带约束的护士排班模型和基于变换规则的优化算法

护士排班是医院不可或缺并且需要反复进行的工作,排班方案的优劣对医院的护理质量、运作成本、护士心身健康、工作积极性等产生重大影响。针对我国护士排班问题缺乏通用模型和排班手段落后的问题,本文首先建立了一个带有一系列劳动法规约束和护士级别差异约束的整数规划模型,该问题被公认为是NP问题;然后增加护士请假约束和护士对工作时段偏好以及护士间配合默契程度的软约束,建立了一个更加人性化的扩展模型;随后设计了一系列变换规则,研制出一个护士优化排班算法。实例验证该模型与算法是可行且有效的,并且扩展模型更受欢迎,有利于提高护士积极性和工作效益。     

集成手术排程和护士排班的中期决策优化研究

在手术需求增大与医护人员短缺的矛盾下如何合理安排手术和配置医护资源,解决手术室实际运作中资源负荷不均衡现象,是当前手术室运作管理中亟待解决的难题。然而手术排程和手术室护士排班作为手术室科学管理的核心决策问题,却有着不同的时间域,并且会相互影响。在考虑科室手术和手术室护士偏好等硬约束和软约束前提下,构建一个集成手术排程和护士排班的手术室中期集成决策模型,设计了具有双层嵌套路径化结构的蚁群算法。通过某三甲医院10天的实际手术室运作数据,进行算法对比和分析评价,验证了算法在解决集成决策问题上的可行性和有效性。     

Measurement of uncertainty by the entropy: application to the classification of MSS data

Uncertainty is imposed simultaneously with multispectral data acquisition in remote sensing. It grows and propagates in processing, transmitting and classification processes. This uncertainty affects the extracted information quality. Usually, the classification performance is evaluated by criteria such as the accuracy and reliability. These criteria can not show the exact quality and certainty of the classification results. Unlike the correctness, no special criterion has been propounded for evaluation of the certainty and uncertainty of the classification results. Some criteria such as RMSE, which are used for this purpose, are sensitive to error variations instead of uncertainty variations. This study proposes the entropy, as a special criterion for visualizing and evaluating the uncertainty of the results. This paper follows the uncertainty problem in multispectral data classification process. In addition to entropy, several uncertainty criteria are introduced and applied in order to evaluate the classification performance.     

Activity-Based Costing and Management applied in a hybrid Decision Support System for order management

This article introduces a new Cost Management and Decision Support System (DSS) applicable to Order Management. This model is better fit and compatible with today's competitive, and constantly changing, business environment. The presented Profitable-To-Promise (PTP) approach is a novel modeling approach which integrates System Dynamics (SD) simulation with Mixed-Integer Programming (MIP). This Order Management model incorporates Activity-Based Costing and Management (ABC/M) as a link to merge the two models, MIP and SD. This combination is introduced as a hybrid Decision Support System. Such a system can evaluate the profitability of each Order Fulfillment policy and generate valuable cost information. Unlike existing optimization-based DSS models, the presented hybrid modeling approach can perform on-time cost analysis. This will lead to better business decisions based on the updated information.     

求解护士分配问题的矩阵编码进化算法

护士分配问题是护理人力资源配置中的一个优化问题,也是计算机科学中的很有挑战性的NP难问题。根据中国实际医院需求日益增加的情况,研究改良了随机规划（SPA）模型,建立了优化的多场景护士分配模型。基于护士与病人的对应关系,设计了0/1矩阵作为算法编码;采用矩阵编码进化算法（EAs with Matrix Coding）框架对矩阵编码进行迭代。基于求同存异的思想,运用随机编码部分介入技术实现了矩阵型染色体的变异算子。实验结果表明,与目前的随机贪心算法、基于Bender's分解的启发式算法和随机扰动遗传算法相比,提出的矩阵编码进化算法在求解护士分配问题时能得到更高质量、更稳定的解;在多场景和多约束前提下,其平均性能优势更加明显。     

Incorporating uncertainty in optimal decision making: Integrating mixed integer programming and simulation to solve combinatorial problems

We introduce a novel methodology that integrates optimization and simulation techniques to obtain estimated global optimal solutions to combinatorial problems with uncertainty such as those of facility location, facility layout, and scheduling. We develop a generalized mixed integer programming (MIP) formulation that allows iterative interaction with a simulation model by taking into account the impact of uncertainty on the objective function value of previous solutions. Our approach is generalized, efficient, incorporates the impact of uncertainty of system parameters on performance and can easily be incorporated into a variety of applications. For illustration, we apply this new solution methodology to the NP-hard multi-period multi-product facility location problem (MPP-FLP). Our results show that, for this problem, our iterative procedure yields up to 9.4% improvement in facility location-related costs over deterministic optimization and that these cost savings increase as the variability in demand and supply uncertainty are increased.     

Using hybrid algorithm for Pareto efficient multi-objective test suite minimisation

Test suite minimisation techniques seek to reduce the effort required for regression testing by selecting a subset of test suites. In previous work, the problem has been considered as a single-objective optimisation problem. However, real world regression testing can be a complex process in which multiple testing criteria and constraints are involved. This paper presents the concept of Pareto efficiency for the test suite minimisation problem. The Pareto-efficient approach is inherently capable of dealing with multiple objectives, providing the decision maker with a group of solutions that are not dominated by each other. The paper illustrates the benefits of Pareto efficient multi-objective test suite minimisation with empirical studies of two and three objective formulations, in which multiple objectives such as coverage and past fault-detection history are considered. The paper utilises a hybrid, multi-objective genetic algorithm that combines the efficient approximation of the greedy approach with the capability of population based genetic algorithm to produce higher-quality Pareto fronts.     

A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand

This paper presents a novel reliability-based stochastic user equilibrium traffic assignment model in view of the day-to-day demand fluctuations for multi-class transportation networks. In the model, each class of travelers has a different safety margin for on-time arrival in response to the stochastic travel times raised from demand variations. Travelers' perception errors on travel time are also considered in the model. This model is formulated as an equivalent variational inequality problem, which is solved by the proposed heuristic solution algorithm. Numerical examples are presented to illustrate the applications of the proposed model and the efficiency of solution algorithm.     

A genetic algorithm for a bicriteria supplier selection problem

In this paper, we discuss the problem of selecting suppliers for an organisation, where a number of suppliers have made price offers for supply of items, but have limited capacity. Selecting the cheapest combination of suppliers is a straightforward matter, but purchasers often have a dual goal of lowering the number of suppliers they deal with. This second goal makes this issue a bicriteria problem – minimisation of cost and minimisation of the number of suppliers. We present a mixed integer programming (MIP) model for this scenario. Quality and delivery performance are modelled as constraints. Smaller instances of this model may be solved using an MIP solver, but large instances will require a heuristic. We present a multi-population genetic algorithm for generating Pareto-optimal solutions of the problem. The performance of this algorithm is compared against MIP solutions and Monte Carlo solutions.     

uBench: exposing the impact of CUDA block geometry in terms of performance

The choice of thread-block size and shape is one of the most important user decisions when a parallel problem is written for any CUDA architecture. The reason is that thread-block geometry has a significant impact on the global performance of the program. Unfortunately, the programmer has not enough information about the subtle interactions between this choice of parameters and the underlying hardware. This paper presents uBench, a complete suite of micro-benchmarks, in order to explore the impact on performance of (1) the thread-block geometry choice criteria, and (2) the GPU hardware resources and configurations. Each micro-benchmark has been designed to be as simple as possible to focus on a single effect derived from the hardware and thread-block parameter choice. As an example of the capabilities of this benchmark suite, this paper shows an experimental evaluation and comparison of Fermi and Kepler architectures. Our study reveals that, in spite of the new hardware details introduced by Kepler, the principles underlying the block geometry selection criteria are similar for both architectures.     

Uncertain programming models for portfolio selection with uncertain returns

In an indeterminacy economic environment, experts’ knowledge about the returns of securities consists of much uncertainty instead of randomness. This paper discusses portfolio selection problem in uncertain environment in which security returns cannot be well reflected by historical data, but can be evaluated by the experts. In the paper, returns of securities are assumed to be given by uncertain variables. According to various decision criteria, the portfolio selection problem in uncertain environment is formulated as expected-variance-chance model and chance-expected-variance model by using the uncertainty programming. Within the framework of uncertainty theory, for the convenience of solving the models, some crisp equivalents are discussed under different conditions. In addition, a hybrid intelligent algorithm is designed in the paper to provide a general method for solving the new models in general cases. At last, two numerical examples are provided to show the performance and applications of the models and algorithm.     

Branching strategies in a branch-and-price approach for a multiple objective nurse scheduling problem

The efficient management of nursing personnel is of critical importance in a hospital’s environment comprising a vast share of the hospital’s operational costs. The nurse scheduling process affects highly the nurses’ working conditions, which are strongly related to the provided quality of care. In this paper, we consider the rostering over a mid-term period that involves the construction of duty timetables for a set of heterogeneous nurses. In scheduling nursing personnel, the head nurse is typically confronted with various (conflicting) goals complying with different priority levels which represent the hospital’s policies and the nurses’ preferences. In constructing a nurse roster, nurses need to be assigned to shifts in order to maximize the quality of the constructed timetable satisfying the case-specific time related constraints imposed on the individual nurse schedules. Personnel rostering in healthcare institutions is a highly constrained and difficult problem to solve and is known to be NP-hard. In this paper, we present an exact branch-and-price algorithm for solving the nurse scheduling problem incorporating multiple objectives and discuss different branching and pruning strategies. Detailed computational results are presented comparing the proposed branching strategies and indicating the beneficial effect of various principles encouraging computational efficiency.     

A cutting plane algorithm for the site layout planning problem with travel barriers

Site layout planning is an imperative procedure that may significantly impact the productivity and the efficiency of logistical operations undertaken on a construction site. This paper considers the site layout planning problem (SLPP) which entails the allocation of temporary facilities on a construction site in the presence of travel barriers such that the total transportation cost between facilities is minimised. In order to account for travel barriers, the SLPP is typically solved under the assumption that the available region for facility layout can be discretised. In this paper, we propose a general Mixed Integer Programming (MIP) model to represent the SLPP, accounting for the presence of barriers, and we show how space-discretised formulations can be derived from this model. In particular, we propose a novel MIP model, which permits facilities to cover multiple locations. This is then benchmarked against a commonly adopted MIP model in the literature. We also highlight a systematic procedure to convert the continuous feasible space in SLPP to a set of discretised locations based on the concept of d-visibility, enabling us to approximate the barrier distance function embedded in the objective function. In particular, we focus on presenting a simple space discretisation approach for converting the continuous SLP into a discrete problem for which the discrete SLP models would be applicable. Space-discretised MIP formulations are highly combinatorial and we introduce a cutting plane algorithm to improve their tractability. Specifically, we propose a novel exact location-decomposition algorithm which works from a relaxed MIP formulation and iteratively generates feasibility cuts to converge to an optimal solution. Both space-discretised MIP models and the decomposition algorithm are tested on a large group of instances to analyse their effectiveness in solving the SLPP. Computational results indicate that the proposed location-decomposition algorithm improves on the pure MIP approach and provides a competitive framework to solve realistic SLPP instances.     

The optimization of warehouse location and resources distribution for emergency rescue under uncertainty

China is one of the countries that suffer the most natural disasters in the world. The situation of emergency response and rescue is extremely tough. Establishing the emergency warehouse is one of the important ways to cope with rapid-onset disasters. In this paper, a mixed integer programming (MIP) model based on time cost under uncertainty is proposed, which help solve the emergency warehouse location and distribution problem. Comprehensive consideration of factors such as time cost, penalty cost for lack of resources, alternative origins of resources from both suppliers and emergency warehouses, different means of transportation and multiple resources types are involved in our study. We also introduce uncertain scenarios to describe the severity of the disaster. Particle swarm optimization (PSO) and variable neighborhood search (VNS) are designed to solve the MIP model of different scales of instances. Numerous examples have been tested to compare two heuristics with commercial solver (CPLEX). Both of two algorithms can obtain the exact solution same as CPLEX in small-scale instances while show great performance on larger instances with 10 candidate warehouses, 25 disasters and 50 scenarios.     

基于视点的多分辨率纹理选择方法

MIP Mapping技术是纹理映射中一种有效的纹理反走样技术。但是MIP Mapping只是根据被渲染区域的大小来选择相应分辨率的纹理,在初始化的时候必须把所有的纹理细节层次调入内存,这种情况下会降低计算机的效率。提出了一种基于视点的三维地图控制方法,根据与视点相关的渲染区域大小以及视觉重要度来选择相应分辨率的纹理。试验证明该方法在不降低显示质量的同时能有效减少纹理的渲染量,提高了计算效率。     

Development of a hybrid expert system for nurse shift scheduling

In this article, we discuss the effect of nurse shift job on circadian rhythm, work stress, and some important ergonomics criteria. We also review and compare different nurse shift scheduling methodologies via the criteria of flexibility, consideration of nurse preference, and consideration of ergonomics principles. A hybrid expert system, entitled NURSE-HELP, is developed to facilitate the nurse scheduling process with an emphasis on considering ergonomics criteria. Moreover, the combination of a linear zero-one goal programming and an expert system program reduces the program run time while maintaining the quality of the schedule. The evaluation of the system is done by comparing 18 sets of four-week schedules generated by the head nurses manually and by NURSE-HELP. Concerning the amount of time to generate the schedules, NURSE-HELP averages less than 20 minutes while the head nurses spend about two to four hours. The quality of the schedules is measured by the following four criteria; minimum staff level not satisfied, day off request not granted, backward rotation, and maximum consecutive work periods on the night shift. The results show that NURSE-HELP is superior than the head nurses in preparing schedules, both in terms of time and quality.     

Solving two-machine assembly scheduling problems with inventory constraints

This paper considers a scheduling problem with component availability constraints in a supply chain consisting of two manufacturing facilities and a merge-in-transit facility. Three mixed-integer programming (MIP) models and a constraint programming (CP) model are compared in an extensive numerical study. Results show that when there are no components shared among the two manufacturers, the MIP model based on time-index variables is the best for proving optimality for problems with short processing times whereas the CP model tends to perform better than the others for problems with a large range of processing times. When shared components are added, the performance of all models deteriorates, with the time-indexed MIP providing the best results. By explicitly modelling the dependence of scheduling decisions on the availability of component parts, we contribute to the literature on the integration of inventory and scheduling decisions, which is necessary for solving realistic supply chain problems.     

A Stochastic Vehicle Routing Problem with Travel Time Uncertainty: Trade-Off Between Cost and Customer Service

On-time shipment delivery is critical for just-in-time production and quick response logistics. Due to uncertainties in travel and service times, on-time arrival probability of vehicles at customer locations can not be ensured. Therefore, on-time shipment delivery is a challenging job for carriers in congested road networks. In this paper, such on-time shipment delivery problems are formulated as a stochastic vehicle routing problem with soft time windows under travel and service time uncertainties. A new stochastic programming model is proposed to minimize carrier’s total cost, while guaranteeing a minimum on-time arrival probability at each customer location. The aim of this model is to find a good trade-off between carrier’s total cost and customer service level. To solve the proposed model, an iterated tabu search heuristic algorithm was developed, incorporating a route reduction mechanism. A discrete approximation method is proposed for generating arrival time distributions of vehicles in the presence of time windows. Several numerical examples were conducted to demonstrate the applicability of the proposed model and solution algorithm.     

A two-stage stochastic programming model for the parallel machine scheduling problem with machine capacity

This paper proposes a two-stage stochastic programming model for the parallel machine scheduling problem where the objective is to determine the machines' capacities that maximize the expected net profit of on-time jobs when the due dates are uncertain. The stochastic model decomposes the problem into two stages: The first (FS) determines the optimal capacities of the machines whereas the second (SS) computes an estimate of the expected profit of the on-time jobs for given machines' capacities. For a given sample of due dates, SS reduces to the deterministic parallel weighted number of on-time jobs problem which can be solved using the efficient branch and bound of M’Hallah and Bulfin [16]. FS is tackled using a sample average approximation (SAA) sampling approach which iteratively solves the problem for a number of random samples of due dates. SAA converges to the optimum in the expected sense as the sample size increases. In this implementation, SAA applies a ranking and selection procedure to obtain a good estimate of the expected profit with a reduced number of random samples. Extensive computational experiments show the efficacy of the stochastic model.