Generalized Facility Location and Design Problem




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Generalized Facility Location and Design Problem


Dmitry Krass

University of Toronto

Dmitry Krass is a Professor of Operations Management and Statistics at Rotman School of Management, University of Toronto.  Obtaining his Ph.D. in Operations Research from Johns Hopkins University, he joined UT in 1989.  His research and teaching interests include facility location models, transportation, reliability and inventory location modeling and humanitarian logistics. He is also interested in environmental modeling, including regulation of pollution fines, marketing mix management and optimization, and predictive/ prescriptive analytics using “big data” and other tools in business decision making. 


We consider the problem of optimal design and location of a set of facilities.  The goal is to optimally allocate the available budget to maximize customer demand (alternatively, the program can be stated as net revenue optimization).  Customer demand is assumed to be concave in the attractiveness of the facilities, where the latter is a function of both, the convenience (proximity) and the design of the facilities. Available budget can be spent on both, locating new facilities or improving the design of the existing ones.


The resulting problem is formulated as a non-linear integer program and solved in several steps.  First we address optimal design of a single facility and develop closed-form solutions for this problem.  Then, we show how the results can be used to reduce the dimensionality of the original problem.  Finally, we apply “double TLA” technique to obtain a linearized version with a provable error bound.  Computational results are presented to show the effectiveness of each step in this procedure.