As supply chains have become more dynamic the difference in the time horizon for strategic decisions has diminished, resulting in supply chains that are more flexible with no/low fixed facility costs. This trend requires the development of solution approaches that can combine the traditionally separate strategic, tactical, and operational decisions in an integrative manner, incorporating a range of decision variables and cost considerations while producing good, and possibly near-optimal, solutions in reasonable time.;This research begins to address these issues through the development of heuristic approaches to solve large-scale facility location problems that reflect economies of scale in the per-unit costs of processing goods and/or holding safety stock of those goods to protect against uncertainty in demand. Such non-linear economies of scale are well known in practice, but are often excluded or overly simplified in location models due to their non-linear nature. Combining and extending existing heuristic approaches, we develop and analyze several meta-heuristics to solve a location problem with a non-linear, concave cost function, which is used as a surrogate for more computationally complex cost functions. The resulting solution methods offer near-optimal solutions with relatively modest computational effort. These meta-heuristics are then applied to a focused study on the use of approximations to represent safety stock inventory costs in location models. This research evaluates the commonly used "Square Root Law" and a more general concave cost function against the explicit safety stock inventory calculation in models with and without inter-customer demand correlation. The results highlight the conditions for which these functions accurately approximate actual inventory costs and/or when they generate location solutions that are close to those generated by the explicit computation of inventory levels. The meta-heuristics are then applied to a reverse logistics location problem for the carpet industry. This application requires us to recommend locations for processing used carpet in a setting where the recycling facilities to be located exhibit economies of scale in processing. We use our modeling approach to analyze an existing, smaller-scale used carpet collection network and also evaluate a larger hypothetical national collection network, providing insight into the number of recycling facilities that should be located and their respective size. We compare the results of formulating and solving models with and without economies of scale, highlighting the value of their inclusion on the results.
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