | Bauso D, Giarre L, Pesenti R. Neurodynamic programming for cooperative inventory control. In: 2004 American control conference, June 30-July 2, Boston, MA, USA, 2004. p. 5527-32. |

[186] | Bauso, D.; Giarre, L.; Pesenti, R., Cooperative inventory control, () · Zbl 1367.90004 |

[187] | Olfati Saber R, Murray RM. Consensus protocols for networks of dynamic agents. In: Proceedings of American control conference, vol. 2, Denver, Colorado, 2003. p. 951-6. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.