A network-based approach to the multi-activity combined timetabling and crew scheduling problem: Workforce scheduling for public health policy implementation

This paper introduces the multi-activity combined timetabling and crew scheduling problem. The goal of this problem is to schedule the minimum number of workers required in order to successfully visit a set of customers characterized by services needed matched against schedule availability. Two solution strategies are proposed. The first is based on mathematical programming whilst the second uses a heuristic procedure in order to reduce computational time. The proposed model combines timetabling with crew scheduling decisions in one mixed integer programming model which considers multiple activities. The algorithms are tested on randomly generated and real instances provided by the Health to School Initiative, a program based at Bogotá’s local Health Department. The results show that the Initiative can increase its coverage by up to 68% using the proposed heuristic approach as a planning process tool.     

Two-machine flowshop scheduling with bicriteria problem

This paper attempts to solve a two-machine flowshop bicriteria scheduling problem with release dates for the jobs, in which the objective function is to minimize a weighed sum of total flow time and makespan. To tackle this scheduling problem, an integer programming model with N²+3N variables and 5N constraints where N is the number of jobs, is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, a heuristic scheduling algorithm is presented. Experimental results show that the proposed heuristic algorithm can solve this problem rapidly and accurately. The average solution quality of the heuristic algorithm is above 99% and is much better than that of the SPT rule as a benchmark. A 15-job case requires only 0.018 s, on average, to obtain an ultimate or even optimal solution. The heuristic scheduling algorithm is a more practical approach to real world applications than the integer programming model.     

Earliness–tardiness minimization on scheduling a batch processing machine with non-identical job sizes

This paper considers the scheduling problem of minimizing earliness–tardiness (E/T) on a single batch processing machine with a common due date. The problem is extended to the environment of non-identical job sizes. First, a mathematical model is formulated, which is tested effectively under IBM ILOG CPLEX using the constraint programming solver. Then several optimal properties are given to schedule batches effectively, and by introducing the concept of ARB (Attribute Ratio of Batch), it is proven that the ARB of each batch should be made as small as possible in order to minimize the objective, designed as the heuristic information for assigning jobs into batches. Based on these properties, a heuristic algorithm MARB (Minimum Attribute Ratio of Batch) for batch forming is proposed, and a hybrid genetic algorithm is developed for the problem under study by combining GA (genetic algorithm) with MARB. Experimental results demonstrate that the proposed algorithm outperforms other algorithms in the literature, both for small and large problem instances.     

The two-stage assembly scheduling problem to minimize total completion time with setup times

We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.     

An efficient heuristic for a two-stage assembly scheduling problem with batch setup times to minimize makespan

This paper considers a two-stage assembly scheduling problem of N products with setup times to minimize the makespan. In this problem, there is a machining machine which produces components in the first stage. When the required components are available, a single assembly machine can assemble these components into products in the second stage. A setup time is needed whenever the machining machine starts processing components, or the item of component is switched on the machine. The problem is formulated as a mixed integer programming model, and several properties for finding optimal solutions are developed. Moreover, an efficient heuristic based on these optimal properties is proposed. A lower bound is derived to evaluate the performance of the proposed heuristic. Computational results show that the proposed heuristic can obtain a near optimal solution in almost zero time and the average percentage deviation is only 0.478.     

A hybrid meta-heuristic algorithm for optimization of crew scheduling

Crew scheduling problem is the problem of assigning crew members to the flights so that total cost is minimized while regulatory and legal restrictions are satisfied. The crew scheduling is an NP-hard constrained combinatorial optimization problem and hence, it cannot be exactly solved in a reasonable computational time. This paper presents a particle swarm optimization (PSO) algorithm synchronized with a local search heuristic for solving the crew scheduling problem. Recent studies use genetic algorithm (GA) or ant colony optimization (ACO) to solve large scale crew scheduling problems. Furthermore, two other hybrid algorithms based on GA and ACO algorithms have been developed to solve the problem. Computational results show the effectiveness and superiority of the proposed hybrid PSO algorithm over other algorithms.     

染缸排产建模及滑动时间窗启发式调度算法

针对染缸排产问题约束复杂、任务规模大、排产效率要求高的特点,为了提高问题模型和算法在实际场景中的适用性,建立了染缸排产增量调度模型,提出了滑动时间窗启发式调度（STWS）算法。该算法以最小化延误代价、洗缸成本、染缸切换成本为优化目标,使用启发式调度规则,按照优先级顺序调度产品;对于每个产品的调度,先用动态拼缸算法和拆缸算法进行批次划分,然后调用批次最佳排序算法调度批次。使用某染纱企业车间实际生产数据仿真调度,所提算法可在10 s内完成月度计划的调度。相对于人工排产方式,所提算法提高了排产效率,显著优化了三个目标,在增量调度中洗缸成本和染缸切换成本也有明显优化。实验结果表明所提算法具有很好的调度能力。     

A tabu search heuristic for the hybrid flowshop scheduling with finite intermediate buffers

This paper investigates the hybrid flowshop scheduling with finite intermediate buffers, whose objective is to minimize the sum of weighted completion time of all jobs. Since this problem is very complex and has been proven strongly NP-hard, a tabu search heuristic is proposed. In this heuristic there are two main features. One is that a scatter search mechanism is incorporated to improve the diversity of the search procedure. And the other is that a permutation of N jobs representing their processing order in the first stage instead of a complex complete schedule is used to denote a solution. Computational experiments on randomly generated instances with different structures show that the proposed tabu search heuristic can provide good solutions compared to both the lower bounds and the algorithm proposed for this problem in a lately published literature.     

A genetic algorithm for multiprocessor scheduling

The problem of multiprocessor scheduling can be stated as finding a schedule for a general task graph to be executed on a multiprocessor system so that the schedule length can be minimized. This scheduling problem is known to be NP-hard, and methods based on heuristic search have been proposed to obtain optimal and suboptimal solutions. Genetic algorithms have recently received much attention as a class of robust stochastic search algorithms for various optimization problems. In this paper, an efficient method based on genetic algorithms is developed to solve the multiprocessor scheduling problem. The representation of the search node is based on the order of the tasks being executed in each individual processor. The genetic operator proposed is based on the precedence relations between the tasks in the task graph. Simulation results comparing the proposed genetic algorithm, the list scheduling algorithm, and the optimal schedule using random task graphs, and a robot inverse dynamics computational task graph are presented     

An artificial immune system heuristic for two-stage multi-machine assembly scheduling problem to minimize total completion time

We address the two-stage multi-machine assembly scheduling problem. The first stage consists of m independently working machines where each machine produces its own component. The second stage consists of two independent and identical assembly machines. The objective is to come up with a schedule that minimizes total or mean completion time for all jobs. The problem has been addressed in the scheduling literature and several heuristics have been proposed. In this paper, we propose a new heuristic called artificial immune system (AIS). We conduct experimental analysis for comparing the newly proposed heuristic AIS with the best known heuristic in the literature. Experimental results show that our proposed heuristic AIS performs better than the best known existing heuristic. More specifically, our new heuristic AIS reduces the error of the best known heuristic by 60% while the computational times of both AIS and the best known heuristic are almost the same.     

Minimizing the makespan on a single machine with flexible maintenances and jobs’ release dates

This paper addresses the production scheduling problem on a single machine with flexible periodic preventive maintenances (PM), where jobs’ release dates are also considered. Both resumable and non-resumable cases are studied. For the resumable case, it is proved that the problem can be solved in polynomial time with Earliest Release Date (ERD) rule. For the non-resumable case, it is proved to be NP-Hard in strong sense. And, a mixed integer programming (MIP) mathematical model is provided. Then, an effective heuristic ERD-LPT based on the properties of optimal solution is proposed. Meanwhile, a branch-and-bound algorithm (B and B) that utilizes several dominance rules is developed to search the optimal schedule for small-to-medium sized problems. Computational results indicate that the proposed heuristic is highly accurate and the two algorithms are complementary in dealing with different sized problems. Furthermore, the improvement of the integration between production scheduling and PM is significant compared with the First-in-First-out (FIFO) rule which is adopted commonly in industry.     

A two-stage hybrid flowshop scheduling problem in machine breakdown condition

This paper considers a two-stage hybrid flowshop scheduling problem in machine breakdown condition. By machine breakdown condition we mean that the machine may not always be available during the scheduling period. Machine failure may occur with a known probability after completing a job. Probability of machine failure depends on the previous processed job. The problem to be studied has one machine at the first stage and M parallel identical machines at the second stage. The objective is to find the optimal job combinations and the optimal job schedule such that the makespan is minimized. The proposed problem is compatible with a large scope of real world situations. To solve the problem, first, we introduce one optimal approach for job precedence when there is one machine in both stages and then provide a heuristic algorithm when there are M machines in stage two. To examine the performance of the heuristic, some experiments used are provided as well.     

Group shops scheduling with makespan criterion subject to random release dates and processing times

This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.     

Addressing the N/1 scheduling problem—A heuristic approach

The problem of sequencing n-jobs on one machine (n/1) to minimize maximum job lateness has been the subject of much prior research. Most of this research has been directed at identifying optimal solutions to the problem via algorithmic search techniques. A weakness in employing an algorithm for solving the problem, however, is that lengthy computational times may result because of the necessity of searching n! sequences. By employing a multiple heuristic approach this limitation can be avoided. An optimal or near optimal schedule can be identified in a finite number of steps.This paper describes a multiple heuristic model that is effective more than eighty-ninety percent of the time in providing an optimal schedule for the N/l/L max scheduling program. Ten separate heuristics are described, and the results of testing the heuristics over fifteen hundred and sixty randomly generated problems is presented. Three of the heuristics are combined to form the heuristic-scheduling model.     

Pharmacy duty scheduling problem

In this study, we define the pharmacy duty scheduling problem, which requires a subset of pharmacies to be on duty on national holidays, at weekends, and at nights, in order to be able to satisfy the emergency medicine needs. We model the pharmacy duty scheduling problem as a multiperiod p‐median problem with special side constraints, and analyze the computational complexity. We propose a Tabu Search heuristic and develop lower bound (LB) algorithms. We test the performance of mathematical models, Tabu Search heuristic, and the LBs on randomly generated instances. We analyze the current system in ?zmir, the third largest city in Turkey, with a population of 3.5 million, and apply solution methods. Our results show that the proposed Tabu Search algorithm suggests improvements on the current system.     

A graph coloring model for a feasibility problem in monthly crew scheduling with preferential bidding

We consider a monthly crew scheduling problem with preferential bidding in the airline industry. We propose a new methodology based on a graph coloring model and a tabu search algorithm for determining if the problem contains at least one feasible solution. We then show how to combine the proposed approach with a heuristic sequential scheduling method that uses column generation and branch-and-bound techniques.     

侦察卫星探测资源调度研究

侦察卫星探测资源调度是一类基于约束满足的优化问题。对卫星探测资源和探测任务的特点进行分析,在此基础上构建卫星探测资源调度的目标函数和约束条件,利用约束满足问题的建模思想对该调度问题进行建模。针对约束满足模型规模大、求解复杂的情况,结合卫星探测资源调度问题的特征,提出一种基于启发式禁忌搜索算法的模型求解方法,并通过仿真算例进行说明与分析。该调度模型和算法充分考虑了星载资源与对应任务的特点,尽量回避假设与简化条件的提出,具有较好的适用性,将为侦察与预警卫星网络任务规划与资源调度的研究奠定基础。     

A variable neighborhood search approach for planning and scheduling of jobs on unrelated parallel machines

In this paper, we study a planning and scheduling problem for unrelated parallel machines. There are n jobs that have to be assigned and sequenced on m unrelated parallel machines. Each job has a weight that represents the priority of the corresponding customer order, a given due date, and a release date. An Automated Guided Vehicle is used to transport at maximum Load _max jobs into a storage space in front of the machines in a given period of time. We consider t _max consecutive periods. We are interested in minimizing the total weighted tardiness of the jobs across the periods. This measure is important when we are interested in a good on-time delivery performance. We present an appropriate mixed integer program. To solve this NP-hard problem, we develop a heuristic methodology based on decomposition and variable neighborhood search (VNS). The proposed approaches are assessed using randomly generated problem instances. We compare them with a simple heuristic based on decomposition and list scheduling using the Apparent Tardiness Cost dispatching rule. The results demonstrate that the heuristic approach based on VNS performs comparably to the mixed integer program while having reasonable solution times and outperforms the simple heuristic and a genetic algorithm (GA) from previous research.     

带约束的清洁排班问题模型及其求解

保洁服务公司的清洁任务往往具有不同级别、不同时长和不同周期等特点,缺乏通用清洁排班问题模型,现阶段主要依赖人工排班方案,存在耗时费力且排班质量不稳定等问题。因此提出了属于NP难问题的带约束的清洁排班问题的数学模型,并使用模拟退火算法（SA）、蜂群算法（BCO）、蚁群算法（ACO）和粒子群优化算法（PSO）对该模型进行求解,最后以某清洁服务公司实际排班情况进行了实证分析。实验结果表明,与人工排班方案进行对比,启发式智能优化算法求解带约束的清洁排班问题具有明显优势,获得的清洁排班表的人力需求明显减少。具体来说,在一年排班周期内这些算法比人工排班方案可节省清洁人力218.62~513.30 h。可见基于启发式智能优化算法的数学模型对带约束的清洁排班问题的求解可行且有效,能为保洁服务公司提供科学管理的决策支持。     

Network service scheduling and routing

Real‐life vehicle routing problems generally have both routing and scheduling aspects to consider. Although this fact is well acknowledged, few heuristic methods exist that address both these complicated aspects simultaneously. We present a graph theoretic heuristic to determine an efficient service route for a single service vehicle through a transportation network that requires a subset of its edges to be serviced, each a specified (potentially different) number of times. The times at which each of these edges are to be serviced should additionally be as evenly spaced over the scheduling time window as possible, thus introducing a scheduling consideration to the problem. Our heuristic is based on the tabu search method, used in conjunction with various well‐known graph theoretic algorithms, such as those of Floyd (for determining shortest routes) and Frederickson (for solving the rural postman problem). This heuristic forms the backbone of a decision support system that prompts the user for certain parameters from the physical situation (such as the service frequencies and travel times for each network link as well as bounds in terms of acceptability of results) after which a service routing schedule is suggested as output. The decision support system is applied to a special case study, where a service routing schedule is sought for the South African national railway system by Spoornet (the semi‐privatised South African national railways authority and service provider) as part of their rationalisation effort, in order to remain a lucrative company.