Economic model predictive inventory routing and control.

*(English)*Zbl 1397.90034Summary: The paper proposes an economic model predictive control (EMPC) strategy for the inventory routing problem under demand uncertainty. The strategy is illustrated using an application on industrial gas distribution systems, where the product is transported to customers in small tanks and the inventory levels at the customers’ sites are monitored and controlled by the supplier following a vendor managed inventory approach. The objective is to produce balanced decisions for the joint routing and the inventory control problem over the planning horizon with respect to the decision maker’s perspective against stock-out risk. The proposed EMPC strategy makes use of a mixed integer mathematical programming optimization model that describes the deterministic inventory routing problem with simultaneous pickups and deliveries over a specific planning horizon. A time series decomposition forecasting model is used for predicting future demand and an exact linearization of the quadratic term of the objective function guarantees optimality of the solutions. The proposed methodology is illustrated using two examples featuring a single distribution centre, and three customers with simple and complex demand profiles. It is shown that EMPC offers a useful tool for producing balanced decisions between transportation and inventory costs and tracking of the safety inventory levels.

##### MSC:

90B05 | Inventory, storage, reservoirs |

90B06 | Transportation, logistics and supply chain management |

90C11 | Mixed integer programming |

##### Keywords:

inventory routing; industrial gas distribution; mathematical modelling; inventory control; mixed integer programming; economic model predictive control
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\textit{A. Nikolakopoulos} and \textit{I. Ganas}, CEJOR, Cent. Eur. J. Oper. Res. 25, No. 3, 587--609 (2017; Zbl 1397.90034)

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##### References:

[1] | Agrawal, S; Singh, RK; Murtaza, Q, A literature review and perspectives in reverse logistics, Resour Conserv Recycl, 97, 76-92, (2015) |

[2] | Ammouri, F; Macron, J, Estimation of the quantity of product within cryogenic storage vessels, Chem Eng Res Des, 89, 2003-2011, (2011) |

[3] | Amrit, R; Rawlings, JB; Angeli, D, Economic optimization using model predictive control with a terminal cost, Annu Rev Control, 35, 178-186, (2011) |

[4] | Applegate DL, Bixby RE, Chvátal V, Cook WJ (2011) The traveling salesman problem: a computational study. Princeton University Press, Princeton |

[5] | Archetti, C; Bertazzi, L; Hertz, A; Grazia Speranza, M, A hybrid heuristic for an inventory routing problem, INFORMS J Comput, 24, 101-116, (2012) · Zbl 06599258 |

[6] | Archetti, C; Bertazzi, L; Laporte, G; Speranza, MG, A branch-and-cut algorithm for a vendor-managed inventory-routing problem, Transp Sci, 41, 382-391, (2007) |

[7] | Axsater, S, Control theory concepts in production and inventory control, Int J Syst Sci, 16, 161-169, (1985) · Zbl 0557.90043 |

[8] | Berbeglia, G; Cordeau, JF; Laporte, G, Dynamic pickup and delivery problems, Eur J Oper Res, 202, 8-15, (2010) · Zbl 1176.90048 |

[9] | Bertazzi L, Speranza M (2011) Matheuristics for inventory routing problems. In: Montoya-Torres JR, Juan AA, Huatuco LH, Faulin J, Rodriguez-Verjan GL (eds) Hybrid algorithms for service, computing and manufacturing systems: routing and scheduling solutions. IGI Global, Hershey, pp 1-336. doi:10.4018/978-1-61350-086-6.ch001 |

[10] | Bertazzi, L; Speranza, M, Inventory routing problems: an introduction, EURO J Transp Logist, 1, 307-326, (2012) |

[11] | Bertazzi L, Savelsbergh M, Speranza MG (2008) Inventory routing. In: Hybrid algorithms for service, computing and manufacturing systems. Routing and scheduling solutions, pp 49-72 · Zbl 1187.90039 |

[12] | Braun, MW; Rivera, DE; Flores, ME; etal., A model predictive control framework for robust management of multi-product, multi-echelon demand networks, Annu Rev Control, 27, 229-245, (2003) |

[13] | Burbidge JL (1991) Period batch control (PBC) with GT—the way forward from MRP. In: Proceedings of the BPCIS annual conference, Birmingham |

[14] | Camacho EF, Bordons C (2007) Model predictive control. Springer, London |

[15] | Coelho, LC; Laporte, G, The exact solution of several classes of inventory-routing problems, Comput Oper Res, 40, 558-565, (2013) · Zbl 1349.90016 |

[16] | Coelho, LC; Laporte, G, Improved solutions for inventory-routing problems through valid inequalities and input ordering, Int J Prod Econ, 155, 391-397, (2014) |

[17] | Coelho, LC; Cordeau, JF; Laporte, G, Consistency in multi-vehicle inventory-routing, Transp Res Part C Emerg Technol, (2012) |

[18] | Coelho, LC; Cordeau, JF; Laporte, G, Thirty years of inventory routing, Transp Sci, 48, 1-19, (2014) |

[19] | Coelho, LC; Cordeau, JF; Laporte, G, Heuristics for dynamic and stochastic inventory-routing, Comput Oper Res, 52, 55-67, (2014) · Zbl 1348.90024 |

[20] | Disney, SM; Towill, DR, Vendor-managed inventory and bullwhip reduction in a two-level supply chain, Int J Oper Prod Manag, 23, 625-651, (2003) |

[21] | Dong, Y; Pinto, JM; Sundaramoorthy, A; Maravelias, CT, MIP model for inventory routing in industrial gases supply chain, Ind Eng Chem Res, 53, 17214-17225, (2014) |

[22] | Dunbar WB, Desa S (2007) Distributed model predictive control for dynamic supply chain management. In: Findeisen R, Allgöwer F, Biegler L (eds) Assessment and future directions of nonlinear model predictive control. Springer, Germany. doi:10.5424/fs/2015243-08148 |

[23] | Edghill, J; Towill, D, The use of system dynamics in manufacturing systems engineering, Trans Inst Meas Control, 11, 208-216, (1989) |

[24] | Ellis, M; Durand, H; Christofides, PD, A tutorial review of economic model predictive control methods, J Process Control, 24, 1156-1178, (2014) |

[25] | Federgruen A, Simchi-Levi D (1995) Chapter 4 analysis of vehicle routing and inventory-routing problems. In: Handbooks in operations research and management science. pp 297-373 · Zbl 0870.90057 |

[26] | Fu, D; Ionescu, CM; Aghezzaf, E-H; Keyser, R, Decentralized and centralized model predictive control to reduce the bullwhip effect in supply chain management, Comput Ind Eng, 73, 21-31, (2014) |

[27] | Govindan, K, Vendor-managed inventory: a review based on dimensions, Int J Prod Res, 51, 3808-3835, (2013) |

[28] | Houlihan, JB, International supply chain management, Int J Phys Distrib Mater Manag, 17, 51-66, (1987) |

[29] | Hyndman RJ, Koehler AB, Ord JK, Snyder RD (2008) Forecasting with exponential smoothing?: The state space approach. Springer, Berlin |

[30] | Kleywegt, AJ; Non, VS; Savelsbergh, MWP, Dynamic programming approximations for a stochastic inventory routing problem, Transp Sci, 38, 42-70, (2004) |

[31] | Laporte, G, Fifty years of vehicle routing, Transp Sci, 43, 408-416, (2009) |

[32] | Lee, HL; Padmanabhan, V; Whang, S, Information distortion in a supply chain: the bullwhip effect, Manag Sci, 50, 1875-1886, (2004) |

[33] | Maestre JM, Muñoz De La Peña D, Camacho EF (2009) Distributed MPC: a supply chain case study. In: Proceedings of the IEEE conference on decision and control. pp 7099-7104 |

[34] | Maestre, JM; Muñoz De La Peña, D; Camacho, EF, Distributed model predictive control based on a cooperative game, Optim Control Appl Methods, 32, 153-176, (2011) · Zbl 1225.93045 |

[35] | Mestan, E; Türkay, M; Arkun, Y, Optimization of operations in supply chain systems using hybrid systems approach and model predictive control, Ind Eng Chem Res, 45, 6493-6503, (2006) |

[36] | Miranbeigi, M; Moshiri, B; Rahimi-Kian, A, Decentralized manufacturing management by a multi-agent optimal control method, Trans Inst Meas Control, 36, 935-945, (2014) |

[37] | Miranbeigi, M; Moshiri, B; Rahimi-Kian, A; Razmi, J, Demand satisfaction in supply chain management system using a full online optimal control method, Int J Adv Manuf Technol, 77, 1401-1417, (2015) |

[38] | Moin, NH; Salhi, S, Inventory routing problems: a logistical overview, J Oper Res Soc, 58, 1185-1194, (2007) · Zbl 1192.90012 |

[39] | Montgomery DC, Johnson LA, Gradiner JS (1990) Forecasting and time series analysis. McGraw-Hill, New York |

[40] | Nikolakopoulos A (2015) A metaheuristic reconstruction algorithm for solving bi-level vehicle routing problems with backhauls for army rapid fielding. Oper Res Comput Sci Interfaces Ser 56:141-157. doi:10.1007/978-3-319-12075-1_8 |

[41] | Ortega, M; Lin, L, Control theory applications to the production-inventory problem: a review, Int J Prod Res, 42, 2303-2322, (2004) · Zbl 1060.90011 |

[42] | Perea-López, E; Ydstie, BE; Grossmann, IE, A model predictive control strategy for supply chain optimization, Comput Chem Eng, 27, 1201-1218, (2003) |

[43] | Rawlings JB, Amrit R (2009) Optimizing process economic performance using model predictive control. In: Nonlinear model predictive control. Lecture notes in control and information sciences, Springer, pp 119-138 · Zbl 1195.93023 |

[44] | Rawlings JB, Mayne DQ, Section OI, Offset Z (2012) Getting Started with model predictive control. Postface to “ Model Predict Control Theory Des ” Chapter 1 |

[45] | Sarimveis, H; Patrinos, P; Tarantilis, CD; Kiranoudis, CT, Dynamic modeling and control of supply chain systems: a review, Comput Oper Res, 35, 3530-3561, (2008) · Zbl 1146.90353 |

[46] | Seferlis, P; Giannelos, NF, A two-layered optimisation-based control strategy for multi-echelon supply chain networks, Comput Chem Eng, 28, 799-809, (2004) |

[47] | Singh, RK, Analyzing the factors for VMI implementation: a framework, Glob Bus Rev, 14, 169-186, (2013) |

[48] | Solyali, O; Cordeau, JF; Laporte, G, Robust inventory routing under demand uncertainty, Transp Sci, 46, 327-340, (2012) |

[49] | Stadtler, H, Supply chain management and advanced planning—basics, overview and challenges, Eur J Oper Res, 163, 575-588, (2005) · Zbl 1071.90006 |

[50] | Subramanian, K; Rawlings, JB; Maravelias, CT; etal., Integration of control theory and scheduling methods for supply chain management, Comput Chem Eng, 51, 4-20, (2013) |

[51] | Subramanian, K; Rawlings, JB; Maravelias, CT, Economic model predictive control for inventory management in supply chains, Comput Chem Eng, 64, 71-80, (2014) |

[52] | You, F; Pinto, JM; Capón, E; Grossmann, IE; Arora, N; Megan, L, Optimal distribution-inventory planning of industrial gases. I. fast computational strategies for large-scale problems, Ind Eng Chem Res, 50, 2910-2927, (2011) |

[53] | You, F; Pinto, JM; Grossmann, IE; Megan, L, Optimal distribution-inventory planning of industrial gases. II. MINLP models and algorithms for stochastic cases, Ind Eng Chem Res, 50, 2928-2945, (2011) |

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.