##
**Supply chain design considering economies of scale and transport frequencies.**
*(English)*
Zbl 1244.90030

Summary: We consider a 3-echelon, multi-product supply chain design model with economies of scale in transport and warehousing that explicitly takes transport frequencies into consideration. Our model simultaneously optimizes locations and sizes of tank farms, material flows, and transport frequencies within the network. We consider all relevant costs: product cost, transport cost, tank rental cost, tank throughput cost, and inventory cost. The problem is based on a real-life example from a chemical company. We show that considering economies of scale and transport frequencies in the design stage is crucial and failing to do so can lead to substantially higher costs than optimal. We solve a wide variety of problems with branch-and-bound and with the efficient solution heuristics based on iterative linearization techniques we develop. We show that the heuristics are superior to the standard branch-and-bound technique for large problems like the one of the chemical company that motivated our research.

### MSC:

90B06 | Transportation, logistics and supply chain management |

90B05 | Inventory, storage, reservoirs |

90C59 | Approximation methods and heuristics in mathematical programming |

PDF
BibTeX
XML
Cite

\textit{K. Baumgartner} et al., Eur. J. Oper. Res. 218, No. 3, 789--800 (2012; Zbl 1244.90030)

Full Text:
DOI

### References:

[1] | Balakrishnan, A.; Graves, S.C., A composite algorithm for a concave-cost network flow problem, Networks, 19, 175-202, (1989) · Zbl 0673.90034 |

[2] | BASF, 2007. Company website - News and Media Relations. <http://corporate.basf.com/de/presse/?id=WGK-HBY8Wbcp*xP> (accessed 15.03.08). |

[3] | Baumol, W.J.; Wolfe, P., A warehouse-location problem, Operations research, 6, 252-263, (1958) · Zbl 1414.90190 |

[4] | Baxter, J., Depot location: A technique for the avoidance of local optima, European journal of operational research, 18, 208-214, (1984) |

[5] | Bayer, 2007. Bayer will Kapazität der geplanten TDI-Produktion in Shanghai auf 300.000 Jahrestonnen erweitern (February 6, 2007). <http://www.investor.bayer.de/de/news/investor-news/investor-news/showNewsItem/738/1170745507/5dc1abb86f/> (accessed 15.03.08). |

[6] | Broek, J.; Schütz, P.; Stougie, L.; Tomasgard, A., Location of slaughterhouses under economies of scale, European journal of operational research, 175, 740-750, (2006) · Zbl 1142.90441 |

[7] | Correia, I.; Captivo, M.E., A Lagrangian heuristic for a modular capacitated location problem, Annals of operations research, 122, 141-161, (2003) · Zbl 1039.90024 |

[8] | Drysdale, J.K.; Sandiford, P.J., Heuristic warehouse location - A case history using a new method, Infor, 7, 45-61, (1969) |

[9] | Efroymson, M.A.; Ray, T.L., A branch-bound algorithm for plant location, Operations research, 14, 361-368, (1966) |

[10] | Feldman, E.; Lehrer, F.A.; Ray, T.L., Warehouse location under continuous economies of scale, Management science, 12, 670-684, (1966) |

[11] | Fleischmann, B., Designing distribution systems with transport economies of scale, European journal of operational research, 70, 31-42, (1993) · Zbl 0800.90398 |

[12] | Geoffrion, A.M., Objective function approximations in mathematical programming, Mathematical programming, 13, 23-37, (1977) · Zbl 0356.90062 |

[13] | Gümüs, M.; Bookbinder, J.H., Cross-docking and its implications in location-distribution systems, Journal of business logistics, 25, 199-228, (2004) |

[14] | Holmberg, K. 1984. Capacitated facility location with staircase costs. Research Report LiTH-MAT-R-1984-26, Department of Mathematics, Linkoping Institute of Technology, Sweden. |

[15] | Holmberg, K., Solving the staircase cost facility location problem with decomposition and piecewise linearization, European journal of operational research, 75, 41-61, (1994) · Zbl 0809.90093 |

[16] | Holmberg, K.; Ling, J., A Lagrangean heuristic for the facility location problem with staircase costs, European journal of operational research, 97, 63-74, (1997) · Zbl 0923.90104 |

[17] | Kelly, D.L.; Khumawala, B.M., Capacitated warehouse location with concave costs, The journal of the operational research society, 33, 817-826, (1982) · Zbl 0489.90039 |

[18] | Khumawala, B.M.; Kelly, D.L., Warehouse location with concave costs, Infor, 12, 55-65, (1974) |

[19] | Kim, D.; Pardalos, P.M., Dynamic slope scaling and trust interval techniques for solving concave piecewise linear network flow problems, Networks, 35, 216-222, (2000) · Zbl 0963.90011 |

[20] | Kim, D.; Pardalos, P.M., A dynamic domain contraction algorithm for nonconvex piecewise linear network flow problems, Journal of global optimization, 17, 225-234, (2000) · Zbl 0988.90002 |

[21] | Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P., Optimization by simulated annealing, Science, 220, 671-680, (1983) · Zbl 1225.90162 |

[22] | Klincewicz, J.G., A large-scale distribution and location model, AT&T technical journal, 64, 1705-1730, (1985) |

[23] | Klincewicz, J.G., Solving a freight transport problem using facility location techniques, Operations research, 38, 99-109, (1990) · Zbl 0715.90044 |

[24] | Klincewicz, J.G., Enumeration and search procedures for a hub location problem with economies of scale, Annals of operations research, 110, 107-122, (2002) · Zbl 1013.90078 |

[25] | Klincewicz, J.G.; Luss, H.; Yu, C.S., A large-scale multilocation capacity planning model, European journal of operational research, 34, 178-190, (1988) · Zbl 0642.90037 |

[26] | Lapierre, S.D.; Ruiz, A.B.; Soriano, P., Designing distribution networks: formulations and solution heuristics, Transportation science, 38, 174-187, (2004) |

[27] | Lin, J.R.; Nozick, L.K.; Turnquist, M.A., Strategic design of distribution systems with economies of scale in transportation, Annals of operations research, 144, 161-180, (2006) · Zbl 1146.90333 |

[28] | O’Kelley, M.E.; Bryan, D.L., Hub location with flow economies of scale, Transportation research part B, 8, 605-616, (1998) |

[29] | Paraschis, I.N., Optimale gestaltung von mehrprodukt-distributionssystemen: modelle – methoden – anwendungen, (1989), Physica-Verlag Heidelberg |

[30] | Romeijin, H.E.; Shu, J.; Teo, C.P., Designing two-echelon supply networks, European journal of operational research, 178, 449-462, (2007) · Zbl 1107.90006 |

[31] | SABIC, 2006. Annual Report 2006. |

[32] | SABIC, 2007. Company website - News and Media Relations. <http://www.sabic.com/corporate/en/newsandmediarelations/news/default.aspx> (accessed 15.03.08). |

[33] | Soland, R.M., Optimal facility location with concave costs, Operations research, 22, 373-382, (1974) · Zbl 0278.90079 |

[34] | Spielberg, K., An algorithm for the simple plant location problem with some side conditions, Operations research, 17, 85-111, (1969) · Zbl 0165.54104 |

[35] | Spielberg, K., Plant location with generalized search origin, Management science, 16, 165-178, (1969) |

[36] | Syam, S.S., A model and methodologies for the location problem with logistical components, Computers and operations research, 29, 1173-1193, (2002) · Zbl 0994.90089 |

[37] | Whitaker, R.A., Some add-drop and drop-add interchange heuristics for non-linear warehouse location, Journal of the operational research society, 36, 61-70, (1985) · Zbl 0557.90024 |

[38] | Zangwill, W.I., Minimum concave cost flows in certain networks, Management science, 14, 429-450, (1968) · Zbl 0159.49102 |

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.