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  A novel optimal single machine replacement policy using a single as well as a two-stage decision making process is proposed based on the quality of items produced. In a stage of this policy, if the number of defective items in a sample of produced items is more than an upper threshold, the machine is replaced. However, the machine is not replaced if the number of defective items is less than a lower threshold. Nonetheless, when the number of defective item falls between the upper and the lower thresholds, the decision making process continues inspecting and possibly repairing the machine and the decision making process goes on to collect more samples. The primary objective of own work is to determine the optimal values of both the upper and the lower thresholds using a Markov process to minimize the total cost associated with a machine replacement policy.

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We develop an optimization model based on Markovian approach to determine the optimum value of thresholds in a proposed acceptance sampling design. Consider an acceptance sampling plan where items are inspected and when the number of conforming items between successive defective items falls below a lower control threshold value, then the batch is rejected, and if it falls above a control threshold value, then the batch is accepted and if it falls within the thresholds, the process of inspecting the items continues. A decision is made to accept or reject the batch. We begin with developing a Markov model for determining performance measures of sampling designs, resulting in an acceptance sampling plan optimized based on the minimum angle method. Then, the performance measures of the acceptance sampling plan are determined and the optimum values of thresholds are selected in order to optimize the objective functions. In order to demonstrate the application of the proposed methodology, numerical examples are illustrated.

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A genetic algorithm is proposed to optimize a tree-structured power distribution network considering optimal cable sizing. For minimizing the total cost of the network, a mixed-integer programming model is presented determining the optimal sizes of cables with minimized location-allocation cost. For designing the distribution lines in a power network, the primary factors must be considered as maximum allowable electrical flow in cables, permitted length of cables, maximum permitted voltage drops, and balance of load. The relationship between rates of electric current and cable sizes with consideration of constraints such as voltage drops and length are our essential data. To create a network with a minimum number of arcs and no closed loop such that all the nodes are covered, a minimum spanning tree technique is utilized. Here, we solve the problem using a genetic optimization algorithm and apply the offered approach to a real problem. By comparing the two extracted results from the proposed approach and an exact method, effectiveness of the genetic algorithm for optimization of power distribution network is shown. To demonstrate the validity of the offered model, a case study in Tehran power distribution company in Iran is made.

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Resource allocation is a problem that commonly appears in organization with a centralized decision making (CDM), who controls the units. The aim of central decision making is to allocate resources in such a way that the organization get the most benefit. Some Data Envelopment Analysis (DEA) researchers presented DEA-based resource allocation models by paying attention to energy saving and environmental pollution reduction. In this paper, we expanded a resource allocation model for 25 branches of an Iranian Tejarat bank, so that determined how much decision making (DM) can save on energy and manpower hours, so that undesirable outputs like non-performing loans are significantly reduced in a way that achieve the minimum reduction of desirable outputs while unchanged the performance of each unit after re-allocation. The result of the implementation of the model shows that in total with a 10% and 23% reduction in staff and costs respectively can result in the 0.09% reduction of deposits and 56% of non-performing loans.

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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.

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Using the experiences of successful and unsuccessful companies can be a criterion for predicting the situation of emerging companies. Each company can have a vector include both financial and non-financial characteristics. Accordingly, for an active or emerging company, it is possible to determine the characteristic vector and predict which group it is likely to belong to. The techniques used in this research are discriminant analysis and data envelopment analysis. Based on this technique, discriminant functions are designed to separate known sets. The main idea for finding discriminant functions is from data envelopment analysis, which makes a limit of efficiency for separating efficient units from inefficient ones. The discriminant functions of this method are used to predict the state of the company. Hyper planes are obtained as discriminant functions to separate companies. These hyper planes are based on multiple indicators. Each of these indicators can also apply in certain situations. The modeling used in this paper was used on oil companies listed on the Iran Stock Exchange. 15 indicators and criteria have been defined for each company. The data were for 2015 and 2016, and the number of oil companies was 18, of which 9 were successful and 9 were bankrupt. In this paper, with the help of data envelopment analysis and discriminant analysis, a new modeling was designed to find hyper planes for separating two sets. Modeling has been performed based on the different criteria that have existed, and each one applies in certain circumstances. In the following, the properties of the designed model are expressed and proved. The specific conditions of the criteria have become limitations that have been added to the multiplicative form of the designed model.

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This study aims to develop a capacitated hub location-routing model to design a rapid transit network under uncertainty. The mathematical model is formulated by making decisions about the location of the hub and spoke (non-hub) nodes, the selection of the hub and spoke edges, the allocation of the spoke nodes to the hub nodes, the determination of the hub and spoke lines, the determination of the percentage of satisfied origin-destination demands, and the routing of satisfied demand flows through the lines. Capacity constraints are considered in the hub and spoke nodes and also the hub and spoke edges. Uncertainty is assumed for the demands and transportation costs, represented by a finite set of scenarios. The aim is to maximize the total expected profit, where transfers between the lines are penalized by including their costs in the objective function. The performance of the proposed model is evaluated by computational tests and some managerial insights are also provided through the analysis of the resulting networks under various parameter settings.