Optimal mathematical programming for the warehouse location problem with Euclidean distance linearization

Abstract The warehouse location problem (WLP) involves determining one (or multiple) locations as the materials/products collecting/distributing centers for serving a group of customers scattered geographically in a region, at a minimum total transportation cost. The most conventional and widely used approach for solving the WLP is the weighted k-means algorithm. However, this is not a global approach, because it always traps into local optima and is sensitive to the initial settings. Our numeric examples demonstrated that the solutions obtained by the weighted k-means could depart from the optimal values by as much as 16.8% on average. In this paper, we present an optimal programming approach based on mixed-integer linear programming (MILP) for the WLP, which is irrelative to the initial solution and can be optimally solved by commercial solvers. For large-sized datasets, we developed an MILP-based dynamic iterative partial optimization (MILP-DIPO) to search for the near-optimal results with controllable computational time. Experiments on 14 datasets, including 6 small-sized synthesized datasets and 8 variants of the known benchmark datasets in the UEF repository, were performed to validate the proposed model and heuristics. The computational results confirm that improvements with the proposed method could be as great as –22.9% (−14.0% on average) for small-sized datasets. For the eight benchmark datasets, the MILP-DIPO algorithm delivered near-optimal solutions in a reasonable computational time, with up to −8.0% (−2.6% on average) improvement compared to the results obtained by the conventional weighted k-means algorithm.

[1]  J. Krarup,et al.  The simple plant location problem: Survey and synthesis , 1983 .

[2]  Yuchun Xu,et al.  Optimal mathematical programming and variable neighborhood search for k-modes categorical data clustering , 2019, Pattern Recognit..

[3]  Ikou Kaku,et al.  Neighborhood search techniques for solving uncapacitated multilevel lot-sizing problems , 2012, Comput. Oper. Res..

[4]  Sakir Esnaf,et al.  Integrated use of fuzzy c-means and convex programming for capacitated multi-facility location problem , 2012, Expert Syst. Appl..

[5]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[6]  R. Sridharan The capacitated plant location problem , 1995 .

[7]  Lawrence V. Snyder,et al.  Facility location under uncertainty: a review , 2006 .

[8]  Wensheng Yin,et al.  Weighted k-Means Algorithm Based Text Clustering , 2009, 2009 International Symposium on Information Engineering and Electronic Commerce.

[9]  Li,et al.  A Review of the Discrete Facility Location Problem , 2006 .

[10]  Anupam Gupta,et al.  Simpler Analyses of Local Search Algorithms for Facility Location , 2008, ArXiv.

[11]  Abdullah Konak,et al.  The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion , 2016 .

[12]  M. Brandeau,et al.  An overview of representative problems in location research , 1989 .

[13]  Jully Jeunet,et al.  Solving large unconstrained multilevel lot-sizing problems using a hybrid genetic algorithm , 2000 .

[14]  Ellsworth Faris Social Psychology.Bernard C. Ewer , 1930 .

[15]  Yuchun Xu,et al.  A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems , 2014, Eur. J. Oper. Res..

[16]  Nicola Volta,et al.  The multi-airline p-hub median problem applied to the African aviation market , 2018 .

[17]  Miloš Herda Parallel Genetic Algorithm for Capacitated P-median Problem , 2017 .

[18]  M. Horner,et al.  Pet- and special needs-friendly shelter planning in south florida: A spatial capacitated p-median-based approach , 2017, International Journal of Disaster Risk Reduction.

[19]  Ikou Kaku,et al.  A variable neighborhood search based approach for uncapacitated multilevel lot-sizing problems , 2011, Comput. Ind. Eng..

[20]  Kung-Jeng Wang,et al.  A two-stage stochastic optimization model for warehouse configuration and inventory policy of deteriorating items , 2018, Comput. Ind. Eng..

[21]  Abdullah Konak,et al.  A genetic algorithm with exact dynamic programming for the green vehicle routing & scheduling problem , 2017 .

[22]  Krista Rizman Zalik Fuzzy C-means clustering and facility location problems , 2006, Artificial Intelligence and Soft Computing.

[23]  Abdullah Konak,et al.  A β-accurate linearization method of Euclidean distance for the facility layout problem with heterogeneous distance metrics , 2018, Eur. J. Oper. Res..

[24]  Cengiz Kahraman,et al.  Multi-criteria warehouse location selection using Choquet integral , 2010, Expert Syst. Appl..

[25]  Ikou Kaku,et al.  Model and heuristic algorithm of the joint replenishment problem with complete backordering and correlated demand , 2012 .

[26]  Sakir Esnaf,et al.  Fuzzy C-Means Algorithm with Fixed Cluster Centers for Uncapacitated Facility Location Problems: Turkish Case Study , 2014, Supply Chain Management Under Fuzziness.

[27]  Shinya Hanaoka,et al.  Warehouse location determination for humanitarian relief distribution in Nepal , 2017 .

[28]  Mark S. Daskin,et al.  Strategic facility location: A review , 1998, Eur. J. Oper. Res..

[29]  Ikou Kaku,et al.  A new approach of inventory classification based on loss profit , 2011, Expert Syst. Appl..

[30]  Stephen D. Boyles,et al.  Joint Production-inventory-location Problem with Multi-variate Normal Demand , 2018 .

[31]  Qian Wang,et al.  An integrated model for site selection and space determination of warehouses , 2015, Comput. Oper. Res..

[32]  Diansheng Guo,et al.  A Clustering‐Based Approach to the Capacitated Facility Location Problem 1 , 2008, Trans. GIS.

[33]  Christian Sohler,et al.  Theoretical Analysis of the k-Means Algorithm - A Survey , 2016, Algorithm Engineering.

[34]  Emilio Jiménez,et al.  Multi-attribute evaluation and selection of sites for agricultural product warehouses based on an Analytic Hierarchy Process , 2014 .

[35]  A. Weber,et al.  Alfred Weber's Theory of the Location of Industries , 1930 .

[36]  Pablo Adasme,et al.  p-Median based formulations with backbone facility locations , 2018, Appl. Soft Comput..

[37]  Pierre Hansen,et al.  The p-median problem: A survey of metaheuristic approaches , 2005, Eur. J. Oper. Res..