Vehicle routing

Traditionally, global tolerances have been specified for any point on the floor relative to datum and local tolerances specified relative to a 3 m straight edge. For VNA type requirements tolerances distinguish between areas of defined movement (i.e. predetermined vehicle routes) and areas of free movement (the rest of the slab). 

To apply these ideas to a general optimization problem, let the system state vector q correspond to the objects to be optimized (job sequences, vehicle routes, or vectors of decision variables), denoted by x. The system energy level corresponds to the objective function fix). As in Section 10.5.1, let N(x) denote a neighborhood of x. The following procedure (Floquet et al., 1994) specifies a basic SA algorithm ... 

Wasner M, Zapfel G (2003) An integrated multi-depot hub-location vehicle routing model for network planning of parcel service. International Journal of Production Economics 90 403-419... 

Once a chemical enters the body of animal or human, it undergoes metabolic reaction. A host of factors modulate the reaction rate and the induction of toxicological effects. These factors have been termed intrinsic factors and include animal species, gender, age, nutritional status, pregnancy, other health status, and circadian rhythms. In addition, there are certain extrinsic factors (e.g., physicochemical properties of chemicals, solvent or vehicle, route of exposure, temperature, and humidity) during exposure to chemicals that also influence the effect of a test chemical. We shall discuss these factors in greater detail. 

Set-Partitioning Formulation with Side Constraints 813 12.1. Vehicle Routing 819... 

The pickup-and-delivery problem can be modeled as a variation of the vehicle routing problem with time windows (VRPTW) and a single depot. Inputs for the VRPTW include matrices that specify the distance and travel time between every pair of customers (including the depot) service time and time window for each customer maximum (or specified) number of drivers starting time of the workday and maximum on-road time of the workday. The maximum on-road time of the workday can be implemented as a time window on the depot, so that the pickup and delivery problem described above can be considered as a traveling salesman problem with time windows and multiple routes (m-TSPTW). However, the term VRPTW will be used in this section for this uncapadtated pickup-and-delivery problem. 

Because clustering is based primarily on purely spatial criteria, the cluster-first, route-second strategy is often more appropriate for the vehicle routing problem (VRP), where time windows are not present than for the VRPTW. However, cluster-first strategies can play a useful role in some instances of the VRPTW, as will be discussed later. 

Heuristic route-improvement procedures play a fimdamental role in vehicle routing algorithms. Such procedures take as input a feasible solution consisting of a route or set of routes and seek to transform this initial solution into a lower-cost feasible solution. 

It is evident, on the basis of the discussion in this section, that for vehicle-routing applications one may require a suite of algorithms, each of which best serves a somewhat different objective. Furthermore, to make the best use of these algorithms, it is important that the actual user be specially trained for the application. 

Several software vendors have developed vehicle-routing software. In 1997, Hall and Partyka surveyed several vendors in order to compare the characteristics of their respective software systems. Table 4 presents an extract of this survey. The complete survey appeared in the June 1997 issue of OR/MS Today. 

The transportation community has turned to the deployment of inteihgent transportation systems (ITS) to increase the efficiency of existing highway, transit, and rail systems. One of the key variables in the vehicle-routing models described above is travel time. With the use of information from ITS, dispatchers can make better decisions. The U.S. Department of Transportation (DOT) has indicated that ITS uses advanced electronics and information technologies to improve the performance of vehicles, highways, and transit systems. ITS provides a variety of products and services in metropolitan and rural areas. ... 

Jaillet, R, and Odoni, A. (1988), The Probabilistic Vehdle Routing Problem, in Vehicle Routing Methods and Studies, B. Golden and A. Assad, Eds., North-Holland, Amsterdam, pp. 293-318. 

Kontoravdis, G., and Bard, J. (1995), A GRASP for the Vehicle Routing Problem with Time Windows, ORSA Journal on Computing, Vol. 7, pp. 10-23. 

Potvin, J., and Rousseau, J. (1993), A Parallel Route Building Algorithm for the Vehicle Routing and Scheduling Problem with Time Windows, European Journal of Operational Research, Vol. 66, pp. 331-340. 

Potvin, J., Kervahut, T, Garcia, B., and Rousseau, J. (1996), The Vehicle Routing Problem with Time Windows—Part 1 Tabu Search, INFORMS Journal on Computing, Vol. 8, pp. 158-164. 

Rochat, Y., and TaiUard, E. (1995), Probabdistic Diversification and Intensification in Local Search for Vehicle Routing, Journal of Heuristics, Vol. 1, pp. 147-167. 

Solomon, M. (1987), Algorithms for the Vehicle Routing and Scheduhng Problems with Time Window Constraints, Operations Research, Vol. 35, pp. 254-265. 

TaiUard, E., Badeau, P., Gendreau, M., Guertin, R, and Potvin, J. (1997), A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows, Transportation Science, Vol. 31, pp. 170-186. 

Thangiah, S., Osman, I., and Sun, T. (1995), Metaheuristics for Vehicle Routing Problems with Time Windows, Technical Report, Computer Science Department, Shppery Rock University, Slippery Rock, PA. 

The required speed of the DSS. Particularly for operational systems such as lead-time quotation and vehicle routing, speed may be essential. 

This problem can be modeled as a vehicle routing problem (VRP) with numerous side constraints. Recognizing that the VRP is notoriously hard, the size and scope of the real-world data sets can make it impractical to just formulate the problem as an integer program (IP) and use an advanced IP solver to get an optimal solution. Therefore, practitioners usually seek solution techniques that yield acceptable solutions within a reasonable time frame (see Chapter 30). Some of these techniques include ... 

Thankfully, industrial engineers and software developers are aware of these real constraints, which are handled by various extensions of the TSP (Ball et rd. 1995 Golden and Assad 1988). For example, route capacities and times are considered by the vehicle routing problem (VRP), while time window constraints are included in the TSP with time windows (TSPTW) and the VRP with time windows (VRPTW). Advances in telecommunications make it now possible to implement models that take into account the dynamic aspects of vehicle routing, while time-dependent vehicle routing problems take into account time-dependent travel times and costs. The stochastic aspects of cost, time, demand... 

The vehicle routing problem (VRP) (Christofides 1985) is a capacitated version of the TSP. A fleet of vehicles is available at one or more terminals to serve a set of defined stops. A shipment size is associated with each stop, and a cost is associated with the movement between each peiir of stops (and between a stop and a terminal). The goal is to deliver the shipments to all the stops at minimum total cost in a set of cycles without violating vehicle capacity. The VRP formulation matches well local pickup and delivery problems where the pickup stops are known before the vehicle starts on the route. 

While the previous description represents a generic implementation, specific vehicle routing applications may have their own individual characteristics, requiring that transportation management and shipment planning software be customized to reflect the operating environment, customer needs, and the characteristics of the transportation mode (Hall and Partyka 1997). 

Vehicle routing can be divided into three primary categories service vehicles, passenger vehicles, and freight vehicles. Service vehicles usually do not move things or people from place to place... 

Christofides, N. (1985), Vehicle Routing, in E. Lawler, J. Lenstra, A. Rinnooy Kan, and D. Shmoys, Eds., The Traveling Salesman Problem A Guided Tour cf Combinatorial Optimization, John Wiley Sons, New York, pp. 431-448. 

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