Dynamics in Logistics pp 327-336 | Cite as

# A Multi-Level Programming Model and Solution Algorithm for the Location of Distribution Centers with Uncertainty Demand

## Abstract

The tri-level programming model is presented to seek the optimal location for distribution centers. The objective of top level model is to determine the optimal location by minimizing the total logistic cost which consists of the fixed operating cost to open distribution centers, the penalty cost and the transportation cost. The middle level model gives an equilibrium demand distribution center by maximizing the total customer demand (in %) that can be delivered on time and to maximize customer satisfaction in the bottom level model. The proposed algorithm is applied to solve this model to obtain the optimal solution. Finally, the tri-level programming model and its algorithm are demonstrated by a numerical example.

### Keywords

Multi-level programming Optimization model Location problem Distribution network## Notes

### Acknowledgments

This research is supported by the Center of Excellence in Mathematics (CEM), Faculty of Science at Mahidol University, Phayathai Campus, Ratchathewi, Bangkok 10400.

### References

- Afshari H, Amin-Nayeri M, Jaafari A (2010) A multi-objective approach for multi-commodity location within distribution network design problem. In: Proceeding of the international conference of engineers and computer scientists, Hong Kong, 17–19 Mar 2010Google Scholar
- Aryanezhad MB, Roghanian E (2008) A bi-level linear multi-objective decision making model with interval coefficients for supply chain coordination. Int Eng Spec Issue 19(1–2):6–74Google Scholar
- Chen Z, Zhang D, Li S (2007) An optimization model and its solution algorithm for distribution network design problem with uncertainty demand. In: Proceeding of the IEEE international conference on automation and logistics, Jinan, China, pp 2170–2175, 18–21 Aug 2007Google Scholar
- Lasunon P, Remsungnen T, Akararungruangkul R (2011) A stochastic tri-level programming model to minimize total cost in a supply chain planning with uncertainty demand. In: Proceeding of 2nd international conference on logistics and transport, Queenstown, New Zealand, pp 693–701, 16–18 Dec 2011Google Scholar
- Lasunon P, Wetweerapong J, Remsungnen T (2011) A new algorithm for solving bi-level linear programming problems. In: Proceeding of 16th annual meeting in mathematics, Khon Kaen, Thailand, 10–11 Mar 2011Google Scholar
- Roghanian E, Sadjadi SJ, Aryanezhad MB (2007) A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl Math Comput 188:786–800Google Scholar
- Shun HJ, Gao ZY (2003) Bi-level programming optimization model for distribution systems in supply chain. J Manage Sci Chin 6(2):66–70Google Scholar
- Sun H, Gao Z, Wu J (2008) A bi-level programming model and solution algorithm for the location of logistics distribution centers. Appl Math Model 32:610–616MathSciNetMATHCrossRefGoogle Scholar
- Zhang G, Jie L, Montero J, Zen Y (2010) Model, solution concept, and K
^{th}-best algorithm for linear tri-level programming. Inf Sci 180:418–492Google Scholar