Simulation Systems for the Vehicle

¶ … 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 demonstrate that the algorithm is quite effective "on a set of standard test problems." (Bramel and Simchi-Levi, 1993)

The work of Wolsey (2006) reports a study of two lot-sizing problems and that each of these have time windows that have been recently proposed. It is stated that for the case of production time windows, both of which the client's specific order is required to have reached the end of production in a specified time period and it is reported by Wolsey that derived is "tight extended formulations for both the constant capacity and uncapacitated problems to the problem in which the time windows can be ordered by time." p.471

According to Wolsey, also demonstrated is "equivalence to the basic lot-sizing problem with upper bounds on the stocks. It is related that here derived is "polynomial time dynamic programming algorithms and tight extended formulation for the uncapacitated and constant capacity problems with general costs." (Wolsey, 2006, p.471) a similar approach is used to derive tight extended formulation for the problem and uncapacitated problems with non-speculative costs with delivery time windows. (Wolsey, 2006, paraphrased)

The work of Terzi and Cavalieri (2004) entitled: "Simulation in the Supply Chain Context: A Survey" states that "modern industrial enterprises operate in a rapidly changing world, stressed by even more global competition, managing world-wide procurement and unforeseeable markets, supervising geographically distributed production plants, striving for the provision of outstanding products and high quality customer service." p.2

Companies that are not willing to adapt to these changes through periodically revising their strategies and modifying processes in the organization are at a critical risk of losing their competitive edge. (Terzi and Cavalieri, 2004, paraphrased) There has been a great deal of emphasis on the last ten years on the needs of organizations to "smooth their physical boundaries in favor of a more integrated perspective..." (Terzi and Cavalieri, 2004) p.3