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In this paper bus scheduling problem under the constraints that the total number of buses needed to perform all trips is known in advance and the energy level of buses is limited, is considered. Each depot has a different time processing cost. The goal of this problem is to find a minimum cost feasible schedule for buses. A mathematical formulation of the problem is developed. When there are two depots, a polynomial time algorithm is developed for the problem and theoretical results about the complexity and correctness of the algorithm is presented. Also, several examples are introduced for illustrating validity of the algorithm.

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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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A new integer program is presented to model an independent resources assignment problem with resource shortages in the context of municipal fire service. When shortage in resources exists, a critical task for fire department's administrator in a city is to assign the available resources to the fire stations such that the effect of the shortage to cover (in providing service, in extinguishing fire and so on) is minimized. To solve the problem, we propose a polynomial time greedy algorithm.

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Linear programming problems with interval grey numbers have recently attracted some interest. In this paper, we study linear programs in which right hand sides are interval grey numbers. This model is relevant when uncertain and inaccurate factors make difficult the assignment of a single value to each right hand side. Some methods have been developed for solving these problems. In this paper, we propose a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. A numerical example is provided to illustrate the proposed approach.

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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.  

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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.

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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.

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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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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.

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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 $sqrt{n}$.

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This paper analyzes the performance of a robotic system with two machines in which machines are configured in a circular layout and produce non-identical parts repetitively. The non-destructive testing (NDT) is performed by a stationary robotic arm located in the center of the circle, or a cluster tool. The robotic arm integrates multiple tasks, mainly the NDT of the part and its transition between a pair of machines. The robotic arm cannot complete the transition if it identifies a fault in the part. The main feature of the NDT technology is that its required time is changed by altering the testing cost. This generates a trade-off between cost and cycle time. Initially, the problem of robotic arm scheduling and part sequencing is jointly solved to supports the decision making for reliability improvement of small-scale robotic systems with NDT technologies. We show how the case of non-identical parts can be converted into a travelling salesman problem (TSP). Then, we provide a generalization of the framework based on three characteristics: pickup criterion, layout and travel time metric. The results are extended for the interval and no-wait pickup criteria, and then some notes are provided for travel time saving of different layout and travel time metric. It is shown whether circular systems are equivalent to linear systems, or they dominate linear cases in general terms.

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Nowadays, airline industries should overcome different barriers regarding the fierce competition and changing consumer behavior. Thus, they attempt to focus on joint decision making which enables them to set pricing and capacity allocation to maximize their profits. In this research, we develop a model to optimize pricing and capacity allocation in a duopoly of single-flight leg for two competitive airlines. The problem considers actual assumptions about flexible partitions in flight’s cabins and additionally demand uncertainty. There is a flexible partitioning of business and economy cabins and demand is assumed price-dependent with additive uncertainty. The capacity and pricing decisions are simultaneously determined through indirect channels. Moreover, a numerical study is developed to investigate how market components and competition conditions change pricing, capacity, and profit levels. The results show that increasing market volume like decreasing price sensitivity provides higher levels of price and profits. Moreover, intensified competition never leads to higher prices. Thus, a competitive network of airlines provides better impact on market mechanism to achieve competitive prices for both economy and business classes.

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This paper presents a structure that empower designing supervisory groups to survey the estimation of real options in projects of enormous scale, incompletely standardized frameworks actualized a couple of times over the medium term. Specific options writing is done using a methodology of planning the design and making prior decisions regarding the arrangements of specific options, with a recreation-based value measure designed to be near-current construction rehearsals and to resolve financial problems in particular cases. To study the case and demonstrate the actual application of this method, drug chain modeling at the tactical level was investigated. The physical and financial flow and their disturbance are simultaneously modulated. In order to complete the financial flow, financial ratios are also entered into the model. Problem uncertainty has been modeled using one of the most recent robust optimization approaches called Robust Possibilistic Programming (RPP) in combination with real options theory. The model was applied to a case study and its results were analyzed and validated by GAMS software. The results show that without violating the limitations of the problem, it shows appropriate decisions to deal with the problem.

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One important step to achieve a sustainable transportation system is to control the impact and evaluate the effect of various influencing factors toward three dimensions of sustainability. Within this context, diverse analytical approaches have been developed to assess the sustainability level of various transportation systems, however, sustainability evaluation based on fuzzy multiple criteria decision-making approaches are still limited. In current research activity, an integrated quantitative evaluation technique is proposed to narrow the identified gap. The developed decision-making approach is consisted of two main phases. Firstly, fuzzy analytic hierarchy process is utilized to weigh the sustainability dimensions resulting in the incorporation of the experts’ knowledge along with the evaluation process. Then, a proposed fuzzy inference mechanism is proposed to provide an indication on the performance of an evaluated road transportation system. The developed approach is applied on a real-world case study. Finally, future works are presented together with some concluding remarks.

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Nowadays, manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of supply chain planning. On the other hand, increasing worldwide environmental, lack of food resources and social concerns are motivating manufacturers and consumers to implement recycling strategies such as product recovery, waste management, or usage of recycled materials. In this study, the closed-loop supply chain network has been proposed which consists of four echelons (suppliers, plants, distribution centers, and customers) in the forward chain and three echelons (collection centers, inspection centers, and disposal centers) in the backward chain. We present a multi-product and multi-period mixed-integer linear programming problem in this paper. The objective of this study is to maximize the profit in the closed-loop supply chain network. The proposed model is applied to an illustrative example based on inspiration from the dairy industry in Iran. The solution of the proposed model is achieved by using Gams software. The results give important insight for fostering the decision making process.

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Nowadays, due to population increase and expansion of the transportation networks, the monitoring of this network, control, and prevention of accidents and crimes are very important. The main tasks of traffic patrols, like other emergency-security facilities, are the monitoring and prevention of crime as well as handling and fining in the case of committing crimes. Traffic patrols should be present in the scene and also in high traffic congestion, to reduce accidents and crimes. This paper presents a bi-objective and stochastic optimization model to design an emergency-security system. This network includes traffic patrol vehicles and manpower in patrol vehicles. The objective of the proposed model is to maximize the number of vehicles passing through patrols and minimize the costs according to different scenarios. To solve the model, the epsilon-constraint method is used which simultaneously determines the location of the patrols, allocation of demand points to patrols, and determining the number of existing manpower in patrols. To evaluate and analyze the proposed model, a numerical example is used.

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Capacitated vehicle routing problem (CVRP) is one of the most well-known and applicable issues in the field of transportation. It has been proved to be an NP-Complete problem. To this end, it is needed to develop a high-performance algorithm to solve the problem, particularly in large scales. This paper develops a novel mathematical model for the CVRP considering the satisfaction level of demand nodes. Then, the proposed model is validated using a numerical example and sensitivity analyses that are implemented by CPLEX solver/GAMS software. To solve the problem efficiently, a Genetic Algorithm (GA) is designed and implemented. The obtained results demonstrate that the proposed GA can yield high-quality solutions compared to exact solutions.

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Here, a new mathematical model for cellular manufacturing systems considering three important features of part priority, levels of machine’s technology, and the operator’s skill is developed. Simultaneous consideration of these features provides a more realistic analysis of the problems in cellular manufacturing systems. A model with multiple design features including cell formation, human resources flexibility with different skills, machines flexibility, operational sequence, processing time, and the capacity of machine and manpower is proposed in this article. Ourfocus is on the design of cells to implementtwo dissimilar goals. The first goal is the reduction of inter-cellular movements of parts and workers. The second goal is the creation of efficient cellsby making cell’s quality level identical for produced products so that the production of all the different parts have good quality. Two approaches of augmented ε-constraint and non-dominated sorting genetic algorithm II (NSGA-II) are used to solve this model. By comparison of these two approaches, we realizethat the multi-objective evolutionary optimization algorithm creates a Pareto-optimal front in a reasonable amount of time forlarge-scale problems

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This contribution gathers some of the ingredients presented during the Iranian Operational Research community gathering in Babolsar in 2019.It is a collection of several previous publications on how to set up an uncertainty quantification (UQ) cascade with ingredients of growing computational complexity for both forward and reverse uncertainty propagation.