Pricing bridges to cross a river.

We consider a Stackelberg pricing problem in directed, uncapacitated networks. Tariffs have to be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs are assumed to be given. There are n clients, the followers, that route their demand independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by problems in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + lnD)–approximation. Here, D is upper bounded by the total demand of all clients. We furthermore discuss some polynomially solvable special cases, and present a short computational study with instances from France Télécom. In addition, we consider the problem under the additional restriction that the operator must serve all clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless NP = ZPP, and we prove the existence of an n–approximation algorithm.Pricing; Networks; Tariffs; Costs; Cost; Demand; Problems; Order; Yield; Studies; Approximation; Algorithms; Performance;

Tariff Optimization in Networks

We consider the problem of determining a set of optimal tariffs for an agent in the network, who owns a subset of all the arcs, and who receives revenue by setting the tariffs on the arcs he owns. Multiple rational clients are active in the network, who route their demands on the least expensive paths from source to destination. The cost of a path is determined by fixed costs and tariffs on the arcs of the path. We introduce a remodeling of the network, using shortest paths. We develop three algorithms based on this shortest-path graph model: a combinatorial branch-and-bound algorithm, a path-oriented mixed integer program, and a known-arc-oriented mixed integer program. Combined with reduction methods, this remodeling enables us to solve the problem to optimality, for quite large instances. We provide computational results for the methods developed and compare them with the results of the arc-oriented mixed integer programming formulation of the problem, applied to the original network

Pricing bridges to cross a river

We consider a Stackelberg pricing problem in directed, uncapacitated networks. Tariffs have to be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs are assumed to be given. There are n clients, the followers, that route their demand independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by problems in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + lnD)–approximation. Here, D is upper bounded by the total demand of all clients. We furthermore discuss some polynomially solvable special cases, and present a short computational study with instances from France Télécom. In addition, we consider the problem under the additional restriction that the operator must serve all clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless NP = ZPP, and we prove the existence of an n–approximation algorithm.status: publishe

აკადემიკოსი ნოდარ ამაღლობელი მაღალი ენერგიების ფიზიკის ინსტიტუტის სამეცნიერო საბჭოს წევრებთან ერთად

მარცხნიდან დგანან: შუქრი ბარაბაძე, მიხეილ ნიორაძე, ბადრი ჭილაძე, ირაკლი მაჩაბელი, ჯემალ მებონია, ლევან ღლონტი, აკადემიკოსი ნოდარ ამაღლობელი, თემურ კოპალეიშვილი და ომარ შუდრანოდარ ამაღლობელი - ფიზიკა-მათემატიკის მეცნიერებათა დოქტორი, პროფესორი, საქართველოს მეცნიერებათა აკადემიის აკადემიკოსი, თსუ-ს რექტორი. ომარ შუდრა - ფიზიკა-მათემატიკურ მეცნიერებათა დოქტორი. თემურ კოპალეიშვილი - აკადემიკოსი, ფიზიკის მეცნიერებათა დოქტორი. ჯემალ მებონია - ფიზიკა-მათემატიკის მეცნიერებათა დოქტორი. მიხეილ ნიორაძე - ფიზიკა-მათემატიკის მეცნიერებათა დოქტორი, პროფესორი. ბადრი ჭილაძე - ფიზიკა-მათემატიკის მეცნიერებათა კანდიდატ