Hard Time Windows Research Articles

Appointment scheduling and routing optimization of attended home delivery system with random customer behavior

Attended home delivery (AHD) has been identified as a crucial delivery mode of the last mile problem. As the name implies, AHD involves delivery of needed goods at the customer's doorsteps or nearby via walking or short-distance vehicle. Considering no-show and random response time, this article presents an integrative approach that combines appointment scheduling and vehicle routing problem with soft time windows. We also propose an intuitive heuristic dynamic programming to tackle the appointment scheduling problem whose optimal decision is expected to be very complicated, embed it into tabu search and formulate a hybrid heuristic algorithmto solve this integrative model. Moreover, an extension to hard time windows has also been discussed. Our results indicate that the integrative approach could lead to high-quality solutions in a reasonable amount of runtimeas compared to the hierarchical approach.

Robust Dynamic Multi-Objective Vehicle Routing Optimization Method.

For dynamic multi-objective vehicle routing problems, the waiting time of vehicle, the number of serving vehicles, and the total distance of routes were normally considered as the optimization objectives. Except for the above objectives, fuel consumption that leads to the environmental pollution and energy consumption was focused on in this paper. Considering the vehicles' load and the driving distance, a corresponding carbon emission model was built and set as an optimization objective. Dynamic multi-objective vehicle routing problems with hard time windows and randomly appeared dynamic customers, subsequently, were modeled. In existing planning methods, when the new service demand came up, global vehicle routing optimization method was triggered to find the optimal routes for non-served customers, which was time-consuming. Therefore, a robust dynamic multi-objective vehicle routing method with two-phase is proposed . Three highlights of the novel method are: (i) After finding optimal robust virtual routes for all customers by adopting multi-objective particle swarm optimization in the first phase, static vehicle routes for static customers are formed by removing all dynamic customers from robust virtual routes in next phase. (ii) The dynamically appeared customers append to be served according to their service time and the vehicles' statues. Global vehicle routing optimization is triggered only when no suitable locations can be found for dynamic customers. (iii) A metric measuring the algorithms robustness is given. The statistical results indicated that the routes obtained by the proposed method have better stability and robustness, but may be sub-optimum. Moreover, time-consuming global vehicle routing optimization is avoided as dynamic customers appear.

Heuristics for the robust vehicle routing problem with time windows

Uncertainty is frequently present in logistics and transportation, where vehicle routing problems play a crucial role. However, due to the complexity inherent in dealing with uncertainty, most research has been devoted to deterministic problems. This paper considers a robust version of the vehicle routing problem with hard time windows, in which travel times are uncertain. A budget polytope uncertainty set describes the travel times, to limit the maximum number of sailing legs that can be delayed. This makes sure that improbable scenarios are not considered, while making sure that solutions are immune to delays on a given number of sailing legs. Existing exact methods are only able to solve small instances of the problem and can be computationally demanding. With the aim of solving large instances with reduced running times, this paper proposes an efficient heuristic based on adaptive large neighborhood search. The computational study performed on instances with different uncertainty levels compares and analyzes the performance of four versions of the heuristic and shows how good quality solutions can be obtained within short computational times.

A unified framework for routing problems with a fixed fleet size

Vehicle routing problems constitute the core of many operations research efforts. Early studies introduced tailor-made solutions for each variant of a vehicle routing problem, but unified frameworks have emerged more recently. These approaches typically generalise across many vehicle routing problems and implement a method for tackling the generalised problem. In line with this, this research proposes a generic method for solving several fixed fleet vehicle routing problems - capacitated vehicle routing, open vehicle routing, vehicle routing with soft and hard time windows, open vehicle routing with soft and hard time windows, and time-dependent vehicle routing with soft and hard time windows - by transforming them into a time-dependent vehicle routing problem with soft time windows, solved by a variable neighbourhood search using a unique parameter setting, regardless of the original problem. Computational tests using standard benchmark instances from prior literature show that genericity does not come at the expense of solution quality. Moreover, the algorithm yields competitive results and some new best known solutions are obtained for the vehicle routing problem with soft time windows, the open vehicle routing problem with hard time windows, and time-dependent vehicle routing problem with hard time windows.

A unified framework for routing problems with a fixed fleet size

Vehicle routing problems constitute the core of many operations research efforts. Early studies introduced tailor-made solutions for each variant of a vehicle routing problem, but unified frameworks have emerged more recently. These approaches typically generalise across many vehicle routing problems and implement a method for tackling the generalised problem. In line with this, this research proposes a generic method for solving several fixed fleet vehicle routing problems - capacitated vehicle routing, open vehicle routing, vehicle routing with soft and hard time windows, open vehicle routing with soft and hard time windows, and time-dependent vehicle routing with soft and hard time windows - by transforming them into a time-dependent vehicle routing problem with soft time windows, solved by a variable neighbourhood search using a unique parameter setting, regardless of the original problem. Computational tests using standard benchmark instances from prior literature show that genericity does not come at the expense of solution quality. Moreover, the algorithm yields competitive results and some new best known solutions are obtained for the vehicle routing problem with soft time windows, the open vehicle routing problem with hard time windows, and time-dependent vehicle routing problem with hard time windows.

A hybrid metaheuristic for the time-dependent vehicle routing problem with hard time windows

This article paper presents a hybrid metaheuristic algorithm to solve the time-dependent vehicle routing problem with hard time windows. Time-dependent travel times are influenced by different congestion levels experienced throughout the day. Vehicle scheduling without consideration of congestion might lead to underestimation of travel times and consequently missed deliveries. The algorithm presented in this paper makes use of Large Neighbourhood Search approaches and Variable Neighbourhood Search techniques to guide the search. A first stage is specifically designed to reduce the number of vehicles required in a search space by the reduction of penalties generated by time-window violations with Large Neighbourhood Search procedures. A second stage minimises the travel distance and travel time in an ‘always feasible’ search space. Comparison of results with available test instances shows that the proposed algorithm is capable of obtaining a reduction in the number of vehicles (4.15%), travel distance (10.88%) and travel time (12.00%) compared to previous implementations in reasonable time

A novel method to handle route failure in fuzzy vehicle routing problem with hard time windows and uncertain demand

In this paper, a fuzzy vehicle routing problem with hard time windows (FVRPTW) having uncertain demand is addressed. Since customer's demand is assumed to be known only upon arrival at customer location, a planned route may fail to meet realised demand of customer. This situation is known as route failure. Instead of adopting simple recourse methods to handle route failure, this paper proposes a novel method titled 'non-restocking' to solve route failure. The problem is formulated as a two stage recourse model with an objective of minimising the total cost and at the same time maximising the obtained sale in a competitive environment. Uncertainty in demand is represented by fuzzy numbers. Route construction for the modelled problem is done by ant colony system. The computational results show that the proposed two stage model with the proposed new recourse scheme produces high quality solutions. Benefits of the proposed method are demonstrated by applying it to milk routing problem.

A novel method to handle route failure in fuzzy vehicle routing problem with hard time windows and uncertain demand

A novel method to handle route failure in fuzzy vehicle routing problem with hard time windows and uncertain demand

Possibilistic scheduling routing for short-notice bushfire emergency evacuation under uncertainties: An Australian case study

This paper aims to develop a capacitated vehicle routing solution to evacuate short-notice evacuees with time windows and disruption risks under uncertainties during a bushfire. A heuristic solution technique is applied to solve the triangular possibilistic model to optimise emergency delivery service. The effectiveness of the proposed algorithm is evaluated by comparing it with a designed genetic algorithm on sets of 20 numerical examples. The model is then applied to the real case study of 2009 Black Saturday bushfires in Victoria, Australia. The results show that it is possible to transfer the last-minute evacuees during the Black Saturday bushfires under the hard time window constraint. Network disruptions however have impact on resource utilisation. The modelling outputs will be useful in the development of emergency plans and evacuation strategies to enhance rapid response to last-minute evacuation in a bushfire emergency.

The vehicle routing problem with hard time windows and stochastic service times

In this paper we consider the vehicle routing problem with hard time windows and stochastic service times (VRPTW-ST); in this variant of the classic VRPTW the service times are random variables. In particular, given a set of vehicle routes, some of the actual service times might not lead to a feasible solution, given the customer time windows. We consider a chance-constrained program to model the VRPTW-ST and provide a new set partitioning formulation that includes a constraint on the minimum success probability of the set of vehicle routes. Under some mild conditions, we develop a method to exactly compute the success probability of the routes. We then solve the VRPTW-ST by a branch-price-and-cut algorithm, where the main challenges are in the solution of the subproblems of the column generation procedure. We adapt the dynamic programming algorithm to account for the probabilistic resource consumption by extending the label dimension and by providing new dominance rules. Extensive computational experiments prove the effectiveness of both the solution method and the stochastic model.

A Partial Delivery Bi-Objective Vehicle Routing Model with Time Windows and Customer Satisfaction Function

We present a new bi-objective model for vehicle routing problem with partial delivery and time windows considering customer’s satisfaction. Objectives are to maximize the customer satisfaction and minimize the travel time. Hard time windows and the possibility of multiple visits are considered and the customer needs could be more than the vehicle’s capacity. A mixed-integer nonlinear programming model is provided which is linearized to obtain the optimal solutions. A number of random instances are generated and solved by the LINGO to assess and validate the effectiveness of the proposed model. DOI: 10.5901/mjss.2016.v7n4S2p102

The vehicle routing problem with hard time windows and stochastic travel and service time

In real-world environments, the variability is always present and influences the level and cost service offered to customers. In this scenario, the present work develops a strategy to solve the Vehicle Routing Problem with Time Windows (VRPTW) in which the travel time among the customers is known only probabilistically and the vehicles are not allowed to start the service before the earliest time windows. The fact there is waiting time brings a challenge to the model because the arrival time distribution at a customer can be truncated, affecting the arrival time in the following customers. A new method is developed to estimate the vehicle arrival time at each customer and to estimate the vehicle's probability to respect the customer's time window. The metaheuristic based on Iterated Local Search finds the best route with minimal expected cost, and it guarantees that certain levels of service are met. A benchmark is used to evidence the superior performance and accuracy of the proposed method.

Enhancing emergency evacuation response of late evacuees: Revisiting the case of Australian Black Saturday bushfire

This paper develops a multi-objective integer programming model to support tactical planning decision-making during a short-notice evacuation using the situated context of the 2009 Black Saturday bushfires in Victoria. Various bushfire scenarios and sensitivity analysis considering short time windows, availability of resources and road disruptions were implemented to demonstrate the robustness and reliability of the model. The ε-constraint technique was applied to solve the problem. Results showed that it would be possible to evacuate all late evacuees during the Black Saturday bushfire events, even if one or two resources are disrupted within the hard time window constraint.

A branch-and-price based heuristic for the stochastic vehicle routing problem with hard time windows

In the Vehicle Routing Problem with Hard Time Windows and Stochastic travel times, a disruption occurs if, due to stochastic events, a vehicle arrives too late at a customer. In this case a recourse action is required such that the service starts within the time window, and a relevant penalty cost is incurred. Despite the problem has been inspired by a real-life application in airport ground handling optimization, it has never been addressed before in literature, to the best of our knowledge. We discuss how the expected penalty cost can be evaluated and how this computation can be integrated in a branch-and-price procedure to obtain heuristic solutions. Preliminary tests on literature instances show the effectiveness of the approach.

Analysis of OpenMP and MPI implementations of meta-heuristics for vehicle routing problems

The parallelization of heuristic methods allows the researchers both to explore the solution space more extensively and to accelerate the search process. Nowadays, there is an increasing interest on developing parallel algorithms using standard software components that take advantage of modern microprocessors including several processing cores with local and shared cache memories. The aim of this paper is to show it is possible to parallelize algorithms included in computational software using standard software libraries in low-cost multi-core systems, instead of using expensive high-performance systems or supercomputers. In particular, it is analyzed the benefits provided by master-worker and island parallel models, implemented with MPI and OpenMP software libraries, to parallelize population-based meta-heuristics. The capacitated vehicle routing problem with hard time windows (VRPTW) has been used to evaluate the performance of these parallel strategies. The empirical results for a set of Solomon's benchmarks show that the parallel approaches executed on a multi-core processor produce better solutions than the sequential algorithm with respect to both the quality of the solutions obtained and the runtime required to get them. Both MPI and OpenMP parallel implementations are able to obtain better or at least equal solutions (in terms of distance traveled) than the best known ones for the considered benchmark instances.

Shippers’ collaboration in city logistics

To remain competitive, shippers must reduce their costs and in particular transportation costs. Collaborating between each other and grouping their demands may help to reach this goal. This can be addressed by solving pickup and delivery problems with multiple time windows (PDPMTW) with paired demands, where vehicles have to transport loads from pickup locations to delivery locations while respecting capacity and time constraints. This paper presents an exact model to solve a PDPTW with soft period and hard time windows. The objective is to minimize the total cost including transportation and penalty costs. The obtained results are encouraging for such problems in an urban context.

Multi-depot time dependent vehicle routing problem with heterogeneous fleet and time windows

Extensive research has been devoted to the vehicle routing problem (VRP). Most of these researches assume a homogenous fleet with constant travel times and single depot. In this paper, we consider the time dependent multi-depot vehicle routing problem. The objective is to minimise the total heterogeneous fleet cost assuming that the travel time between two locations depends on the departure time of vehicles. Also, hard time window constraints for the customers and transit restrictions should be satisfied. The problem is formulated as a mixed integer programming model. Due to NP-hardness of the problem a parameters-tuned simulated annealing (SA) is proposed to obtain a satisfying solution. The efficiency of the proposed SA is evaluated on 180 test problems. The obtained computational results indicate that the proposed procedure is efficient.

Daily scheduling of home health care services using time-dependent public transport

This paper presents a real-world optimization problem in home health care that is solved on a daily basis. It can be described as follows: care staff members with different qualification levels have to visit certain clients at least once per day. Assignment constraints and hard time windows at the clients have to be observed. The staff members have a maximum working time and their workday can be separated into two shifts. A mandatory break that can also be partitioned needs to be scheduled if the consecutive working time exceeds a certain threshold. The objective is to minimize the total travel- and waiting times of the care staff. Additionally, factors influencing the satisfaction of the clients or the care staff are considered. Most of the care staff members from the Austrian Red Cross (ARC) in Vienna use a combination of public transport modes (bus, tram, train, and metro) and walking. We present a novel model formulation for this problem, followed by an efficient exact solution approach to compute the time-dependent travel times out of the timetables from public transport service providers on a minute-basis. These travel time matrices are then used as input for three Tabu Search based solution methods for the scheduling problem. Extensive numerical studies with real-world data from the ARC show that the current planning can be improved significantly when these methods are applied.

A priori optimization with recourse for the vehicle routing problem with hard time windows and stochastic service times

The vehicle routing problem with hard time windows and stochastic service times (VRPTW-ST) introduced by Errico et al. (2013) in the form of a chance-constrained model mainly differs from other vehicle routing problems with stochastic service or travel times considered in the literature by the presence of hardtime windows. This makes the problem extremely challenging. In this paper, we model the VRPTW-ST as a two-stage stochastic program and define two recourse policies to recover operations feasibility when the first stage plan turns out to be infeasible. We formulate the VRPTW-STas a set partitioning problem and solve it by exact branch-cut-and-price algorithms. Specifically, we developed efficient labeling algorithms by suitably choosing label components, determining extension functions, and developing lower and upper bounds on partial route reduced cost to be used in the column generation step. Results on benchmark data show that our methods are able to solve instances with up to 50 customers for both recourse policies.

A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience

Organizations providing home care services are inclined to optimize their activities in order to meet the constantly increasing demand for home care. In this context, home care providers are confronted with multiple, often conflicting, objectives such as minimizing their operating costs while maximizing the service level offered to their clients by taking into account their preferences. This paper is the first to shed some light on the trade-off relationship between these two objectives by modeling the home care routing and scheduling problem as a bi-objective problem. The proposed model accounts for qualifications, working regulations and overtime costs of the nurses, travel costs depending on the mode of transportation, hard time windows, and client preferences on visit times and nurses. A distinguishing characteristic of the problem is that the scheduling problem for a single route is a bi-objective problem in itself, thereby complicating the problem considerably. A metaheuristic algorithm, embedding a large neighborhood search heuristic in a multi-directional local search framework, is proposed to solve the problem. Computational experiments on a set of benchmark instances based on real-life data are presented. A comparison with exact solutions on small instances shows that the algorithm performs well. An analysis of the results reveals that service providers face a considerable trade-off between costs and client convenience. However, starting from a minimum cost solution, the average service level offered to the clients may already be improved drastically with limited additional costs.