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Models and Methods for Merge–in–Transit Operations

Fisher College of Business, The Ohio State University, Suite 518, Fisher Hall, 2100 Neil Avenue, Colombus, Ohio 43210–1144
Département d'informatique et de recherche opérationnelle, and Centre de recherche sur les transports, Université de Montréal, C.P. 6128, succ. Centre–ville, Montreal, Quebec, Canada H3C 3J7
School of Engineering, and Sloan School of Management, Massachusetts Institute of Technology, Room 1–206, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139–4307
croxton{at}cob.osu.edu
bernard{at}crt.umontreal.ca
magnanti{at}mit.edu

We develop integer programming formulations and solution methods for addressing operational issues in merge–in–transit distribution systems. The models account for various complex problem features, including the integration of inventory and transportation decisions, the dynamic and multimodal components of the application, and the nonconvex piecewise linear structure of the cost functions. To accurately model the cost functions, we introduce disaggregation techniques that allow us to derive a hierarchy of linear programming relaxations. To solve these relaxations, we propose a cutting–plane procedure that combines constraint and variable generation with rounding and branch–and–bound heuristics. We demonstrate the effectiveness of this approach on a large set of test problems with instances derived from actual data from the computer industry that contain almost 500,000 integer variables.

History: Received: September 2000; revised: April 2001; accepted: October 2001.

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