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

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

Efficient Duration-Based Workload Balancing for Interdependent Vehicle Routes

Vehicle routing and scheduling problems with interdependent routes arise when some services must be performed by at least two vehicles and temporal synchronization is thus required between the starting times of these services. These problems are often coupled with time window constraints in order to model various real-world applications such as pickup and delivery with transfers, cross-docking and home care scheduling. Interdependent routes in these applications can lead to large idle times for some drivers, unnecessarily lengthening their working hours. To remedy this unfairness, it is necessary to balance the duration of the drivers\u27 routes. However, quickly evaluating duration-based equity functions for interdependent vehicle routes with time windows poses a significant computational challenge, particularly when the departure time of routes is flexible. This paper introduces models and algorithms to compute two well-known equity functions in flexible departure time settings: min-max and range minimization. We explore the challenges and algorithmic complexities of evaluating these functions both from a theoretical and an experimental viewpoint. The results of this paper enable the development of new heuristic methods to balance the workload of interdependent vehicle routes with time windows

Scheduling and Routing of Truck Drivers Considering Regulations on Drivers’ Working Hours

In many countries, truck drivers are obliged by law to take a break or a rest regularly. In the European Union, for example, this is governed by Regulation (EC) No. 561/2006. It states that, after 4.5 hours of driving a truck, it is prohibited to continue driving until a 45-minute break is taken. After accumulating a driving time of 9 hours, a rest of 11 hours is mandatory. These are only two rules of a considerably longer list of break rules set out in this regulation, and it is only one of many regulations there are worldwide. Such breaks and rests have to be planned into the work schedules of the drivers. In general, the task of a dispatcher is to find routes and schedules for the truck drivers such that every customer is served in time. With the regulations on drivers’ working hours, both the routing and the scheduling parts of the task become more challenging. In this thesis, we study several optimization problems that arise in the context of drivers’ working hours. One is known as the truck driver scheduling problem. Here, a sequence of customers is given, and the task is to find a schedule for a driver such that every customer is visited within one of the customer’s time windows and the applicable break rules are complied with. Depending on the regarded break rules, we get different variants of the truck driver scheduling problem. Little is known about the complexity of the individual problem variants. One of the two focal points of this thesis is to present polynomial-time algorithms for different variants of the problem, for which polynomial-time algorithms are not yet known. With this, we can falsify the NP-hardness conjecture of Xu et al. (2003) for an important special case of their considered problem variant. But this thesis is not only about scheduling, it is also about routing. This constitutes the second focal point of this thesis. We present an integrated approach for the vehicle routing and truck driver scheduling problem. Here, a route refers to the order in which the customers are visited. However, the meaning of route is twofold. In another studied problem, the truck driver scheduling and routing problem, it means the sequence of road segments that the driver takes to drive from one customer to the other. In this problem, we take into account that, before taking a break, truck drivers need to head for a rest area or at least a spot where their vehicle can be parked. We even consider the time-dependent scenario in which driving times on road segments vary over the day due to rush hours. Both an exact approach and a heuristic for this problem are presented, and both are evaluated on a recent road network instance of Germany. It turns out that the heuristic is at least two orders of magnitude faster but still hardly worse than the exact approach. Our main motivation is the application in practice. It is our aim – and this is especially true for the second focal point – to provide helpful algorithms that may find their way into software products for dispatchers, like the described approach for the vehicle routing and truck driver scheduling problem is already integrated into the vehicle route planning tools of a commercial provider of logistics optimization software

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

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

Optimizing departure times in vehicle routes

Most solution methods for the vehicle routing problem with time\ud windows (VRPTW) develop routes from the earliest feasible departure time. However, in practice, temporal traffic congestions make\ud that such solutions are not optimal with respect to minimizing the\ud total duty time. Furthermore, VRPTW solutions do not account for\ud complex driving hours regulations, which severely restrict the daily\ud travel time available for a truck driver. To deal with these problems,\ud we consider the vehicle departure time optimization (VDO) problem\ud as a post-processing step of solving a VRPTW. We propose an ILP-formulation that minimizes the total duty time. The obtained solutions are feasible with respect to driving hours regulations and they\ud account for temporal traffic congestions by modeling time-dependent\ud travel times. For the latter, we assume a piecewise constant speed\ud function. Computational experiments show that problem instances\ud of realistic sizes can be solved to optimality within practical computation times. Furthermore, duty time reductions of 8 percent can\ud be achieved. Finally, the results show that ignoring time-dependent\ud travel times and driving hours regulations during the development of\ud vehicle routes leads to many infeasible vehicle routes. Therefore, vehicle routing methods should account for these real-life restrictions

The Influence of Multi-agent Cooperation on the Efficiency of Taxi Dispatching

The paper deals with the problem of the optimal collaboration scheme in taxi dispatching between customers, taxi drivers and the dispatcher. The authors propose three strategies that differ by the amount of information exchanged between agents and the intensity of cooperation between taxi drivers and the dispatcher. The strategies are evaluated by means of a microscopic multi-agent transport simulator (MATSim) coupled with a dynamic vehicle routing optimizer (DVRP Optimizer), which allows to realistically simulate dynamic taxi services as one of several different transport means, all embedded into a realistic environment. The evaluation is carried out on a scenario of the Polish city of Mielec. The results obtained prove that the cooperation between the dispatcher and taxi drivers is of the utmost importance, while the customer–dispatcher communication may be reduced to minimum and compensated by the use of more sophisticated dispatching strategies, thereby not affecting the quality of service