Iranian Journal Of Operations Research
Volume:1 Issue: 1, Winter and Spring 2008

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.

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.

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.

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.

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.