Estimating bed requirements for an intermediate care facility

Concern has been expressed in the United Kingdom regarding the proportion of beds intended for acute care that are occupied by patients who do not require acute care. One solution to this problem that is being investigated by some hospitals is the establishment of an intermediate care facility devoted to non-acute care. A key question faced by hospital planners is how many beds such an intermediate care facility should have. We report on a study consisting of a bed use survey and a stochastic analysis exercise that was conducted at the Whittington Hospital NHS Trust in London in order to address this question. Rather than focus on the whether patients in acute beds required acute care throughout their stay in hospital, the study concentrated on identifying periods in patients’ stays when they would have been transferred to an intermediate care facility if one had been available.     

Labour scheduling at an airport refuelling installation

We have developed an automatic assignment procedure for labour scheduling at a continously operating airport refuelling installation. Different types of workers are subject to different conditions on the shifts they can do (morning, evening or night), shift lengths, days-off, holidays, terms of contract and working hours. The scheduling process is carried out on a weekly basis, but there are mid-term and long-term conditions and objectives which link each week with the preceding and following weeks. Our package uses firstly a tabu search algorithm to find the best schemes of shifts/days-off to be used to cover the requirements. Secondly, an assignment problem is solved to match the schemes with available workers. Finally, the starting and finishing times for each working day are determined for each worker. The system has been designed to run on a personal computer and gives good quality solutions in very short computing times.     

Optimal response against bioterror attack on airport terminal

We consider a potential bioterror attack on an airport. After the attack is identified, the government is faced with the problem of how to allocate limited emergency resources (human resources, vaccines, etc.) efficiently. The government is assumed to make a one-time resource allocation decision. The optimal allocation problem is discussed and it is shown how available information on the number of infected passengers can be incorporated into the model. Estimation for parameters of the cost function (number of deaths after the epidemic is over) is provided based on known epidemic models. The models proposed in the paper are demonstrated with a case study using real airport data.     

Assigning arriving flights at an airport to the available gates

Unexpected changes in the flight schedules may disrupt the initial aircraft-gate assignments, and result in congestions and delays in getting aircraft onto gates. A mathematical model is developed to assign the flights with the minimum range of unutilised time periods of gates, subject to the level of service offered to passengers and other physical and managerial considerations. (The assignments are expected to be flexible enough to absorb the minor modifications in the flight schedules.) Interactive optimum and heuristic procedures, both utilising lower bounds on the ranges of future solutions, are proposed to cope with the major changes in disrupting the initial gate-assignments. Over randomly generated schedules, 74 flights can be optimally assigned to seven gates within 17 seconds when the gates are re-utilised within 30 minutes after each departure. The heuristic reaches the optimal solution after evaluating at most 20 partial solutions at one level. Over data obtained from Riyadh’s International Airport, the heuristic outperforms the existing practice: On average, 72.03% and 54.28% improvements are obtained on the number of remote served aircraft and towed aircraft, respectively.     

Using Singular Spectrum Analysis to obtain staffing level requirements in emergency units

Many operational research (OR) techniques use historical data to populate model input parameters. Although the majority of these models take into account stochastic variation of the inputs, they do not necessarily take into account seasonal variations and other stochastic effects that might arise. One of the major applications of OR lies within healthcare, where ever increasing pressure on healthcare systems is having major implications on those who plan the provision of such services. Coping with growing demand for healthcare, as well as the volatile nature of the number of arrivals at a healthcare facility makes modelling healthcare provision one of the most challenging fields of OR. This paper proposes the use of a relatively modern time series technique, Singular Spectrum Analysis (SSA), to improve existing algorithms that give required staffing levels. The methodology is demonstrated using data from a large teaching hospital's emergency unit. Using time dependent queueing theory, as well as SSA, staffing levels are obtained. The performance of our technique is analysed using a weighted mean square error measure, introduced in this paper.     

Virtual queuing at airport security lanes

Airports continuously seek opportunities to reduce the security costs without negatively affecting passenger satisfaction. In this paper, we investigate the possibilities of implementing virtual queuing at airport security lanes, by offering some passengers a time window during which they can arrive to enter a priority queue. This process could result in a smoother distribution of arriving passengers, such that the required security personnel (costs) can be decreased. While this concept has received attention in a number of settings, such as theme parks, virtual queuing at airports bears an additional level of complexity related to the flight schedules, i.e., passengers can only be transferred forward in time to a limited extent, which we denote by the transfer time limit. We conducted a major simulation study in collaboration with a large international airport in Western Europe to determine the potential impact of virtual queuing and find that nearly one million Euro can be saved on security personnel cost without negatively impacting the passenger waiting time.     

Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments

An incentive scheme aimed at reducing patients’ waiting times in accident and emergency departments was introduced by the UK government in 2000. It requires 98% of patients to be discharged, transferred, or admitted to inpatient care within 4 hours of arrival. Setting the minimal hour by hour medical staffing levels for achieving the government target, in the presence of complexities like time-varying demand, multiple types of patients, and resource sharing, is the subject of this paper. Building on extensive body of research on time dependent queues, we propose an iterative scheme which uses infinite server networks, the square root staffing law, and simulation to come up with a good solution. The implementation of this algorithm in a typical A&E department suggests that significant improvement on the target can be gained, even without increase in total staff hours.     

Estimating returns to scale of Chinese airport airside activities using the CCR-0-objective RTS method

The returns to scale (RTS) nature of 41 Chinese airport airsides is investigated in this paper. We introduce take-off distance available and landing distance available into RTS estimation. To deal with the existence of multiple optimal solutions when estimating RTS using the CCR (Charnes, Cooper and Rhodes) RTS method in Data Envelopment Analysis, we introduce the CCR-0-objective RTS method. The empirical study shows that all those airsides with two runway operate under decreasing RTS. Those airsides with only one runway either show constant RTS or show increasing RTS.     

Parametric shortest path algorithms with an application to cyclic staffing

Let G=(V, E) be a digraph with n vertices including a special vertex s. Let E′ ? E be a designated subset of edges. For each e?E there is an associated real number $\text{?}{}_1\text{(e)}$. Furthermore, let $\text{?}{}_2\text{(e)=1}$ if e?E′ and $\text{?}{}_2\text{(e)=0}$ if e?E ? E′. The length of edge e is $\text{?}{}_1\text{(e)? λ?}{}_2\text{(e)}$, where λ is a parameter that takes on real values. Thus the length varies additively in λ for each edge of E′.We shall present two algorithms for computing the shortest path from s to each vertex υ?V parametrically in the parameter λ, with respective running times O(n³) and O(n|E|log n). For dense digraphs the running time of the former algorithm is comparable to the fastest (non-parametric) shortest path algorithm known.This work generalizes the results of Karp [2] concerning the minimum cycle mean of a digraph, which reduces to the case that E′=E. Furthermore, the second parametric algorithm may be used in conjunction with a transformation given by Bartholdi, Orlin, and Ratliff [1] to give an O(n² log n) algorithm for the cyclic staffing problem.     

Passenger grouping with risk levels in an airport security system

This is a follow-up to the recent paper by Lazar Babu et al. [V.L. Lazar Babu, R. Batta, L. Lin, Passenger grouping under constant threat probability in an airport security system, European Journal of Operational Research 168 (2006) 633–644] which investigated the benefit of classifying passengers into different groups, with the idea that the number of checks and the degree of inspection may vary for different groups. A basic assumption in that paper was that the threat probability is constant across all passengers. In this paper, we relax this assumption and consider the case where passenger risk levels are incorporated. We assume that passengers are classified into several risk classes via some passenger prescreening system, for example, Computer-Assisted Passenger Prescreening System II (CAPPS II). We consider the separate grouping of every class of passengers such that the overall false alarm probability is minimized while maintaining the overall false clear probability within specifications set by a security authority. Meanwhile, we consider the staffing needs at each check station. The problem is formulated as a mixed integer linear program. An illustrative example of the model is presented with comparisons to the model in Lazar Babu et al. (2006) using two performance measures: probability of false alarm and total number of screeners needed. Our conclusion is that incorporation of risk levels through passenger grouping strategies leads to a more efficient security check system.     

Passenger grouping under constant threat probability in an airport security system

In a typical security system at a US airport, there are a series of inspections done on passengers as well as on baggage to check whether any item of threat is entering into the system. Considering the large number of passengers and items using our airports, one hundred percent check on all the items is not practical. This paper investigates the benefit of classifying passengers into different groups, with the idea that the number of checks and the degree of inspection may vary for different groups. The threat probability is assumed to be known and identical for all passengers. We develop a model to determine the number of groups, the fractions of passengers and the assignment of check stations for each group. The constraint is that the false clear probability is within Federal of Aviation Administration (FAA) specifications, and the objective is that the number of false alarms (a surrogate measure of passenger inconvenience) in the system is minimized. The model studies the effect of the system parameters on the number of items checked at various check stations and on the false alarm rate. The major conclusion of this paper is that passenger grouping is beneficial even when the threat probability is assumed constant across all passengers. A further conclusion is that the optimal grouping and check station assignments can depend on the overall threat probability.     

IBM journey management library: an arena system for airport simulations

Airline passenger terminal congestion caused by increasing passenger traffic results in unsatisfactory levels of customer service. We discuss a simulation modelling tool to help airlines and airports to use advanced technology to improve service to passengers. The tool consists of custom designed, reusable modules that represent the most common airline and airport system data, logic and processes. A model of an actual airline operation based on this approach is described.     

Estimating an interaction parameter of an infinite particle system

This article deals with the estimation of a parameter in the stochastic motion affecting an infinite number of particles. An estimator, based on a nonstationary time-series is considered and shown to be consistent. A comparison with more well-known estimates, via asymptotic variances, is also carried out.     

Human resources management at a marine container terminal

We consider the manpower planning problem in the real context of a marine container terminal. The main features of this problem are the uncertainty of workforce demand and the need of ensuring a time continuous efficiency of the terminal, which enforces to decompose the problem into two phases: a long-period planning first and then a daily planning.We propose mathematical programming models for both problems and suitably tailor them to the container terminal at the Gioia Tauro port. We derive solution algorithms by exploiting the mathematical properties of the models: a heuristic approach to a set-covering type problem for the long-term planning, and a branch-and-bound algorithm for the short-term planning. Finally, we report computational results on some real instances.     

Optimizing yard assignment in an automotive transshipment terminal

This paper studies a yard management problem in an automotive transshipment terminal. Groups of cars arrive to and depart from the terminal in a given planning period. These groups must be assigned to parking rows under some constraints resulting from managerial rules. The main objective is the minimization of the total handling time. Model extensions to handle application specific issues such as a rolling horizon and a manpower leveling objective are also discussed. The main features of the problem are modeled as an integer linear program. However, solving this formulation by a state-of-the-art solver is impractical. In view of this, we develop a metaheuristic algorithm based on the adaptive large neighborhood search framework. Computational results on real-life data show the efficacy of the proposed metaheuristic algorithm.