Andrey Melnikov

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• PhD
• Senior Researcher at Russian Academy of Sciences

We consider the discrete competitive facility location problem with finitely many consumers and finitely many locations of the facilities. Two competing companies are opening the facilities in some of these locations consequently; i.e., the first company does it first, then does second company. The goal of both is to maximize their profit obtained...

We consider a mathematical model similar in a sense to competitive location problems. There are two competing parties that sequentially open their facilities aiming to “capture” customers and maximize profit. In our model, we assume that facilities’ capacities are bounded. The model is formulated as a bilevel integer mathematical program, and we st...

In the mathematical model under study, the two competing sides consecutively place their facilities aiming to capture consumers and maximize profits. The model amounts to a bilevel integer programming problem. We take the optimal noncooperative solutions as optimal to this problem. To find approximate and optimal solutions, we propose a branch-and-...

Consider a finite set of consumers that two competing companies are willing to service. The companies open facilities one by one. The set of locations available to open facilities is finite. The problem is to find a facility location for the first company that maximizes its profit given that the second company also makes its decision by maximizing...

Eternal vertex cover problem is a variant of the graph vertex cover problem that can be considered as a dynamic game between two players (Attacker and Defender) with an infinite number of turns. At each turn, there is an arrangement of guards over the vertices of the graph, forming a vertex cover. Attacker attacks one of the graph’s edges, and Defe...

We have a directed graph describing a network and an origin-destination matrix for customer internet traffic demands. Our aim is to optimize the routing of the traffic by adjusting the weights of the graph links. Though the internal design of the routing protocol is unavailable, we have access to the simulator to model it. Given the link weights, t...

We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenario. The problem to find the best solutions for the parties is formulated as a discrete bi-level mathematical programming problem. In the paper, we suggest a procedure to compute an upper bound for the objective function...

We consider a two-echelon inventory management problem, where customers’ requests for spare parts of different types must be fulfilled within a given service level threshold. The supply system is composed of multiple warehouses in the first echelon, where the customers’ requests are processed, and a single second-echelon warehouse, replenishing sto...

We study a dynamic vector bin packing (DVBP) problem. We show hardness for shrinking arbitrary DVBP instances to size polynomial in the number of request types or in the maximal number of requests overlapping in time. We also present a simple polynomial-time data reduction algorithm that allows to recover (1+ε)-approximate solutions for arbitrary ε...

We study a dynamic vector bin packing (DVBP) problem. We show hardness for shrinking arbitrary DVBP instances to size polynomial in the number of request types or in the maximal number of requests overlapping in time. We also present a simple polynomial-time data reduction algorithm that allows to recover $(1 + {\varepsilon})$-approximate solutions...

We consider a bilevel model of estimating the costs of the attacking party (the Attacker) for a successful attack of a given set of objects protected by the other party (the Defender). The Attacker and the Defender have multiple means to, correspondingly, attack and protect the objects, and the Attacker’s costs depend on the Defender’s means of pro...

We consider a model of two parties’ competition organized as a Stackelberg game. The parties open their facilities intending to maximize profit from serving the customers that behave following a binary rule. The set of customers is unknown to the party which opens its facilities first and is called the Leader. Instead, a finite list of possible sce...

We consider a modification to the classic medianoid problem, where facilities of different types are present on the market. A newcomer firm opens facilities providing a specific type of products and competes with existing facilities of that type. Each customer requires multiple products of different types and chooses the shortest route visiting fac...

We consider a mathematical model of market competition between two parties. The parties sequentially bring their products to the market while aiming to maximize profit. The model is based on the Stackelberg game and formulated as a bilevel integer mathematical program. The problem can be reduced to the competitive facility location problem (CompFLP...

We investigate a bi-level optimization program that models a two parties’ competition in the form of a Stackelberg game. Each of the parties must decide where to open facilities and how to assign them to service customers in a way that maximizes a profit. A party can service a customer only by a facility which is preferable to all the competitor's...

We consider a bilevel “defender-attacker” model built on the basis of the Stackelberg game. In this model, given is a set of the objects providing social services for a known set of customers and presenting potential targets for a possible attack. At the first step, the Leader (defender) makes a decision on the protection of some of the objects on...

A competitive facility location model formulated as a bilevel programming problem is considered. A new approach to the construction of estimating problems for bilevel competitive location models is proposed. An iterative algorithm for solving a series of mixed integer programming problems to obtain a pessimistic optimal solution of the model under...

We consider a competition between two parties maximizing their profit from servicing customers. A decision making process is assumed to be organized in a Stackelberg game framework. In the model, we are given with two finite sets: a set of customers and a set of potential facilities’ locations. The parties, called the Leader and the Follower, seque...

A new mathematical model is considered related to competitive location problems where two competing parties, the Leader and the Follower, successively open their facilities and try to win customers. In the model, we consider a situation of several alternative demand scenarios which differ by the composition of customers and their preferences.We ass...

We consider the capacitated competitive facility location problem (CCFLP) where two competing firms open facilities to maximize their profits obtained from customer service. The decision making process is organized as a Stackelberg game. Both the set of candidate sites where firms may open facilities and the set of customers are finite. The custome...

We consider a new load balancing model that arises in the processing of user requests for files located on a given set of servers. The optimization criterion is the total excess of actual load over the limit load. In order to redistribute the load and minimize the criterion, files can be moved between the servers. We show that if there are no other...

In this paper, we consider a competitive location problem in a form of Stackelberg game. Two parties open facilities with the goal to capture customers and maximize own profits. One of the parties, called Leader, opens facilities first. The set of customers is specified after Leader’s turn with random realization of one of possible scenarios. Leade...

We consider a mathematical model belonging to the family of competitive location problems. In the model, there are two competing parties called Leader and Follower, which open their facilities with the goal to capture customers and maximize profit. In our model we assume that Follower is able to open own facilities as well as to close the Leader’s...

In the optimization problem for pseudo-Boolean functions we consider a local search algorithm with a generalized neighborhood. This neighborhood is constructed for a locally optimal solution and includes nearby locally optimal solutions. We present some results of simulations for pseudo-Boolean functions whose optimization is equivalent to the prob...

We consider the competitive facility location problem in which two competing sides (the Leader and the Follower) open in succession their facilities, and each consumer chooses one of the open facilities basing on its own preferences. The problem amounts to choosing the Leader’s facility locations so that to obtain maximal profit taking into account...