Optimal design of multi-echelon supply chain networks under normally distributed demand.

*(English)*Zbl 1314.90085Summary: This paper addresses the optimal design of a multiproduct, multi-echelon supply network under uncertainty of demand. The network consists of multiproduct production sites, warehouses and distribution centers and decisions about the selection of facilities and their capacity are taken. Furthermore, information about the flows of products transferred and the safety stock at each distribution center is derived. The lead time of an order to a customer is computed, using the probabilities of overstocking and understocking. All these decisions are incorporated into a single period mixed integer non-linear programming problem (MINLP) which minimizes cost. Linearization techniques for selected highly non-linear terms of the models are explored in order to reduce the computational effort for the solution of the model. Finally, a sensitivity analysis is performed by changing product demand parameters and assessing their effect on the supply chain structure.

##### MSC:

90C35 | Programming involving graphs or networks |

90C15 | Stochastic programming |

90B05 | Inventory, storage, reservoirs |

Full Text:
DOI

##### References:

[1] | Axsäter, S., Using the deterministic EOQ formula in stochastic inventory control, Management Science, 42, 830-834, (1996) · Zbl 0880.90030 |

[2] | Bassett, M.; Gardner, A., Designing optimal global supply chains at dow agrosciences, Annals of Operations Research, (2012) · Zbl 1269.90018 |

[3] | Baud-Lavigne, B.; Agard, B.; Penz, B., Mutual impacts of product standardization and supply chain design, International Journal of Production Economics, 153, 50-60, (2012) |

[4] | Beamon, B. M., Measuring supply chain performance, International Journal of Operations & Production Management, 19, 275-292, (1999) |

[5] | Brook, A.; Kendrick, D.; Meeraus, A., GAMS, a user’s guide, SIGNUM Newsletter, 23, 10-11, (1988) |

[6] | Chaabane, A.; Ramudhin, A.; Paquet, M., Design of sustainable supply chains under the emission trading scheme, International Journal of Production Economics, 135, 37-49, (2012) |

[7] | Cachon, G. P.; Fisher, M., Supply chain inventory management and the value of shared information, Management Science, 46, 1032-1048, (2000) · Zbl 1232.90028 |

[8] | Cachon, G. P.; Zipkin, P. H., Competitive and cooperative inventory policies in a two-stage supply chain, Management Science, 45, 936-953, (1999) · Zbl 1231.90013 |

[9] | Charnes, A.; Cooper, W. W., Deterministic equivalents for optimizing and satisficing under chance constraints, Operations Research, 11, 18-39, (1963) · Zbl 0117.15403 |

[10] | Chen, C. L.; Lee, W. C., Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices, Computers & Chemical Engineering, 28, 1131-1144, (2004) |

[11] | Chen, C. W.; Fan, Y., Bioethanol supply chain system planning under supply and demand uncertainties, Transportation Research. Part E, Logistics and Transportation Review, 48, 150-164, (2012) |

[12] | Chen, Y.; Mockus, L.; Orcun, S.; Reklaitis, G. V., Simulation optimization approach to clinical trial supply chain management with demand scenario forecast, Computers & Chemical Engineering, 40, 82-96, (2012) |

[13] | Christopher, M., The agile supply chain: competing in volatile markets, Industrial Marketing Management, 29, 37-44, (2000) |

[14] | Daskin, M. S.; Coullard, C. R.; Shen, Z. J., An inventory-location model: formulation, solution algorithm and computational results, Annals of Operations Research, 110, 83-106, (2002) · Zbl 1013.90001 |

[15] | Diabat, A.; Richard, J. P.; Codrington, C., A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design, Annals of Operations Research, (2011) · Zbl 1269.90053 |

[16] | Duclos, L. K.; Vokurka, R. J.; Lummus, R. R., A conceptual model of supply chain flexibility, Industrial Management & Data Systems, 103, 446-456, (2003) |

[17] | Duran, M. A.; Grossmann, I. E., An outer approximation algorithm for a class of mixed integer nonlinear programs, Mathematical Programming, 36, 307, (1986) · Zbl 0619.90052 |

[18] | Federgruen, A.; Graves, S. C. (ed.); Rinnooy Kan, A. H. G. (ed.); Zipkin, P. H. (ed.), Centralized planning models for multi-echelon inventory systems under uncertainty, 133-173, (1993), Amsterdam |

[19] | Ganeshan, R., Managing supply chain inventories: a multiple retailer, one warehouse, multiple supplier model, International Journal of Production Economics, 59, 341-354, (1999) |

[20] | Georgiadis, M. C.; Tsiakis, P.; Longinidis, P.; Sofioglou, M. K., Optimal design of supply chain networks under uncertain transient demand variations, Omega, 39, 254-272, (2011) |

[21] | Glover, F., Improved linear integer programming formulations of nonlinear integer problems, Management Science, 22, 455-460, (1975) · Zbl 0318.90044 |

[22] | Graves, S. C.; Tomlin, B. T., Process flexibility in supply chains, Management Science, 49, 907-919, (2003) · Zbl 1232.90183 |

[23] | Grossmann, I. E., Viswanathan, J., Vecchietti, A., Raman, R., & Kalvelagen, E. (2002). GAMS/DICOPT: a discrete continuous optimization package. GAMS Development Corporation, Washington, DC. · Zbl 1232.90183 |

[24] | Gruen, T.; Corsten, D., Stock outs cause walkouts, Harvard Business Review, 82, 26-27, (2004) |

[25] | Handfield, R. B.; Bechtel, C., The role of trust and relationship structure in improving supply chain responsiveness, Industrial Marketing Management, 31, 367-382, (2002) |

[26] | 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 |

[27] | Lee, Y. H.; Kim, S. H., Production-distribution planning in supply chain considering capacity constraints, Computers & Industrial Engineering, 43, 169-190, (2002) |

[28] | Liu, S.; Papageorgiou, L. G., Multiobjective optimisation of production, distribution and capacity planning of global supply chains in the process industry, Omega, 41, 369-382, (2013) |

[29] | Lummus, R. R.; Vokurka, R. J.; Duclos, L. K., Delphi study on supply chain flexibility, International Journal of Production Research, 43, 2687-2708, (2005) |

[30] | Martin, M. J. C. (1994). Managing innovation and entrepreneurship in technology-based firms. New York: Wiley-Interscience. |

[31] | Miranda, P. A.; Garrido, R. A., Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand, Transportation Research. Part E, Logistics and Transportation Review, 40, 183-207, (2004) |

[32] | Nagurney, A.; Masoumi, A. H.; Yu, M., Supply chain network operations management of a blood banking system with cost and risk minimization, Computational Management Science, 9, 205-231, (2012) · Zbl 1273.90028 |

[33] | Olivares-Benitez, E.; González-Velarde, J. L.; Ríos-Mercado, R. Z., A supply chain design problem with facility location and bi-objective transportation choices, TOP, 20, 729-753, (2012) · Zbl 1262.90005 |

[34] | Özekici, S.; Parlar, M., Inventory models with unreliable suppliers in a random environment, Annals of Operations Research, 91, 123-136, (1999) · Zbl 0970.90005 |

[35] | Pan, F.; Nagi, R., Robust supply chain design under uncertain demand in agile manufacturing, Computers & Operations Research, 37, 668-683, (2010) · Zbl 1175.90049 |

[36] | Petkov, S. B.; Maranas, C. D., Design of single-product campaign batch plants under demand uncertainty, AIChE Journal, 44, 896-911, (1998) |

[37] | Prater, E.; Biehl, M.; Smith, M. A., International supply chain agility—tradeoffs between flexibility and uncertainty, International Journal of Operations & Production Management, 21, 823-839, (2001) |

[38] | Ramezani, M.; Bashiri, M.; Tavakkoli-Moghaddam, R., A new multi-objective stochastic model for a forward/reverse logistic network design with responsiveness and quality level, Applied Mathematical Modeling, 37, 328-344, (2013) · Zbl 1349.90123 |

[39] | Schmitt, A. J.; Singh, M., A quantitative analysis of disruption risk in a multi-echelon supply chain, International Journal of Production Economics, 139, 22-32, (2012) |

[40] | Shen, Z. J. M.; Coullard, C.; Daskin, M. S., A joint location-inventory model, Transportation Science, 37, 40-55, (2003) |

[41] | Tsiakis, P.; Papageorgiou, L. G., Optimal production allocation and distribution supply chain networks, International Journal of Production Economics, 111, 468-483, (2008) |

[42] | Tsiakis, P.; Shah, N.; Pantelides, C. C., Design of multi-echelon supply chain networks under demand uncertainty, Industrial & Engineering Chemistry Research, 40, 3585-3604, (2001) |

[43] | Uskonen, J.; Tenhiälä, A., The price of responsiveness: cost analysis of change orders in make-to-order manufacturing, International Journal of Production Economics, 135, 420-429, (2012) |

[44] | Xanthopoulos, A.; Vlachos, D.; Iakovou, E., Optimal newsvendor policies for dual-sourcing supply chains: a disruption risk management framework, Computers & Operations Research, 39, 350-357, (2012) · Zbl 1251.90042 |

[45] | You, F.; Grossmann, I. E., Mixed-integer nonlinear programming models and algorithms for large-scale supply chain design with stochastic inventory management, Industrial & Engineering Chemistry Research, 47, 7802-7817, (2008) |

[46] | You, F.; Grossmann, I. E., Design of responsive supply chains under demand uncertainty, Computers & Chemical Engineering, 32, 3090-3111, (2008) |

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.