Finding good nurse duty schedules: a case study

Constructing duty schedules for nurses at large hospitals is a difficult problem. The objective is usually to ensure that there is always sufficient staff on duty, while taking into account individual preferences with respect to work patterns, requests for leave and financial restrictions, in such a way that all employees are treated fairly. The problem is typically solved via mixed integer programming or heuristic (local) search methods in the operations research literature. In this paper the problem is solved using a tabu search approach as a case study at Stikland Hospital, a large psychiatric hospital in the South African Western Cape, for which a computerized decision support system with respect to nurse scheduling was developed. This decision support system, called NuRoDSS (short for Nurse Rostering Decision Support System) is described in some detail.     

Variable neighborhood search for the pharmacy duty scheduling problem

In this paper, we study on the Pharmacy Duty Scheduling (PDS) problem, where a subset of pharmacies should be on duty on national holidays, at weekends and at nights in order to be able to satisfy the emergency drug needs of the society. PDS problem is a multi-period p-median problem with special side constraints and it is an NP-Hard problem. We propose four Variable Neighborhood Search (VNS) heuristics. The first one is the basic version, BVNS. The latter two, Variable Neighborhood Decomposition Search (VNDS) and Variable Neighborhood Restricted Search (VNRS), aim to obtain better results in less computing time by decomposing or restricting the search space. The last one, Reduced VNS (RVNS), is for obtaining good initial solutions rapidly for BVNS, VNDS and VNRS. We test BVNS, VNRS and VNDS heuristics on randomly generated instances and report the computational test results. We also use VNS heuristics on real data for the pharmacies in central İzmir and obtain significant improvements.     

A tabu search algorithm for the multi-period inspector scheduling problem

This paper introduces a multi-period inspector scheduling problem (MPISP), which is a new variant of the multi-trip vehicle routing problem with time windows (VRPTW). In the MPISP, each inspector is scheduled to perform a route in a given multi-period planning horizon. At the end of each period, each inspector is not required to return to the depot but has to stay at one of the vertices for recuperation. If the remaining time of the current period is insufficient for an inspector to travel from his/her current vertex A to a certain vertex B, he/she can choose either waiting at vertex A until the start of the next period or traveling to a vertex C that is closer to vertex B. Therefore, the shortest transit time between any vertex pair is affected by the length of the period and the departure time. We first describe an approach of computing the shortest transit time between any pair of vertices with an arbitrary departure time. To solve the MPISP, we then propose several local search operators adapted from classical operators for the VRPTW and integrate them into a tabu search framework. In addition, we present a constrained knapsack model that is able to produce an upper bound for the problem. Finally, we evaluate the effectiveness of our algorithm with extensive experiments based on a set of test instances. Our computational results indicate that our approach generates high-quality solutions.     

A very fast TS/SA algorithm for the job shop scheduling problem

The job shop scheduling problem (JSP) is one of the most notoriously intractable NP-complete optimization problems. Over the last 10–15 years, tabu search (TS) has emerged as an effective algorithmic approach for the JSP. However, the quality of solutions found by tabu search approach depends on the initial solution. To overcome this problem and provide a robust and efficient methodology for the JSP, the heuristics search approach combining simulated annealing (SA) and TS strategy is developed. The main principle of this approach is that SA is used to find the elite solutions inside big valley (BV) so that TS can re-intensify search from the promising solutions. This hybrid algorithm is tested on the standard benchmark sets and compared with the other approaches. The computational results show that the proposed algorithm could obtain the high-quality solutions within reasonable computing times. For example, 17 new upper bounds among the unsolved problems are found in a short time.     

A tabu search algorithm with a new neighborhood structure for the job shop scheduling problem

Tabu search (TS) algorithms are among the most effective approaches for solving the job shop scheduling problem (JSP) which is one of the most difficult NP-complete problems. However, neighborhood structures and move evaluation strategies play the central role in the effectiveness and efficiency of the tabu search for the JSP. In this paper, a new enhanced neighborhood structure is proposed and applied to solving the job shop scheduling problem by TS approach. Using this new neighborhood structure combined with the appropriate move evaluation strategy and parameters, we tested the TS approach on a set of standard benchmark instances and found a large number of better upper bounds among the unsolved instances. The computational results show that for the rectangular problem our approach dominates all others in terms of both solution quality and performance.     

A tabu search approach for scheduling hazmat shipments

Vehicle routing and scheduling are two main issues in the hazardous material (hazmat) transportation problem. In this paper, we study the problem of managing a set of hazmat transportation requests in terms of hazmat shipment route selection and actual departure time definition. For each hazmat shipment, a set of minimum and equitable risk alternative routes from origin to destination points and a preferred departure time are given. The aim is to assign a route to each hazmat shipment and schedule these shipments on the assigned routes in order to minimize the total shipment delay, while equitably spreading the risk spatially and preventing the risk induced by vehicles traveling too close to each other. We model this hazmat shipment scheduling problem as a job-shop scheduling problem with alternative routes. No-wait constraints arise in the scheduling model as well, since, supposing that no safe area is available, when a hazmat vehicle starts traveling from the given origin it cannot stop until it arrives at the given destination. A tabu search algorithm is proposed for the problem, which is experimentally evaluated on a set of realistic test problems over a regional area, evaluating the provided solutions also with respect to the total route risk and length.     

A tabu search heuristic for the quay crane scheduling problem

This paper proposes a tabu search heuristic for the Quay Crane Scheduling Problem (QCSP), the problem of scheduling a fixed number of quay cranes in order to load and unload containers into and from a ship. The optimality criterion considered is the minimum completion time. Precedence and non-simultaneity constraints between tasks are taken into account. The former originate from the different kind of operations that each crane has to perform; the latter are needed in order to avoid interferences between the cranes. The QCSP is decomposed into a routing problem and a scheduling problem. The routing problem is solved by a tabu search heuristic, while a local search technique is used to generate the solution of the scheduling problem. This is done by minimizing the longest path length in a disjunctive graph. The effectiveness of our algorithm is assessed by comparing it to a branch-and-cut algorithm and to a Greedy Randomized Adaptive Search Procedure (GRASP).     

A tabu search approach to the truck scheduling problem with multiple docks and time windows

While organizing the cross-docking operations, cross-dock managers are confronted with many decision problems. One of these problems is the truck scheduling problem. This paper presents a truck scheduling problem that is concerned with both inbound and outbound trucks at multiple dock doors. The objective is to minimize the total travel time and the total tardiness. The truck scheduling problem under study is described in detail and a mathematical model of the problem is provided which can be solved to optimality with a mixed integer programming solver, at the expense of a high computation time. Next, a tabu search approach is presented. Experimental results on new benchmark instances indicate that the proposed tabu search is able to find good quality results in a short time period, thus offering potential for integration in cross-docking decision support systems.     

Path-relinking Tabu search for the multi-objective flexible job shop scheduling problem

The multi-objective flexible job shop scheduling problem is solved using a novel path-relinking algorithm based on the state-of-the-art Tabu search algorithm with back-jump tracking. A routing solution is identified by problem-specific neighborhood search, and is then further refined by the Tabu search algorithm with back-jump tracking for a sequencing decision. The resultant solution is used to maintain the medium-term memory where the best solutions are stored. A path-relinking heuristics is designed to generate diverse solutions in the most promising areas. An improved version of the algorithm is then developed by incorporating an effective dimension-oriented intensification search to find solutions that are located near extreme solutions. The proposed algorithms are tested on benchmark instances and its experimental performance is compared with that of algorithms in the literature. Comparison results show that the proposed algorithms are competitive in terms of its computation performance and solution quality.     

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.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

Improving simulated annealing with variable neighborhood search to solve the resource-constrained scheduling problem

The purpose of this paper is to improve the simulated annealing method with a variable neighborhood search to solve the resource-constrained scheduling problem. We also compare numerically this method with other neighborhood search (local search) techniques: threshold accepting methods and tabu search. Furthermore, we combine these techniques with multistart diversification strategies and with the variable neighborhood search technique. A thorough numerical study is completed to set the parameters of the different methods and to compare the quality of the solutions that they generate. The numerical results indicate that the simulated annealing method improved with a variable neighborhood search technique is indeed the best solution method. This research was supported by NSERC grant (OGP 0008312) the first author received a FCAR fellowship during her M.Sc. studies.     

A search heuristic for just-in-time scheduling in parallel machines

In recent years the Just-in-Time (JIT) production philosophy as been adopted by many companies around the world. This has motivated the study of scheduling models that embrace the essential components of JIT systems. In this paper, we present a search heurustic for the weighted earliness penalty problem with deadlines in parallel identical machines. Our approach combines elements of the solution methods known as greedy randomized adaptive search procedure (GRASP) and tabu search. It also uses a branch-and-bound post-processor to optimize individually the sequence of the jobs assigned to each machine.     

Problem difficulty for tabu search in job-shop scheduling

Tabu search algorithms are among the most effective approaches for solving the job-shop scheduling problem (JSP). Yet, we have little understanding of why these algorithms work so well, and under what conditions. We develop a model of problem difficulty for tabu search in the JSP, borrowing from similar models developed for SAT and other NP-complete problems. We show that the mean distance between random local optima and the nearest optimal solution is highly correlated with the cost of locating optimal solutions to typical, random JSPs. Additionally, this model accounts for the cost of locating sub-optimal solutions, and provides an explanation for differences in the relative difficulty of square versus rectangular JSPs. We also identify two important limitations of our model. First, model accuracy is inversely correlated with problem difficulty, and is exceptionally poor for rare, very high-cost problem instances. Second, the model is significantly less accurate for structured, non-random JSPs. Our results are also likely to be useful in future research on difficulty models of local search in SAT, as local search cost in both SAT and the JSP is largely dictated by the same search space features. Similarly, our research represents the first attempt to quantitatively model the cost of tabu search for any NP-complete problem, and may possibly be leveraged in an effort to understand tabu search in problems other than job-shop scheduling.     

An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems

This paper proposes an effective hybrid tabu search algorithm (HTSA) to solve the flexible job-shop scheduling problem. Three minimization objectives – the maximum completion time (makespan), the total workload of machines and the workload of the critical machine are considered simultaneously. In this study, a tabu search (TS) algorithm with an effective neighborhood structure combining two adaptive rules is developed, which constructs improved local search in the machine assignment module. Then, a well-designed left-shift decoding function is defined to transform a solution to an active schedule. In addition, a variable neighborhood search (VNS) algorithm integrating three insert and swap neighborhood structures based on public critical block theory is presented to perform local search in the operation scheduling component. The proposed HTSA is tested on sets of the well-known benchmark instances. The statistical analysis of performance comparisons shows that the proposed HTSA is superior to four existing algorithms including the AL + CGA algorithm by Kacem, Hammadi, and Borne (2002b), the PSO + SA algorithm by Xia and Wu (2005), the PSO + TS algorithm by Zhang, Shao, Li, and Gao (2009), and the Xing’s algorithm by Xing, Chen, and Yang (2009a) in terms of both solution quality and efficiency.     

A multiobjective hybrid ant colony optimization approach applied to the assignment and scheduling problem

The assignment and scheduling problem is inherently multiobjective. It generally involves multiple conflicting objectives and large and highly complex search spaces. The problem allows the determination of an efficient allocation of a set of limited and shared resources to perform tasks, and an efficient arrangement scheme of a set of tasks over time, while fulfilling spatiotemporal constraints. The main objective is to minimize the project makespan as well as the total cost. Finding a good approximation set is the result of trade‐offs between diversity of solutions and convergence toward the Pareto‐optimal front. It is difficult to achieve such a balance with NP‐hard problems. In this respect, and in order to efficiently explore the search space, a hybrid bidirectional ant‐based approach is proposed in this paper, which is an improvement of a bi‐colony ant‐based approach. Its main characteristic is that it combines a solution construction developed for a more complicated problem with a Pareto‐guided local search engine.     

A comparison of five heuristics for the multiple depot vehicle scheduling problem

Given a set of timetabled tasks, the multi-depot vehicle scheduling problem consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristics for this well-known problem, namely, a truncated branch-and-cut method, a Lagrangian heuristic, a truncated column generation method, a large neighborhood search heuristic using truncated column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are new in the context of this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for good quality solutions in relatively fast computational times.     

蛙跳算法与批量无等待流水线调度问题的优化*

针对以makespan为指标的批量无等待流水线调度问题,提出了一种有效的离散蛙跳算法。首先采用基于工序的编码方式使蛙跳算法直接应用于调度问题;其次采用基于NEH与改进NEH和随机产生相结合的初始化方法,保证了初始解的高质量和分布性;再次采用交叉或变异方法产生新解,保持了种群的优越性和多样性;最后对全局最优解执行快速局部搜索,有效地降低了算法的时间复杂度,平衡算法的全局和局部开发能力。对随机生成不同规模的实例进行广泛的实验,通过仿真实验结果的比较,表明所得蛙跳算法的有效性和高效性。     

作业车间调度问题的布谷鸟搜索算法求解

布谷鸟搜索算法是一种新型元启发式优化算法,该算法受到自然界中布谷鸟的巢寄生行为启发而提出。首先分析了布谷鸟搜索算法的仿生原理和数学描述,采用基于工序的编码方式对最小化最大完工时间的作业车间调度问题进行布谷鸟搜索算法求解。通过典型算例进行仿真实验,测试结果表明布谷鸟搜索算法求解作业车间调度问题的可行性和有效性,优于萤火虫算法和基本粒子群算法,是解决生产调度问题的一种有效方法。