Multiple-Square-Root Minimization Problem
Abstract: The Multiple-Square-Root Minimization Problem (MSR) has an objective function that consists of a sum of a linear term and at least two square root terms. The Lagrangian sub-problem for the LMRP is a typical MSR problem and there are other MSR problems in real life. A simple example is that we add other concave costs besides the safety stock cost to the LMRP, such as the labor cost and even minimize the negation of the revenue. We tested a sort of heuristic involved, similar to the method to solve the problem of the LMRP vibrational days, and we explore the heuristic is probably the most optimal condition. The accuracy of this approach is declining at a slow rate, because the number of square roots is increasing, and when the number is not too large, it stays at a higher level.
Cite this paper: Zhang, X. , Tian, X. , Wang, C. and Li, T. (2017) Multiple-Square-Root Minimization Problem. American Journal of Industrial and Business Management, 7, 927-943. doi: 10.4236/ajibm.2017.77066.
References

[1]   Daskin, M.S. (1982) Application of an Expected Covering Model to Emergency Medical Service System Design. Decision Sciences, 13, 416-439.
https://doi.org/10.1111/j.1540-5915.1982.tb00159.x

[2]   Daskin, M.S. (1983) A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution. Transportation Science, 17, 48-70.
https://doi.org/10.1287/trsc.17.1.48

[3]   Daskin, M.S., Coullard, C.R. and Shen, Z.-J.M. (2002) An Inventory-Location Model Formulation, Solution Algorithm and Computational Results. Annals of Operations Research, 110, 83-106.
https://doi.org/10.1023/A:1020763400324

[4]   Ozsen, L., Coullard, C.R. and Daskin, M.S. (2008) Capacitated Warehouse Location Odel with Risk Pooling. Naval Research Logistics, 55, 295-312.
https://doi.org/10.1002/nav.20282

[5]   Shen, Z.-J.M. (2007) Integrated Supply Chain Design Models: A Survey and Future Research Directions. Journal of Industrial and Management Optimization, 3.
https://doi.org/10.3934/jimo.2007.3.1

[6]   Shen, Z.-J.M., Coullard, C.R. and Daskin, M.S. (2003) A Joint Location-Inventory Model. Transportation Science, 37, 40-50.
https://doi.org/10.1287/trsc.37.1.40.12823

[7]   Shu, J., Teo, C.-P. and Shen, Z.-J.M. (2005) Stochastic Transportation-Inventory Net-Work Design Problem. Operations Research, 53, 48-60.
https://doi.org/10.1287/opre.1040.0140

[8]   Snyder, L.V., Daskin, M.S. and Teo, C.-P. (2007) The Stochastic Location Model with Risk Pooling. European Journal of Operational Research, 179, 1221-1238.
https://doi.org/10.1016/j.ejor.2005.03.076

Top