Johnson’s rule,composite jobs and the relocation problem

Two-machine flowshop scheduling to minimize makespan is one of the most well-known classical scheduling problems. Johnson’s rule for solving this problem has been widely cited in the literature. We introduce in this paper the concept of composite job, which is an artificially constructed job with processing times such that it will incur the same amount of idle time on the second machine as that incurred by a chain of jobs in a given processing sequence. This concept due to Kurisu first appeared in 1976 to deal with the two-machine flowshop scheduling problem involving precedence constraints among the jobs. We show that this concept can be applied to reduce the computational time to solve some related scheduling problems. We also establish a link between solving the two-machine flowshop makespan minimization problem using Johnson’s rule and the relocation problem introduced by Kaplan. We present an intuitive interpretation of Johnson’s rule in the context of the relocation problem.     

具有恶化效应和凸资源分配关系的单机排序问题

研究工件加工时间具有恶化效应和凸资源关系的单机排序问题,其中工件的实际加工时间是其正常的加工时间,工件开工时间(具有恶化效应)及消耗资源量的函数。目标为在最大完工时间(总完工时间、总等待时间、完工时间总绝对差与等待时间总绝对差)小于或等于给定常数的条件下找到工件的最优排序和最优的资源分配使工件的总资源消耗量最少。在单机状态下,证明了此问题是多项式时间可解的,并给出了求解该问题的算法和数值实例。     

考虑路径冲突的AGV配置与调度优化

合理调度有限的码头资源以满足船舶的装卸时间要求是自动化集装箱码头的重要目标之一。针对自动化集装箱码头自动导引车(automated guided vehicle,AGV)配置与调度问题,考虑船舶装卸时间要求和AGV运输过程中的路径冲突,提出分阶段调度策略。将船舶装卸作业分为卸船阶段、装卸同步阶段、装船阶段三个阶段,在每个阶段中,建立以最小化最大完工时间和最小化AGV空载和等待时间为双目标的调度优化模型,并设计基于NSGA-Ⅱ的启发式算法求解。根据本阶段的实际完工时间,从最优解集中选择下一阶段AGV的配置与调度方案。最后对比其他调度方案表明本文调度方案能够满足集装箱船的装卸时间要求,且提高了AGV的利用率,更符合码头实际作业要求。     

A general model for cyclic machine scheduling problems

A general framework for modeling and solving cyclic scheduling problems is presented. The objective is to minimize the cycle time. The model covers different cyclic versions of the job-shop problem found in the literature, robotic cell problems, the single hoist scheduling problem and tool transportation between the machines.It is shown that all these problems can be formulated as mixed integer linear programs which have a common structure. Small instances are solved with CPLEX. For larger instances tabu search procedures have been developed. The main ideas of these methods are indicated.     

Optimal appointment scheduling in continuous time: The lag order approximation method

We study appointment scheduling problems in continuous time. A finite number of clients are scheduled such that a function of the waiting time of clients, the idle time of the server, and the lateness of the schedule is minimized. The optimal schedule is notoriously hard to derive within reasonable computation times. Therefore, we develop the lag order approximation method, that sets the client’s optimal appointment time based on only a part of his predecessors. We show that a lag order of two, i.e., taking two predecessors into account, results in nearly optimal schedules within reasonable computation times. We illustrate our approximation method with an appointment scheduling problem in a CT-scan area.     

单向航道散货港口船舶调度优化

为提高单向航道散货港口的泊位利用率,研究多港池的散货港口船舶调度优化问题。考虑船舶间需保持安全航行距离、进出港时段交替条件和成簇进出港规则等现实约束,以进港船舶总等待时间最小为目标,构建了混合整数线性规划模型。基于问题的特点,设计了启发式规则与模拟退火算法相结合的混合算法进行求解。在数值实验中分别将该算法的结果同下界值和两种现实调度方案对比。结果表明,运用混合算法求解的结果与下界值的平均相对偏差为5.28%,较两种现实调度方案的目标值优化率提升显著,且平均泊位优化率分别为6.74%和4.71%,验证了方案及算法的有效性。     

An evolutionary approach to rehabilitation patient scheduling: A case study

Focusing on real settings, this study aimed to develop an evolutionary approach based on genetic algorithm for solving the problem of rehabilitation patient scheduling to increase service quality by reducing patient waiting time and improve operation efficiency by increasing the therapy equipment utilization. Indeed, due to partial precedence constraints of rehabilitation therapies, the problem can be structured as a hybrid shop scheduling problem that has received little attention to date. In addition, a mixed integer programming model was also constructed as a benchmark to validate the solution quality with small problems. Based on empirical data from a Medical Center in Taiwan, several experiments were conducted to estimate the validity of the proposed algorithm. The results showed that the proposed algorithm can reduce patient waiting time and enhance resource utilization and thus demonstrated the practicality of the proposed algorithm. Indeed, a decision support system embedded with the developed algorithm has been implemented in this medical center.     

Heuristic approaches for solving transit vehicle scheduling problem with route and fueling time constraints

Electric bus scheduling problem can be defined as vehicle scheduling problem with route and fueling time constraints (VSPRFTC). Every vehicle’s travel miles (route time) after charging is limited, thus the vehicle must be recharged after taking several trips and the minimal charging time (fueling time) must be satisfied. A multiple ant colony algorithm (ACA) was presented to solve VSPRFTC based on ACA used to solve traveling salesman problem (TSP), a new metaheuristic approach inspired by the foraging behavior of real colonies of ants. The VSPRFTC considered in this paper minimizes a multiple, hierarchical objective function: the first objective is to minimize the number of tours (or vehicles) and the second is to minimize the total deadhead time. New improvement of ACA as well as detailed operating steps was provided on the basis of former algorithm. Then in order to settle contradiction between accelerating convergence and avoiding prematurity or stagnation, improvement on route construction rule and Pheromone updating rule was adopted. A group feasible trip sets (blocks) had been produced after the process of applying ACA. In dealing with the fueling time constraint a bipartite graphic model and its optimization algorithm are developed for trip set connecting in a hub and spoke network system to minimize the number of vehicle required. The maximum matching of the bipartite graph is obtained by calculating the maximum inflow with the Ford–Fulkerson algorithm. At last, an example was analyzed to demonstrate the correctness of the application of this algorithm. It proved to be more efficient and robust in solving this problem.     

On the characterization and generation of nurse scheduling problem instances

Due to its complexity and relevance in practice, many different procedures have been proposed in the operations research literature to solve the well-known nurse scheduling problem (NSP). The NSP assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The often highly case-specific workplace conditions in hospital departments have resulted in the development of dedicated (meta-)heuristics to find a workable schedule in an acceptable time limit. However, in spite of research community posing a growing need for benchmarking, these procedures lack any base for comparison.     

Single-facility scheduling by logic-based Benders decomposition

Logic-based Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size scales up. We solve single-facility non-preemptive scheduling problems with time windows and long time horizons. The Benders master problem assigns jobs to predefined segments of the time horizon, where the subproblem schedules them. In one version of the problem, jobs may not overlap the segment boundaries (which represent shutdown times, such as weekends), and in another version, there is no such restriction. The objective is to find feasible solutions, minimize makespan, or minimize total tardiness.     

考虑老年人感知满意度的社区居家养老护理人员调度策略研究

近年来,随着人口老龄化进程不断加快,社区居家养老模式越来越受到社会各界的高度关注。为了向社区居家养老服务中心护理人员调度提供决策支持,研究考虑老年人感知满意度的护理人员调度问题。以社区居家养老预约服务为背景,首先融合前景理论和模糊理论分别从老年人等待时间、老年人对护理人员偏好和老年人对服务价格偏好三个方面建立老年人感知满意度函数;其次确定主要目标为最大化老年人综合感知满意度,次要目标为最小化社区居家养老服务中心运营成本的优化调度问题,并且构建了相应的混合整数非线性规划数学模型;最后综合应用遗传算法和模拟植物生长算法(PGSA)对该模型进行求解,其中遗传算法用于求解护理人员的服务顺序,PGSA用于求解护理人员调度方案,并且利用MATLAB软件进行仿真,同时引入粒子群算法与PGSA进行计算对比,发现PGSA在性能参数和计算时间方面都有明显的优势。通过算例验证分析,结果表明该模型在考虑老年人感知满意度的基础上,能够获得最优的护理人员调度方案,证明了上述优化模型和算法的可行性和有效性。     

Modeling and solution of the joint quay crane and truck scheduling problem

This paper addresses the joint quay crane and truck scheduling problem at a container terminal, considering the coordination of the two types of equipment to reduce their idle time between performing two successive tasks. For the unidirectional flow problem with only inbound containers, in which trucks go back to quayside without carrying outbound containers, a mixed-integer linear programming model is formulated to minimize the makespan. Several valid inequalities and a property of the optimal solutions for the problem are derived, and two lower bounds are obtained. An improved Particle Swarm Optimization (PSO) algorithm is then developed to solve this problem, in which a new velocity updating strategy is incorporated to improve the solution quality. For small sized problems, we have compared the solutions of the proposed PSO with the optimal solutions obtained by solving the model using the CPLEX software. The solutions of the proposed PSO for large sized problems are compared to the two lower bounds because CPLEX could not solve the problem optimally in reasonable time. For the more general situation considering both inbound and outbound containers, trucks may go back to quayside with outbound containers. The model is extended to handle this problem with bidirectional flow. Experiment shows that the improved PSO proposed in this paper is efficient to solve the joint quay crane and truck scheduling problem.     

基于物流AGV的“货到人”订单拣选系统任务调度研究

基于物流AGV的“货到人”订单拣选模式由于其高效率和灵活性,逐渐成为电商物流配送中心订单拣选系统发展趋势。本文通过对基于物流AGV的电商物流配送中心订单拣选作业流程分析,提出多拣选台同步拣选和多拣选台异步拣选两种作业模式。然后对基于物流AGV的订单拣选任务调度问题进行描述,以物流AGV完成所有任务的时间最短为目标,分别建立同步和异步两种拣选模式下物流AGV任务调度模型;针对物流AGV任务调度问题特性,对共同进化遗传算法粗粒度模型进行改进用于模型求解。最后,通过改进前后算法的对比,验证了改进共同进化遗传算法在求解物流AGV任务调度问题中的有效性;通过在求解速度和优化结果上对多拣选台同步拣选和异步拣选两种作业模式进行比较,得出同步拣选优于异步拣选的结果。     

Non-block scheduling with priority for radiotherapy treatments

In this paper, a quite challenging operational problem within health care delivery has been considered: the optimal management of patients waiting for radiotherapy treatments. Long waiting times for radiotherapy treatments of several cancers are largely documented all over the world. This problem is mainly due to an imbalance between supply and demand of radiotherapy services, which negatively affects the effectiveness and the efficiency of the health care delivered. Within this context, the paper presents an innovative solution approach for effectively scheduling a set of patients waiting to start the radiotherapy plan. The proposed approach is based on a well tailored integer linear optimization program, modelling a non-block scheduling strategy, with the aim to minimize the mean waiting time or maximize the number of new scheduled patients. The model has been tested and evaluated by carrying out some numerical experiments on suitable use-case scenarios, and the obtained results demonstrate the effectiveness and reliability of the proposed approach.     

Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations

This paper is concerned with the problem of assigning employees to gas stations owned by the Kuwait National Petroleum Corporation (KNPC), which hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. Although similar employee scheduling problems have been addressed in the literature, certain peculiarities of the problem require novel mathematical models and algorithms to deal with the specific nature and size of this problem. The problem is modeled as a mixed-integer program, and a problem size analysis based on real data reveals that the formulation is too complex to solve directly. Hence, a two-stage approach is proposed, where the first stage assigns employees to stations, and the second stage specifies shifts and off-days for each employee. Computational results related to solving the two-stage models directly via CPLEX and by specialized heuristics are reported. The two-stage approach provides daily schedules for employees for a given time horizon in a timely fashion, taking into consideration the employees’ expressed preferences. This proposed modeling approach can be incorporated within a decision support system to replace the current manual scheduling practice that is often chaotic and has led to feelings of bias and job dissatisfaction among employees.     

Solving the discrete-continuous project scheduling problem via its discretization

In this paper a discrete-continuous project scheduling problem is considered. In this problem activities simultaneously require discrete and continuous resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resources are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a classical (i.e. discrete) project scheduling problem in the multi-mode version is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. In the former case a nonlinear solver is used for solving a corresponding convex programming problem. The results are compared with the results obtained using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each iteration. The results of a computational experiment are analyzed and some conclusions are included.     

Multi-mode resource-constrained project scheduling using RCPSP and SAT solvers

This paper reports on a new solution approach for the well-known multi-mode resource-constrained project scheduling problem (MRCPSP). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and non-renewable) resource feasible project schedule with a minimal makespan. The problem type is known to be NP-hard and has been solved using various exact as well as (meta-)heuristic procedures.The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean non-renewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.     

On the complexity of project scheduling to minimize exposed time

We consider project scheduling where the project manager’s objective is to minimize the time from when an adversary discovers the project until the completion of the project. We analyze the complexity of the problem identifying both polynomially solvable and NP-hard versions of the problem. The complexity of the problem is seen to be dependent on the nature of renewable resource constraints, precedence constraints, and the ability to crash activities in the project.     

具有两种运输方式选择的物流排序问题

本文研究了单机环境下,有两种运输方式可供选择的集成生产和运输的排序问题。有多个工件需要在一台机器上进行加工,工件生产完后需要分批运到客户处。有两种运输方式,普通运输和特快运输可供选择。制造商需要安排工件的加工顺序,选择合适的运输方式和出发时间,以极小化相应的时间目标与运输费用的加权和。研究了排序理论中主要的两个目标函数,分析了问题的复杂性,对于这些问题给出了它们的最优算法。