Iranian Journal of Operations Research

Special Issue for 11th International Conference of Iranian Operations Research Society

Nezam Mahdavi-Amiri

This is a special issue of the Iranian Journal of Operations Research that includes some of the
invited talks presented at the 11th international conference of the Iranian Operations Research Society
(IORS), organized jointly by IORS and Razi University of Kermanshah and held at the Razi
University, Kermanshah, Iran, May 2-4, 2018. The IORS conference is held annually and is the main
event for presentation of new theoretical and applied developments of OR. International participation
is enhanced by some invited talks presented by international scholars. There were over 400
participants, 170 accepted talks and 69 poster presentations. The selected papers for this special issue
were reviewed going through the usual reviewing process and 6 papers were accepted for publication.

On SOCP/SDP Formulation of the Extended Trust Region Subproblem

Maziar Salahi

We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examples are provided.

On Optimality Conditions via Weak Subdifferential and Augmented Normal Cone

Ali Farajzadeh

In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator function. Relation between weak subifferential and augmented normal cone and epigraph is also explored. We also obtain optimality conditions via weak subdifferential and augmented normal cone. Finally, we define the Stampacchia and Minty solution via weak subdifferential and investigate the relation between Stampacchia and Minty solution and the minimal point.

Intelligent Mapping

Abolfazl Fathollahzadeh

This paper is directed to the question of how to model and design an efficient tool for the intelligent mapping which is based on both dynamic and efficient storage of data and soft computing. The former is performed by our method that learns how to store, search and delete the data. After pointing out the limitation of the crisp evaluation of the distance between two points, we argue in favor of soft computing which is based on the extension of metric space to
interval one and then to the fuzzy metric. A-Star algorithm is used to illustrate our model along with the injection of competitive data structures.

A Scenario-Based Nonlinear Programming Model for a Two-Level Inventory Control Problem: A Case in Dairy Product Industry

Seyed Taghi Akhavan Niaki

In this paper, a novel scenario-based two-level inventory control model with a limited budget is formulated. The demand during the selling period is considered to follow a uniform probability distribution. In addition, it is assumed that there will be some customers who are willing to wait for their demands to be satisfied; thus a service level is considered for these customers. The aim is to find the optimal order quantities of the products and the required raw materials such that the relevant expected total profit obtained during the period is maximized. After proving the convexity of the proposed formulation, a penalty function and the Barrier method is proposed to solve the developed nonlinear stochastic programming problem. The problem is solved under different demand scenarios defined in three states of good, fair, and low. Finally, a case study in a dairy manufacturing company is provided to illustrate the application of the proposed methodology in real-world inventory control systems.

Comparison of Selected Advanced Numerical Methods for Greeks Calculation of Vanilla Options

Ales Kresta

Option valuation has been a challenging issue of financial engineering and optimization for a long
time. The increasing complexity of market conditions requires utilization of advanced models that,
commonly, do not lead to closed-form solutions. Development of novel numerical procedures, which prove to be efficient within various option valuation problems, is therefore worthwhile. Notwithstanding, such novel approaches should be tested as well, the most natural way being to assume simple plain vanilla options under the Black and Scholes model first; because of its simplicity the analytical solution is available and the convergence of novel numerical approaches can be analyzed easily. Here, we present the methodological concepts of two relatively modern numerical techniques, i.e., discontinuous Galerkin and fuzzy transform approaches, and compare their performance with the standard finite difference scheme in the case of sensitivity calculation
(a so-called Greeks) of plain vanilla option price under Black and Scholes model conditions. The results show some interesting properties of the proposed methods.

Using Nesterov's Excessive Gap Method as Basic Procedure in Chubanov's Method for Solving a Homogeneous Feasibility Problem

Cornelis Roos

We deal with a recently proposed method of Chubanov [1], for solving linear homogeneous systems with positive variables. We use Nesterov's excessive gap method in the basic procedure. As a result, the iteration bound for the basic procedure is reduced by the factor $nsqrt{n}$. The price for this improvement is that the iterations are more costly, namely $O(n^2 )$ instead of $O(n)$. The overall gain in the complexity hence becomes a factor of $sqrt{n}$.