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(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...
(1992) p.154
The process repeats "as long as feasible and profitable exchanges have been found." (1992) p.154 Salvesbergh states that while this method is not sophisticated in the least that it is suitable for the present purposes. Investigation of the varying effect of objective function differences compared were the solutions "obtained with minimizing route duration as objective to those obtained with minimizing travel time and minimizing completion time. The results are stated to clearly demonstrate the importance of "being able to handle different objective functions." (1992) p.153
Efficiency is stated to have been assessed through comparison of running times of the implementation that has been proposed "of iterative improvement techniques with a straightforward implementation of these techniques, i.e. (temporarily) perform an exchange and test its feasibility and profitability, for various types." (1992) p.153 CPU findings on times include the generation of the first set of routes and this is stated to demonstrate "the efficiency" of the implementation that is proposed in Salvesbergh's work. The chosen solution is one in which profitable exchanges are identified resulting in CPU times increasing when there are time windows present.
Bibliography
Brahimi, N., Dauz'ere-P'er'es, S., Najid, N.M.: Capacitated multi-item lot-sizing problems with time windows. Technical report, Ecole des Mines de Nantes, 2005
Brahimi, N.: Planification de la production: mod'eles et algorithmes pour les problemes de dimensionnement de lots. PhD thesis, Universit'e de Nantes, 2004
Dauz'ere-P'er'es, S., Brahimi, N., Najid, N.M., Nordli, a.: Uncapacitated lot-sizing problems with time windows. Technical report, Ecole des Mines de Saint-Etienne, 2005
Lee, C.-Y., Cetinkaya, S.,Wagelmans, a.P.M.: A dynamic lot-sizing model with demand time windows. Manage. Sci. 47, 1384 -- 1395 (2001)
Cordeau, J., Desaulniers, G., Desrosiers, J., Solomon, M. & Soumis, F. (2002) the VRP With Time Windows. The Vehicle Routing Problem, 157-193.
Savelsbergh, M. (1992) the Vehicle Routing Problem With Time Windows: Minimizing Route Duration. Informs Journal on Computing, 4, 146.
Wolsey, L. (2006) Lot-Sizing With Production…
Bibliography
Brahimi, N., Dauz'ere-P'er'es, S., Najid, N.M.: Capacitated multi-item lot-sizing problems with time windows. Technical report, Ecole des Mines de Nantes, 2005
Brahimi, N.: Planification de la production: mod'eles et algorithmes pour les problemes de dimensionnement de lots. PhD thesis, Universit'e de Nantes, 2004
Dauz'ere-P'er'es, S., Brahimi, N., Najid, N.M., Nordli, a.: Uncapacitated lot-sizing problems with time windows. Technical report, Ecole des Mines de Saint-Etienne, 2005
Lee, C.-Y., Cetinkaya, S.,Wagelmans, a.P.M.: A dynamic lot-sizing model with demand time windows. Manage. Sci. 47, 1384 -- 1395 (2001)
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