Flexible Time Windows Research Articles

A rich heterogeneous fleet vehicle routing problem with flexible time windows: a case study of dairy supply chain

Routing is a particularly important concept of cargo transport and has always enticed the interest of researchers and decision makers from different industries. The rich vehicle routing problem considers more realistic features of the real-world problems than the conventional problem. This article aims at solving a vehicle routing problem with heterogeneous fleet and flexible hard and soft time windows where flexible time windows allow for early and tardy deliveries in a given tolerance interval considering earliness and tardiness penalties through defining the earliness and tardiness as decision variables. In this paper, the proposed mathematical programming model is verified through several numerical examples using GAMS software. In order to demonstrate the applicability of the model, a real-world case study is provided. The results show the high potential of the proposed model for real-life application. Specifically, by applying the results of the case study, a 156,000 USD annual cost reduction is possible.

Tree growth and its climate signal along latitudinal and altitudinal gradients: comparison of tree rings between Finland and the Tibetan Plateau

Abstract. Latitudinal and altitudinal gradients can be utilized to forecast the impact of climate change on forests. To improve the understanding of how these gradients impact forest dynamics, we tested two hypotheses: (1) the change of the tree growth–climate relationship is similar along both latitudinal and altitudinal gradients, and (2) the time periods during which climate affects growth the most occur later towards higher latitudes and altitudes. To address this, we utilized tree-ring data from a latitudinal gradient in Finland and from two altitudinal gradients on the Tibetan Plateau. We analysed the latitudinal and altitudinal growth patterns in tree rings and investigated the growth–climate relationship of trees by correlating ring-width index chronologies with climate variables, calculating with flexible time windows, and using daily-resolution climate data. High latitude and altitude plots showed higher correlations between tree-ring chronologies and growing season temperature. However, the effects of winter temperature showed contrasting patterns for the gradients. The timing of the highest correlation with temperatures during the growing season at southern sites was approximately 1 month ahead of that at northern sites in the latitudinal gradient. In one out of two altitudinal gradients, the timing for the strongest negative correlation with temperature at low-altitude sites was ahead of treeline sites during the growing season, possibly due to differences in moisture limitation. Mean values and the standard deviation of tree-ring width increased with increasing mean July temperatures on both types of gradients. Our results showed similarities of tree growth responses to increasing seasonal temperature between latitudinal and altitudinal gradients. However, differences in climate–growth relationships were also found between gradients due to differences in other factors such as moisture conditions. Changes in the timing of the most critical climate variables demonstrated the necessity for the use of daily-resolution climate data in environmental gradient studies.

The vehicle routing problem with multiple prioritized time windows: A case study

This paper addresses Multi-objective Vehicle Routing Problem with Multiple Prioritized Time Windows (VRPMPTW) in which the distributer proposes a set of all non-overlapping time windows with equal or different lengths and the customers prioritize these delivery time windows. VRPMPTW aims to find a set of routes of minimal total traveling cost and maximal customer satisfaction (with regard to the prioritized time windows), starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. This problem is inspired from a real life application. The contribution of this paper lies in its addressing the VRPMPTW from a problem definition, modeling and methodological point of view. We developed a mathematical model for this problem. This model can simply be used for a wide range of applications where the customers have multiple flexible time windows and violation of time windows may drop the satisfaction levels of customers and lead to profit loss in the long term. A Cooperative Coevolutionary Multi-objective Quantum-Genetic Algorithm (CCMQGA) is also proposed to solve this problem. A new local search is designed and used in CCMQGA to reach an appropriate pareto front. Finally, the proposed approach is employed in a real case study and the results of the proposed CCMQGA are compared with the current solution obtained from managerial experience, the results of NSGA-II and the multi-objective quantum-inspired evolutionary algorithm.

A Vehicle Routing Problem with Flexible Time Windows

In this paper, we introduce the Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW), in which vehicles are allowed to deviate from customer time windows by a given tolerance. This flexibility enables savings in the operational costs of carriers, since customers may be served before and after the earliest and latest time window bounds, respectively. However, as time window deviations are undesired from a customer service perspective, a penalty proportional to these deviations is accounted for in the objective function. We develop a solution procedure, in which feasible vehicle routes are constructed via a tabu search algorithm. Furthermore, we propose a linear programming model to handle the detailed scheduling of customer visits for given routes. We validate our solution procedure by a number of Vehicle Routing Problem with Time Windows (VRPTW) benchmark instances. We highlight the costs involved in integrating flexibility in time windows and underline the advantages of the VRPFlexTW, when compared to the VRPTW.

A decision support system for optimizing dynamic courier routing operations

In this paper, we propose a prototype of a decision support system (DSS) that integrates a hybrid neighborhood search algorithm to solve the offline and online routing problems arising in courier service. In the dynamic operational environment of courier service, new customer orders and order cancellations continually arrive over time and thus disrupt the optimal routing schedule that was originally designed. This calls for the real-time re-optimization of routes. As service level is sensitive to whether allowable service time intervals are wide or narrow, it is valuable to study how adjustable and flexible time windows influence the courier service efficiency in a dynamic environment. To capture these dynamic features, a dynamic vehicle routing problem (DVRP) that simultaneously considers new customer orders and order cancellations is investigated in this study. Meanwhile, fuzzy time windows are formulated in the DVRP model to quantify the service level and explore the service efficiency. To tackle the new problem, we propose a competitive hybrid neighborhood search heuristic for (re)optimizing the offline and online routes. Numerical computational experiments and the comparison with results from Lingo show that our algorithm is capable of re-optimizing dynamic problems effectively and accurately in a very short time. The proposed model and algorithms are able to enhance courier service level without further expense of a longer traveling distance or a larger number of couriers.

A Branch-and-Price Algorithm for Capacitated Arc Routing Problem with Flexible Time Windows

Abstract In this paper we study Capacitated Arc Routing Problem with Flexible Time Windows where violating a time windows implies some extra cost. We propose a branch-and-price algorithm due to the Dantzig-Wolfe decomposition. The subproblem is a non-elementary capacitated shortest path problem. Experimental results are presented on the instances up to 40 nodes and 69 required edges.

Resource co-allocation using advance reservations with flexible time-windows

Co-allocations require the availability of more than one resource for utilization in a time interval. We show that co-allocations increase the blocking probability and analyze the use of flexible windows to lower blocking probability in spite of co-allocations.

HANDLING IMPRECISION IN VEHICLE ROUTING PROBLEMS: FUZZY LOGIC APPROACH

In this article, we are interested in the dynamic management of a vehicles fleet, dedicated to the pick-up and/or delivery of parcels in a customers set. In order to have a more realistic model, travel times and time windows are subject to variations: we will present a realistic vehicle routing problem model obtained by introducing uncertainties data (flexible time windows and fuzzy travel times) modelled by using fuzzy logic. In the last, we will present a resolution preliminary results obtained by two approaches (heuristic insertion and genetic algorithm).

Flexible time-windows for advance reservation in LambdaGrids

Advance-reservation requests are an essential feature of LambdaGrids, where resources may need to be co-allocated at pre-determined times. In this paper, we discuss unconstrained advance reservations, which use flexible time-windows to lower blocking probability and, consequently, increase resource utilization. We claim and show using simulations that the minimum window size, which theoretically brings the blocking probability to 0, in a first-come-first-served advance reservation model without time-slots, equals the waiting time in a queue-based on-demand model. We also show, with simulations, the window sizes, which bring the blocking probability to its minimum, for an advance reservation model with time-slots.

The vehicle routing problem with flexible time windows and traveling times

We generalize the standard vehicle routing problem by allowing soft time window and soft traveling time constraints, where both constraints are treated as cost functions. With the proposed generalization, the problem becomes very general. In our algorithm, we use local search to determine the routes of vehicles. After fixing the route of each vehicle, we must determine the optimal start times of services at visited customers. We show that this subproblem is NP-hard when cost functions are general, but can be efficiently solved with dynamic programming when traveling time cost functions are convex even if time window cost functions are non-convex. We deal with the latter situation in the developed iterated local search algorithm. Finally we report computational results on benchmark instances, and confirm the benefits of the proposed generalization.

A note on an iterative forward/backward scheduling technique with reference to a procedure by Li and Willis

In this note we propose an iterative scheduling technique which consists of consecutive forward/backward scheduling passes aimed at reducing the project duration by smoothing out the project's resource profile. The idea of iterative scheduling is initiated by Li and Willis in their related paper. The only common point between their scheduling technique and the one proposed here is the iterative feature. The two techniques differ both in algorithmic aspects and in the way activities are selected for scheduling at a decision point. In the technique proposed here activities are evaluated by well-reputed dispatching rules and a conflict based decision-making process called Local Constraint Based Analysis (LCBA). The results on benchmark problems from the literature demonstrate that LCBA specifically exploits the flexible activity time windows provided by the iterative scheduling technique.