Time Window Constraints Research Articles

Matheuristics to optimize refueling and maintenance planning of nuclear power plants

Planning the maintenance of nuclear power plants is a complex optimization problem, involving a joint optimization of maintenance dates, fuel constraints and power production decisions. This paper investigates Mixed Integer Linear Programming (MILP) matheuristics for this problem, to tackle large size instances used in operations with a time scope of five years, and few restrictions with time window constraints for the latest maintenance operations. Several constructive matheuristics and a Variable Neighborhood Descent local search are designed. The matheuristics are shown to be accurately effective for medium and large size instances. The matheuristics give also results on the design of MILP formulations and neighborhoods for the problem. Contributions for the operational applications are also discussed. It is shown that the restriction of time windows, which was used to ease computations, induces large over-costs and that this restriction is not required anymore with the capabilities of matheuristics or local search to solve such size of instances. Our matheuristics can be extended to a bi-objective optimization extension with stability costs, for the monthly re-optimization of the maintenance planning in the real-life application.

The Split Delivery Vehicle Routing Problem with Three-Dimensional Loading and Time Windows Constraints

Besides routing and packing plans, synthetically considering the requirements of customers about service time is absolutely necessary. An order split delivery plan can not only better satisfy the service time requirements, but also improve the full-load rate of vehicles. The split delivery vehicle routing problem with three-dimensional loading constraints (3L-SDVRP) combines vehicle routing and three-dimensional loading with additional packing constraints. In the 3L-SDVRP splitting deliveries of customers is basically possible, i.e., a customer can be visited in two or more tours. The vehicle routing problem with three-dimensional loading constraints that are based on the time window and considering split delivery of orders (3L-CVRPTWSDO) and its optimization algorithm are studied in this paper. We established mathematical model of the problem and designed the tabu search algorithm. Based on the examples used in Gendreau et al. (2006), examples was constructed to test our algorithm. The experimental results have expressed that, in the 3L-CVRP problem, the results of split delivery is better than those of non-split delivery, and it is easier to satisfy the time window constraints. The algorithm in this paper generates high quality solutions, it provides a effective method to solve the 3L-CVRPTWSDO problems.

The flexible and real-time commute trip sharing problems

The Commute Trip Sharing Problem (CTSP) was introduced to remove parking pressure on cities, as well as corporate and university campuses. Its goal is to reduce the number of vehicles being used for daily commuting activities. Given a set of inbound and outbound requests, which consists of origin and destination pairs and their departure and return times, the CTSP assigns riders and a driver, as well as inbound and outbound routes, to each vehicle in order to satisfy time-window, capacity, and ride-duration constraints. The CTSP guarantees a ride back for each rider, which is a critical aspect of such a ride-sharing system. This paper generalizes the CTSP to account for uncertainties about the return trip. Each rider is assumed to have a return time specified by a distribution (learned from historical data) and, each day, a percentage of riders will want to preprone or postpone their return trip to accommodate some schedule changes. The paper proposes two generalizations of the CTSP: the Flexible CTSP (FCTSP) and the Real-Time CTSP (RT-CTSP). In the FCTSP, riders must confirm their final return times by a fixed deadline. In the RT-CTSP, riders confirm their new return times in real time with some prior notice. The paper proposes a two-step approach to address the FCTSP and the RT-CTSP. The first step uses a scenario-based stochastic program to choose the drivers and the morning routes in order to maximize the robustness of the driver assignment. The second step reoptimizes the plan at the fixed deadline or in real time once the return times are confirmed. Experiments on a real-world dataset of commute trips demonstrate the effectiveness of the algorithm in generating robust plans and reveal a trade-off between vehicle reduction and plan robustness as the robust plans tend to be conservative. A method is then proposed to evaluate this trade-off using the per-unit price ratio of vehicle increase to uncovered riders.

A new constraint programming model and a linear programming-based adaptive large neighborhood search for the vehicle routing problem with synchronization constraints

We consider a vehicle routing problem which seeks to minimize cost subject to time window and synchronization constraints. In this problem, the fleet of vehicles is categorized into regular and special vehicles. Some customers require both vehicles’ services, whose service start times at the customer are synchronized. Despite its important real-world application, this problem has rarely been studied in the literature. To solve the problem, we propose a Constraint Programming (CP) model and an Adaptive Large Neighborhood Search (ALNS) in which the design of insertion operators is based on solving linear programming (LP) models to check the insertion feasibility. A number of acceleration techniques is also proposed to significantly reduce the computational time. The computational experiments show that our new CP model finds better solutions than an existing CP-based ALNS, when used on small instances with 25 customers and with a much shorter running time. Our LP-based ALNS dominates the CP-based ALNS, in terms of solution quality, when it provides solutions with better objective values, on average, for all instance classes. This demonstrates the advantage of using linear programming instead of constraint programming when dealing with a variant of vehicle routing problems with relatively tight constraints, which is often considered to be more favorable for CP-based methods. We also adapt our algorithm to solve a well-studied variant of the problem, and the obtained results show that the algorithm provides good solutions as state-of-the-art approaches and improves four best known solutions.

The long-haul full-load vehicle routing and truck driver scheduling problem with intermediate stops: An economic impact evaluation of Brazilian policy

Abstract This paper presents a methodology to identify the economic impact of different policies for heavy vehicle routing and driver scheduling in long-haul full-load trips with intermediate stops for refueling and for regulation-driven meal and rest periods. This methodology can be used both as a planning tool to help policy-makers define policies through scenario simulations, and as an evaluation tool to examine ex-post economic impact once policies have been changed as illustrated herein for the Brazilian case. The paper introduces a mathematical formulation, proposes a state-space graph search approach, and develops an algorithmic solution for a variant of the vehicle routing and truck driver scheduling problem with intermediate stops (VRTDSPIS), which is especially important in countries with vast territory where long-range freight trucking trips are common. In addition, it is particularly relevant for the economies of emerging markets that may have evolving regulatory frameworks and suboptimal infrastructure environments. Regulatory maximum driving and minimum driver resting time windows impose significant constraints to trucker routines, especially in sparsely populated regions through which long range vehicle trips with full load are common. Such trips can take days to be concluded and numerous alternative routes are possible, each with very different alternatives for refueling and rest. While the literature to date has focused mostly on truck driver scheduling given pre-determined routes and individual country’s laws and regulations, this paper proposes a joint solution for the routing and scheduling problem with time window constraints, determining simultaneously a routing and scheduling plan that meets all maximum driving and minimum resting time interval regulatory requirements at minimum cost. An illustration applying the methodology to evaluate the economic impact of truck driver regulatory changes in Brazil is presented.

Research on Coordination and Optimization of Order Allocation and Delivery Route Planning in Take-Out System

This paper studies the take-out route delivery problem (TRDP) with order allocation and unilateral soft time window constraints. The TRDP considers the order allocation and delivery route optimization in the delivery service process. The TRDP is a challenging version of vehicle routing problem. In order to solve this problem, this paper aims to minimize the total cost of delivery, builds an optimization model of this problem by using cumulative time, and adds time dimension in order allocation and path optimization dimensions. It can not only track the real-time location of delivery personnel but also record the delivery personnel to perform a certain task. The main algorithm is the dynamic allocation algorithm designed from the perspective of dispatch efficiency, and the subalgorithm is the improved genetic algorithm. Finally, some experiments are designed to verify the effectiveness of the established model and the designed algorithm, the order allocation and route optimization are calculated with/without the consideration of traffic jam, and the results show that the algorithm can generate better solution in each scene.

In-port multi-ship routing and scheduling problem with draft limits

ABSTRACT This paper addresses an in-port multi-ship routing and scheduling problem in maritime transportation. The key objective is to find an optimal routing and schedule for multiple ships that are planned to pick up or deliver cargos located in the various terminals of a port with different draft limits. Using the multiple traveling salesman problem (mTSP) as a base, we formulate a multi-ship routing and scheduling model with draft limits and time windows constraints. To solve the developed model, a two-stage solution method based on dynamic programming and branch-and-bound algorithms is developed. The solution approach is applied to 41 real-sized problem instances. Our experiments revealed that the proposed method outperforms CPLEX by accurately solving the problem instances in a reasonable time. The formulated problem and presented solution can be implemented in fleet operations of autonomous ships in smart maritime transportation systems of the future.

Multi-objective Tourist Trip Design Problem in Chiang Mai City

This study aims to solve a multi-objective tourist trip design problem (MO-TTDP) in order to simultaneously maximize tourist satisfaction and minimize total traveling cost. The goal is to identify optimal routing for tourist under time window and time horizon constraints. The mathematical model is first presented to find optimal routing under limited budget. However, the exact algorithm cannot find solution with multiple objectives simultaneously. Therefore, this study applies a metaheuristic, called Global Local and Near-Neighbour Particle Swarm Optimization (GLNPSO), to solve the MO-TTDP. Several local search strategies are also proposed to enhance the solution quality. The proposed algorithm is implemented on the real-case study in Chiang Mai City, Thailand. The experimental results show that the proposed algorithm yields a set of diverse and high quality non-dominated solutions.

Effective neighborhood search with optimal splitting and adaptive memory for the team orienteering problem with time windows

The Team Orienteering Problem with Time Windows (TOPTW) is an extension of the well-known Orienteering Problem. Given a set of locations, each one associated with a profit, a service time and a time window, the objective of the TOPTW is to plan a set of routes, over a subset of locations, that maximizes the total collected profit while satisfying travel time limitations and time window constraints. Within this paper, we present an effective neighborhood search for the TOPTW based on (1) the alternation between two different search spaces, a giant tour search space and a route search space, using a powerful splitting algorithm, and (2) the use of a long term memory mechanism to keep high quality routes encountered in elite solutions. We conduct extensive computational experiments to investigate the contribution of these components, and measure the performance of our method on literature benchmarks. Our approach outperforms state-of-the-art algorithms in terms of overall solution quality and computational time. It finds the current best known solutions, or better ones, for 89% of the literature instances within reasonable runtimes. Moreover, it is able to achieve better average deviation than state-of-the-art algorithms within shorter computation times. Moreover, new improvements for 57 benchmark instances were found.

Two-echelon vehicle routing problem with satellite bi-synchronization

In considering route optimization at a series of express stages from pickup to delivery via the intercity linehaul, we introduce the two-echelon vehicle routing problem with satellite bi-synchronization (2E-VRP-SBS) from the perspective of modeling the routing problems of two-echelon networks. The 2E-VRP-SBS involves the inter-satellite linehaul on the first echelon, and the pickups from senders to origin satellites (i.e., satellites for cargo collection) and deliveries from destination satellites (i.e., satellites for cargo deliveries) to receivers on the second echelon. The 2E-VRP-SBS integrates satellite bi-synchronization constraints, multiple vehicles, and time window constraints on the two-echelon network and aims to find cost-minimizing routes for various types of trucks. Satellite bi-synchronization constraints, which synchronously guarantee the synchronization at origin satellites and the synchronization at destination satellites, provide an innovative method to formulate the two-echelon routing problem. In this study, we develop a mixed-integer programming model for the 2E-VRP-SBS. An exact method using CPLEX solver is presented and a modified adaptive large neighborhood search is conducted. Furthermore, the effectiveness of the 2E-VRP-SBS formulation and the applicability of the heuristic for various instances are experimentally evaluated.

Towards delivery-as-a-service: Effective neighborhood search strategies for integrated delivery optimization of E-commerce and static O2O parcels

In this paper, we investigate a new variant of last-mile delivery that integrates the scheduling of static E-commerce parcels and Online-to-Offline(O2O) parcels. The O2O parcels, such as flowers and cakes, are often delivered intra city with a time window constraint. It is driven by the concept of delivery-as-a-service, which targets at building consolidated infrastructure and using the same fleet of vehicles to provide standardized delivery services for different types of merchants. We formulate it as an integration of Multi-Depot Multi-Trip Vehicle Routing Problem (MDMTVRP) and Paired Pickup and Delivery Problem with Time Window (PPDPTW). To solve the mixed problem of MDMTVRP and PPDPTW, we present its Mixed-Integer Programming (MIP) model to obtain the optimal solution for small-scale instances. To solve large-scale problems, we propose a hybrid neighborhood search strategy to effectively combine the merits of ALNS and tabu search. We also present a two-level pruning strategy that can significantly accelerate the local search procedure. We conduct extensive numeric experiments on multiple datasets, and results showed that our hybrid approach achieved near-optimal performance and established clear superiority over ALNS and tabu search.

On the one-to-one pickup-and-delivery problem with time windows and trailers

This paper studies an extension of the well-known one-to-one pickup-and-delivery problem with time windows. In the latter problem, requests to transport goods from pickup to delivery locations must be fulfilled by a set of vehicles with limited capacity subject to time window constraints. Goods are not interchangeable: what is picked up at one particular location must be delivered to one particular other location. The discussed extension consists in the consideration of a heterogeneous vehicle fleet comprising lorries with detachable trailers. Trailers are advantageous as they increase the overall vehicle capacity. However, some locations may be accessible only by lorries. Therefore, special locations are available where trailers can be parked while lorries visit accessibility-constrained locations. This induces a nontrivial tradeoff between an enlarged vehicle capacity and the necessity of scheduling detours for parking and reattaching trailers. The contribution of the paper is threefold: (i) it studies a practically relevant generalization of the one-to-one pickup-and-delivery problem with time windows. (ii) It develops an exact amortized constant-time procedure for testing the feasibility of an insertion of a transport task into a given route with regard to time windows and lorry and trailer capacities. (iii) It provides a comprehensive set of new benchmark instances on which the runtime of the constant-time test is compared with a naïve one that requires linear time by embedding both tests in an adaptive large neighbourhood search algorithm. Computational experiments show that the constant-time test outperforms its linear-time counterpart by one order of magnitude on average.

Discrete scenario-based optimization for the robust vehicle routing problem: The case of time windows under delay uncertainty

In this paper we propose a robust optimization strategy for the vehicle routing problem with time windows, where the travel time is considered as uncertain. The objective is to minimize the risk of delay related to the time windows constraint. We first present a robust model in which the uncertain travel time is related to a discrete set of scenarios: each scenario can be viewed as an observation of time required to complete a current route. Such a model is based upon a mixed-integer linear programming that can handle an optimal (solution) value related to the worst observation of the total travel time over all available scenarios. Second, in order to evaluate the effects on the scenario model, a guided neighborhood search-based heuristic is adapted for solving the model and tested on a variety of instances obtained by using Solomon’s standard generator, where a total of 5040 instances are considered. Finally, we study the behavior of the adapted algorithm to solve the robust model and highlight the interaction between the number of scenarios used which are based upon uncertain events and the uncertainty of the problem.

Transit-Based Evacuation for Urban Rail Transit Line Emergency

Urban rail systems are the backbone of urban transit networks and are characterized by large passenger volumes, high speeds, punctuality, and low environmental impacts. However, unforeseen events such as rail transit line emergencies can lead to unexpected costs and delays. As a means of disruption management, we divide the decision support system for urban rail transit line emergency situations into two stages—transit-based evacuation and bus bridging management. This paper focuses on the transit-based evacuation under emergency scenarios on a single rail line. The model determines the vehicles and routes within traditional transit systems required to evacuate stranded passengers within a given time window. In addition, the proposed method ensures the reliability of traditional transit systems by considering the operating fleet and reserve fleet in the traditional transit systems. Therefore, the proposed optimization model is established with the objective of maximizing the total number of stranded passengers transferred within the given time window and headway constraint. Herein, we present the optimization model and solution method, and the proposed method is validated. The effectiveness of the proposed control method is evaluated in the Changchun urban transit network. By analyzing stranded passengers at stations under different numbers of vehicles and time periods, the results show that the proposed model can significantly provide routing arrangements to maximize the number of passengers evacuated from stations. The results are useful in the development of emergency evacuation plans to prevent secondary accidents and evacuate stranded passengers during a rail transit line emergency.

Vessel routing and optimization for marine debris collection with consideration of carbon cap

Marine debris pollution is becoming an increasingly serious problem, affecting not only navigational safety but also the health of marine ecosystems. Carbon emission causes ocean acidification, which greatly harms marine lives. In order to respond to these environmental issues, this paper studies marine debris collection with consideration of carbon cap using logistics network. To the most of our knowledge, this is first work to study marine debris removal from logistics way. We proposed a three-phase marine debris collection framework: (1) identifying initial locations of the debris; (2) utilizing GNOME software to predict the drifting trajectory of the debris; and (3) formulating vessel routing as a mixed integer nonlinear programming with consideration of carbon emission. The model seeks to minimize the total costs including fuel cost, berth cost, unloading cost in the harbor, vessel rent, vessel insurance, and labor cost, with respect to the constraints of carbon cap, vessel capacities, and time windows. After the linearization process, a Branch-and-Cut (B&C) algorithm with multiple variable fixing techniques and valid inequalities is used to solve the proposed model. The debris dispersion located in Boston vicinity is used as a case study to validate the proposed model and algorithm. The results reveal that the farther away the debris location is from the shore, the higher the collection cost and the more the carbon emission would be. The daily collection cost in the closest location and in the farthest location is $140 lower and $210 higher than that in the initial location. The carbon emission in the farthest location is 21% and 32% higher than that in the initial location and in the closest location. Sensitivity analysis is also carried out for the fuel price and carbon cap to test their impact on total costs These results show that proposed model and algorithm can significantly improve the efficiency of marine debris collection process, reduce carbon emission and total costs.

Intelligent decision support systems for determining tour bus route with time windows: A metaheuristic approach

The transportation routing problem is a very popular field in operations research and management science area. Many previous researches are still continuing to develop model and algorithm to produce the best transportation route optimization in various research objects. Technology has enabled the development of the intelligent decision support system (I-DSS) to optimize transportation route. Although technology has evolved, there are still few researches that build I-DSS software to minimize transportation distance and fuel consumption, especially using the metaheuristic approach. Thus, this paper aims to develop I-DSS software to minimize fuel consumption and travel distance by considering time-windows constraint using metaheuristic approach. The software can receive input dynamically to evaluate and select the best transportation route. The results of this software have been tested using real historical data from one of tour and travel company in Indonesia. The company provides travel services using a bus to visit several tourist attractions based on the opening hours of the destinations. I-DSS software output shows that the travel distance is 25.64% more efficient than the current real conditions. In addition, the fuel consumption produced by I-DSS is better than the actual conditions, which is 17.35% more efficient.

An efficient heuristic method for joint optimization of train scheduling and stop planning on double-track railway systems

In this study, a new mathematical programming approach for solving the joint timetabling and train stop planning problem in a railway line with double-track segments is proposed. This research aims to design an optimized train timetable subject to the station-capacity and time-dependent dwell time constraints. The objective function is to maximize the railway infrastructure capacity by minimizing the schedule makespan. The problem is formulated as a particular case of blocking permutation flexible flow shop scheduling model with dynamic time window constraints. Due to the combinatorial nature of the problem, heuristic algorithm and bound tightening methods are proposed that generate approximate solutions, which are computationally efficient for large-size instances of the problem. Computational experiments based on the Iranian railway data set are conducted to examine the performance of the heuristic method. The results of the numerical experiments verified the efficiency of the heuristic method in solving moderately large instances of the problem. The outcomes show that the heuristic method works efficiently in finding high-quality solutions with optimality gaps of 2.1% on average.

A mixed integer robust programming model for two-echelon inventory routing problem of perishable products

To solve the inventory routing problem of perishable products with time window constraints, a mixed integer linear programming (MILP) model is constructed to minimize the total cost. Due to the uncertainty of market demand, the MILP model is further transformed into mixed integer robust programming (MIRP) model by introducing uncertain sets (box, ellipsoid and polyhedron). Experiments with actual data show that as demand uncertainty increases, although MIRP models will pay corresponding robust costs, they can achieve better robustness. In addition, the comparison shows that the ellipsoid set MIRP model can achieve a higher level of logistics and distribution services.

Single machine workpieces sorting problem with time window

In the research process of sorting problem, on the one hand is the development of the diversity of solving methods, on the other hand is the continuous generation of modern problem model due to the emergence of many practical problems, the basic assumptions of the classical sorting problem has been constantly breakthrough, a large number of modern sorting problems. The problem with time window constraint is studied. The sorting of only one machine workpieces is discussed, this paper designed a 3/2-approximation algorithm, the algorithm complexity is.

A Matheuristic Algorithm for the Inventory Routing Problem

This work addresses a challenging inventory routing problem that arises from a practical application faced by air-product companies, including Air Liquide. Given its computational complexity and industrial importance, this problem (denoted as IRP-Challenge2016) was presented as the topic of the French Operational Research and Decision Support Society/European Operational Research Society (ROADEF/EURO) Challenge 2016. The IRP-Challenge2016 seeks an optimal delivery schedule to minimize the unit distribution cost, while satisfying various hard constraints. It involves a single product, a heterogeneous fleet, heterogeneous drivers, multiperiods, a deterministic consumption forecast, and time-window constraints. We present a new mathematical formulation of the problem and introduce a matheuristic algorithm that integrates a local search-based metaheuristic with mathematical programming. Our algorithm combines mixed integer programming and linear programming as slave methods to optimize timing and delivery and embeds these procedures within a multineighborhood search metaheuristic to adjust routes. The method extends and enhances a preliminary version of our algorithm, which ranked third in the final round of the ROADEF/EURO Challenge 2016. Computational results for 20 challenge benchmark instances demonstrate the value of the proposed algorithm in terms of both effectiveness and efficiency with respect to the results reported in the competition. We additionally analyze several key components of our matheuristic to gain an insight into its operation.