Showing papers in "OR Spectrum in 2012"

Line planning in public transportation: models and methods

Abstract: The problem of defining suitable lines in a public transportation system (bus, railway, tram, or underground) is an important real-world problem that has also been well researched in theory Driven by applications, it often lacks a clear description, but is rather stated in an informal way This leads to a variety of different published line planning models In this paper, we introduce some of the basic line planning models, identify their characteristics, and review literature on models, mathematical approaches, and algorithms for line planning Moreover, we point out related topics as well as current and future directions of research

An integer programming approach to elective surgery scheduling

Abstract: The scope of this work covers a real case of elective surgery planning in a Lisbon hospital The aim is to employ more efficiently the resources installed in the surgical suite of the hospital in question besides improving the functioning of its surgical service Such a planning sets out to schedule elective surgeries from the waiting list on a weekly time horizon with the objective of maximizing the use of the surgical suite For this purpose, the authors develop an integer linear programming model The model is tested using real data obtained from the hospital's record The non-optimal solutions are further improved by developing a custom-made, simple and efficient improvement heuristic Application of this heuristic effectively improves almost all non-optimal solutions The results are analyzed and compared with the actual performance of the surgical suite This analysis reveals that the solutions obtained using this approach comply with the conditions imposed by the hospital and improve the use of the surgical suite It also shows that in this case study the plans obtained from the proposed approach may be implemented in real life

The impact of client choice on preventive healthcare facility network design

Abstract: In contrast with sick people who need urgent medical attention, the clientele of preventive healthcare have a choice in whether to participate in the programs offered in their region. In order to maximize the total participation to a preventive care program, it is important to incorporate how potential clients choose the facilities to patronize. We study the impact of client choice behavior on the configuration of a preventive care facility network and the resulting level of participation. To this end, we present two alternative models: in the "probabilistic-choice model" a client may patronize each facility with a certain probability, which increases with the attractiveness of the available facilities. In contrast, the "optimal-choice model" stipulates that each client will go to the most attractive facility. In this paper, we assume that the proximity to a facility is the only attractiveness attribute considered by clients. To ensure the quality of care, we impose a bound on the mean waiting time as well as a minimum workload requirement at each open facility. Subject to a total capacity limit, the number of open facilities as well as the location and the capacity (number of servers) of each open facility is the main determinant of the configuration of a facility network. Both models are formulated as a mixed-integer program. To solve the problems efficiently, we propose a probabilistic search algorithm and a genetic algorithm. Finally, we use the models to analyze the network of mammography centers in Montreal.

Models and algorithms for the heterogeneous dial-a-ride problem with driver-related constraints

Abstract: This paper introduces models and algorithms for a static dial-a-ride problem arising in the transportation of patients by non-profit organizations such as the Austrian Red Cross. This problem is characterized by the presence of heterogeneous vehicles and patients. In our problem, two types of vehicles are used, each providing a different capacity for four different modes of transportation. Patients may request to be transported either seated, on a stretcher or in a wheelchair. In addition, some may require accompanying persons. The problem is to construct a minimum-cost routing plan satisfying service-related criteria, expressed in terms of time windows, as well as driver-related constraints expressed in terms of maximum route duration limits and mandatory lunch breaks. We introduce both a three-index and a set-partitioning formulation of the problem. The linear programming relaxation of the latter is solved by a column generation algorithm. We also propose a variable neighborhood search heuristic. Finally, we integrate the heuristic and the column generation approach into a collaborative framework. The column generation algorithm and the collaborative framework provide tight lower bounds on the optimal solution values for small-to-medium-sized instances. The variable neighborhood search algorithm yields high-quality solutions for realistic test instances.

Efficiency evaluation for pooling resources in health care

Abstract: Hospitals traditionally segregate resources into centralized functional departments such as diagnostic departments, ambulatory care centers, and nursing wards. In recent years this organizational model has been challenged by the idea that higher quality of care and efficiency in service delivery can be achieved when services are organized around patient groups. Examples include specialized clinics for breast cancer patients and clinical pathways for diabetes patients. Hospitals are struggling with the question of whether to become more centralized to achieve economies of scale or more decentralized to achieve economies of focus. In this paper we examine service and patient group characteristics to study the conditions where a centralized model is more efficient, and conversely, where a decentralized model is more efficient. This relationship is examined analytically with a queuing model to determine the most influential factors and then with simulation to fine-tune the results. The tradeoffs between economies of scale and economies of focus measured by these models are used to derive general management guidelines.

A (μ, λ)-coordination mechanism for agent-based multi-project scheduling

Abstract: A new generic negotiation-based mechanism to coordinate project planning software agents to share resources among projects is described. The mechanism, which takes into account asymmetric information and opportunistic behavior, is concretized for the decentralized resource constrained multi-project scheduling problem, and evaluated on 80 benchmark instances taken from the literature and 60 newly generated instances. Computational tests show that the proposed mechanism comes close to results obtained by central solution methods. For twelve benchmark instances new best solutions could be computed.

Effects of storage block layout and automated yard crane systems on the performance of seaport container terminals

Abstract: As a decoupling point between waterside and landside transport, the container yard plays a major role for the competitiveness of container terminals. One of the latest trends in container yard operations is the automated rail-mounted-gantry-crane system, which offers dense stacking along with high productivity. In this paper, the strategic design of rail-mounted-gantry-crane systems is investigated. A simulation study is conducted to evaluate the effects of four rail-mounted-gantry-crane systems and 385 yard block layouts--differing in block length, width, and height--on the yard and terminal performance.

Optimized load planning of trains in intermodal transportation

Abstract: In this paper the problem of load planning for trains in intermodal container terminals is studied. The objective is to assign load units to wagons of a train such that the utilization of the train is maximized, and setup and transportation costs in the terminal are minimized. Contrary to previous approaches additionally weight restrictions for the wagons are integrated into our model. We present three different integer linear programming formulations and test them on some real-world instances. It is shown that even non-commercial MIP-solvers can solve our models to optimality in reasonable time.

Organizing hospitals into networks: a hierarchical and multiservice model to define location, supply and referrals in planned hospital systems

Abstract: Health care planners in countries with a system based on a National Health Service (NHS) have to make decisions on where to locate and how to organize hospital services, so as to improve the geographic equity of access in the delivery of care while accounting for efficiency and cost issues. This study proposes a hierarchical multiservice mathematical programming model to inform decisions on the location and supply of hospital services, when the decision maker wants to maximize patients' geographical access to a hospital network. The model considers the multiservice structure of hospital production (with hospitals producing inpatient care, emergency care and external consultations) and the costs associated with reorganizing the hospital network. Moreover, it considers the articulation between different hospital services and between hospital units, and the ascendant and descendent flows related to two-way referrals of patients in the hospital hierarchy. The proposed approach differs from previous literature by accounting simultaneously for these issues and provides crucial information for health care planners on referral networks, on hospital catchment areas, on the location and structure of hospital supply as well as on the costs required to improve access. The results from applying the model are illustrated in an application to the South region of the Portuguese NHS. Three scenarios are portrayed to describe how the model can be used in distinct institutional settings and policy contexts and when there is uncertainty concerning the key parameters of the model.

Project scheduling with flexible resources: formulation and inequalities

Abstract: In this paper, we study a variant of the resource-constrained project scheduling problem in which resources are flexible, i.e., each resource has several skills. Each activity in the project may need several resources for each required skill. We present a mixed-integer linear programming formulation for this problem. Several sets of additional inequalities are also proposed. Due to the fact that some of the above-mentioned inequalities require a valid upper bound to the problem, a heuristic procedure is proposed. Computational experience is reported based on randomly generated data, showing that for instances of reasonable size the proposed model enlarged with the additional inequalities can be solved efficiently.

Using flexible products to cope with demand uncertainty in revenue management

Abstract: While flexible products have been popular for many years in practice, they have only recently gained attention in the academic literature on revenue management. When selling a flexible product, a firm retains the right to specify some of its details later. The relevant point in time is after the sale, but often before the provision of the product or service, depending on the customers' need to know the exact specification in advance. The resulting flexibility can help to increase revenues if capacity is fixed and the demand to come difficult to forecast. We present several revenue management models and control mechanisms incorporating this kind of flexible products. An extensive numerical study shows how the different approaches can mitigate the negative impact of demand forecast errors.

Trapezoidal fuzzy DEMATEL method to analyze and correct for relations between variables in a composite indicator for disaster resilience

Abstract: Indicator systems of disaster vulnerability are important for monitoring and increasing the capacity in risk management. Various composite indicators have been developed to operationalize social vulnerability at national and sub-national level. Problems with relations between the sub-indicators of the composite indicator are a common phenomenon. The fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) method analyzes the structure of complex cause-effect relationships between the sub-indicators based on perceived direct influences. The results provide insight into the composite indicators and can be used to correct the sub-indicator weighting for relations between the sub-indicators and allow the identification of cause- and effect-group sub-indicators which is an important information for selecting mitigation measures in risk management. The fuzzy DEMATEL method is generalized to take into account trapezoidal membership functions. A composite indicator originally developed to determine the disaster resilience in US counties is adapted, operationalized and used to assess the resilience of Germany at county level using corrected weights. Resilience is highest in urban areas and in southern Germany and lowest in rural areas, in particular in eastern Germany.

An implementation of the iterated tabu search algorithm for the quadratic assignment problem

Abstract: In this paper, we describe an implementation of the iterated tabu search (ITS) algorithm for the quadratic assignment problem (QAP), which is one of the well-known problems in combinatorial optimization. The medium- and large-scale QAPs are not, to this date, practically solvable to optimality, therefore heuristic algorithms are widely used. In the proposed ITS approach, intensification and diversification mechanisms are combined in a proper way. The goal of intensification is to search for good solutions in the neighbourhood of a given solution, while diversification is responsible for escaping from local optima and moving towards new regions of the search space. In particular, the following enhancements were implemented: new formula for fast evaluation of the objective function and efficient data structure; extended intensification mechanisms (including randomized tabu criterion, combination of tabu search and local search, dynamic tabu list maintaining); enhanced diversification strategy using periodic tabu tenure and special mutation procedure. The ITS algorithm is tested on the different instances taken from the QAP library QAPLIB. The results from the experiments demonstrate promising efficiency of the proposed algorithm, especially for the random QAP instances.

The single-day surgery scheduling problem: sequential decision-making and threshold-based heuristics

Abstract: Scheduling elective surgeries is a dynamic, sequential decision-making process that must balance the costs of deferring waiting cases and blocking higher-priority cases. Although other surgery scheduling problems have received extensive treatment in the literature, this paper presents the first single-day scheduling problem formulation to capture this aspect of the scheduling process while also incorporating surgical block schedules, block release policies, and waiting lists. Theoretical results for the special case in which all cases have the same duration motivate a range of threshold-based heuristics for the general problem with multiple case durations. Our computational results demonstrate the effectiveness of the proposed heuristics and show how block release dates affect the quality of the scheduling decisions. Based on these results, we propose a new approach to surgery scheduling. In particular, to make more equitable waiting list decisions, operating room (OR) managers should gradually release unused OR time over the course of several days leading up to the day of surgery.

Value-at-Risk optimization using the difference of convex algorithm

Abstract: Value-at-Risk (VaR) is an integral part of contemporary financial regulations. Therefore, the measurement of VaR and the design of VaR optimal portfolios are highly relevant problems for financial institutions. This paper treats a VaR constrained Markowitz style portfolio selection problem when the distribution of returns of the considered assets are given in the form of finitely many scenarios. The problem is a non-convex stochastic optimization problem and can be reformulated as a difference of convex (D.C.) program. We apply the difference of convex algorithm (DCA) to solve the problem. Numerical results comparing the solutions found by the DCA to the respective global optima for relatively small problems as well as numerical studies for large real-life problems are discussed.

Decision support for rehabilitation hospital scheduling

Abstract: We present a detailed analysis of the patient and resource scheduling problem in rehabilitation hospitals. In practice, the predominantly therapeutical treatments and activities which are prescribed for the patients are typically scheduled manually. This leads to rigid and inefficient schedules which can have negative effects on the quality of care and the patients' satisfaction. We outline the conceptual framework of a decision support system for the scheduling process that is based on formal optimization models. To this end, we first develop a large-scale monolithic optimization model. Then we derive a numerically tractable hierarchical model system in order to deal with problem instances of realistic sizes. We report numerical results with respect to solution times, model sizes and solution quality.

Trade-off analysis approach for interactive nonlinear multiobjective optimization

Abstract: When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the right ones for the DM, it is important to understand the trade-offs related to different Pareto optimal solutions. We first propose a trade-off analysis approach that can be connected to various multiobjective optimization methods utilizing a certain type of scalarization to produce Pareto optimal solutions. With this approach, the DM can conveniently learn about local trade-offs between the conflicting objectives and judge whether they are acceptable. The approach is based on an idea where the DM is able to make small changes in the components of a selected Pareto optimal objective vector. The resulting vector is treated as a reference point which is then projected to the tangent hyperplane of the Pareto optimal set located at the Pareto optimal solution selected. The obtained approximate Pareto optimal solutions can be used to study trade-off information. The approach is especially useful when trade-off analysis must be carried out without increasing computation workload. We demonstrate the usage of the approach through an academic example problem.

Staffing a call center with uncertain non-stationary arrival rate and flexibility

Abstract: We consider a multi-period staffing problem in a single-shift call center. The call center handles inbound calls, as well as some alternative back-office jobs. The call arrival process is assumed to follow a doubly non-stationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the back-office jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboy-type model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboy-type formulation as a stochastic program. Second, we develop a robust programming formulation. The characteristics of the two methods and the associated optimal solutions are illustrated through a numerical study based on real-life data. In particular we focus on the numerical tractability of each formulation. We also show that the alternative workload of back-office jobs offers an interesting flexibility allowing to decrease the total operating cost of the call center.

A new achievement scalarizing function based on parameterization in multiobjective optimization

Abstract: This paper addresses a general multiobjective optimization problem. One of the most widely used methods of dealing with multiple conflicting objectives consists of constructing and optimizing a so-called achievement scalarizing function (ASF) which has an ability to produce any Pareto optimal or weakly/properly Pareto optimal solution. The ASF minimizes the distance from the reference point to the feasible region, if the reference point is unattainable, or maximizes the distance otherwise. The distance is defined by means of some specific kind of a metric introduced in the objective space. The reference point is usually specified by a decision maker and contains her/his aspirations about desirable objective values. The classical approach to constructing an ASF is based on using the Chebyshev metric L ?. Another possibility is to use an additive ASF based on a modified linear metric L 1. In this paper, we propose a parameterized version of an ASF. We introduce an integer parameter in order to control the degree of metric flexibility varying from L 1 to L ?. We prove that the parameterized ASF supports all the Pareto optimal solutions. Moreover, we specify conditions under which the Pareto optimality of each solution is guaranteed. An illustrative example for the case of three objectives and comparative analysis of parameterized ASFs with different values of the parameter are given. We show that the parameterized ASF provides the decision maker with flexible and advanced tools to detect Pareto optimal points, especially those whose detection with other ASFs is not straightforward since it may require changing essentially the reference point or weighting coefficients as well as some other extra computational efforts.

Quantifying the impact of inland transport times on container fleet sizing in liner shipping services with uncertainties

Abstract: Container fleet sizing is a key issue in liner shipping industry. Although container shipping is an intermodal transport system, inland container movements are often beyond the control of shipping lines. It is vital to understand how the inland transport times and their variability affect the container fleet sizing. This paper first formulates the container fleet sizing problem in liner services with uncertain customer demands and stochastic inland transport times. Simulation-based optimisation approaches are then employed to solve the problem. Two typical shipping services, one cyclic route in trans-Pacific lane and the other more complicated route in Europe---Asia lane, are used as case studies. A quantitative relationship between the optimal container fleet size and the inland transport time is established. The impact of uncertainties in inland times on the fleet sizing is also investigated. The results provide shipping companies useful insights into making strategic decisions.

A branch-and-bound algorithm for the single-row equidistant facility layout problem

Abstract: In this paper, we deal with the single-row equidistant facility layout problem (SREFLP), which asks to find a one-to-one assignment of n facilities to n locations equally spaced along a straight line so as to minimize the sum of the products of the flows and distances between facilities. We develop a branch-and-bound algorithm for solving this problem. The lower bound is computed first by performing transformation of the flow matrix and then applying the well-known Gilmore---Lawler bounding technique. The algorithm also incorporates a dominance test which allows to drastically reduce redundancy in the search process. The test is based on the use of a tabu search procedure designed to solve the SREFLP. We provide computational results for problem instances of size up to 35 facilities. For a number of instances, the optimal value of the objective function appeared to be smaller than the best value reported in the literature.

Learning non-monotonic additive value functions for multicriteria decision making

Abstract: Multiattribute additive value functions constitute an important class of models for multicriteria decision making. Such models are often used to rank a set of alternatives or to classify them into pre-defined groups. Preference disaggregation techniques have been used to construct additive value models using linear programming techniques based on the assumption of monotonic preferences. This paper presents a methodology to construct non-monotonic value function models, using an evolutionary optimization approach. The methodology is implemented for the construction of multicriteria models that can be used to classify the alternatives in pre-defined groups, with an application to credit rating.

DEA based models for reallocations of police personnel

Abstract: A difficult aspect of improving the efficiency of service organisations in the developed world is the need to lay-off experienced people, whose training had significant costs and where later replacements are both costly and time consuming. This paper shows a novel way to reallocate personnel resources between tasks within a specific unit as well as between similar units using a data envelopment analysis model set. As there are many different ways to reallocate people, we propose six different scenarios to provide for different circumstances or policy objectives that may exist in the organisations. The method is illustrated using police units in a major metropolitan area and the results herein illustrate how efficiency improvements can be made in the police units' operations with very different impacts on the people involved for the various scenarios. This method saves resources and improves operating efficiency while allowing management to consider or compare the results following from different objectives. In some cases it may also preserve morale amongst the personnel, when the necessary productivity and efficiency improvements are made in ways that specifically aims at also minimising the impact on the personnel.

The shape of the utility or value function in stochastic multicriteria acceptability analysis

Abstract: Stochastic multicriteria acceptability analysis (SMAA) is a decision support method that allows representing uncertain, imprecise, and partially missing criteria measurements and preference information as probability distributions. In this paper, we test how the assumed shape of the utility or value function affects the results of SMAA in two different problem settings: identifying the most preferred alternative and ranking all the alternatives. A linear value function has been most frequently applied, because more precise shape information can be difficult to obtain in real-life applications. In this paper, we analyse one past real-life problem and a large number of randomly generated test problems of different size using additive functions of different shape. The shape varies from linear to increasingly concave and convex exponential utility or value functions corresponding to different attitudes on marginal value or risk. The results indicate that in most cases slight non-linearity does not significantly affect the results. The proposed method can be used for evaluating how robust a particular real-life decision problem is with respect to the shape of the function. Based on this information, it is possible to determine how accurately the DMs' preferences need to be assessed in a particular problem, and if it is possible to assume a simple linear shape.

Mean sojourn times in two-queue fork-join systems: bounds and approximations

Abstract: This paper considers a fork-join system (or: parallel queue), which is a two-queue network in which any arrival generates jobs at both queues and the jobs synchronize before they leave the system. The focus is on methods to quantify the mean value of the `system's sojourn time' S: with S i denoting a job's sojourn time in queue i, S is defined as max{S 1, S 2}. Earlier work has revealed that this class of models is notoriously hard to analyze. In this paper, we focus on the homogeneous case, in which the jobs generated at both queues stem from the same distribution. We first evaluate various bounds developed in the literature, and observe that under fairly broad circumstances these can be rather inaccurate. We then present a number of approximations, that are extensively tested by simulation and turn out to perform remarkably well.

How to park freight trains on rail---rail transshipment yards: the train location problem

Abstract: In modern rail---rail transshipment yards huge gantry cranes spanning all railway tracks allow for an efficient transshipment of containers between different freight trains This way, multiple trains loaded with cargo for varying destinations can be consolidated to a reduced number of homogeneous trains, which is an essential requirement of hub-and-spoke railway systems An important problem during the daily operations of such a transshipment yard is the train location problem, which assigns each train of a given pulse to a railway track (vertical position) and decides on each train's parking position on the track (horizontal position), so that the distances of container movements are minimized and the overall workload is equally shared among cranes For this problem a mathematical model is presented; different heuristic solution procedures are described and tested in a comprehensive computational study The results show that our procedures allow for a remarkable reduction of train processing time compared with typical real-world train location policies

Health care operations management

Abstract: Health care operations management has become a major topic for health care service providers and society. Operations research already has and further will make considerable contributions for the effective and efficient delivery of health care services. This special issue collects seven carefully selected papers dealing with optimization and decision analysis problems in the field of health care operations management.

Analytical models to determine room requirements in outpatient clinics

Abstract: Outpatient clinics traditionally organize processes such that the doctor remains in a consultation room while patients visit for consultation, we call this the Patient-to-Doctor policy (PtD-policy). A different approach is the Doctor-to-Patient policy (DtP-policy), whereby the doctor travels between multiple consultation rooms, in which patients prepare for their consultation. In the latter approach, the doctor saves time by consulting fully prepared patients. We use a queueing theoretic and a discrete-event simulation approach to provide generic models that enable performance evaluations of the two policies for different parameter settings. These models can be used by managers of outpatient clinics to compare the two policies and choose a particular policy when redesigning the patient process. We use the models to analytically show that the DtP-policy is superior to the PtD-policy under the condition that the doctor's travel time between rooms is lower than the patient's preparation time. In addition, to calculate the required number of consultation rooms in the DtP-policy, we provide an expression for the fraction of consultations that are in immediate succession; or, in other words, the fraction of time the next patient is prepared and ready, immediately after a doctor finishes a consultation. We apply our methods for a range of distributions and parameters and to a case study in a medium-sized general hospital that inspired this research.

DEA based on strongly efficient and inefficient frontiers and its application on port efficiency measurement

Abstract: Data envelopment analysis (DEA) is a non-parametric analytical methodology widely used in efficiency measurement of decision making units (DMUs). Conventionally, after identifying the efficient frontier, each DMU is compared to this frontier and classified as efficient or inefficient. This paper first introduces the strongly efficient frontier (SEF) and strongly inefficient frontier (SIF), and then proposes several models to calculate various distances between DMUs and both frontiers. Specifically, the distances considered in this paper include: (1) both the distance to SEF and the distance to SIF, where the former reveals a unit's potential opportunity to become a best performer while the latter reveals its potential risk to become a worst performer, and (2) both the closest distance and the farthest distance to frontiers, which may provide different valuable benchmarking information for units. Subsequently, based on these distances, eight efficiency indices are suggested to rank DMUs. Due to different distances adopted in these indices, the efficiency of units can be evaluated from diverse perspectives with different indices employed. In addition, all units can be fully ranked by these indices. The efficiency of 24 major Asian container ports is analyzed with our study, where the potential opportunities and potential crises of these ports are revealed and some new insights about their efficiency are provided.

The variance of inter-departure times of the output of an assembly line with finite buffers, converging flow of material, and general service times

Abstract: In this paper, we propose an approximation for the variability of the inter-departure times of finished products in an assembly line with finite buffers, converging flow of material, and general service times. We use the coefficient of variation as the relevant measure of variability. Exact procedures are not available for that case. The quality of the proposed approximation is tested against the results of various simulation experiments.