(Wolsey, 2006) p.472
The work of Savelsbergh (1992) entitled: "The Vehicle Routing Problem with Time Windows: Minimizing Route Duration" reports the investigation of the implementation of "edge-exchange improvement methods for the vehicle routing problem with time windows with maximization of route duration as the objective." During the past decade, researchers investigating vehicle routing and scheduling have highlighted use of algorithms for problems in real-life however, the problems have increased in size and constraints of practicality are no longer brushed aside in consideration of the research in this area of study.
Stated as one such constraint is "the specification of time window at customers, i.e., time intervals during which they must be served. These lead to mixed routing and scheduling problems." (Savelsbergh, 1992) p.146 the introduction of time windows at customers is stated to allow "the specification of more realistic objective functions, compared to minimizing distance, such as minimizing waiting time, minimizing completion time, and minimizing route duration." (Savelsbergh, 1992)
Savelsbergh states that edge-exchange improvement methods are that which form both an important as well as a popular class or algorithms in the area of vehicle routing problems. (1992, paraphrased) Previous studies in this area focus on efficient implementations of edge-exchange improvement methods for the vehicle routing problem with time windows...." however, Savelsbergh states that these studies focus completely on the aspect of feasibility and fail to identify "profitable exchanges for realistic objective functions." (1992) p.146
Salvesbergh states that the growing importance of 'side constraints as well as realistic objectives in practical distribution management and the need for fast implementation of algorithms in the context of interactive planning systems justify the current research." (1992) p.153 More realistic objective functions are critically needed. The model presented by Salvesbergh is one in which "the iterative improvement methods were embedded in a two phase approximation algorithm for the VRPTW." (1992) p.153 Salvesbergh states: (1) the relevant iterative improvement methods are applied to all possible combinations of two routes; and (2) the relevant iterative improvement methods are...
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If the cost values satisfy the symmetry, such that for any I and j ? V, cij = cji, then the problem is said to be symmetric VRP, else, it is called an asymmetric VRP. In several practical cases the cost matrix satisfies the triangle inequality, such that cik + ckj ? cij for any i, j, k ? V." (Toth and Vigo, 1998, cited in Vural (2003). Vural (2003)
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