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  Abstract

  Extended Oligopoly models will be introduced and examined in which the firms might face capacity limits, thresholds for minimal and maximal moves, and antitrust thresholds in the case of partial cooperation. Similar situation occurs when there is an additional cost of output adjustment, which is discontinuous at zero due to set-up costs. In these cases the payoff functions of the firms are nondifferentiable and in some cases even discontinuous. Under the usual concavity assumptions Cournot oligopolies have monotonic response functions and unique Cournot-Nash equilibrium. However the introduction of these more realistic additions into the oligopoly models creates a fundamentally new situation: the existence of no equilibrium or the presence of multiple, in some cases even infinitely many, equilibria. It also results in a very different asymptotic behavior of the dynamic extensions. The paper gives a brief survey of the relevant models, derives the response functions of the firms, and examines the existence and the number of equilibria. In the case of infinitely many equilibria the equilibrium-set will be also determined and characterized.

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 Abstract

  We consider an application of the ABS procedure to the linear systems arising from the primal-dual interior point methods where Newton method is used to compute path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS class can reduce the ill conditioning. Preliminary numerical experiments show that the proposed approach can provide a residual in the computed solution up to sixteen orders lower.

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Abstract

  We extend the concept of dynamic pricing by integrating it with “overselling with opportunistic cancellation” option, within the framework of dynamic policy. Under this strategy, to sell a stock of perishable product (or capacity) two prices are offered to customers at any given time period. Customers are categorized as high-paying and low-paying ones. The seller deliberately oversells its capacity if high paying customers show up, even when the capacity is already fully booked by low-paying customers. In that case, the sale to some low-paying customers is canceled, although an appropriate compensation must be provided. A dynamic programming approach is applied to formulate and solve this problem. We develop two models for continuous and periodic pricing, depending on the frequency of price changing. The advantage of this system over dynamic pricing model is investigated through some numerical examples. We also study some structural properties of the optimal policies.

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 Abstract 

  This paper gives a survey of the theory and practice of nonlinear ABS methods including various types of generalizations and computer testing. We also show three applications to special problems, two of which are new.

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Abstract

  The Analytic Network Process (ANP) is a generalization of the Analytic Hierarchy Process (AHP). The basic structure is an influence network of clusters and nodes contained within the clusters. Priorities are established in the same way they are in the AHP using pairwise comparisons and judgment. Many decision problems cannot be structured hierarchically because they involve the interaction and dependence of higher-level elements in a hierarchy on lower-level elements. Not only does the importance of the criteria determine the importance of the alternatives as in a hierarchy, but also the importance of the alternatives themselves determines the importance of the criteria. Feedback enables us to factor the future into the present to determine what we have to do to attain a desired future. To illustrate ANP, one example is also presented. 

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Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. It is proved that nonsmooth complementary approximate Karush-Kuhn-Tucker conditions are stronger than nonsmooth approximate gradient projection conditions. Sufficiency for differentiable generalized convex programming is established.

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An availability model is developed to optimize the availability of a series repairable system with multiple k-out-of-n subsystems in this paper. There are two types of decision variables that determine the system designer’s decision to allocate the number of repairmen and to allocate the number of redundant components in each subsystem in the presence of weight, volume and cost constraints. As per the nonlinear structure of the objective in the model, the model is located into the nonlinear programming category. A classical Particle Swarm Optimization (PSO) algorithm is proposed to solve seven various instances of the model. The aim of this study is to illustrate the model and to propose an applicable algorithm for the problem. The efficiency of the proposed PSO is illustrated by comparison with Simulated Annealing (SA) method.

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The traffic assignment problem is one of the most important problems for analyzing and optimizing the transportation network to find optimal flows. This study presented a new formulation based on a generalized Benders' decomposition approach to solve its important part, i.e. user equilibrium problems, in deterministic and stochastic cases. The new approach decomposed the problem into a master problem and a sub problem. The first one was a nonlinear and the latter a linear programming problem. Iteratively, the master problem was solved and its outputs were used to solve the sub-problem in which to form appropriate cuts and add them to the master problem for solving it in the next iteration. Based on the convergence of Benders' decomposition, the iterative process was terminated in a finite number of steps. In this manner, some numerical examples were explained and compared with other methods.

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We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory of the original problem. Numerical results are also given to demonstrate the applicability and the efficiency of the proposed method.

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     This special issue is a collection of refereed articles selected from the 13th International Industrial Engineering Conference (IIEC 2017). The initial selection was made by Dr. Hamed Fazlollahtabar who also wrote the following description. The accepted articles were reviewed going through the usual reviewing process of IJOR.

Nezam Mahdavi-Amiri
Editor-in-Chief


     The 13th International Industrial Engineering Conference (IIEC 2017) hosted by Mazandaran University of Science and Technology, Babol, Iran, was held on 22nd and 23rd of February 2017 at Mizban Complex, Babolsar, Mazandaran, Iran. The total number of papers received was 805, among which 378 papers were accepted in two categories of oral presentations (185 papers) and poster presentations (193 papers). The scientific committee of the conference selected a number of papers to be extended and considered for a special issue of the Iranian Journal of Operations Research (IJOR). For this, 25 selected papers were considered and 17 papers were chosen for the second round of review. Having strict review criteria, 11 papers were then selected and refereed for a final decision. After the review process, 6 papers were finally accepted for the special issue. The contents of the accepted papers follow here. Vehicle routing and scheduling in an environmentally friendly manner attracted researchers to develop both mathematical programming models and heuristics as solution approaches. Green supply network design under uncertainty was considered for a multi-mode production system. Facility planning and hub location problem in competitive conditions and multiple allocations were investigated. Robust optimization philosophy as an uncertainty treatment approach was studied using event-driven and attribute-driven concepts. An interesting application of operations research in forestry was studied developing stochastic dynamic programming with Markov chains.

     My special gratitude goes to Professor Nezam Mahdavi-Amiri, Editor-in-chief, and the editorial board members of IJOR for their cooperation and support during the past 10 months of preparing this special issue.

Hamed Fazlollahtabar
Coordinator for Special Issues IIEC2017
Department of Industrial Engineering
School of Engineering, Damghan University
Damghan, Iran

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The definition of ordered weighted averaging (OWA) operators and their applications in decision making are reviewed. Also, some generalizations of OWA operators are studied and then, the notion of 2-symmetric OWA operators is introduced. These generalizations are illustrated by some examples.

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We present a stochastic optimal control approach to wildlife management. The objective value is
the present value of hunting and meat, reduced by the present value of the costs of plant damages
and traffic accidents caused by the wildlife population. First, general optimal control functions and
value functions are derived. Then, numerically specified optimal control functions and value
functions of relevance to moose management in Sweden are calculated and presented.

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Here, we collect two parts of a research project on the pedestrian flow modeling. Rapid growth in the volume of public transport and the need for its reasonable, efficient planning have made the description and modeling of transport and pedestrian behaviors as important research topics in the past twenty years. First, we present a macroscopic model for the pedestrian flow based on continuum mechanical balances. Second, we present a new microscopic modelling method to describe the interaction among pedestrians in conflicting situations. A local navigation based on a continuous density estimator is adopted for the configuration of pedestrians’ temporary route choices on the tactical level. On the operational level, a balancing mechanism is installed to ensure correct execution of the planned position transitions of the pedestrians. A comparison of the test results of our simulation with a real-world video clip is provided.