Systemic Risk and Stochastic Games with Delay

We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into account a quadratic cost for lending or borrowing and a linear incentive to borrow if the reserve is low or lend if the reserve is high relative to the average capitalization of the system. As such, our problem is a finite-player linear–quadratic stochastic differential game with delay. An open-loop Nash equilibrium is obtained using a system of fully coupled forward and advanced-backward stochastic differential equations. We then describe how the delay affects liquidity and systemic risk characterized by a large number of defaults. We also derive a closed-loop Nash equilibrium using a Hamilton–Jacobi–Bellman partial differential equation approach.     

Multiobjective vendor allocation in multiechelon inventory systems: a spreadsheet model

The vendor selection problem (VSP) is a critical element of the numerous managerial decisions in the consideration of both outsourcing and integrated supply chain management. Many papers in the literature have dealt with VSPs from a multicriteria perspective, but few have looked into the implications of such decisions in a multiechelon supply chain with the explicit consideration of multiple time-phased demands. A new integrated supply chain model is proposed for a multiechelon supply chain. This model takes into account the usual cost objective and other important criteria in a multiechelon supply chain ranging from the most upstream suppliers' quality to end customers' satisfaction level through a large-scale multiobjective linear programme (MOLP). Furthermore, various Pareto optimal solutions can be graphically presented to facilitate decision making and negotiations with existing and potential suppliers.     

On the optimality of algorithms for finite state sequential decision processes

A finite state sequential decision process (sdp) is a model which is able to represent a wide variety of combinatorial optimization problems. Four known and two new algorithms for obtaining optimal policies of three subclasses of sdp's, r-lmsdp, r-pmsdp, and r-psmsdp, are considered, and their optimality in the sense of minimizing the number of evaluations of cost functions associated with state transitions is proved.     

Spatial Point Process Models of Defensive Strategies: Detecting Changes

The study of stochastic processes can take many forms. Theoretical properties are important to ensure consistent model definition. Statistical inference on unknown parameters is equally important but can be difficult. This is principally because many of the standard assumptions for proving consistency and asymptotic normality of estimators involve independence and homogeneity. In the case where inference is concerned with detecting change in a spatial process from one time point to another, a statistical-computing approach can be rewarding. Regardless of the complexity of the stochastic process, if simulating from it is relatively easy, then detecting change is possible using a Monte Carlo approach. The methodology is applied in a military scenario, where a country’s defensive posture changes as a function of its perceived threat. For tactical-decision purposes, it is extremely important to know whether the country’s perceived threat level has changed.     

Optimal monopoly pricing with congestion and random utility via partial mass transport

We consider a bilevel optimization framework corresponding to a monopoly spatial pricing problem: the price for a set of given facilities maximizes the profit (upper level problem) taking into account that the demand is determined by consumers' cost minimization (lower level problem). In our model, both transportation costs and congestion costs are considered, and the lower level problem is solved via partial transport mass theory. The partial transport aspect of the problem comes from the fact that each consumer has the possibility to remain out of the market. We also generalize the model and our variational analysis to the stochastic case where utility involves a random term.     

Multiobjective optimization and marginal pollution abatement cost in the electricity sector – An Israeli case study

The multiple objective optimization models for capacity expansion problem of power generation system in the long run as a base for setting up the marginal abatement cost were examined. In the optimization model the objective function is considered as the weighted sum of several objective functions. Air pollutants are taken into account in both the objective function and the constraints. Different scenarios of pollutant reduction were analyzed. The periods of the years 2003–2013 were taken into account and the results are based on the real data of the Israel electricity sector. Several environmental policies were considered by using the CAPEX system to evaluate the environmental and economic deficiencies in different abatement cost scenarios. The following are obtained: abatement cost for each pollutant, amount of emissions and additional cost connected with the pollutants. Modern decision tools are implemented, such as data envelopment analysis (DEA) and reasonable goal method/interactive decision maps (RGM/IDM) technique as a base for decision-makers to make decisions on energy and environmental policy.     

An a posteriori decision support methodology for solving the multi-criteria supplier selection problem

This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting.     

A Markov decision algorithm for optimal inspections and revisions in a maintenance system with partial information

This paper deals with a gradually deteriorating equipment whose actual degree of deterioration can be revealed by inspections only. An inspection can be succeeded by a revision depending on the system's degree of deterioration. In the absence of inspections and revisions, the working condition of the system evolves according to a Markov chain whose changes of state are not observable with the possible exception of a breakdown. Examples of this model include production machines subject to stochastic breakdowns, and maintenance of communication systems. The cost structure of the model consists of inspection, revision and operating costs. It is intuitively reasonable that in many applications a simple control-limit rule will be optimal. Such a rule prescribes a revision only when inspection reveals that the degree of deterioration has exceeded some critical level. A special-purpose Markov decision algorithm operating on the class of control-limit rules is developed for the computation of an average cost optimal schedule of inspections and revisions.     

Multiobjective stochastic programming for feed formulation

The minimum cost linear programming model used traditionally for feed formulation does not take account of variability of nutrients in feed ingredients. Therefore, it may be that the nutrient requirements of the animal are not adequately met. In this paper, we show how a multiobjective stochastic model that permits confronting the cost of the ration with the probabilities of meeting the nutrient requirements of the animal can enhance the process of animal diet formulation. The model presented here does not require any a priori information from the decision maker, eliciting his preferences through an interactive process. This is the main advantage in relation to other models found in the literature for treating the problem of nutrient variability, which introduce stochastic constraints in the single objective minimum cost model requiring fixing the level of probability desired for each one of the nutrients in advance.     

Optimal Investment by the Principal in Order to Increase the Probability of Favourable States of Nature in the Principal-Agent Model with Moral Hazard

In this paper we analyse the single agent, principal-agent model with moral hazard. This model differs from other models that have been formulated in that in this model the principal is allowed to make an investment that increases the probability of higher levels of output. The principal must take into account the agent's reaction to the investment in making the investment decision. We also show that conventional wisdom about the relationship between compensation and uncertainty, and the optimal level of investment may only hold under restrictive assumptions when the principal is allowed to invest.     

A finite element approach to Burgers' equation

Because of its similarity to the Navier-Stokes equation Burgers' equation often arises in the mathematical modelling used to solve problems in fluid dynamics involving turbulence. Difficulties have been experienced in the past in the numerical solution of Burgers' equation for small values of the parameter v. It is therefore useful to attempt a piecewise polynomial approximation (i.e. finite element) where the size of the elements are chosen to take into account the nature of the solution. The aim is to ‘chase the peak’ by altering the size of the elements at each stage using information from the previous step.     

Decision analysis models in reinsurance

Decision analysis models are developed and illustrated for the reinsurance (risk transfer) decisions made by insurance companies. Decision analytic models were found to be useful tools both for structuring multistage reinsurance decisions and for comparing alternative options. The insurer is faced with many possible choices involving reinsurance type and extent, and an expected utility model provided insight both as a screening device and as an evaluation criterion. Decision analytic models appeared to be superior to other approaches such as mean/variance and risk of ruin models both because of their flexibility and their more comprehensive treatment the important elements of the decision, namely the complete claims distribution, the cost of reinsurance and the insurer's risk attitude.     

搜寻成本下可替代产品的定价策略与库存决策

为探寻存在搜寻成本情况下消费者购买可替代产品时的定价与库存问题,从消费者效用出发,对厂商收益构建了基于马尔可夫决策过程的优化模型。在消费者方面,分析了其购买与继续搜寻的条件,并分别在搜寻成本不变和搜寻成本边际递减的情况下研究了消费者保留效用的变化情况以及购买相应产品的概率。此外,与很多相关文献不同的是,由于搜寻成本的存在,该情形下的消费者并不一定会在完成购买之前搜寻完所有的产品。在厂商方面,根据实际情况构建不同搜寻顺序下的收益模型并求解出最优定价策略与库存策略,并将定价模型与库存策略扩展到了动态的环境,为厂商制定价格及库存方案提供相应的决策支持。     

Soft-sensing of level of satisfaction in TOC product-mix decision heuristic using robust fuzzy-LP

Product-mix decision through theory of constraints (TOC) should take into account considerations like the decision-maker’s (DM) level of satisfaction in order to make product-mix decision a robust one. Sensitivity of the decision made, needs to be focused for a bottle-neck-free, optimal product-mix solution of TOC problem. A membership function (MF) has been suitably designed in the present work, first in finding out the degree of imprecision in the product-mix decision, and thereafter to sense the level of satisfaction of the DM. Inefficiency of traditional linear programming (LP) in handling multiple-bottleneck problem through TOC has been discussed through an illustrative example. Comparison of traditional LP over fully fuzzified-LP (FLP) model has also been addressed to elucidate the advantages of FLP in TOC. Key objective of this work is to guide DMs in finding out the optimal product-mix with higher degree of satisfaction with lesser degree of fuzziness under tripartite fuzzy environment.     

Multicriteria modelling for a repair contract problem based on utility and the ELECTRE I method

Each alternative for a repair contract implies a specific responsetime and related cost. The response time is associated withthe commitment of repair time, based on the contract. A decisionmaker chooses the best alternative taking into account the systemperformance and the cost of the contract. This problem has beenanalysed through a multicriteria decision model. This decisionmodel supports decision makers in the determination of the bestcombination of contracting conditions. The decision model proposedallows the decision maker to quantify the consequences of anaction taking into account two basic criteria: the cost of thecontract and the system performance. Two different decisionmodels have been built to support decision makers. These decisionmodels are based on different multicriteria approaches. Thefirst, reported in a previous paper, is based on the multiattributeutility theory (MAUT). The model presented in this paper isbased on the ELECTRE I method combined with utility functions.The paper presents the main theoretical aspects related to bothapproaches and practical implications related to model building.A numerical application is presented in order to illustratethe use of the decision model.     

A framework for predicting gross institutional long-term care cost arising from known commitments at local authority level

As the UK population ages, it is forecasted that there will be an unsustainable increase in the need for, and therefore in the costs of long-term care. Although several studies have been performed to estimate these costs, they do not take into account the impact of survival patterns on costs. Focussing only on residents already in care (known commitments), we have developed, in association with an English local authority, a framework for estimating the future gross cost incurred by this group, built around a survival model. We apply this framework to forecast the cost over a given period of time, of maintaining a group of individuals in residential and nursing care, funded by the local authority. One of the novelties in the model is that it translates survival inputs and unit fees for care into cost in a manner, which was useful and meaningful to decision makers.     

A model of the executive's decision processes in new product development

This paper introduces the concept of fuzziness to deal quantitatively with the imprecision of the meaning of the executive's judgment stated in a natural language and presents a model of the executive's decision processes for the new product introduction which contain fuzzy-2 states, fuzzy-2 information systems, fuzzy-2 information signals, fuzzy-2 strategy are presented. The committee decision problem under fuzzy-2 constraints is dealt with.     

Location of courts of justice: The making of the new judiciary map of Portugal

Location modeling techniques have been applied to an extremely wide variety of public facilities. However, their application to one of the most ubiquitous public facilities – courts of justice – has been very rare. In this paper, we describe a study promoted by the Ministry of Justice of Portugal to define a proposal for the country's new judiciary map – that is, the spatial organization of the judicial system. The new map aims to promote the efficiency and specialization of the justice system (leading to better and faster court decisions) and to provide a good level of accessibility to courts. We developed two optimization models addressing those goals – a districting model, to determine the borders of new, large judicial districts; and a court location model, to determine the location, type, size, and coverage area of the courts included in each new district. Both models are discrete facility location models and consider hierarchical facilities – generic courts and specialized courts of multiple types. Our study was publicly acknowledged by the Portuguese government as having contributed to the new judiciary map that has since been approved and implemented.     

An arithmetic-geometric mean inequality approach for determining the optimal production lot size with backlogging and imperfect rework process

Some classical studies on economic production quantity (EPQ) models with imperfect production processes have focused on determining the optimal production lot size. However, these models neglect the fact that the total production-inventory costs can be reduced by reworking imperfect items for a relatively small repair and holding cost. To account for the above phenomenon, we take the out of stock and rework into account and establish an EPQ model with imperfect production processes, failure in repair and complete backlogging. Furthermore, we assume that the holding cost of imperfect items is distinguished from that of perfect ones, as well as, the costs of repair, disposal, and shortage are all included in the proposed model. In addition, without taking complex differential calculus to determine the optimal production lot size and backorder level, we employ an arithmetic-geometric mean inequality method to determine the optimal solutions. Finally, numerical examples and sensitivity analysis are analyzed to illustrate the validity of the proposed model. Some managerial insights are obtained from the numerical examples.     

A two-stage stochastic model for labour wastage

A stochastic model for labour wastage is presented which accounts for the employee's variability on the propensity to leave through dependence on both his length of service and his tenure-in-current-state. The basic assumption underlying the model is that the employee's personal characteristics, the job characteristics and the external labour market conditions are stochastic over time, therefore affecting his decision to stay or leave the company. It is shown that the model provides a good fit to a variety of observed leaving patterns for several companies reported in the literature, explains the relationships among a number of important occupational variables, and is useful for planning purposes in predicting future developments.