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In the running of multiple automated guided vehicles (AGVs) in warehouses, delay problems in motions happen unavoidably as there might exist some disabled components of robots, the instability of networks and the interference of people walking. Under this case, robots would not follow the designed paths and the coupled relationship between temporal and space domain for paths is broken. And there is no doubt that other robots are disturbed by the ones where delays happen. Finally, this brings about chaos or even breakdown of the whole system. Therefore, taking the delay disturbance into consideration in the path planning of multiple robots is an issue worthy of attention and research.

This paper proposes a prioritized path planning algorithm based on time windows to solve the delay problems of multiple AGVs. The architecture is a unity consisting of three components which are focused on scheduling AGVs under normal operations, delays of AGVs, and recovery of AGVs. In the components of scheduling AGVs under normal operations and recovery, this paper adopts a dynamic routing method based on time windows to ensure the coordination of multiple AGVs and efficient completion of tasks. In the component for scheduling AGVs under delays, a dynamical prioritized local path planning algorithm based on time windows is designed to solve delay problems. The introduced planning principle of time windows would enable the algorithm to plan new solutions of trajectories for multiple AGVs, which could lower the makespan. At the same time, the real-time performance is acceptable based on the planning principle which stipulates the parameters of local time windows to ensure that the computation of the designed algorithm would not be too large.

The simulation results demonstrate that the proposed algorithm is more efficient than the state-of-the-art method based on homotopy classes, which aims at solving the delay problems. What is more, it is validated that the proposed algorithm can achieve the acceptable real-time performance for the scheduling in warehousing applications.

By introducing the planning principle and generating delay space and local adjustable paths, the proposed algorithm in this paper can not only solve the delay problems in real time, but also lower the makespan compared with the previous method. The designed algorithm guarantees the scheduling of multiple AGVs with delay disturbance and enhances the robustness of the scheduling algorithm in multi-AGV system.

The traveling purchaser problem (TPP) has gained attention in academics to deal with different variants in real business world. This study aims to study a green TPP with quantity discounts and soft time windows (TPPQS), in which a firm needs to purchase products from a set of available markets and deliver the products to a set of customers.

Vehicles are available to visit the markets, which offer products at different prices and with different quantity discount schemes. Soft time windows are present for the markets and the customers, and earliness cost and tardiness may incur if a vehicle cannot arrive a market or a customer within the designated time interval. The environmental impact of transportation activities is considered. The objective of this research is to minimize the total cost, including vehicle-assigning cost, vehicle-traveling cost, purchasing cost, emission cost, earliness cost and tardiness cost, while meeting the total demand of the customers and satisfying all the constraints. A mixed integer programming (MIP) model and a genetic algorithm (GA) approach are proposed to solve the TPPQS.

The results show that both the MIP and the GA can obtain optimal solutions for small-scale cases, and the GA can generate near-optimal solutions for large-scale cases within a short computational time.

The proposed models can help firms increase the performance of customer satisfaction and provide valuable supply chain management references in the service industry.

The proposed models for TPPQS are novel and can facilitate firms to design their green traveling purchasing plans more effectively in today’s environmental conscious and competitive market.

This paper, considers the multi-depot vehicle routing problem with time window considering two repair and pickup vehicles (CMDVRPTW).

The objective of this problem is minimization of the total traveling cost and the time window violations. Two meta-heuristic algorithms, namely, simple genetic algorithm (GA) and hybrid genetic algorithm (HGA) are used to find the best solution for this problem. A comparison on the results of these two algorithms has been done and based on the outcome, it has been proved that HGA has better performance than GA.

A comparison on the results of these two algorithms has been done and based on the outcome, it has been proved that HGA has better performance than GA.

This paper, considers the multi-depot vehicle routing problem with time window considering two repair and pickup vehicles (CMDVRPTW). The defined problem is a practical problem in the supply management and logistic. The repair vehicle services the customers who have goods, while the pickup vehicle visits the customer with nonrepaired goods. All the vehicles belong to an internal fleet of a company and have different capacities and fixed/variable cost. Moreover, vehicles have different limitations in their time of traveling. The objective of this problem is minimization of the total traveling cost and the time window violations. Two meta-heuristic algorithms (simple genetic algorithm and hybrid one) are used to find the best solution for this problem.

The purpose of this paper is to provide an effective solution for a complex planning problem encountered in heavy industry. The problem entails selecting a set of projects to produce from a larger set of solicited projects and simultaneously scheduling their production to maximize profit. Each project has a due window inside of which, if accepted, it must be shipped. Additionally, there is a limited inventory buffer where lots produced early are stored. Because scheduling affects which projects may be selected and vice-versa, this is a particularly difficult combinatorial optimization problem.

The authors develop an algorithm based on the Metaheuristic for Randomized Priority Search (Meta-RaPS) as well as a greedy heuristic and an integer programming (IP) model. The authors then perform computational experiments on a large set of benchmark problems over a wide range of characteristics to compare the performance of each method in terms of solution quality and time required.

The paper shows that this problem is very difficult to solve using IP, with even small instances unable to be solved optimally. The paper then shows that both proposed algorithms will in seconds often outperform IP by a large margin. Meta-RaPS is particularly robust, consistently producing the best or very near-best solutions.

The Meta-RaPS algorithm developed enables companies facing this problem to achieve higher profits through improved decision making. Moreover, this algorithm is relatively easy to implement.

This research provides an effective solution for a difficult combinatorial optimization problem encountered in heavy industry which has not been previously addressed in the literature.

Being the final end of the logistic distribution, attended home delivery (AHD) plays an important role in the distribution network. AHD typically refers to the service provided by the distribution service provider to the recipient's doorstep. Researchers have always identified AHD as a bottleneck for last-mile delivery. This paper addresses a real-life stochastic multi-objective AHD problem in the context of the Indian public distribution system (PDS).

Two multi-objective models are proposed. Initially, the problem is formulated in a deterministic environment, and later on, it is extended to a multi-objective AHD model with stochastic travel and response time. This stochastic AHD model is used to extensively analyze the impact of stochastic travel time and customer response time on the total expected cost and time-window violation. Due to the NP-hard nature of the problem, an ant colony optimization (ACO) algorithm, tuned via response surface methodology (RSM), is proposed to solve the problem.

Experimental results show that a change in travel time and response time does not significantly alter the service level of an AHD problem. However, it is strongly correlated with the planning horizon and an increase in the planning horizon reduces the time-window violation drastically. It is also observed that a relatively longer planning horizon has a lower expected cost per delivery associated.

The paper does not consider the uncertainty of supply from the warehouse. Also, stochastic delivery failure probabilities and randomness in customer behavior have not been taken into consideration in this study.

In this paper, the role of uncertainty in an AHD problem is extensively studied through a case of the Indian PDS. The paper analyzes the role of uncertain travel time and response time over different planning horizons in an AHD system. Further, the impact of the delivery planning horizon, travel time and response time on the overall cost and service level of an AHD system is also investigated.

This paper investigates a unique and practical AHD problem in the context of Indian PDS. In the present context of AHD, this study is highly relevant for real-world applications and can help build a more efficient delivery system. The findings of this study will be of particular interest to the policy-makers to build a more robust PDS in India.

The most challenging part of an AHD problem is the requirement of the presence of customers during the time of delivery, due to which the probability of failed delivery drastically increases if the delivery deviates from the customer's preferred time slot. The paper modelled an AHD system to incorporate uncertainties to attain higher overall performance and explore the role of uncertainty in travel and response time with respect to the planning horizon in an AHD, which has not been considered by any other literature.

The current air traffic management (ATM) operational approach is changing; “time” is now integrated as an additional fourth dimension on trajectories. This notion will impose on aircraft the compliance of accurate arrival times over designated checkpoints (CPs), called time windows (TWs). This paper aims to clarify the basic requirements and foundations for the practical implementation of this functional framework.

This paper reviews the operational deployment of 4D trajectories, by defining its relationship with other concepts and systems of the future ATM and communications, navigation and surveillance (CNS) context. This allows to establish the main tools that should be considered to ease the application of the 4D-trajectories approach. This paper appraises how 4D trajectories must be managed and planned (negotiation, synchronization, modification and verification processes). Then, based on the evolution of a simulated 4D trajectory, the necessary corrective measures by evaluating the degradation tolerances and conditions are described and introduced.

The proposed TWs model can control the time tolerance within less than 100 s along the passing CPs of a generic trajectory, which is in line with the expected future ATM time-performance requirements.

The main contribution of this work is the provision of a holistic vision of the systems and concepts that will be necessary to implement the new 4D-trajectory concept efficiently, thus enhancing performance. It also proposes tolerance windows for trajectory degradation, to understand both when an update is necessary and what are the conditions required for pilots and air traffic controllers to provide this update.

The pace of booking is a critical element in the accuracy of revenue management (RM) systems. Anecdotal evidence suggests that booking windows exhibit persistent shifts due to a variety of macro and micro factors. The article outlines several causes and tests the impact of the shifts on forecasting accuracy.

A novel methodological approach is utilized to empirically shift hotel reservation windows into smaller increments. Forecasts are then estimated and tested on the incremental shifts with popular RM techniques characteristic of advance booking data. A random effects model assesses the impact of the shifts on forecast accuracy.

The results show that shifts in booking behavior can cause the accuracy of forecasting models to deteriorate. The findings stress the importance of considering these shifts in model estimation and evaluation.

The results demonstrate that changes in booking behavior can be detrimental to the accuracy of RM forecasting algorithms. It is recommended that revenue managers monitor booking window shifts when forecasting with advanced booking data.

This study is the first to systematically assess the impact of booking window shifts on forecasting accuracy. The demonstrated approach can be implemented in future research to assess model accuracy as booking behavior changes.

The vehicle routing problem (VRP) has been widely investigated during last decades to reduce logistics costs and improve service level. In addition, many researchers have realized the importance of green logistic system design in decreasing environmental pollution and achieving sustainable development.

In this paper, a bi-objective mathematical model is developed for the capacitated electric VRP with time windows and partial recharge. The first objective deals with minimizing the route to reduce the costs related to vehicles, while the second objective minimizes the delay of arrival vehicles to depots based on the soft time window. A hybrid metaheuristic algorithm including non-dominated sorting genetic algorithm (NSGA-II) and teaching-learning-based optimization (TLBO), called NSGA-II-TLBO, is proposed for solving this problem. The Taguchi method is used to adjust the parameters of algorithms. Several numerical instances in different sizes are solved and the performance of the proposed algorithm is compared to NSGA-II and multi-objective simulated annealing (MOSA) as two well-known algorithms based on the five indexes including time, mean ideal distance (MID), diversity, spacing and the Rate of Achievement to two objectives Simultaneously (RAS).

The results demonstrate that the hybrid algorithm outperforms terms of spacing and RAS indexes with p-value <0.04. However, MOSA and NSGA-II algorithms have better performance in terms of central processing unit (CPU) time index. In addition, there is no meaningful difference between the algorithms in terms of MID and diversity indexes. Finally, the impacts of changing the parameters of the model on the results are investigated by performing sensitivity analysis.

In this research, an environment-friendly transportation system is addressed by presenting a bi-objective mathematical model for the routing problem of an electric capacitated vehicle considering the time windows with the possibility of recharging.

In the present research, location and routing problems, as well as the supply chain, which includes manufacturers, distributor candidate sites and retailers, are explored. The goal of addressing the issue is to reduce delivery times and system costs for retailers so that routing and distributor location may be determined.

By adding certain unique criteria and limits, the issue becomes more realistic. Customers expect simultaneous deliveries and pickups, and retail service start times have soft and hard time windows. Transportation expenses, noncompliance with the soft time window, distributor construction, vehicle purchase or leasing, and manufacturing costs are all part of the system costs. The problem's conceptual model is developed and modeled first, and then General Algebraic Modeling System software (GAMS) and Multiple Objective Particle Swarm Optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGAII) algorithms are used to solve it in small dimensions.

According to the mathematical model's solution, the average error of the two suggested methods, in contrast to the exact answer, is less than 0.7%. In addition, the performance of algorithms in terms of deviation from the GAMS exact solution is pretty satisfactory, with a divergence of 0.4% for the biggest problem (N = 100). As a result, NSGAII is shown to be superior to MOSPSO.

Since this paper deals with two bi-objective models, the priorities of decision-makers in selecting the best solution were not taken into account, and each of the objective functions was given an equal weight based on the weighting procedures. The model has not been compared or studied in both robust and deterministic modes. This is because, with the exception of the variable that indicates traffic mode uncertainty, all variables are deterministic, and the uncertainty character of demand in each level of the supply chain is ignored.

The suggested model's conclusions are useful for any group of decision-makers concerned with optimizing production patterns at any level. The employment of a diverse fleet of delivery vehicles, as well as the use of stochastic optimization techniques to define the time windows, demonstrates how successful distribution networks are in lowering operational costs.

According to a multi-objective model in a three-echelon supply chain, this research fills in the gaps in the link between routing and location choices in a realistic manner, taking into account the actual restrictions of a distribution network. The model may reduce the uncertainty in vehicle performance while choosing a refueling strategy or dealing with diverse traffic scenarios, bringing it closer to certainty. In addition, two modified MOPSO and NSGA-II algorithms are presented for solving the model, with the results compared to the exact GAMS approach for medium- and small-sized problems.

This study aims to investigate a locating-routing-allocating problems and the supply chain, including factories distributor candidate locations and retailers. The purpose of this paper is to minimize system costs and delivery time to retailers so that routing is done and the location of the distributors is located.

The problem gets closer to reality by adding some special conditions and constraints. Retail service start times have hard and soft time windows, and each customer has a demand for simultaneous delivery and pickups. System costs include the cost of transportation, non-compliance with the soft time window, construction of a distributor, purchase or rental of a vehicle and production costs. The conceptual model of the problem is first defined and modeled and then solved in small dimensions by general algebraic modeling system (GAMS) software and non-dominated sorting genetic algorithm II (NSGAII) and multiple objective particle swarm optimization (MOPSO) algorithms.

According to the solution of the mathematical model, the average error of the two proposed algorithms in comparison with the exact solution is less than 0.7%. Also, the algorithms’ performance in terms of deviation from the GAMS exact solution, is quite acceptable and for the largest problem (N = 100) is 0.4%. Accordingly, it is concluded that NSGAII is superior to MOSPSO.

In this study, since the model is bi-objective, the priorities of decision makers in choosing the optimal solution have not been considered and each of the objective functions has been given equal importance according to the weighting methods. Also, the model has not been compared and analyzed in deterministic and robust modes. This is because all variables, except the one that represents the uncertainty of traffic modes, are deterministic and the random nature of the demand in each graph is not considered.

The results of the proposed model are valuable for any group of decision makers who care optimizing the production pattern at any level. The use of a heterogeneous fleet of delivery vehicles and application of stochastic optimization methods in defining the time windows, show how effective the distribution networks are in reducing operating costs.

This study fills the gaps in the relationship between location and routing decisions in a practical way, considering the real constraints of a distribution network, based on a multi-objective model in a three-echelon supply chain. The model is able to optimize the uncertainty in the performance of vehicles to select the refueling strategy or different traffic situations and bring it closer to the state of certainty. Moreover, two modified algorithms of NSGA-II and multiple objective particle swarm optimization (MOPSO) are provided to solve the model while the results are compared with the exact general algebraic modeling system (GAMS) method for the small- and medium-sized problems.