Dynamic programming algorithm for the vehicle routing problem with time windows and EC social legislation

In practice, apart from the problem of vehicle routing, schedulers also face the problem of nding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a dynamic programming approach for the vehicle routing problem with time windows including the EC social legislation on drivers' driving and working hours. Our algorithm includes all optional rules in these legislations, which are generally ignored in the literature. To include the legislation in the dynamic programming algorithm we propose a break scheduling method that does not increase the time-complexity of the algorithm. This is a remarkable eect that generally does not hold for local search methods, which have proved to be very successful in solving less restricted vehicle routing problems. Computational results show that our method finds solutions to benchmark instances with 18% less vehicles and 5% less travel distance than state of the art approaches. Furthermore, they show that including all optional rules of the legislation leads to an additional reduction of 4% in the number of vehicles and of 1.5%\ud regarding the travel distance. Therefore, the optional rules should be exploited in practice

Vehicle Routing with Traffic Congestion and Drivers' Driving and Working Rules

For the intensively studied vehicle routing problem (VRP), two real-life restrictions have received only minor attention in the VRP-literature: traffic congestion and driving hours regulations. Traffic congestion causes late arrivals at customers and long travel times resulting in large transport costs. To account for traffic congestion, time-dependent travel times should be considered when constructing vehicle routes. Next, driving hours regulations, which restrict the available driving and working times for truck drivers, must be respected. Since violations are severely fined, also driving hours regulations should be considered when constructing vehicle routes, even more in combination with congestion problems. The objective of this paper is to develop a solution method for the VRP with time windows (VRPTW), time-dependent travel times, and driving hours regulations. The major difficulty of this VRPTW extension is to optimize each vehicle’s departure times to minimize the duty time of each driver. Having compact duty times leads to cost savings. However, obtaining compact duty times is much harder when time-dependent travel times and driving hours regulations are considered. We propose a restricted dynamic programming (DP) heuristic for constructing the vehicles routes, and an efficient heuristic for optimizing the vehicle’s departure times for each (partial) vehicle route, such that the complete solution algorithm runs in polynomial time. Computational experiments emonstrate the trade-off between travel distance minimization and duty time minimization, and illustrate the cost savings of extending the depot opening hours such that traveling before the morning peak and after the evening peak becomes possible

Distributed Decision Making in Combined Vehicle Routing and Break Scheduling

The problem of combined vehicle routing and break scheduling comprises three subproblems: clustering of customer requests, routing of vehicles, and break scheduling. In practice, these subproblems are usually solved in the interaction between planners and drivers. We consider the case that the planner performs the clustering and the drivers perform the routing and break scheduling. To analyze this problem, we embed it into the framework of distributed decision making proposed by Schneeweiss (2003). We investigate two different degrees of anticipation of the drivers’ planning behaviour using computational experiments. The results indicate that in this application a more precise anticipation function results in better objective values for both the planner and the drivers

Analyzing combined vehicle routing and break scheduling from a distributed decision making perspective

We analyze the problem of combined vehicle routing and break scheduling from a distributed decision making perspective. The problem of combined vehicle routing and break scheduling can be defined as the problem of finding vehicle routes to serve a set of customers such that a cost criterion is minimized and legal rules on driving and working hours are observed. In the literature, this problem is always analyzed from a central planning perspective. In practice, however, this problem is solved interactively between planners and drivers. In\ud many practical scenarios, the planner first clusters the customer requests and instructs the drivers which customers they have to visit. Subsequently, the drivers decide upon the routes to be taken and their break schedules. We apply a framework for distributed decision making to model this planning scenario and propose various ways for planners to anticipate the drivers' planning behavior. Especially in the case of antagonistic objectives, which are often encountered in practice, a distributed decision making perspective is necessary to analyze this planning process. Computational experiments demonstrate that a high degree of anticipation by the planner has a strong positive impact on the overall planning quality, especially in the case of conflicting planner's and drivers' objectives

Dynamic Collection Scheduling Using Remote Asset Monitoring: Case Study in the UK Charity Sector

Remote sensing technology is now coming onto the market in the waste collection sector. This technology allows waste and recycling receptacles to report their fill levels at regular intervals. This reporting enables collection schedules to be optimized dynamically to meet true servicing needs in a better way and so reduce transport costs and ensure that visits to clients are made in a timely fashion. This paper describes a real-life logistics problem faced by a leading UK charity that services its textile and book donation banks and its high street stores by using a common fleet of vehicles with various carrying capacities. Use of a common fleet gives rise to a vehicle routing problem in which visits to stores are on fixed days of the week with time window constraints and visits to banks (fitted with remote fill-monitoring technology) are made in a timely fashion so that the banks do not become full before collection. A tabu search algorithm was developed to provide vehicle routes for the next day of operation on the basis of the maximization of profit. A longer look-ahead period was not considered because donation rates to banks are highly variable. The algorithm included parameters that specified the minimum fill level (e.g., 50%) required to allow a visit to a bank and a penalty function used to encourage visits to banks that are becoming full. The results showed that the algorithm significantly reduced visits to banks and increased profit by up to 2.4%, with the best performance obtained when the donation rates were more variable

Vehicle routing under time-dependent travel times: the impact of congestion avoidance

Daily traffic congestions form major problems for businesses such\ud as logistical service providers and distribution firms. They cause\ud late arrivals at customers and additional hiring costs for the truck\ud drivers. The additional costs of traffic congestions can be reduced\ud by taking into account and avoid well-predictable traffic congestions\ud within off-line vehicle route plans. In the literature, various strategies\ud are proposed to avoid traffic congestions, such as selecting alternative routes, changing the customer visit sequences, and changing the\ud vehicle-customer assignments. We investigate the impact of these and\ud other congestion avoidance strategies in off-line vehicle route plans on\ud the performance of these plans in reality. For this purpose, we develop\ud a set of VRP instances on real road networks, and a speed model that\ud inhabits the main characteristics of peak hour congestion. The instances are solved for different levels of congestion avoidance using a\ud modified Dijkstra algorithm and a restricted dynamic programming\ud heuristic. Computational experiments show that 99% of late arrivals\ud at customers can be eliminated if traffic congestions are accounted for\ud off-line. On top of that, almost 70% of the extra duty times caused by\ud the traffic congestions can be eliminated by clever avoidance strategies

A dynamic programming heuristic for vehicle routing with time-dependent travel times and required breaks.

For the intensively studied vehicle routing problem (VRP), two real-life restrictions have received only minor attention in the VRP-literature: traffic congestion and driving hours regulations. Traffic congestion causes late arrivals at customers and long travel times resulting in large transport costs. To account for traffic congestion, time-dependent travel times should be considered when constructing vehicle routes. Next, driving hours regulations, which restrict the available driving and working times for truck drivers, must be respected. Since violations are severely fined, also driving hours regulations should be considered when constructing vehicle routes, even more in combination with congestion problems. The objective of this paper is to develop a solution method for the VRP with time windows (VRPTW), time-dependent travel times, and driving hours regulations. The major difficulty of this VRPTW extension is to optimize each vehicle’s departure times to minimize the duty time of each driver. Having compact duty times leads to cost savings. However, obtaining compact duty times is much harder when time-dependent travel times and driving hours regulations are considered. We propose a restricted dynamic programming (DP) heuristic for constructing the vehicle routes, and an efficient heuristic for optimizing the vehicle’s departure times for each (partial) vehicle route, such that the complete solution algorithm runs in polynomial time. Computational experiments demonstrate the trade-off between travel distance minimization and duty time minimization, and illustrate the cost savings of extending the depot opening hours such that traveling before the morning peak and after the evening peak becomes possible