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Title: Routing problems : theoretical analysis and case studies of Coventry City Council
Author: Aziz, Azmin Azliza
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2012
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The Travelling Salesman Problem (TSP) is a special case of the Vehicle Routing Problem (VRP) which concerns with finding a tour from one city to another in such a way that each city is visited exactly once and the total travel length is minimal. The literature has established that, thus far, studies that consider both practical and theoretical aspects of routing problems have received relatively little attention from the researchers and practitioners. This thesis aims to bridge a gap between the two aspects by exploring two case studies of Coventry City Council (CCC), namely the Meals Delivery and Incontinence Laundry services as well as investigating the robustness of the routing plan by exploiting relevant theoretical concepts of TSP. The Meals Delivery service was modelled as the multiple TSP with time windows (m-TSPTW) and optimized using Trapeze® PASS with regard to the objective of identifying possible improvement for the current practice. Several alternative optimization scenarios were proposed by varying the delivery time windows and number of vehicles in searching for the solutions that minimize the total distance travelled by the vehicles. Experimental results revealed that huge savings could be obtained by employing the commercial, off-the-shelf software package in the scheduling exercise. The Incontinence Laundry (IL) service was modelled as the Periodic TSP with Simultaneous Pick-up and Delivery (PTSPSPD). The problem is unique in the sense that it involves clients with multiple visits. The study aims to improve the current routing scheme by rescheduling this service using alternative approaches, namely Trapeze® PASS, Microsoft® MapPoint 2009 and Decision Support System (DSS), with the objective of minimizing the total distance travelled. In each approach, the problem was solved in two stages, specifically without and with the insertion of a break event in the middle of the daily trip while considering the balancing of demands. Unlike Trapeze and MapPoint, the DSS approach scheduled the clients on a weekly basis, hence implying that the resulting DSS routes could correspond to any service days. Due to this reason, a further analysis was proposed to allocate the routes into relevant days by formulating the problem as the assignment and transportation problems and solving it using Microsoft® Excel Solver. Experimental results revealed that DSS offers significant mileage reductions for the IL routes by 52.4% and 41.6% for solutions without and with break insertion, respectively, as compared to manual implementation. This thesis also explores the TSP from the theoretical perspective. In particular, the robustness of the TSP routes is investigated by recognizing the special combinatorial structures of Kalmanson and Burkard matrices. A recognition algorithm encompassing four procedures, namely combinatorial-based Kalmanson, combinatorial-based Burkard and two approaches of LP-based Kalmanson was developed and executed on a number of randomly generated instances. These procedures produce four lower bounds which provide guarantees on the quality of the solutions. Computational experiments have shown that the proposed LP-based procedure performs consistently well across all problem dimensions and provides the best lower bounds to the TSP solutions. This is supported by an average deviation of less than 7% between the TSP tour lengths and the lower bounds. Furthermore, the study also recognizes the cases of permuted Kalmanson matrices in the distance matrices of TSP in order to suggest a reasonable characterization of robust tours. The algorithm was developed based on relaxed Kalmanson condition and executed on the TSP instances with data distributed across several regions as well as data clustered within a region. Our observation demonstrates that the within-region and cross-region cases are more likely to form a tree and convex structures, respectively. Also, the former is more likely to possess Kalmanson permutations which guarantee the existence of master tours as compared to the latter. In addition to the above, this study has successfully improved the time complexity of the Burkard algorithm from O(n5) to O(n4).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: HD28 Management. Industrial Management ; QA Mathematics