Window Assignment Research Articles

Common due window assignment and single machine scheduling with delivery time, resource allocation, and job-dependent learning effect

Common due window assignment and single machine scheduling with delivery time, resource allocation, and job-dependent learning effect

Multi-period time window assignment for attended home delivery

We study a multi-period stochastic variant of the Time Window Assignment Vehicle Routing Problem, where customers’ demands, locations, and service times are uncertain. Customers are partitioned into geographical zones, each of which has to be visited a predetermined number of times over a planning period of several days. Whenever a zone is visited, a time window is assigned. Time windows are decided before knowing customers and their demands. A fleet of homogeneous vehicles is available to serve customers each day. At a tactical level, the problem looks for a static time window assignment that minimizes the expected traveling costs plus the expected penalty costs for unserved customers. We propose a two-stage formulation and a solution approach, which relies on the Sample Average Approximation Method, while encompassing a perturbation method to assign time windows in the first stage and an Adaptive Large Neighborhood Search to optimize routes in the second stage. We experimentally evaluate three instance sets, including real ones from a Canadian company, comparing our results to lower bounds from the exact solution of a deterministic equivalent formulation over a finite number of scenarios. Our method outperforms the manual approach used by the company.

Slack due window assignment scheduling in the single-machine with controllable processing times

Slack due window assignment scheduling in the single-machine with controllable processing times

Single machine slack due window assignment and deteriorating jobs

Single machine slack due window assignment and deteriorating jobs

Delivery Times Scheduling with Deterioration Effects in Due Window Assignment Environments

In practical problems, in addition to the processing time of the job, the impact of the time required for delivering the service to customers on the cost is also considered, i.e., delivery time, where the job processing time is a simple linear function of its starting time. This paper considers the impact of past-sequence-dependent delivery times (which can be referred to as psddt) on the studied objectives in three types of due windows (common, slack and different due windows). This serves to minimize the weighted sum of earliness, tardiness, starting time and size of due window, where the weights (coefficients) are related to the location. Through the theoretical analysis of the optimal solution, it is found that these three problems can be solved in time O(NlogN), respectively, where N is the number of jobs.

Single machine SLK/DIF due window assignment problem with general job-dependent positional effect and outsourcing operations

This paper considers the SLK/DIF due window assignment problems on a single machine with a general job-dependent positional effect, where the actual processing time of a job is subject to a job-dependent and positional effect. Production schedulers may decide to outsource/reject some jobs by paying the corresponding costs. Based on whether to accept the tardiness jobs, we consider two different objectives under slack and different due window assignment, respectively. The first objective function is to minimize the weighted sum of earliness, tardiness, due window starting time, due window size, and outsourcing costs, while the second objective function is to minimize the cost function that includes earliness, due window starting time, due window size and outsourcing costs. We study the structural properties of two due window assignment methods and develop polynomial-time solution algorithms for the considered problems. A numerical example proves the advantage of the outsourcing decision and the distinction between two different objectives.

RCC: Enabling Receiver-Driven RDMA Congestion Control With Congestion Divide-and-Conquer in Datacenter Networks

The development of datacenter applications leads to the need for end-to-end communication with microsecond latency. As a result, RDMA is becoming prevalent in datacenter networks to mitigate the latency caused by the slow processing speed of the traditional software network stack. However, existing RDMA congestion control mechanisms are either far from optimal in simultaneously achieving high throughput and low latency or in need of additional in-network function support. In this paper, by leveraging the observation that most congestion occurs at the last hop in datacenter networks, we propose RCC, a receiver-driven rapid congestion control mechanism for RDMA networks that combines explicit assignment and iterative window adjustment. Firstly, we propose a network congestion distinguish method to classify congestions into two types, last-hop congestion and in-network congestion. Then, an Explicit Window Assignment mechanism is proposed to solve the last-hop congestion, which enables senders to converge to a proper sending rate in one-RTT. For in-network congestion, a PID-based iterative delay-based window adjustment scheme is proposed to achieve fast convergence and near-zero queuing latency. RCC does not need additional in-network support and is friendly to hardware implementation. In our evaluation, the overall average FCT (Flow Completion Time) of RCC is <inline-formula> <tex-math notation="LaTeX">$4{\sim}79\%$</tex-math> </inline-formula> better than Homa, ExpressPass, DCQCN, TIMELY, and HPCC.

Emergency logistics network optimization with time window assignment

During natural disasters or accidents, an emergency logistics network aims to ensure the distribution of relief supplies to victims in time and efficiently. When the coronavirus disease 2019 (COVID-19) emerged, the government closed the outbreak areas to control the risk of transmission. The closed areas were divided into high-risk and middle-/low-risk areas, and travel restrictions were enforced in the different risk areas. The distribution of daily essential supplies to residents in the closed areas became a major challenge for the government. This study introduces a new variant of the vehicle routing problem with travel restrictions in closed areas called the two-echelon emergency vehicle routing problem with time window assignment (2E-EVRPTWA). 2E-EVRPTWA involves transporting goods from distribution centers (DCs) to satellites in high-risk areas in the first echelon and delivering goods from DCs or satellites to customers in the second echelon. Vehicle sharing and time window assignment (TWA) strategies are applied to optimize the transportation resource configuration and improve the operational efficiency of the emergency logistics network. A tri-objective mathematical model for 2E-EVRPTWA is also constructed to minimize the total operating cost, total delivery time, and number of vehicles. A multi-objective adaptive large neighborhood search with split algorithm (MOALNS-SA) is proposed to obtain the Pareto optimal solution for 2E-EVRPTWA. The split algorithm (SA) calculates the objective values associated with each solution and assigns multiple trips to shared vehicles. A non-dominated sorting strategy is used to retain the optimal labels obtained with the SA algorithm and evaluate the quality of the multi-objective solution. The TWA strategy embedded in MOALNS-SA assigns appropriate candidate time windows to customers. The proposed MOALNS-SA produces results that are comparable with the CPLEX solver and those of the self-learning non-dominated sorting genetic algorithm-II, multi-objective ant colony algorithm, and multi-objective particle swarm optimization algorithm for 2E-EVRPTWA. A real-world COVID-19 case study from Chongqing City, China, is performed to test the performance of the proposed model and algorithm. This study helps the government and logistics enterprises design an efficient, collaborative, emergency logistics network, and promote the healthy and sustainable development of cities.

A Group-Dependent Due Window Assignment Scheduling Problem with Controllable Learning Effect

In this paper, we study a single machine scheduling problem with group-dependent due window assignment and further incorporate autonomous and induced learning effects. Here, autonomous learning refers to learning by doing, while induced learning denotes that proactive investments can promote the learning effect, i.e., the learning effect is controllable. The proactive spending could include any management efforts like professional training programs, among others. The objective is to find optimal strategies of due window assignments, sequence of groups and jobs, and level of induced learning that optimize the total cost comprising the due window-related penalty costs and the investment cost. We present a polynomial-time algorithm capable of solving this problem and an improved idea to further reduce the time complexity. In addition, a detailed numerical example is conducted. Our study shows that the learning effect can be tuned to fit the demand of the manufacturing system better and lead to a more flexible operating system.

Partition window assignment in hierarchically scheduled time-partitioned distributed real-time systems with multipath flows

Time and space partitioning techniques are implemented in the development of safety-critical applications to ensure isolation among components. A suitable arrangement of the execution of such partitions is a key challenge so that applications meet the timing requirements imposed to software. In this work, the effect of window sizes and context switch overheads in the partition window configuration is studied, with the aim of analyzing their impact when the response-time analysis and priority assignment techniques are applied. Then, a heuristic algorithm is proposed, in order to obtain a partition window configuration that enables the schedulability of partition-based safety critical systems. This algorithm is evaluated in synthetic test scenarios and it is also applied to a safety-critical use-case in the railway domain.

The Due Window Assignment Problems with Deteriorating Job and Delivery Time

This paper considers the single machine scheduling problem with due window, delivery time and deteriorating job, whose goal is to minimize the window location, window size, earliness and tardiness. Common due window and slack due window are considered. The delivery time depends on the actual processing time of past sequences. The actual processing time of the job is an increasing function of the start time. Based on the small perturbations technique and adjacent exchange technique, we obtain the propositions of the problems. For common and slack due window assignment, we prove that the two objective functions are polynomial time solvable in O(nlogn) time. We propose the corresponding algorithms to obtain the optimal sequence, window location and window size.

A combined intelligent and game theoretical methodology for collaborative multicenter pickup and delivery problems with time window assignment

Collaborative multicenter pickup and delivery problems with time window assignment (CMPDPTWA) are introduced in this paper and formulated and solved as a two-stage optimization problem. First, the collaborative mechanism achieves optimal transportation resource configuration in a multicenter logistics network. Second, open-closed mixed pickup and delivery routes satisfying the demands and time windows of customers are proposed to enhance transportation efficiency and reduce the total logistics operating cost. A set of candidate-time windows is assigned to the corresponding customers through time window assignment (TWA) strategy to increase the operational efficiency of logistics network. A bi-objective programming model for CMPDPTWA is formulated to minimize the number of vehicles and total operating cost. An improved k-means clustering algorithm is used to cluster customers according to their proximities to pickup and delivery centers for reducing the computational complexity to solve the abovementioned problem. A self-learning non-dominated sorting genetic algorithm-II (SNSGA-II) is proposed to optimize the open-closed mixed pickup and delivery routes in CMPDPTWA. An update mechanism for the probabilities of crossover and mutation is devised to improve the efficiency of searching the solution space, and thus to accelerate the convergence of SNSGA-II. The performance of the proposed algorithm is compared with that of other algorithms, and the results indicate that it can generate near-optimal solutions for CMPDPTWA. A game theoretical method involving a cost gap allocation model and the strictly monotonic path strategy is proposed to find the best profit allocation scheme and the optimal coalition sequence for stabilizing the collaborative coalition. Finally, the proposed method is applied to a case study using the real-world logistics network in Chongqing City, China. Six scenarios with and without the collaborative mechanism and TWA strategy are simulated and compared with one another to verify the efficacy of the proposed method. The results show that the collaborative mechanism and TWA strategy can improve the utilization of transportation resources and operational efficiency. Thus, they can facilitate an efficient and sustainable urban logistics network.

Multidepot Recycling Vehicle Routing Problem with Resource Sharing and Time Window Assignment

This study aims to provide tactical and operational decisions in multidepot recycling logistics networks with consideration of resource sharing (RS) and time window assignment (TWA) strategies. The RS strategy contributes to efficient resource allocation and utilization among recycling centers (RCs). The TWA strategy involves assigning time windows to customers to enhance the operational efficiency of logistics networks. A biobjective mathematical model is established to minimize the total operating cost and number of vehicles for solving the multidepot recycling vehicle routing problem with RS and TWA (MRVRPRSTWA). A hybrid heuristic algorithm including 3D k-means clustering algorithm and nondominated sorting genetic algorithm- (NSGA-) II (NSGA-II) is designed. The 3D k-means clustering algorithm groups customers into clusters on the basis of their spatial and temporal distances to reduce the computational complexity in optimizing the multidepot logistics networks. In comparison with NSGA algorithm, the NSGA-II algorithm incorporates an elitist strategy, which can improve the computational speed and robustness. In this study, the performance of the NSGA-II algorithm is compared with the other two algorithms. Results show that the proposed algorithm is superior in solving MRVRPRSTWA. The proposed model and algorithm are applied to an empirical case study in Chongqing City, China, to test their applicability in real logistics operations. Four different scenarios regarding whether the RS and TWA strategies are included or not are developed to test the efficacy of the proposed methods. The results indicate that the RS and TWA strategies can optimize the recycling services and resource allocation and utilization and enhance the operational efficiency, thus promoting the sustainable development of the logistics industry.

Multitasking scheduling problems with a common due-window

We study multitasking scheduling and due-window assignment problems in a single machine, which can be found in various application domains. In multitasking environment, unfinished job always interrupts in-processing job. In common due window assignment, the aim is to find optimal due window to minimise the value of the earliness and tardiness penalty. In this paper, we study two problems, where the objective of the first problem is minimise the earliness, tardiness, due-window starting time, and due-window size costs, the objective of the second problem is minmax common due-date with completion time penalty, then we obtain some analytical properties and provide polynomial time solutions. Finally, the experimental results show that the proposed methods are effective.

The Robust Vehicle Routing Problem with Time Window Assignments

In practice, there are several applications in which logistics service providers determine the service time windows at the customers, for example, in parcel delivery, retail, and repair services. These companies face uncertain travel times and service times that have to be taken into account when determining the time windows and routes prior to departure. The objective of the proposed robust vehicle routing problem with time window assignments (RVRP-TWA) is to simultaneously determine routes and time window assignments such that the expected travel time and the risk of violating the time windows are minimized. We assume that the travel time probability distributions are not completely known but that some statistics, such as the mean, minimum, and maximum, can be estimated. We extend the robust framework based on the requirements’ violation index, which was originally developed for the case where the specific requirements (time windows) are given as inputs, to the case where they are also part of the decisions. The subproblem of finding the optimal time window assignment for the customers in a given route is shown to be convex, and the subgradients can be derived. The RVRP-TWA is solved by iteratively generating subgradient cuts from the subproblem that are added in a branch-and-cut fashion. Experiments address the performance of the proposed solution approach and examine the trade-off between expected travel time and risk of violating the time windows.

Single machine resource allocation scheduling problems with deterioration effect and general positional effect.

This paper investigates single machine scheduling problems where the actual processing time of a job is dependent on its starting time, processing position and the amount of resource allocation. We present two unified models and provide a bicriteria analysis for the general scheduling criteria and the total weighted resource consumption. We consider two different versions for treating the two criteria and show that the unified models can be applied to solve scheduling problems under various due window assignment considerations. We prove that two different versions of the problems can be solved in polynomial time, respectively.

Collaborative Multidepot Petrol Station Replenishment Problem with Multicompartments and Time Window Assignment

Energy supply is an important system that affects the overall efficiency of urban transportation. To improve the system operational efficiency and reduce costs, we formulate and solve a collaborative multidepot petrol station replenishment problem with multicompartments and time window assignment by establishing a mixed-integer linear programming model. The hybrid heuristic algorithm composed of genetic algorithm and particle swarm optimization is used as a solution, and then the Shapley value method is applied to analyze the profit allocation of each petrol depot under different coalitions. The optimal membership sequence of the cooperation is determined according to the strict monotone path. To analyze and verify the effectiveness of the proposed method, a regional petrol supply network in Chongqing city in China is investigated. Through cooperation between petrol depots in the supply network, the utilization of customer clustering, time window coordination, and distribution truck sharing can significantly reduce the total operation costs and improve the efficiency of urban transportation energy supply. This approach can provide theoretical support for relevant government departments and enterprises to make optimal decisions. The implementation of the joint distribution of energy can promote the sustainable development of urban transportation.

Addressing Orientation Symmetry in the Time Window Assignment Vehicle Routing Problem

The time window assignment vehicle routing problem (TWAVRP) is the problem of assigning time windows for delivery before demand volume becomes known. This implies that vehicle routes in different demand scenarios have to be synchronized such that the same client is visited around the same time in each scenario. For TWAVRP instances that are relatively difficult to solve, we observe many similar solutions in which one or more routes have a different orientation, that is, the clients are visited in the reverse order. We introduce an edge-based branching method combined with additional components to eliminate orientation symmetry from the search tree, and we present enhancements to make this method efficient in practice. Next, we present a branch-price-and-cut algorithm based on this branching method. Our computational experiments show that addressing orientation symmetry significantly improves our algorithm: The number of nodes in the search tree is reduced by 92.6% on average, and 25 additional benchmark instances are solved to optimality. Furthermore, the resulting algorithm is competitive with the state of the art. The main ideas of this paper are not TWAVRP specific and can be applied to other vehicle routing problems with consistency considerations or synchronization requirements.

An effective Progressive Hedging algorithm for the two-layers time window assignment vehicle routing problem in a stochastic environment

This paper presents an effective Progressive Hedging algorithm for vehicle routing problem with two-layers time window assignment and stochastic service times (2L-TWAVRPSST). Based on a predefined exogenous time window determined by the customers, an endogenous time window is assigned to each customer. Endogenous time windows have flexible width and composed of two-layers. The outer layer is wider than inner layer and is determined by violation variable. This approach aims to giving more flexibility to career companies for serving more customers using less vehicles. Customers could be visited even after the end of their assigned time windows by paying proportional penalty, while extra violation from the outer layer is not permitted. This problem is formulated as a two-stage stochastic model with the first-stage decisions of assigning inner and outer layers time window. Then in the second stage, routes are planned for each scenario combination of stochastic demand and service time. The validity and effectiveness of the proposed model was examined by various numerical examples. The problem was solved by a Progressive Hedging (PH) algorithm for large-scale instances. The results confirm efficiency of the considered solution approach in different instances.

Resource allocation flowshop scheduling with learning effect and slack due window assignment

<p style='text-indent:20px;'>We study flowshop scheduling problems with respect to slack due window assignments, which are operations in which jobs are assigned an individual due window. We combine learning effect and controllable processing times, in which the flowshop has a two-machine no-wait setup. The goal is to determine job sequence, slack due window based on common flow allowance, due window size, and resource allocation. We provide a bicriteria analysis for the scheduling and resource consumption costs. We show that the two costs can be solved in polynomial time utilizing three different combinations.