Research Proposal on "Use of Simulation Systems for the Vehicle Routing Problem"

Research Proposal 4 pages (1244 words) Sources: 3 Style: Harvard

[EXCERPT] . . . .

Simulation Systems for the Vehicle Routing Problem

The work of Solomon (1987) entitled: "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints" reports the consideration of the design and analysis of algorithms for vehicle routing and scheduling problems with time windows constraints. Solomon (1987) reports having presented the development of heuristics and test problem sets and computational experiments with results indicating that the "insertion heuristic I1 can be explained with the realization that "while routing problems seems to be driven by the assignment-of-customers-to-vehicles component -- as indicated by the success of the Fisher and Jaikumar generalized assignment heuristic -- the sequencing aspect of the problem seems to drive routing problems dominated by time windows. It is this aspect of the problem that the insertion heuristic II captures so well." (Solomon, 1987)

It is stated that based upon Solomon's study that the use of the insertion heuristic 11 is recommended "to obtain excellent initial VRSPTW solutions in a reasonable amount of computing time." (1985) p.264 Because of the stable behavior of this heuristic it is held by Solomon that it will "perform well on practical problems." (1987) p.264

The work of Desrochers, Desrosiers, and Solomon (1992) entitled: "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows" presents the development of a new optimization algorithm which uses a column generation approach for a set partitioning formulation for the VRPTW." p.353 Results are stated to indicate that this algorithm was successful and "on a variety of practical sized benchmark VRPTW test problems." (Desrochers, Desrosiers, and Solomon, 1992) p.353

The algorithm was stated to have the capacity to problem-solve on a scale that was six times greater than any other reported algorithm. (Desrochers, Desrosiers, and Solomon, 1992) p.353 Stated as a key element of distributions systems is the "routing and scheduling of vehicles through a set of customers requiring service." (Solomon, 1992) p.254 Solomon goes on to relate that the vehicle routing problem (VRP) involves "the design of a set of minimum-cost vehicle routes, originating and terminating at a central depot, for a fleet of vehicles that services a set of customers with known demands. Each customer is serviced exactly once and, furthermore, all the customers must be assigned to vehicles without exceeding vehicle capacities." (Solomon, 1992) p.256

It is necessary to address these issues along with the additional complexity of "...allowable delivery times, or time windows, stemming from the fact that some customers impose delivery deadlines and earliest-delivery-time constraints. In the presence of time windows, the total routing and scheduling costs include not only the total travel distance and time costs considered for routing problems, but also the cost of waiting time incurred when a vehicle arrives too early at a customer location or when the vehicle is loaded or unloaded." (Solomon, 1992) p.256

The work of Bent and Hentenryck (2004) entitled: "A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows" proposes a two-stage hybrid algorithm for the VRP with the minimization of the vehicle number first in the algorithm through use of simulated annealing and followed by minimization of travel cost through use of a large neighborhood search resulting in relocation of some customers. Upon conduction of an experiment results are stated to "demonstrate the effectiveness of the algorithm, which has improved 10 of the 56 best published solutions to the Solomon benchmarks..." (Bent and Hentenryck, 2004) p.515 Conclusions state that this algorithm is robust in nature.

The work of Bramel and Simchi-Levi (1993) entitled: "Probabilistic Analyses and Practical Algorithms for the Vehicle Routing Problem with Time Windows" report use of a new algorithm that is based on the formulation of the problem "as a stylized location problem" and report results that… READ MORE

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