A two-stage heuristic for multi-activity and task assignment to work shifts

The multi-activity assignment problem consists of assigning interruptible activities to given work shifts so as to match as much as possible for each activity a demand curve in function of time. In this paper we consider an extension to this problem, called the multi-activity and task assignment problem, that additionally considers the assignment of uninterruptible pieces of work, called tasks. These possess properties such as worker qualifications, time windows for completion, fixed lengths and precedence relationships. We propose a mixed-integer programming formulation and a two-stage method to solve this problem. The first stage consists of an approximation mixed-integer programming model to assign tasks approximately taking into account the activities and the second involves a column generation heuristic for assigning activities and reassigning tasks at the same time. We suggest four different strategies for reassigning tasks. We conducted extensive computational tests on randomly generated instances in order to validate our method and to compare the various strategies. One strategy proved universally best when compared to the other three policies.     

A two-stage heuristic for multi-activity and task assignment to work shifts

The multi-activity assignment problem consists of assigning interruptible activities to given work shifts so as to match as much as possible for each activity a demand curve in function of time. In this paper we consider an extension to this problem, called the multi-activity and task assignment problem, that additionally considers the assignment of uninterruptible pieces of work, called tasks. These possess properties such as worker qualifications, time windows for completion, fixed lengths and precedence relationships. We propose a mixed-integer programming formulation and a two-stage method to solve this problem. The first stage consists of an approximation mixed-integer programming model to assign tasks approximately taking into account the activities and the second involves a column generation heuristic for assigning activities and reassigning tasks at the same time. We suggest four different strategies for reassigning tasks. We conducted extensive computational tests on randomly generated instances in order to validate our method and to compare the various strategies. One strategy proved universally best when compared to the other three policies.     

Assigning multiple activities to work shifts

In some companies such as large retail stores, the employees perform different activities (e.g., cashier or clerk in a specific department) to respond to a customer demand for each activity that varies over the planning horizon and must be fulfilled as soon as possible. For a given time period, this demand translates into an ideal number of employees required for the corresponding activity. During a work shift, an employee can be assigned to several activities that are interruptible at any time and subject to operational constraints (required skills, minimum and maximum assignment durations). Given work shifts already assigned to the employees, the multi-activity assignment problem (MAAP) consists of assigning activities to the shifts such that the activity demands are satisfied as best as possible over the planning horizon. In this paper, we propose three integer programming models for the MAAP and develop various heuristics based on mathematical programming techniques. Computational results obtained on randomly generated MAAP instances show that a heuristic column generation method embedded into a rolling horizon procedure provides the best results in general.     

A fault-tolerant parallel heuristic for assignment problems

This paper presents a new approach for parallel heuristic algorithms based on adaptive parallelism. Adaptive parallelism was used to dynamically adjust the parallelism degree of the application with respect to the system load. This approach demonstrates that high-performance computing using a hundred of heterogeneous workstations combined with massively parallel machines is feasible to solve large optimization problems with respect to the personal character of workstations. The fault-tolerant algorithm allows a minimal loss of computation in case of failures. The proposed algorithm exploits the properties of this class of applications in order to reduce the complexity of the algorithm in terms of the checkpoint files size and the control messages exchanged. The parallel heuristic algorithm combines different search strategies: simulated annealing and tabu search. Encouraging results have been obtained in solving the quadratic assignment problem. We have improved the best known solutions for some large real-world problems.     

An effective heuristic for flexible job-shop scheduling problem with maintenance activities

Most production scheduling problems, including the standard flexible job-shop scheduling problem (FJSP), assume that machines are continuously available. However, in most realistic situations, machines may become unavailable during certain periods due to preventive maintenance (PM). In this paper, a flexible job-shop scheduling problem with machine availability constraints is considered. Each machine is subject to preventive maintenance during the planning period and the starting times of maintenance activities are either flexible in a time window or fixed beforehand. Moreover, two cases of maintenance resource constraint are considered: sufficient maintenance resource available or only one maintenance resource available. To deal with this variant FJSP problem with maintenance activities, a filtered beam search (FBS) based heuristic algorithm is proposed. With a modified branching scheme, the machine availability constraint and maintenance resource constraint can be easily incorporated into the proposed algorithm. Simulation experiments are conducted on some representative problems. The results demonstrate that the proposed filtered beam search based heuristic algorithm is a viable and effective approach for the FJSP with maintenance activities.     

定位2运输路线安排问题的两阶段启发式算法

重点研究了集成化物流中一类特殊的定位一运输路线安排问题(LRP)的解决方法．LRP问题包括设施定位和运输路线优化两方面决策，属于NP-hard难题．由于问题的复杂性，提出基于假设前提的LRP模型及其两阶段启发式求解算法．该方法分两步实现：首先，采用基于最小包络聚类分析的启发式方法确定被选择的潜在设施及由每一个选中的设施所要提供服务的客户群；其次，运用带有控制开关的遗传算法求解每一确定客户类中的优化运输路线．提出利用两阶段启发式算法求解LRP问题，此方法实现容易、运算简单，一定程度上避免了遗传算法中的“局部最优现象”．仿真实验证明了该算法求解单目标LRP的有效性和准确性．     

A column generation heuristic for a dynamic generalized assignment problem

This paper studies the dynamic generalized assignment problem (DGAP) which extends the well-known generalized assignment problem by considering a discretized time horizon and by associating a starting time and a finishing time with each task. Additional constraints related to warehouse and yard management applications are also considered. Three linear integer programming formulations of the problem are introduced. The strongest one models the problem as an origin–destination integer multi-commodity flow problem with side constraints. This model can be solved quickly for instances of small to moderate size. However, because of its computer memory requirements, it becomes impractical for larger instances. Hence, a column generation algorithm is used to compute lower bounds by solving the linear program (LP) relaxation of the problem. This column generation algorithm is also embedded in a heuristic aimed at finding feasible integer solutions. Computational experiments on large-scale instances show the effectiveness of the proposed approach.     

A two-phase hybrid heuristic algorithm for the capacitated location-routing problem

In this paper, we propose a two-phase hybrid heuristic algorithm to solve the capacitated location-routing problem (CLRP). The CLRP combines depot location and routing decisions. We are given on input a set of identical vehicles (each having a capacity and a fixed cost), a set of depots with restricted capacities and opening costs, and a set of customers with deterministic demands. The problem consists of determining the depots to be opened, the customers and the vehicles to be assigned to each open depot, and the routes to be performed to fulfill the demand of the customers. The objective is to minimize the sum of the costs of the open depots, of the fixed cost associated with the used vehicles, and of the variable traveling costs related to the performed routes. In the proposed hybrid heuristic algorithm, after a Construction phase (first phase), a modified granular tabu search, with different diversification strategies, is applied during the Improvement phase (second phase). In addition, a random perturbation procedure is considered to avoid that the algorithm remains in a local optimum for a given number of iterations. Computational experiments on benchmark instances from the literature show that the proposed algorithm is able to produce, within short computing time, several solutions obtained by the previously published methods and new best known solutions.     

A heuristic algorithm for the distributed and flexible job-shop scheduling problem

The distributed manufacturing takes place in a multi-factory environment including several factories, which may be geographically distributed in different locations, or in a multi-cell environment including several independent manufacturing cells located in the same plant. Each factory/cell is capable of manufacturing a variety of product types. An important issue in dealing with the production in this decentralized manner is the scheduling of manufacturing operations of products (jobs) in the distributed manufacturing system. In this paper, we study the distributed and flexible job-shop scheduling problem (DFJSP) which involves the scheduling of jobs (products) in a distributed manufacturing environment, under the assumption that the shop floor of each factory/cell is configured as a flexible job shop. A fast heuristic algorithm based on a constructive procedure is developed to obtain good quality schedules very quickly. The algorithm is tested on benchmark instances from the literature in order to evaluate its performance. Computational results show that, despite its simplicity, the proposed heuristic is computationally efficient and promising for practical problems.     

复合并行机排序问题的启发式算法研究

为有效解决复合并行机排序的极小化最大完成时间问题,提出了分支定界算法和改进的启发式动态规划算法。利用分支定界算法的3个工具:分支模型、边界和优先规则,构建出分支搜索树。按优先规则进行定界搜索,从而减小了问题求解规模。将原始作业转换为虚拟作业,根据Johnson法则,求解出原问题的最优排序。改进的动态规划算法复杂度分析和计算实验表明,这两个算法可靠性高并且可以解决实际问题。     

A map-reduce lagrangian heuristic for multidimensional assignment problems with decomposable costs

Data association is the problem of identifying when multiple data sources have observed the same entity. Central to this effort is the multidimensional assignment problem, which is often used to formulate data association problems. The nature of data association problems dictate that solution methods for the multidimensional assignment problem must return results promptly, and work on large data sets. The contribution of this work is to describe a Lagrangian relaxation based heuristic for the multi-dimensional assignment problem with decomposable costs that can be largely implemented in a map-reduce framework and thus easily distributed across a cluster of computers. Distribution allows the heuristic to address run time and large data requirements of data association. The developed algorithm is tested on a synthesized dataset, and shown to achieve an optimality gap ranging from 0.00008% to 0.6% for dense (no filtering) problems having 10,000 observation. Distribution of the algorithm was found to offer a significant reduction in run time on 30,000 observation problems for an 8 node computing cluster with 96 processors over a single node with 12 processors.     

A novel two-phase heuristic method for vehicle routing problem with backhauls

This paper raises a novel two-phase heuristic method to solve vehicle routing problems with backhauls. Differing from other vehicle routing problems, we consider the travel speed of vehicle to be time dependent, which will be used for the model of rush hour in an urban city. In the first phase, the original solution is generated by extending traditional heuristic methods and in the second phase, the reactive tabu search algorithm is used to optimize the original solution. We verified that this algorithm is efficient in a number of standard test cases. After comparison with the closest neighboring search algorithm, we found that the results of two-phase heuristic methods are more reasonable.     

A Newton-based heuristic algorithm for multi-objective flexible job-shop scheduling problem

We propose a new hierarchical heuristic algorithm for multi-objective flexible job-shop scheduling problems. The proposed method is an adaptation of the Newton’s method for continuous multi-objective unconstrained optimization problems, belonging to the class of multi-criteria descent methods. Numerical experiments with the proposed method are presented. The potential of the proposed method is demonstrated by comparing the obtained results with the known results of existing methods that solve the same test instances.     

A heuristic procedure for the integrated facility layout design and flow assignment problem

We present an efficient iterative heuristic procedure for solving the integrated layout design and product flow assignment problem. The layout design decisions involve planar location of unequal-area machines with duplicates. The product flows are assigned to machines according to the product processing routes. The integrated decision problem is a nonlinear mixed integer model which cannot be efficiently solved using classical methods for large problems. We propose a novel integrated heuristic procedure based on the alternating heuristic, a perturbation algorithm and sequential location heuristic. Since the alternating heuristic between facility layout design and product-machine assignment sub-problems terminates with local optima, we developed a perturbation algorithm based on assignment decisions. The results of an experimental study show that proposed procedure is both efficient and effective in identifying quality solutions for small to very large-sized problems.     

A hybrid heuristic queue based algorithm for task assignment in mobile cloud

This paper presents a novel algorithm for task assignment in mobile cloud computing environments in order to reduce offload duration time while balancing the cloudlets’ loads. The algorithm is proposed for a two-level mobile cloud architecture, including public cloud and cloudlets. The algorithm models each cloud and cloudlet as a queue to consider cloudlets’ limited resources and study response time more accurately. Performance factors and resource limitations of cloudlets such as waiting time for clients in cloudlets can be determined using queue models. We propose a hybrid genetic algorithm (GA) - Ant Colony Optimization (ACO) algorithm to minimize mean completion time of offloaded tasks for the whole system. Simulation results confirm that the proposed hybrid heuristic algorithm has significant improvements in terms of decreasing mean completion time, total energy consumption of the mobile devices, number of dropped tasks over Queue based Random, Queue based Round Robin and Queue based weighted Round Robin assignment algorithms. Also, to prove the superiority of our queue based algorithm, it is compared with a dynamic application scheduling algorithm, HACAS, which has not considered queue in cloudlets.     

一种启发式多传感器任务实时动态分配算法

传感器任务的分配是传感器管理的重要问题。为提高任务分配的实时性和实效性,基于紧急任务优先、最早完成任务优先、复用能力最小优先和随机分配四条原则,提出了一种启发式多传感器任务实时动态分配算法。计算机模拟仿真表明:该算法既能保证优先级任务较早的执行,又能探测到任务的失败,还能维持传感器负载平衡,是一种快捷、高效的分配算法。     

A heuristic based on multi-exchange techniques for a regional fleet assignment location-routing problem

We deal with a distribution network design problem that involves location, fleet assignment and routing decisions. Specifically, the distribution network under investigation is characterized by one central depot, a set of customers split into regions, and a heterogeneous fleet of vehicles. The goal is to locate one regional depot in each region, to assign some vehicles to each region, and to design the vehicles routes, each starting and ending at the central depot, in such a way that the regional depot is visited once by all vehicles assigned to the corresponding region, the vehicle capacities are not exceeded, the customer demands are satisfied and the overall distribution cost is minimized. The study has been motivated by a real life application related to a company operating in the North of Italy.     

Exact and heuristic algorithms for the interval data robust assignment problem

We consider the Assignment Problem with interval data, where it is assumed that only upper and lower bounds are known for each cost coefficient. It is required to find a minmax regret assignment. The problem is known to be strongly NP-hard. We present and compare computationally several exact and heuristic methods, including Benders decomposition, using CPLEX, a variable depth neighborhood local search, and two hybrid population-based heuristics. We report results of extensive computational experiments.     

Timetabling problem for university as assignment of activities to resources

A mathematical programming approach is presented to solve the timetabling problem in a University. It includes two subproblems that are solved sequentially. Both subproblems have the same structure consisting of a 0–1 assignment problem of conflicting activities to resources. A solution method is derived for a relaxed version of an equivalent 0–1 quadratic assignment programming problem. The paper concludes with implementation remarks, numerical results and extensions.     

Mathematical modeling and heuristic approaches to flexible job shop scheduling problems

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it is quite difficult to achieve an optimal solution to this problem in medium and actual size problem with traditional optimization approaches owing to the high computational complexity. For solving the realistic case with more than two jobs, two types of approaches have been used: hierarchical approaches and integrated approaches. In hierarchical approaches assignment of operations to machines and the sequencing of operations on the resources or machines are treated separately, i.e., assignment and sequencing are considered independently, where in integrated approaches, assignment and sequencing are not differentiated. In this paper, a mathematical model and heuristic approaches for flexible job shop scheduling problems (FJSP) are considered. Mathematical model is used to achieve optimal solution for small size problems. Since FJSP is NP-hard problem, two heuristics approaches involve of integrated and hierarchical approaches are developed to solve the real size problems. Six different hybrid searching structures depending on used searching approach and heuristics are presented in this paper. Numerical experiments are used to evaluate the performance of the developed algorithms. It is concluded that, the hierarchical algorithms have better performance than integrated algorithms and the algorithm which use tabu search and simulated annealing heuristics for assignment and sequencing problems consecutively is more suitable than the other algorithms. Also the numerical experiments validate the quality of the proposed algorithms.