Mixed integer programming (MIP) provides an important modeling and decision support tool for a wide variety of real-life problems. Unfortunately, practical MIPs are large-scale in size and pose serious difficulties to the available solution methodology and software. / This thesis presents a novel solution approach for large-scale mixed integer programming that integrates three bodies of research: interior point methods, decomposition techniques and branch-and-bound approaches. The combination of decomposition concepts and branch-and-bound is commonly known as branch-and-price, while the integration of decomposition concepts and interior point methods lead to the analytic centre cutting plane method (ACCPM). Unfortunately, the use of interior point methods within branch-and-bound methods could not compete with simplex based branch-and-bound due to the inability of "warm" starting. / The motivation for this study stems from the success of branch-and-price and ACCPM in solving integer and non-differentiable optimization problems respectively and the quest for a method that efficiently integrates interior-point methods and branch-and-bound. / The proposed approach is called an Interior Point Branch-and-Price method (IP-B&P) and works as follows. First, a problem's structure is exploited using Lagrangean relaxation. Second, the resulting master problem is solved using ACCPM. Finally, the overall approach is incorporated within a branch-and-bound scheme. The resulting method is more than the combination of three different techniques. It addresses and fixes complications that arise as a result of this integration. This includes the restarting of the interior-point methods, the branching rule and the exploitation of past information as a warm start. / In the first part of the thesis, we give the details of the interior-point branch-and-price method. We start by providing, discussing and implementing new ideas within ACCPM, then detail the IP-B&P method and its different components. To show the practical applicability of IP-B&P, we use the method as a basis for a new solution methodology for the production-distribution system design (PDSD) problem in supply chain management. In this second part of the thesis, we describe a two-level Lagrangean relaxation heuristic for the PDSD. The numerical results show the superiority of the method in providing the optimal solution for most of the problems attempted.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.37887 |
| Date | January 2001 |
| Creators | Elhedhli, Samir. |
| Contributors | Goffin, Jean-Louis (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Faculty of Management.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001846112, proquestno: NQ75629, Theses scanned by UMI/ProQuest. |
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