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The relevance of multiple criteria decision-making/aiding is reinforced by the prominence of these methods in a wide range of applications. Whether by solving problems with a single decision-maker (DM) or a group of DMs, additive modelling, based on value or utility functions, is the most traditional. However, applying this kind of method raises a critical issue: the difficulty in eliciting DM’s preferences and recommending a decision. Actually, it is a hard task for the DM to provide complete information regarding their preferences, because the DM may not be able to provide such information in the detailed way required, or even they may not be willing to do so. From this perspective, the emergence and growth of partial (incomplete or imprecise) information-based methods is indicative that these are a useful way of guiding decision-making as they require less cognitive input from a DM. Thus, this paper systematically reviews the literature on multicriteria decision methods that deal with partial information, focusing on the Multi-Attribute Value/Utility Theory context. Strategic research questions guide a bibliometric and content analysis of 105 peer-reviewed papers selected from the Web of Science (Main Collection). An integrated analysis of the results provides scholars, researchers and other professionals with a deeper comprehension of methodological advances and respective contributions, and of the main challenges and trends in this field of knowledge. Our analysis aims to show that when these methods are applied more reliable decision-making can be achieved.

Organizations have successfully used dynamic pricing to optimize revenues for many years, where research and practice have mainly focused on applications with independent, discrete commodities; for example, an airline ticket. In this research we consider applications where the commodity is continuous and the value of the commodity available to sell depends on the combination of previously accepted demand. We focus on vehicle ferries, where the accepted vehicle bookings are packed in lanes in the ferry to leave a usable space for future bookings. Certain combinations of vehicles may result in areas of unusable space, which will affect future revenue. While this application is the focus of the paper, there are numerous industries that face similar challenges including freight and the sale of advertising on television and radio. In this paper, we simultaneously solve the pricing and resource utilization problem to optimality for a discrete set of product types and stochastic demand. Our approach combines a dynamic pricing model with a mixed-integer linear program to optimize the packing. We present results for real-world examples from the ferry industry and discuss extensions to the method to improve the selection of vehicle configurations.

This paper provides some theoretical foundations for using moving average (MA) rules in the stock market. In particular, the paper analyzes the conditional probability of price increments and examines how this probability varies over time. We prove under certain assumptions that the probability of being in an uptrend is greater than the probability of being in a downtrend. This demonstration partially justifies the common use of MA rules in the stock market. Finally, we propose an ex-post empirical analysis to evaluate and compare the performance of some MA rules and other portfolio strategies in the US stock market. In this context, we also suggest a methodology that incorporates these trading rules as alarm rules to predict potential market failures. Our ex-post results confirm the advantages of using these trading rules to predict market trends and crises.

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance, and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call 'exposure units' to naturally cover manifold scenarios spanning well beyond 'products'. Our findings show, for example, that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e., all are gains) or all negative (i.e., all are losses). In the case of exposure units mixed-sign values, decision rules are much more complex and rely on cataloging the Bell-number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

One of the main problems facing hospital managers is in coping with the variability in demand for the services that the hospital provides. This is particularly the case in the Critical Care Unit (CCU), where inability to provide adequate facilities on demand can lead to serious consequences. Admissions to CCUs may be categorized under two headings: unplanned (emergency) and planned (elective). The length of stay (LoS) in the CCU is heavily dependent on the admission category: unplanned admissions have a much longer LoS on average than elective patients. In this paper, we propose a mathematical model that shows how improvements in bed management may be achieved by distinguishing between these two categories of patients. The vast majority of previous literature in this field is concerned only with steady-state conditions, whereas in reality, activities in virtually all hospital environments are very much time dependent. This paper goes some way to addressing this problem.

Statistical models of football (soccer) match outcomes have potential applications to areas such as the development of team rankings and football betting markets. Much of the published work in this context has typically focused on the use of generalized linear models, which are non-dynamic in the sense that the parameters in the model, which often represent the underlying abilities of each team, are assumed to remain constant over time. Dynamic generalized linear models (DGLMs) on the otherhand allow the abilities of each team to vary over time. This paper illustrates the application of a DGLM in the context of football match outcome prediction and describes improvements on similar work previously presented by the author, in relation to the estimation of a parameter in the model, referred to as the evolution variance, which is crucial in terms of optimizing the predictive performance of these types of models. Match results data from the Scottish Premier League from 2003/2004 to 2005/2006 are used to show that the DGLM approach provides improved predictive probabilities of future match outcomes compared to the non-dynamic form of the model. DGLMs are also Bayesian in terms of their structure and so a Bayesian approach to parameterestimation is required. This paper therefore illustrates a practical implementation of the DGLM model that can easily be deployed using the freely available software WinBUGS.

Aspiring green agendas in conjunction with tremendous economic pressures are resulting in an increased attention to the environment and technological innovations for improving existing logistics systems. Last mile logistics, in particular, are becoming much more than a consumer convenience necessity and a transportation optimization exercise. Rather, this area presents a true opportunity to foster both financial and environmental sustainability. This paper investigates recent technological advancements and pending needs related to business and social innovations, emphasizing green logistics and city logistics concepts. We discuss various pertinent aspects, including drones, delivery robots, truck platooning, collection and pickup points, collaborative logistics, integrated transportation, decarbonization and advanced transport analytics. From a mathematical perspective, we focus on the basic features of the vehicle routing problem and some of its variants. We provide recommendations around strategies that may facilitate the adoption of new effective technologies and innovations.

Integer programming (IP), also known as discrete optimization, is a way of modelling a very wide range of problems involving indivisibilities (e.g. yes/no investment decisions) and non-convexities (e.g. economies of scale and fixed cost allocation). Such problems arise in many areas; these are mentioned in the paper. However, IP demands ingenuity in both building models and in their solution. Much is still not properly understood. This paper investigates the question: ‘Is IP like Linear Programming (LP)? ’ The mathematical and economic properties of IP will be contrasted with LP. It will be suggested that the mathematics and economics of IP are still not properly understood. Many of the results which apply to LP do not apply to IP. It will be asserted that this lack of understanding reveals inadequacies in both the mathematics and economics. Published online October 5th, 2010.

Control tunnelling over firms can be reached through pyramids, cross-ownership, and other complex features. This phenomenon is frequent in Europe and in Asia. However, the theoretical literature has not yet converged toward a well-defined and robust measurement of integrated control that takes into account the threshold for control as applied in practice. Based on graph theory, this paper aims at filling this gap and proposes a new algorithm for evaluating the control tunnelling exerted by the firms' ultimate shareholders. Then, the paper discusses the various forms of control existing next to voting shares, like multiple voting rights, board representation and active monitoring, before suggesting ways to include them into the modelling of control.

In this paper, we use a continuous time stochastic model to study a collective defined contribution pension plan when the interest rate is stochastic, and where the benefit levels are adjusted depending on the performance of the plan, and with risk sharing between different generations. The nominal interest rate is characterized by the Vasicek model, and the pension fund is invested in a financial market consisting of three assets: one risk-free asset, one bond and one risky asset. The participants of the pension plan are the risk bearers, and the plan seeks optimal investment and risk-sharing arrangements for plan sponsors and participants that maximize the expected accumulated discount utility of intermediate benefit adjustments and terminal wealth. Closed-form solutions are derived via the stochastic optimal control approach under constant relative risk aversion utility function. Numerical results show the effects of financial market parameters on the optimal investment strategy and how the optimal benefit changes with respect to different risk aversions and wage increase rates.

In this paper, we present a routing heuristic for the Flying Sidekick Traveling Salesman Problem. This problem combines a single truck with a single drone. The drone may be launched from the truck from a customer location and can make a single package delivery before being recovered by the truck. While the drone is in flight, the truck can deliver packages independently. The problem is one of simultaneously assigning the customers to each vehicle and determining the synchronized routes for both vehicles to satisfy all customer demands in the shortest time possible. The problem is NP-hard. Our main contribution lies in developing a novel split algorithm that utilizes a shortest path approach for determining the optimal routing solution to a given order of customer locations. This split algorithm has polynomial complexity. We develop a heuristic solution to the problem by combining the split algorithm with local search techniques. This overall heuristic is shown to be accurate and computationally scalable to large, realistically sized problems applicable in last-mile logistics.

This paper provides the first optimal portfolio analysis for a constant relative risk-averse and ambiguity-averse investor under the state-of-the-art 4/2 stochastic volatility model in a complete market setting. We determine the robust optimal strategy and the worst case measure by allowing separate levels of uncertainty for variance and stock drivers. Technical conditions for well-defined solutions are detailed together with a verification result. The robust optimal investment exposure displays a dependence on current volatility levels similar to the non-robust case further impacted by the ambiguity-aversion level. Using real-world parameters, the numerical analysis finds that wealth-equivalent losses (WELs) from ignoring uncertainty or market completeness are moderate. On the other hand, WELs for investors who follow simpler but popular strategies, such as Heston (1/2 model) and Merton (geometric Brownian motion [GBM] model), could be quite substantial, of up to 24 and 51%, respectively. This latest analysis comes from new non-affine representations for the suboptimal value function of the 1/2 and GBM strategies.

In higher education, student learning support centres are examples of walk-in services with nonstationary demand. For many centres, the major expenditure is tutor wages; thus, optimizing tutor numbers and ensuring value for money in this area are key. In University College Dublin, the mathematics support centre (MSC) has developed a software system, which electronically records the time each student enters the queue, their start time with a tutor and time spent with a tutor. In this paper, we show how data analysis of 25,702 student visits and tutor timetable data, spanning 6 years, is used to identify busy and quiet periods. Prediction modelling is then used to estimate the waiting time for future MSC visitors. Subsequently, we discuss how this is used for staffing optimization, i.e. to ensure there is sufficient coverage for busy times and no resource wastage during quieter periods. The analysis described resulted in the MSC reducing the number of queue abandonments and releasing funds from overstaffed hours to increase opening hours. The methods used are easily adapted for any busy walk-in service, and the code and data referenced are freely available: https://github.com/ehoward1/Math-Support-Centre-.

Energy quanto options are risk management tools that have a payoff similar to the product of the payoffs of two options, each written on an energy-related underlying. These options, as opposed to standardized contracts that only account for price risk, are designed to manage both volumetric and price risk in energy markets. Since the use of such options enables actors in the energy market also to hedge against production volume risk, they are becoming very popular. This paper considers the valuation of such an option on futures when the underlying futures prices are governed by Markov-modulated additive processes, which have independent but non-stationary increments within each regime. We derive a valuation formula by using the Fast Fourier Transform (FFT) technique under the assumption that the joint characteristic function of the log-futures prices is known analytically. We study this approximation under different regime-switching models. Several numerical case studies illustrate that our FFT-based valuation has a high precision and is much faster than Monte Carlo estimates.

This paper studies the situation in which a manufacturer acts as a dealer and buys a second-hand product from one customer and sells it with a two-dimensional warranty to another customer. The manufacturer plans to inspect the product during the warranty period to identify and remove hidden defects and hence prevent failure as well as their corresponding cost. We describe a two-dimensional delay time model in which the customer’s usage rate affects both the time to defect and delay time. This concept is then used to derive a new class of failure models, namely, the two-dimensional and two-stage failure model. The number and time of inspections are determined to minimize the service cost during the warranty period under periodic and sequential inspection policies. Our approach is illustrated using an example from the automobile industry. A sensitivity analysis evaluates the effect of changes in the parameters of the model. Results indicate that the proposed model can aid the decision-making of a manufacturer, particularly in relation to the effect of customers’ usage and the effect of inspection upon the service cost during the warranty period.

We study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem.

One of the main challenges when applying data envelopment analysis (DEA) is the selection of appropriate input and output variables. This paper addresses this important problem using a novel two-stage method. In the first stage, we use entropy theory to generate a comprehensive efficiency score (CES) of each decision-making unit. In the second stage, we select input and output variables using the Bayesian information criterion, when CES is treated as a dependent variable and the input and output variables are used as explanatory variables. We use stochastic data to demonstrate that our proposed method can improve the discrimination power of DEA and determine the important input and output variables. Finally, we compare the proposed method with principal component analysis using datasets on carbon emissions in China. This comparison demonstrates the practical value of our proposed method.

Traditional efficiency studies on network data envelopment analysis (DEA) consider decision-making units as black boxes that use a set of crisp inputs to produce a set of crisp outputs and that ignore intermediate measures and reverse flows. In real applications, however, we are faced with network systems with reverse flows in an uncertain environment. In this paper, therefore, a chance-constrained multistage DEA model is introduced to analyze the relative performances of supply chains and components in the presence of reverse flows and random factors. A real case in the sugar illustrates the proposed method. The results demonstrate the validity and applicability of the model.

In this paper, we consider the pricing of financial derivatives that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), guaranteed investment certificates (GICs) and American and barrier options are typical examples of these products. Our exploration involves the use and comparison of alternative models that use risk measures. Although the hedging is done for each observation of the input stochastic process, the appropriate mix of risk measures and state dynamic equations helps the issuer to appropriately tailor the overall risk exercise. These different models are solved by a unified backward stochastic dynamic programming framework that we imbed with parametric techniques to shorten the running time and manage the curse of dimensionality in dynamic programming. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs. Finally, by using sampling techniques, optimal hedging strategies and specific indicators of the hedging performance, we make recommendations on how to fine tune the risk measure parameters.

We consider a hybrid preventive maintenance policy. As in the classic model of age-replacement, a system is replaced either on failure or on reaching a predetermined age T. Additionally, it can be replaced on reaching a predetermined level of deterioration at some intermediate time in [0,T). We use a transformed gamma process with dependent increments to model the deterioration. A failure of an item occurs when this process reaches a predetermined deterministic level. We show that the proposed policy outperforms the classical one, that is, it achieves a lower value of the long-run cost rate. A detailed numerical illustration is presented and sensitivity analysis for the main parameters of the model is performed. The work in the paper makes an important contribution to maintenance modelling because dependent increments can better represent deterioration of a real system.

Advance selling activities are becoming more popular, especially in online retailing of new products. During the advance selling process, consumers may be loss averse. This influences the pricing strategy of the members of the supply chain. Using prospect theory and game theory, and considering consumers’ loss aversion, this paper studies the pricing strategy of advance selling in a supply chain consisting of a manufacturer and an e-retailer under a resale contract or an agency contract. The study finds that as consumers’ loss aversion increases, supply chain members set lower prices. Consumers’ loss aversion has a positive impact on the member who directly prices to consumers, but it has a negative impact on the indirect member. Advance selling under an agency contract makes it easier to achieve a Pareto improvement than that under the resale contract. When the unit order fulfilment cost is low, the e-retailer prefers the agency contract.

In this paper, the pricing of foreign exchange options is considered under a modified Heston–Cox–Ingersoll–Ross hybrid model. This modified model reserves all the characteristics of the Heston–Cox–Ingersoll–Ross model and also additionally assumes regime switching in the key parameters of the volatility as well as the domestic and foreign interest rates. Even though complicated, we have derived a closed-form pricing formula for foreign exchange options after the affinity of this new model is verified. Various properties of the newly derived formula are also shown through numerical experiments. To show the performance of this newly proposed model, an empirical study is also conducted, the result of which suggests that our model is a good alternative to the Heston–Cox–Ingersoll–Ross model for practical purpose.

This paper studies alternative procurement modes for emergency supplies in the presence of a public sector and a private supplier. A key feature of such a supply chain is that the private supplier must consider commercial demand in addition to disaster demand. Three procurement modes are analysed: an option mode (OM), an order-before-disaster mode (OBDM) and a procurement-after-disaster mode (PADM). We provide the optimal decisions associated with these three modes. Theoretical results in the OM show that a large order is not always better for the private supplier. From theoretical and numerical comparative analyses, no mode is absolutely superior. For the public sector, there are two thresholds. When the disaster probability is less than the low threshold, the revenues of all procurement modes are the same; when the disaster probability is larger than the high threshold, the OBDM has the highest revenue; otherwise, the OM has the highest revenue. However, for the private supplier, the PADM always has the highest revenue.

This paper contributes to the research on multi-pillar pension systems with main focus on private pension funds (PFs). In this context, the specific objective of this study is to determine which second-pillar private fund is the best for participants in such systems on the basis of their risk profile. Based on the assumptions on utility functions of the participants in a pension scheme, four types of stochastic dominance (SD) relations are considered, specifically first order, second order, third order and SD generated by utility functions with decreasing absolute risk aversion. We conduct an analysis under two distributional assumptions: empirical and stable distribution of returns. Moreover, the investors for which non-dominated funds are the optimal choices are identified. Allowing for diversification, the efficiency of the PFs with respect to several types of SD is tested. Then, the observed behaviour of participants in the last quarter/year is compared to the results of SD analysis. Finally, the identified SD relations are stress-tested using data originating from a period of turmoil. Despite the focus on Lithuanian PFs, the methodology developed in this work can be employed by participants or PF managers in similar markets of other countries.

Models derived from distributions of order-statistics are useful for modelling ranked data. The well-known Bradley–Terry (BT) and Plackett–Luce (PL) models can be derived from the order statistics of the exponential distribution but cannot handle ties. However, ties often occur in sports, and the ability to accommodate them leads to more useful ranking models. In this paper, we use discrete distributions, principally the geometric distribution, to obtain modified BT and PL models and some others that allow tied ranks. Our methodology is introduced for some mathematically tractable and some less tractable distributions and is illustrated using test match cricket.

Data envelopment analysis (DEA) is a mathematical programming technique for efficiency analysis. For dealing with the data in ratio form, the DEA model for ratio data known as DEA-R exists in the literature. However, some ratio data like financial risk may be negative naturally. In this paper, we contribute to the literature in two ways. In the first place, we deal with DEA-R models in the presence of negative ratio data by proposing an inverse DEA model for merger analysis. In the second place, we develop DEA-R models for merger analysis that can deal with negative data. We apply our models in a real-world application of efficiency and merger analysis of an Iranian bank with 66 branches. The proposed models maintain data confidentiality. This motivates managers to participate in the evaluation and merger process. Our models also provide a reasonable endogenous weight restriction framework without restricting weights exogenously.

Parisian options are a useful real-option tool in risk management, particularly for corporate bankruptcy protection. However, in the past, only one barrier with the Parisian feature was studied in the literature, possibly due to the additional complication that arises with the co-existence of two barriers. In this paper, we present an analytic solution for the valuation of European-style double-barrier Parisian options by casting the pricing problem into three inter-coupled partial differential equations. These are then solved using a dimension reduction procedure and the ‘moving window’ technique. Our solution is in an explicit and analytical form that is written in terms of multiple integrals. This represents an important advantage over the purely numerical approaches previously published in the literature.

This paper studies a healthcare system under two priority charging schemes. The first is a fee-for-priority (FFP) scheme under which the patients can choose to buy the priorities or not at their admission or readmission to the healthcare provider (HCP). The second is a bundled priority (BP) scheme under which the HCP receives a lump sum priority payment from patients for the entire episode of priority visits (regardless of the number of readmissions). Under both schemes, a certain proportion of revenue of the HCP (the reimbursement) is used to improve the service quality for patients. A two-stage Stackelberg game is established that captures the non-cooperative interactions between the HCP and patients, where the HCP is the leader who sets a price of priority and patients are the followers who decide whether to buy the priorities or not. We first characterize the Pareto-dominant equilibrium strategy of patients under the FFP and BP schemes, and we find that the total cost (including delay disutility and priority fee) of patients can be reduced if the patient pool is large. Although patients' minimum cost, including waiting cost and priority payment, is obtained under both the FFP and BP schemes, the prices are more flexible under the former than the latter. Finally, we demonstrate that implementing the FFP scheme can induce higher social welfare than the BP scheme.

The modelling of supply chain risk management (SCRM) has attracted increasing attention from researchers and professionals. However, a systematic network analysis of the literature to understand the development of research over time is lacking. Therefore, this study reviews SCRM modelling and its evolution as a scientific field. We collected 566 papers published in the Scopus database and shortlisted 120 for review. We have analysed the field's performance, mapped the most influential studies, as well as the generative and evolutionary research areas, and derived future research directions. Using bibliometric methods and tools for citation network analysis to understand the field's dynamic development, we find that five generative research areas provide the fundamental knowledge for four evolutionary research areas. The interpretation of gaps and trends in these areas provides an SCRM modelling timeline with 14 future research directions, which should consider adopting a holistic SCRM approach and developing prescriptive and normative risk models. The holistic approach enables more research on key factors—like process integration, design, information risk, visibility and risk coordination—that directly impact industry, decision-makers and sustainability needs. Risk models with evolved prescriptive and normative typology should respect both business model strategies and actual supply chain performance.

This paper considers sports matches in which two teams compete to score more points within a set amount of time (e.g. football, ice hockey). We focus on the order in which the competing teams score during the match (order of scoring). This type of order of scoring problem has not been addressed previously, and doing so here gives new insights into sports matches. For example, our analysis can deal with a situation that spectators find matches that involve comebacks particularly exciting. To describe such problems mathematically, we formulate the probabilities of (i) the favourite team leading throughout the match and (ii) the favourite team falling behind the opposing team but then making a comeback. These probabilities are derived using an independent Poisson model and lattice path enumeration, the latter of which involves the well-known ballot theorem. The independence assumption allows lattice path enumeration to be applied directly to the Poisson model and various scoring patterns to be addressed. We confirm that the values obtained from the proposed models agree well with actual sports data from football, futsal and ice hockey.

Although online business has been growing for some time, third-party e-platforms and their impact on e-channels are an under-explored area in the literature on dual-channel supply chains. Considering different combinations of open and self-support e-platform, this paper develops dynamic game models in four dual-channel e-retail structures to study pricing strategies and channel preference for manufacturers. The results provide interesting insights. First, a manufacturer’s optimal prices vary in different e-channels. Second, e-retail prices on the self-support e-platform and open e-platform are both affected by the e-platform’s service quality and commission fee. Regardless of the channel structure, a better service quality by one e-platform leads to an increase in its own e-retail prices and forces the competing e-platform to either improve its service quality or take a lower price. Lastly and more importantly, we compare the manufacturer’s pricing strategies and performances in different dual-channel e-retail structures and identify its preferences. Specifically, if the commission fee is dynamic, we find that the manufacturer always prefers to use two e-channels provided by different e-platforms, and at least one of the e-channels is the self-support model, although it is a sub-optimal strategy.

The complexity of dependence between different types of components results in many challenges to estimate system reliability and to optimize maintenance plans. In this paper, we develop a reliability model to study the failure dependence of a system with a main component and several protective auxiliary components. Damage to the main component caused by random environmental shocks depends on the number of auxiliary components in operation. When the execution of inspection and maintenance actions during system operation is difficult, failures of the main component provide opportunities to inspect and replace the auxiliary components. We derive the system reliability using Laplace transforms and the matrix method. The optimization problem is solved by an enumeration method. A numerical example and sensitivity studies of cost parameters show how the evolution of the parameters influences the optimal maintenance strategy. The results show that a high replacement threshold of the auxiliary components is required when the replacement cost of the main component is high. Conversely, the threshold could be adjusted to a lower level when the replacement cost of the auxiliary components and the downtime cost increase.

In quantitative finance practice, model calibration is a key challenge. This is especially so when a local regime-switching model needs to be calibrated because designing an efficient and reliable algorithm to obtain local volatility values as a function of underlying price and time is important for the model to be successfully used in practice. Therefore, this paper proposes a new algorithm for calibrating local regime-switching models with observed option prices available for a particular market that is suitable for this type of model. The newly proposed algorithm is tested with calibrations performed on synthetic as well as real market data. Our empirical test results indicate that the algorithm has great potential to be used in financial risk management.

In this paper, we construct quantitative models in which the dependence structure of the firms’ default times is incorporated. Such models serve as the underlying frameworks in our proposed approach to price and hedge basket credit derivatives. Through the Gaussian copula-based method, we model the default correlation risk and develop valuation formulas for credit derivatives. Using single-name derivatives in a hedging strategy for basket credit derivatives, the utility of the delta and delta-gamma hedging techniques are examined. This enables the management of risk attributed to the changes in correlation without the need for a large number of hedging instruments. Our research contributions provide insights on how dependent risks in basket credit derivatives could be dealt with effectively.

This paper considers a retrial queueing system with a pay-for-priority option. A queueing-game-theoretic model that captures the interaction among the customers, the service provider (SP) and the social planner is developed. We obtain the equilibrium strategy of customers for any fixed priority premium and identify the unique Pareto-dominant strategy. The optimal pricing strategies for the SP and the social planner are derived and compared extensively. Interestingly, we find that the equilibrium outcome of customers is non-monotone in the service reward and the profit of the SP is bimodal in the priority premium. We reveal the fact that the SP’s optimization makes the system more congested than what is socially desirable. Finally, numerical examples indicate that the customer welfare can be improved by providing priorities when the market size is large.

Decision makers in various sectors, such as manufacturing and transportation, strive to minimize downtime costs. Often, brief-planned stoppage times allow for changes in shifts and line configurations and longer periods are scheduled for major repairs. It is quite important to proactively make use of these downtimes to reduce the costs of unexpected downtimes due to failures. Among many aspects, the availability of spare parts significantly affects the operational costs of such systems. Current sensor technologies enable the condition monitoring of critical components and degradation-based spare parts management. This paper focuses on Bayesian degradation modelling for spare parts inventory management for a new system. We propose a stochastic dynamic program to minimize the expected spare parts inventory cost for a fixed planning horizon. A numerical example illustrates the value of Bayesian analysis in this management setting. The proposed methodology finds the optimal time between long stoppages and optimal spare parts order quantity when the prior information about the degradation process is accurate. The methodology can be used to analyse the sensitivity of the optimal solution to changes in the accuracy and bias of the prior distributions of the model parameters, the cost structure and the number of machines in the system.

Low-rank problems are nonlinear minimization problems in which the objective function, by means of a suitable linear transformation of the variables, depends on very few variables. These problems often arise in quantitative management science applications, for example, in location models, transportation problems, production planning, data envelopment analysis and multiobjective programs. They are usually approached by means of outer approximation, branch and bound, branch and select and optimal level solution methods. The paper studies, from both a theoretical and an algorithmic point of view, a class of large-dimension rank-two nonconvex problems having a polyhedral feasible region and $f(x)=\phi (c^Tx+c_0,d^Tx+d_0)$ as the objective function. The proposed solution algorithm unifies a new partitioning method, an outer approximation approach and a mixed method. The results of a computational test are provided to compare these three approaches with the optimal level solutions method. In particular, the new partitioning method performs very well in solving large problems.

The conventional inverse data envelopment analysis (DEA) model is only applicable to positive data, while negative data are commonly present in most real-world applications. This paper proposes a novel inverse DEA model that can handle negative data. The conventional inverse DEA model is a special case of our model as our model is more general in terms of returns-to-scale properties. The proposed model is used to evaluate the efficiency of the Chinese commercial banks after the global financial crisis, where negative outputs existed. We show that our model is feasible in the presence of negative data and generates empirical findings that are consistent with reality.

Forecasting non-stationary time series, especially when the data generating processes contains a random walk component, is a difficult and sometimes impossible task. In this paper we suggest an intuitive, computationally fast and expedient way of forecasting time series of the above type using distance-based nearest neighbours (NN). We exploit to advantage the path and scale dependence present in a random walk model and so we provide a number of theoretical results (a) on the distances used for selecting the NN, (b) on a number of new forecasting models that use these distances and (c) on the properties of the resulting forecasts. We illustrate the efficacy of our method via a comprehensive empirical application on time series of exchange rates and commodities, where we present the resulting performance enhancements and discuss the importance of such results in a decision-making context, linking our forecasting approach with management mathematics and predictive analytics problems.

In this paper, we formulate an inverse data envelopment analysis (DEA) model for a serially linked two-stage production process operating under constant returns to scale technology. The inverse DEA model determines a set of intermediate and output targets for an input augmented decision-making unit (DMU) to maintain its relative efficiency at a pre-specified level. We solve the inverse DEA model using the constraint method used in multi-objective optimization. The input augmented DMU with intermediate and output targets obtained in the inverse DEA model is a hypothetical DMU. Under our modelling framework, when such a hypothetical DMU established on an inefficient DMU is included in the observed DMU set, the frontier established with observed DMU set remains intact. This is important in practice as the intermediate and output targets of the hypothetical DMU would be feasible. When overall efficiency of the hypothetical DMU is decomposed, individual stages have the same efficiency level as that of the hypothetical DMU. This is important to DMU managers as sub-processes also maintain the desired overall efficiency level. We apply our inverse DEA model to a sample of Australian superannuation funds. We demonstrate that each unique Pareto optimal solution of the inverse DEA model obtained through the constraint method provides a specific set of intermediate and output targets and they may offer trade-off between intermediates and outputs. When fund managers anticipate expansion or growth in their funds, choice of targets allows comparison of different trade-off scenarios and makes informed decisions.

In this paper, the fair price of an American-style resettable convertible bond (CB) under the Black–Scholes model with a particular reset clause is calculated. This is a challenging problem because an unknown optimal conversion price needs to be determined together with the bond price. There is also an additional complexity that the value of the conversion ratio will change when the underlying price touches the reset price. Because of the additional reset clause, the bond price is not always a monotonically increasing function with the underlying price, which is impossible for other types of the CBs. Of course, the problem can be dealt with using the Monte-Carlo simulation. But, a partial differential equation (PDE)/integral equation approach is far superior in terms of computational efficiency. Fortunately, after establishing the PDE system governing the bond price, we are able to present an integral equation representation by applying the incomplete Fourier transform on the PDE system.

We present a novel general inverse data envelopment analysis model for assessing the restructuring of decision-making units (DMUs) while observing predetermined value efficiency targets, under two distinct scenarios: merger and acquisitions and split. By considering the set of efficient DMUs as the Decision Maker’s set of Most Preferred Solutions, virtual new units with desired targets for value efficiency scores and input and output levels can be computed. The innovations of this paper are threefold. First, a comparison between the proposed value efficiency and previous technical efficiency approaches reveals improvement in the estimation of restructured input/output levels. Second, the proposed approach is capable of handling the decision-maker’s preferences during restructuring. Third, an algorithm to determine the worst case-scenario for restructuring is presented. An applied case study in banking operations is presented to illustrate the validity and applicability of the proposed method.

Made available in DSpace on 2020-12-10T16:56:41Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-10-01 radiotherapy Erasto Gaertner Hospital, Curitiba/Parana/Brazil Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Radiotherapy planning is vital for ensuring the maximum level of effectiveness of treatment. In the planning task, there are at least two connected decision problems that can be modelled and solved using operational research techniques: determining the best position of the radiotherapy machine (beam angle problem) and the optimal dose delivered through each beam (dose distribution problem). This paper presents a mathematical optimization model for solving the combined beam angle and dose distribution problems in the presence of multiple objectives. A matheuristic based on Tabu Search (called TSrad) is developed to solve realistic large-scale instances. The performance of the proposed method is assessed on two prostate cancer instances, namely a single computed tomography (CT) slice and a set of CT slices (three-dimensional problem). For the single-slice problem, the results of TSrad are compared to the optimal solutions obtained by an exact method. Our experiments show that TSrad is able to achieve optimality for some instances. For the multi-slice problem, our experiments show that TSrad produces viable solutions that can be attained in a reasonable computational time. Fed Technol Univ Parana, Guarapuava, PR, Brazil Univ Nottingham Ningbo China, Nottingham Univ Business Sch China, 199 Taikang East Rd, Ningbo 315100, Zhejiang, Peoples R China Univ Portsmouth, Dept Math, Ctr Operat Res & Logist, Portsmouth, Hants, England UNESP, Biosci Inst, Botucatu, SP, Brazil Midwestern State Univ, Guarapuava, PR, Brazil Univ Fed Parana, Curitiba, PR, Brazil UNESP, Biosci Inst, Botucatu, SP, Brazil radiotherapy Erasto Gaertner Hospital, Curitiba/Parana/Brazil: 2042

The geometric process has been widely applied in reliability engineering and other areas since its introduction. One of its assumptions is that the times between occurrences of events are independent. This assumption is rather restrictive and can limit its application in the real world. This paper extends the geometric process to a new process, which we call the semi-geometric process, by relaxing this assumption. Some probabilistic properties of the process are derived and parameter estimation is described. A numerical example, based on a real-world dataset, is used to illustrate the model and validate the estimation methodology.

The interest rate and the market price of risk may be stochastic in a real-world financial market. In this paper, the interest rate is assumed to be driven by a stochastic affine interest rate model and the market price of risk from the stock market is a mean-reverting process. In addition, the dynamics of the stock are simultaneously driven by random sources of interest rate and the stock market itself. In pension fund management, different fund managers may have different risk preferences. We suppose risk preference is described by the hyperbolic absolute risk aversion utility, which is a general utility function describing different risk preferences. Legendre transform-dual theory is presented to successfully obtain explicit expressions for optimal strategies. A numerical example illustrates the sensitivity of optimal strategies to market parameters. Theoretical results imply that the risks from stochastic interest rate and stochastic return may be completely hedged by adopting specific portfolios.

This paper is an attempt to gain mathematical insight into the aggregate–disaggregate intermittent demand approach (ADIDA) forecasting framework, by formulating it as a multi-rate signal processing system. After a brief synopsis of the framework's background, an alternative way to perceive ADIDA from a systemic viewpoint is derived by breaking down its managerial steps into fundamental and well-studied components. Mathematical properties stemming from each separate system block are thoroughly explored and their practical effects are then exemplified through simulated paradigms of common time series patterns. Subsequently, theoretical and practical evidence are combined to draw useful conclusions about the framework's performance and make suggestions on its application. Finally, guidelines for further research are proposed.

Radiation accidents such as those at Three Mile Island, Chernobyl and, more recently, Fukushima have emphasized the need for supporting all phases of emergency management from the early phases in which a threat is detected to years and decades after the accident. Several decision-aiding tools have been developed to prevent and mitigate the effects of a radiation accident. This work reviews a range of mathematical models, computing tools and, particularly, multi-criteria decision-making techniques that have been applied in the last 25 years to help politicians, health officials, local authority representatives and emergency planning officers devise better countermeasure strategies in the event of a radiation accident. The paper discusses all phases of a nuclear emergency as well as emergency training and planning. It highlights what has been achieved in the application of multi-criteria decision analysis, mainly through initiatives such as the EU-funded real-time online decision support projects. It examines how such tools that have been developed fit into the formulation, evaluation and appraisal stages of the emergency management process and discusses the complex socio-technical issues that arise from radiation accidents. © The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Whereas the Duckworth-Lewis method (originally designed for one-day cricket) has been adopted in both international T20 matches and in the Indian Premier League, there has been growing objections to itsspecific use in T20. The Duckworth-Lewis method relies on the Duckworth-Lewis resource table which specifies the resources remaining at various stages of a match. In this paper, we consider the estimationof an alternative resource table specifically for T20 cricket. The alternative resource table suggests that there exist meaningful differences in the scoring patterns between one-day cricket and T20, and hence itcalls into question the suitability of the Duckworth-Lewis table for use in T20.

Mathematical models are often used to describe the sales and adoption patterns of products in the years following their launch and one of the most popular of these models is the Bass model. However, using this model to forecast sales time series for new products is problematical because there is no historic time series data with which to estimate the model’s parameters. One possible solution is to fit the model to the sales time series of analogous products that have been launched in an earlier time period and to assume that the parameter values identified for the analogy are applicable to the new product. In this paper, we investigate the effectiveness of this approach by applying four forecasting methods based on analogies (and variants of these methods) to the sales of consumer electronics products marketed in the USA. We found that all the methods tended to lead to forecasts with high absolute percentage errors, which is consistent with other studies of new product sales forecasting. The use of the means of published parameter values for analogies led to higher errors than the parameters we estimated from our own data. When using our own data, averaging the parameter values of multiple analogies rather than relying on a single most-similar, product led to improved accuracy. However, there was little to be gained by using more than five or six analogies.

In this paper we deal with the definition of a decision model for a producer operating in a multi-auction electricity market. The decisions to be taken concern the commitment of the generation plants and the quantity of energy required to offer to each auction and to cover the bilateral contracts. We propose a Multistage Stochastic Programming model in which the randomness of the clearing prices is represented by means of a scenario tree. The risk is modelled using a Conditional Value at Risk term in the objective function. Experimental results are reported to show the validity of our model and to discuss the influence of the risk parameters on the optimal value.