فصلنامه مدل سازی پیشرفته ریاضی
سال سوم شماره 2 (پاییز و زمستان 1392)

In this paper، a semi-Markov model is applied for description the seismicity patterns in the region within (27 °، -30 °) latitude and (55 °، 58 °) longitude، which includes some portion of the Kerman and Hormozgan provinces. The classification of states of the model is based on magnitudes of earthquakes. Because of the features of Weibull distribution and earthquake characteristics، it is assumed that the crossing times between states are Weibull. Some numerical estimates for the semi-Markov kernel and the mean recurrence times of earthquakes have been presented based on the past information. A new computational method which is on the basis of the inverse Laplace transform approximation have been introduced for estimating the expected number of earthquakes، distribution of hitting time of strongest earthquakes and transition functions. Estimation of above functions are rapid by using this method، with short processing times. The past history has been used for prediction while the probabilities of future earthquakes with different magnitudes and time intervals have been calculated. The obtained results are consistent with the latest recent earthquake in this zone، which shows the validity of the employed model.

Nowadays، in public and private sectors، managers require information about the operation، in addition to financial information. Therefore، the independent auditors are facing with increasing demands for doing the operational auditing. General objectives of operational audit are composed of performance evaluation (in terms of the three measurements of economy، efficiency and effectiveness)، the identification of opportunities for operation improvement and offering recommendations for it. Growing trend of attention to this type of audit and performance evaluation implies that every methodology that can help to achieve the objectives of this audit would be valuable. In order to implement operational auditing، this article proposes integrated data envelopment analysis (IDEA) approach under variable returns to scale technologies، namely IBCC model، which considers concepts of three performance measurements. Case analysis results of 18 insurance companies that were examined for the year 1390 demonstrates that the proposed IDEA approach have higher benchmarking power (the measurement power of the companies with the best performance) than the conventional separate DEA (SDEA) approach.

In this paper، by introducing of the double Heston''s stochastic volatility model، since the prices of underlying asset in the financial markets are subject to the abrupt changes caused by different factors، by adding jump term to the double Heston model، we propose a new financial model، called the double Heston''s stochastic volatility model with jumps. Then، by determining the characteristic function of the underlying stock price process، we obtain a formula for the European call option pricing under the proposed model by using the Fast Fourier transform method. Due to existence the jump term in the stock price process، the proposed model can be widely used in the financial markets، such as oil، gold and stock financial markets. Therefore، the model is more flexible than the Heston model and covers the abrupt changes of underlying asset price. The main goal of this paper is to present the model and derive a numerical scheme for the European option pricing.

Data envelopment analysis (DEA) is a method for evaluating performance of organizations and decision making units (DMUs). This method divide decision making units (DMUs) in four different categories: inefficient، weak efficient، extreme efficient and non-extreme efficient. In this paper، we investigate a new DMU category which called «anchor point». An anchor point places on common region between the efficiency frontier and free-disposability. Indeed، an anchor point is extreme efficient which makes weak efficiency frontier. Omission of the anchor points will change efficiency frontier and eliminate a region of generating possibility set. Anchor point also has another characteristic، changing its input or output will change efficiency frontier and by increasing input or decreasing output، the new point will be still on frontier and is extreme efficient. Therefore، the characteristics of the anchor point demonstrate its importance. As for its importance، we propose faster methods to identify these points. At first، we express identifying algorithms for these points and then by using their characteristics، we propose some methods like supper efficiency method which identifies anchor points by using less calculation than others. We will give a numerical example to explain proposed method and compare it with other methods.

Supplier selection is an important decision in the management of a supply chain that is depends on various factors and parameters. Recent emphasis on sustainability in supply chain management has made this selection more complex. Many tools have been developed with a variety of formal modeling techniques. These techniques may be limited for a variety of reasons. An integrated Sustainable supplier selection and order allocation model is discussed in this paper to apply sustainability attributes in supplier selection and develop a bilinear goal programming model for integrated order allocation model. Bilinearity in goal programming is handled with a modified Benders decomposition method and numerical results shows the efficiency of the proposed model. Implications of the model and future research directions conclude the paper

In this article we investigate the positive semirings (a semiring R is called positive if 1+x is unit for all x ε R). In fact، using the intersection of maximal ideals containing an element of a positive semiring، we give the concept of “z-ideal” in such semirings and investigate some properties of these ideals. Furthermore we study th e relations between topological properties of X and algebraic properties of positive semiring τ، where τ is the topology on X. Finally the familiar positive semiring C+ (X) will be studied. Finally the familiar positive semiring C+ (X) will be studied