Motivated by the squeeze on public service expenditure, staffing is an important issue for service systems, which are required to maintain or even improve their service levels in order to meet general public demand. This paper considers Police Patrol Service Systems (PPSSs) where staffing issues are extremely serious and important because they have an impact on service costs, quality and public-safety. Police patrol service systems are of particularly interest because the demand for service exhibits large time-varying characteristics. In this case, incidents with different urgent grades have different targets of patrol officers’ immediate attendances. A new method is proposed which aims to determine appropriate staffing levels. This method starts at a refinement of the Square Root Staffing (SRS) algorithm which introduces the possibility of a delay in responding to a priority incident. Simulation of queueing systems will then be implemented to indicate modifications in shift schedules. The proposed method is proved to be effective on a test instance generated from real patrol activity records in a local police force.
Various recent events have shown the enormous importance of maritime search-and-rescue missions. By reducing the time to find floating victims at sea, the number of casualties can be reduced. A major improvement can be achieved by employing autonomous aerial systems for autonomous search missions, allowed by the recent rise in technological development. In this context, the need for efficient search trajectory planning methods arises. The objective is to maximize the probability of detecting the target at a certain time k, which depends on the estimation of the position of the target. For stationary target search, this is a function of the observation at time k. When considering the target movement, this is a function of all previous observations up until time k. This is the main difficulty arising in solving moving target search problems when the duration of the search mission increases. We present an intermediate result for the single searcher single target case towards an efficient algorithm for longer missions with multiple aerial vehicles. Our primary aim in the development of this algorithm is to disconnect the networks of the target and platform, which we have achieved by applying Benders decomposition. Consequently, we solve two much smaller problems sequentially in iterations. Between the problems, primal and dual information is exchanged. To the best of our knowledge, this is the first approach utilizing dual information within the category of moving target search problems. We show the applicability in computational experiments and provide an analysis of the results. Furthermore, we propose well-founded improvements for further research towards solving real-life instances with multiple searchers.
The knowledge of nucleotides chains that compose the double DNA chain of an individual has a relevant role in detecting diseases and studying populations. However, determining experimentally the single nucleotides chains that, paired, form a certain portion of the DNA is expensive and time-consuming. Mathematical programming approaches have been proposed instead, e.g. formulating the Haplotype Inference by Pure Parsimony problem (HIPP). Abstractly, we are given a set of genotypes (strings over a ternary alphabet {0,1,2}) and we want to determine the smallest set of haplotypes (binary strings over the set {0,1}) so that each genotype can be generated by some pair of haplotypes, meaning that they are compatible with the genotype and can fully explain its structure. A polynomial-sized Integer Programming model was proposed by Catanzaro, Godi and Labbe (2010), which is highly efficient but hardly scalable to instances with a large number of genotypes. In order to deal with larger instances, we propose a new model involving an exponential number of variables to be solved via column generation, where variables are dynamically introduced into the model by iteratively solving a pricing problem. We compared different ways of solving the pricing problem, based on integer programming, smart enumeration and local search heuristic. The efficiency of the approach is improved by stabilization and by a heuristic to provide a good initial solution. Results show that, with respect to the linear relaxations of both the polynomial and exponential-size models, our approach yields a tighter formulation and outperforms in both efficiency and effectiveness the previous model for instances with a large number of genotypes.
The vehicle routing problem comes in varied forms. In addition to usual variants with diverse constraints and specialized objectives, the problem instances themselves – even from a single shared source - can be distinctly different. Heuristic, metaheuristic, and hybrid algorithms that are typically used to solve these problems are sensitive to this variation and can exhibit erratic performance when applied on new, previously unseen instances. To mitigate this, and to improve their applicability, algorithm developers often choose to expose parameters that allow customization of the algorithm behavior. Unfortunately, finding a good set of values for these parameters can be a tedious task that requires extensive experimentation and experience. By deriving descriptors for the problem classes and instances, one would be able to apply learning and adaptive methods that, when taught, can effectively exploit the idiosyncrasies of a problem instance. Furthermore, these methods can generalize from previously learnt knowledge by inferring suitable values for these parameters. As a necessary intermediate step towards this goal, we propose a set of feature extractors for vehicle routing problems. The descriptors include dimensionality of the problem; statistical descriptors of distances, demands, etc.; clusterability of the vertex locations; and measures derived using fitness landscape analysis. We show the relevancy of these features by performing clustering on classical problem instances and instance-specific algorithm configuration of vehicle routing metaheuristics.
From preliminary design through product sustainment to end of life removal, optimal performance through the entire life cycle, is one of the most important design considerations in engineering systems. There are a number of mathematical modelling techniques available to determine the performance of any system, or process design. This paper focuses on the Petri Net technique for the representation and simulation of complex cases with the future aim of automatically generating a model from the system, or process description. If the model can be automatically generated changes can be investigated easily, enabling different designs to be investigated. Within this research, a Petri Net model is developed for a process of recycling IT assets. The model developed here will be used in future work to validate the automation process. This model is simulated and programmed in Matlab. The model enables the simulation of various flow paths through the recycling process, giving an understanding of the current process limiting factors. These can then be used to identify possible ways of improving the efficiency of the recycling process and enhancing the current IT asset management strategy. The future aim of this research is the automatic generation of a system model for complex industrial systems and processes by converting the SysML–based specifications into Petri Nets.
Urban access networks are the external part of worldwide networks that make telecommunication services accessible to end users and represent a critical part of the infrastructures of modern cities. An important recent trend in urban access networks is the integration of fiber and wireless networks, leading to so-called fiber-wireless (Fi-Wi) networks. Fi-Wi networks get the best of both technologies, namely the high capacity offered by optical fiber networks and the mobility and ubiquity offered by wireless networks. The optimal design of fiber and wireless networks has been separately extensively studied. However, there is still a lack of mathematical models and algorithms for the integrated design problem. In this work, we propose a new Power-Indexed optimization model for the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks. The new model includes additional power-indexed variables and constraints to represent the signal-to-interference formulas expressing wireless signal coverage. To solve the problem, which can prove very hard even for a state-of-the art optimization solver, we propose a new heuristic that combines a probabilistic variable fixing procedure, guided by (tight) linear relaxations, with an MIP heuristic, corresponding to an exact very large neighborhood search. Computational experiments on realistic instances show that our heuristic can find solutions of much higher quality than a state-of-the-art solver.
We introduce options on FTSE100 index in portfolio optimisation with shares in which conditional value at risk (CVaR) is minimised. The option considered here is the one that follows FTSE100 Index Option standards. Price of options are calculated under the risk neutral valuation. The efficient portfolio composed under this addition of options shows that put option will be selected as part of the investment for every level of targeted returns. Main finding shows that the use of options does indeed decrease downside risk, and leads to better in-sample portfolio performance. Out-of-sample and back-testing also shows better performance of CVaR efficient portfolios in which index options are included. All models are coded using AMPL and the results are analysed using Microsoft Excel. Data used in this study are obtained from Datastream. We conclude that adding a put index option in addition to stocks, in order to actively create a portfolio, can substantially reduce the risk at a relatively low cost. Further research work will consider the case when short positions are considered, including writing call options.
Model validation is a key activity undertaken during the model development process in simulation. There is a large body of literature on model validation, albeit there exists little convergence in terms of the definitions, types of validity, and tests used. Yet it is not clear what standards should be taken into consideration to avoid developing what could be considered to be invalid or wrong models. In this paper we examine existing literature on model validation with the view to identifying the existing validation approaches and types of tests used to assess model validity. In this review we focus our attention on three domains that usually overlap in methods and techniques: general Operational Research (OR), Modelling & Simulation (M&S) and Computer Science (CS). We analyze each field to identify the aspects of validity considered including the tests used, the validation approach taken, i.e. the suggested level of validity achieved (if this applies) and the reported outcome. The analysis shows that there are common validation practices used in all three fields as well as new ideas that could be adopted in discrete event simulation. Some main points of concurrence include the lack of universal validation, the continuous need for validation, and, the indispensable need for modelers and users to work closely together during the model validation process. This review provides an initial categorization of literature on model validation which can in turn be used as a basis for future work in investigating how and to what extent models are considered sufficiently valid.
We consider a large-scale unit commitment problem arising in medium-term simulation of energy networks, stemming from a joint project between the University of Milan and a major energy research centre in Italy. Optimal plans must be computed for a set of thermal and hydroelectric power plants, located in one or more countries, over a time horizon spanning from a few months to one year, with a hour-by-hour resolution. We propose a mixed-integer linear programming model for the problem. Since the complexity of this unit commitment problem and the size of real-world instances make it impractical to directly optimise this model using general purpose solvers, we devise ad-hoc heuristics and relaxations to obtain approximated solutions and quality estimations. We exploit an incremental approach: at first, a linear relaxation of an aggregated model is solved. Then, the model is disaggregated and the full linear relaxation is computed. Finally, a tighter linear relaxation of an extended formulation is obtained using column generation. At each stage, metaheuristics are run to obtain good integer solutions. Experimental tests on real-world data reveal that accurate results can be obtained by our framework in affordable time, making it suitable for efficient scenario simulations.
The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models. Nevertheless, an issue that has been raised is whether there exist other models that can explain and fit real data better than linear ones. In this paper, new nonlinear time series models are proposed (namely the ExpAR-ARCH and the ExpAR-GARCH), which are combinations of a nonlinear model in the conditional mean and a nonlinear model in the conditional variance and have the potential of explaining observed data in various fields. Simulated data of these models are presented, while different algorithms (the Nelder-Mead simplex direct search method, the Quasi-Newton line search algorithm, the Active-Set algorithm, the Sequential Quadratic Programming algorithm, the Interior Point algorithm and a Genetic Algorithm) are used and compared in order to check their estimation performance when it comes to these suggested nonlinear models. Moreover, an application to the Dow Jones data is considered, showing that the new models can explain real data better than the AR-ARCH and AR-GARCH models.
Supply chain risk management is an active area of research and there is a research gap of exploring established risk quantification techniques in other fields for application in the context of supply chain management. We have developed a novel framework for quantification of supply chain risks that integrates two techniques of Bayesian belief network and Game theory. Bayesian belief network can capture interdependency between risk factors and Game theory can assess risks associated with conflicting incentives of stakeholders within a supply network. We introduce a new node termed ‘Game theoretic risks’ in Bayesian network that gets its qualitative and quantitative structure from the Game theory based analysis of the existing policies and partnerships within a supply network. We have applied our proposed risk modeling framework on the development project of Boeing 787 aircraft. Two different Bayesian networks have been modeled; one representing the Boeing’s perceived supply chain risks and the other depicting real time supply chain risks faced by the company. The qualitative structures of both the models were developed through cognitive maps that were constructed from the facts outlined in a case study. The quantitative parts were populated based on intuition and subsequently updated with the facts. The Bayesian network model incorporating quantification of game theoretic risks provides all the reasons for the delays and financial loss of the project. Furthermore, the proactive strategies identified in various case studies were verified through our model. Such an integrated application of two different quantification techniques in the realm of supply chain risk management bridges the mentioned research gap. Successful application of the framework justifies its potential for further testing in other supply chain risk quantification scenarios.
In this paper a serial, three echelon, push-pull supply chain is investigated. The supply chain consists of a provider, a distribution centre (buffer) and a retailer. The material flow between upstream stages is push type, while between downstream stages it is driven by continuous review, reorder point/order quantity inventory control policy. Exponentially distributed lead times between stages are assumed. External demand occurs according to pure Poisson, while the demand that cannot be met is lost. The system is modelled using matrix analytic methods as a Markov birth-and-death process. An algorithm is developed to generate the transition matrix for different parameters of the system. Then, the corresponding system of stationary linear equations is generated and the solution of the stationary probabilities is provided. Key performance metrics such as average inventories and customer service levels at each echelon of the system can be computed. The algorithm is programmed in Matlab© and its validity is tested using simulation, with the two approaches giving practically identical results. The contribution of our work is an exact algorithm for a lost sales push-pull supply network. This algorithm can be used to evaluate different scenarios for supply chain design, to explore the dynamics of a push-pull system, or as an optimization tool.
The problem can be often formulated as a weighted p-median problem. Real instances of the problem are characterized by big numbers of possible service center locations, which can take the value of several hundreds or thousands. The optimal solution can be obtained by the universal IP solvers only for smaller instances of the problem. The universal IP solvers are very time-consuming and often fail when solving a large instance. Our approach to the problem is based on the Erlenkotter procedure for solving of the uncapacitated facility location problem and on the Lagrangean relaxation of the constraint which limits number of the located center. The suggested approach finds the optimal solution in most of the studied instances. The quality and the feasibility of the resulting solutions of the suggested approach depend on the setting of the Lagrangean multiplier. A suitable value of the multiplier can be obtained by a bisection algorithm. The resulting multiplier cannot guarantee an optimal solution, but provides a near-to-optimal solution and a lower bound. If our approach does not obtain the optimal solution, then a heuristic improves the near-to-optimal solution. The resulting solution of our approach and the optimal solution obtained by the universal IP solver XPRESS-IVE are compared in the computational time and the quality of solutions.
We consider the post-disaster road clearing problem with the goal of restoring network connectivity in shortest time. Given a set of blocked edges in the road network, teams positioned at depot nodes are dispatched to open a subset of them that reconnects the network. After a team finishes working on an edge, others can traverse it. The problem is to find coordinated routes for the teams. We generate a feasible solution using a constructive heuristic algorithm after solving a relaxed mixed integer program. In almost 70 percent of the instances generated both randomly and from Istanbul data, the relaxation solution turned out to be feasible, i.e. optimal for the original problem. 1998 ACM Subject Classification G.1.6 Optimization, G.2.2 Graph Theory, G.2.3 Applications
This paper represents results from our ongoing research project in the foresight area. The goal of the project is to develop web based tools which automatically detect activity and trends regarding given keywords. This knowledge can be used to enable decision makers to react proactively to arising challenges. As for now we can detect trends worldwide in more than 60 languages and assign these trends accordingly to over 100 national states. To reach this goal we utilize the big search engines as their core competence is to determine the relevance of a document regarding the search query. The search engines allow slicing of the results by language and country. In the next step we download some of the proposed documents for analysis. Because of the amount of information required we reach the field of Big Data. Therefore an extra effort is made to ensure scalability of the application. We introduce a new approach to activity and trend detection by combining the data collection and detection methods. To finally detect trends in the gathered data we use data mining methods which allow us to be independent from the language a document is written in. The input of these methods is the text data of the downloaded documents and a specially prepared index structure containing meta data and various other information which accumulate during the collection of the documents. We show that we can reliably detect trends and activities in highly active topics and discuss future research.
Coping with an ageing population is a major concern for healthcare organisations around the world. The average cost of hospital care is higher than social care for older and terminally ill patients. Moreover, the average cost of social care increases with the age of the patient. Therefore, it is important to make efficient and fair capacity planning which also incorporates patient centred outcomes. Predictive models can provide predictions which their accuracy can be understood and quantified. Predictive modelling can help patients and carers to get the appropriate support services, and allow clinical decision-makers to improve care quality and reduce the cost of inappropriate hospital and Accident and Emergency admissions. The aim of this study is to provide a review of modelling techniques and frameworks for predictive risk modelling of patients in hospital, based on routinely collected data such as the Hospital Episode Statistics database. A number of sub-problems can be considered such as Length-of-Stay and End-of-Life predictive modelling. The methodologies in the literature are mainly focused on addressing the problems using regression methods and Markov models, and the majority lack generalisability. In some cases, the robustness, accuracy and re-usability of predictive risk models have been shown to be improved using Machine Learning methods. Dynamic Bayesian Network techniques can represent complex correlations models and include small probabilities into the solution. The main focus of this study is to provide a review of major time-varying Dynamic Bayesian Network techniques with applications in healthcare predictive risk modelling.
Revenue Management (RM) has been successfully applied to many industries and to various problem settings. While this is well reflected in research, RM literature is almost entirely focused on the dynamic pricing problem where a perishable product is priced over a finite selling horizon. In retail however, the static case, in which products are continuously replenished and therefore virtually imperishable is equally relevant and features a unique set of industry-specific problem properties. Different aspects of this problem have been discussed in isolation in various fields. The relevant contributions remain therefore scattered throughout Operations Research, Econometrics, and foremost Marketing and Retailing while a holistic discussion is virtually non-existent. We argue that RM with its interdisciplinary, practical, and systemic approach would provide the ideal framework to connect relevant research across fields and to narrow the gap between theory and practice. We present a review of the static retail pricing problem from an RM perspective in which we focus on the demand model as the core of the retail RM system and highlight its links to the data and the optimization model. We then define five criteria that we consider critical for the applicability of the demand model in the retail RM context. We discuss the relevant models in the light of these criteria and review literature that has connected different aspects of the problem. We identify several avenues for future research to illustrate the vast potential of discussing the static retail pricing problem in the RM context.
A network design problem consists in locating facilities (nodes and arcs) that enable the transfer of flows (passengers and/or goods) from given origin-destination pairs. The topic can have several applications within transportation and logistics contexts. In this work we propose a multi-objective model in which balancing or equity aspects, i.e. measures of the distribution of distances of users from the path, are considered. These kinds of models can be used when there is the need to balance risks or benefits among all the potential users deriving from the location of the path to be designed. The application of the proposed model to a benchmark problem used in the literature to test these kinds of models, shows that it is able to find solutions characterized by significant level of equity but also of efficiency and efficacy.
