M.S. (Master of Science)
Department of Industrial and Systems Engineering
Industrial location; Management science; Lagrangian functions
A common problem in logistics is the Facility Location Problem (FLP). In its most basic form, the problem involves a set of customers who are served by a set of uncapacitated facilities with the objective of locating the facilities so that transportation and fixed facility costs are minimized while satisfying the demand of all the customers. As the problem is generalized to reflect real-world scenarios, a trade-off between solution quality and computation time becomes a relevant concern. This thesis provides a model to solve a two-stage, capacitated FLP using a combination of decomposition and Lagrangian relaxation (LR) methodologies. This research is an expansion of a previously studied problem that looked at a two-stage, supply chain scenario where there were known customer demands for a variety of products that must be met using the most cost effective warehousing and transportation system. The problem has been complicated by constraining the warehouse sizing to discrete levels, with each warehouse also having a total capacity limit to represent situations requiring discrete storage such as cargo containers or specialized shelving which this new model incorporates. The results of this study include a comparison of the LR model's performance against the performance of a commercially provided mixed integer program (MIP) solution, in this case IBM ILOG CPLEX. The results show that regardless of the number of discrete decision variables considered, the LR model provided greatly superior computation times. Similarly, the LR model consistently provided better quality solutions than the commercial solver. The experiments show that the improvement in the quality of solutions becomes more evident as the number of discrete decision variables increases. The contribution of this research is that it provides an approach to reducing computation times without sacrificing solution quality. The new mathematical formulation presented in this research also mirrors the real world needs in terms of discrete storage levels for various products stored at a warehouse. This is promising with respect to providing future research that more realistically encompasses real world generalizations and data set sizes; meaningful solutions could be found in a practical amount of time.
Noe, Christopher, "Lagrangian relaxation for integrated facility location and allocation sizing models" (2016). Graduate Research Theses & Dissertations. 3750.
v, 64 pages
Northern Illinois University
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Advisors: Purushothaman Damodaran.||Committee members: Murali Krishnamurthi; Christine Nguyen.||Includes bibliographical references.||Includes illustrations.