Using the Viable Systems Model to examine multi-agency arrangements for combatting transnational organised crime

Traditionally, most operational research applications in the area of law enforcement and criminal justice have used quantitative techniques to forecast patterns and levels of offending and to optimise various police, judicial and prison processes. This paper seeks to examine the role that more qualitative modelling approaches might contribute in this important application area. Specifically, the paper examines the role that cybernetic theory and viable systems modelling can contribute in helping government bodies and law enforcement agencies to think through how, organisationally, they can best respond to the increasingly complex problem of transnational organised crime. Focussing on new multi-agency collaborative arrangements, the paper argues that there is a need for more informed debate that can account for the complexity of the challenge and point towards more holistic and integrated solutions. Against this background, the paper argues that the viable systems modelling approach has much to offer because it is theoretically grounded in the management of complexity; because its flexibility allows it to accommodate the trend for law enforcement agencies to work more closely with partner agencies, and to do so at multiple organisational levels; and because its user-friendly annotated diagramming conventions allow stakeholders to focus discussion and work towards outcomes that make sense in particular settings.     

Planning sustainable community health schemes in rural areas of developing countries

In this research, we consider the planning of community health schemes by non-governmental or faith-based organisations in rural areas of developing countries, from both top-down and ground level viewpoints. We conclude that both types of planning approach are valid and necessary for sustainability of such developments. With top-down planning in mind, we describe our hierarchical models especially designed for location of community health facilities, with objectives pertaining to both efficiency and equity of provision. As an additional case study, we present modelling of the location of a maximal number of self-sustainable primary healthcare workers in a rural region of India.     

A robust disaster preparedness model for effective and fair disaster response

Humanitarian network design decisions belonging to the preparedness stage of disaster management life-cycle are of critical importance since they set the frame for all further post-disaster operations. Having an adequate number of strategically located storage and distribution centers for critical supplies is the key that enables effectiveness, efficiency and fairness when responding to a disaster situation. The preparedness model proposed in this study selects locations and inventory levels of these facilities such that the right mix of relief items can be supplied at the right time. Our mixed integer linear model aims to find a robust relief network design that satisfies the demand for all given disaster scenarios, and to help achieve a better response during the response stage when the relief items are distributed. The assumptions and the parameters used in the model are justified by authorities of humanitarian organizations. We propose a logic-based Benders decomposition approach to solve this problem to optimality. Although the problem is NP-hard, our numerical studies demonstrate that it is possible to obtain optimal or very good solutions to problem instances with realistic sizes.     

Tactical Planning for a Cutting Stock System

Wood processing on a centralized conversion site can be considered as a cutting stock problem. The multiperiod optimization of the production system is a very hard problem to solve. A balance has to be made between value recovery optimization and service rate maximization. In this research a decision support system was designed and built to support production planning. Strategic, tactical and operational planning are covered, but here the focus is primarily on tactical planning.     

Planning a family visit program for PACU

Hospitals can develop or improve a PACU visitation program by establishing a policy, setting rules for visitation, ensuring patient privacy, educating staff and families, and performing quality control. Resistance from nursing staff is fairly easy to overcome, and visitation in the PACU for all patients seems likely to become standard practice. Sullivan warns that not allowing visitation may be detrimental: "If you don't have a visitor program, you'll probably have people somehow figuring out what your phone number is, lurking outside the door, and trying to see if they can get in." She is confident that "if you have a good program that meets the needs of the patient, the family, and the nurse, it will be successful." PACU visitarion is integral to patient care and consistent with regulations such as those of the Joint Commission on Accreditation of Healthcare Organizations (JCAHO). Jeran explains: "As nurses, we're taught to believe in family-centered care. That's the way nursing programs are set up; that's what JCAHO wants. I think it's unacceptable to have an area [in the hospital] where you don't reunite the family, even if it's just for a few minutes. She adds, "Anything that's going to make the patient and family more comfortable as they go through a very stressful period needs to be instituted, and we just have to figure out a way to make it work for everyone."     

Planning for a Single Specialty in a Health District

This paper discusses planning in the National Health Service. An outline of a general method for planning at the district level is illustrated with a case study in which a strategic plan was produced for the maternity services in Cambridge Health District. Some of the problems of ensuring implementation of proposals are then discussed.     

Towards a framework for developing students' fraction proficiency

The importance of the knowledge of fractions in mathematical learning, coupled with the difficulties students have with them, has prompted researchers to focus on this particular area of mathematics. The term ‘fraction proficiency' used in this article refers to a person's conceptual comprehension, procedural skills and the ability to approach daily situations involving fractions. In the area of fractions, there has been a call for more research to study how, and where, efforts should be focused in order to integrate the various aspects of fraction knowledge for students, and even for teachers, to help them develop proficiency in fractions. Thus, the article presents a theoretical synthesis of the specialized literature in the learning and teaching of fractions, with the aim of proposing a framework for developing students' fraction proficiency. The frameworks presented in the article may shed light upon the implications for the design of fraction instruction, which should focus on developing a multi-faceted knowledge of fractions, rather than simply isolating one facet from the others.     

A model for housing allocation of a homeless population due to a natural disaster

In the present work we derive and analyze a model considering housing allocation of homeless families due to a natural disaster; we use data from the earthquake of September 1999, in Athens, Greece. We derive a non-linear system of ordinary differential equations and analyze the stability of this system. Also we find an approximate solution of the model for a case study as well as and a numerical solution. Finally we consider possible extensions and improvements of the model making it more realistic.     

Planning for meals-on-wheels: algorithms and application

Home-delivered meals provision, also known as meals-on-wheels, is a volunteer-staffed activity for which little strategic planning is performed. We develop a Memetic Algorithm to solve the Home Delivered Meals Location-Routing Problem. This planning model addresses facility location, allocation of demand to facilities, and design of delivery routes, while balancing efficiency and effectiveness considerations. The case study presented on a large data set shows how trade-off curves, which are very useful for decision making, can be obtained by the method developed.     

New models for locating a moving service facility

In this paper we analyze a new location problem which is a generalization of the well-known single facility location model. This extension consists of introducing a general objective function and replacing fixed locations by trajectories. We prove that the problem is well-stated and solvable. A Weiszfeld type algorithm is proposed to solve this generalized dynamic single facility location problem on L ^p spaces of functions, with p ∈(1,2]. We prove global convergence of our algorithm once we have assumed that the set of demand functions and the initial step function belong to a subspace of L ^p called Sobolev space. Finally, examples are included illustrating the application of the model to generalized regression analysis and the convergence of the proposed algorithm. The examples also show that the pointwise extension of the algorithm does not have to converge to an optimal solution of the considered problem while the proposed algorithm does.     

Scheduling preparation of doses for a chemotherapy service

A fast realization of drugs is an important part in the quality of service of a hospital. In this paper we propose a scheduling method for the preparation of chemotherapy doses in order to reduce the patient waiting time. Two approaches have been defined: an off-line approach and a real time approach. The off-line approach is using a linear programming model for minimizing the maximum tardiness of jobs in a production day. This method is re-used during the real-time resolution combined with a greedy algorithm. The solution obtained respects constraints on the production center and the hospital organization. Our model is currently used in software which helps the decision maker of the service and allows increasing the patient satisfaction and the productivity of the service.     

Least-cost network topology design for a new service

We describe an implementation of the tabu search metaheuristic that effectively finds a low-cost topology for a communications network to provide a centralized new service. Our results are compared to those of a greedy algorithm which applies corresponding decision rules, but without the guidance of the tabu search framework. These problems are difficult computationally, representing integer programs that can involve as many as 10,000 integer variables and 2000 constraints in practical applications. The tabu search results approach succeeded in obtaining significant improvements over the greedy approach, yielding optimal solutions to problems small enough to allow independent verification of optimality status and, more generally, yielding both absolute and percentage cost improvements that did not deteriorate with increasing problem size.This research was partially supported by the Air Force Office of Scientific Research and the Office of Naval Research Contract No. F49629-90-C-0033.     

Determining optimal treatment rate after a disaster

From the standpoint of medical services, a disaster is a calamitous event resulting in an unexpected number of casualties that exceeds the therapeutic capacities of medical services. In these situations, effective medical response plays a crucial role in saving life. To model medical rescue activities, a two-priority non-preemptive S-server, and a finite capacity queueing system is considered. After constructing Chapman–Kolmogorov differential equations, Pontryagin's minimum principle is used to calculate optimal treatment rates for each priority class. The performance criterion is to minimize both the expected value of the square of the difference between the number of servers and the number of patients in the system, and also the cost of serving these patients over a determined time period. The performance criterion also includes a final time cost related to deviations from the determined value of the desired queue length. The two point boundary value problem is numerically solved for different arrival rate patterns and selected parameters.     

Heuristic procedures for a stochastic batch service problem

This paper considers a multi-class batch service problem that involves a class-dependent waiting cost and a service cost in determining customer batch sizes. Unlike a fixed service cost used widely in standard models, the service cost considered in this work is incurred only if the total service time is over the capacity. We formulate this problem as an infinite horizon Markov decision process, and exploit its structural properties to establish theoretical results, including bounds on the optimal action space. We use the results to improve the value iteration procedure. Furthermore, we design heuristic algorithms for large problems. The numerical experiments demonstrate that the class-dependent waiting cost has a considerable influence on the optimal customer batch size. Finally, we evaluate the efficiency of the proposed value iteration procedure and the quality of the heuristic solutions.     

Calibration of a Mathematical Model for Urban Planning

The operational value of the mathematical models used in regional or urban planning is mainly dependent upon the possibility of adequate calibration so as to make them actually represent the social and economic problem under study. In this paper we give a formulation of the calibration problem for a singly constrained exponential model, use it to calibrate a specific model that is actually being used to plan the development of a large Italian town, and obtain results that improve by about 30% a standard currently used calibration procedure.     

Motion Planning for a Convex Polygon in a Polygonal Environment

We study the motion-planning problem for a convex m -gon P in a planar polygonal environment Q bounded by n edges. We give the first algorithm that constructs the entire free configuration space (the three-dimensional space of all free placements of P in Q ) in time that is near-quadratic in mn , which is nearly optimal in the worst case. The algorithm is also conceptually simple. Previous solutions were incomplete, more expensive, or produced only part of the free configuration space. Combining our solution with parametric searching, we obtain an algorithm that finds the largest placement of P in Q in time that is also near-quadratic in mn . In addition, we describe an algorithm that preprocesses the computed free configuration space so that reachability queries can be answered in polylogarithmic time. Received September 9, 1997, and in revised form September 24, 1998.     

Teachers' understanding of inflation: developing a crystalline concept

Inflation rates are often reported in the media and interpreted differently by various people. The purpose of the study was to explore mathematical literacy teachers’ written responses to questions based on the concept of percentage increase and inflation. The participants were a group of 59 in-service South African teachers who were enrolled on a course to help them to teach the subject mathematical literacy. The findings show that 95% of the teachers could carry out a percentage increase calculation without any difficulties, but only 37% could correctly work out a two-step calculation using the inflation rate figures. Across all the items, there were only eight teachers (14%) who showed evidence of engagement with all the contextual constraints embedded in the inflation concept. Teachers exhibited poor covariational reasoning with respect to the changes in the inflation rates and changes in the price of goods. The study suggests that opportunities for the development of covariational reasoning should be promoted.     

On a bulk arrival bulk service infinite service queue

This paper considers an infinite server queue in continuous time in which arrivals are in batches of variable size X and service is provided in groups of fixed size R. We obtain analytical results for the number of busy servers and waiting customers at arbitrary time points. For the number of busy servers, we obtain a recursive relation for the partial binomial moments both in transient and steady states. Special cases are also discussed