This paper proposes a new location problem of competitive facilities, e.g. shops and stores, with uncertain demands in the plane. By representing the demands for facilities as random variables, the location problem is formulated to a stochastic programming problem, and for finding its solution, three deterministic programming problems: expectation maximizing problem, probability maximizing prob...

A new heuristic algorithm for solution of bi-objective discrete competitive facility location problems is developed and experimentally investigated by solving different instances of a facility location problem for firm expansion. The proposed algorithm is based on ranking of candidate locations for the new facilities, where rank values are dynamically adjusted with respect to behaviour of the a...

This paper presents a deterministic and efficient algorithm for online facility location. The algorithm is based on a simple hierarchical partitioning and is extremely simple to implement. It also applies to a variety of models, i.e., models where the facilities can be placed anywhere in the region, or only at customer sites, or only at fixed locations. The paper shows that the algorithm is O(l...

A single facility has to be located in competition with fixed existing facilities of similar type. Demand is supposed to be concentrated at a finite number of points, and consumers patronise the facility to which they are attracted most. Attraction is expressed by some function of the quality of the facility and its distance to demand. For existing facilities quality is fixed, while quality of ...

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 the subsequent facility location by the Follow...

We study a mathematical model generalizing the well-known facility location problem. In this model we consider two competing sides successively placing their facilities and aiming to ‘‘capture’’ consumers, in order to make maximal profit. We state the problem as a bilevel integer programming problem, regarding optimal noncooperative solutions as optimal solutions. We propose a branch-andbound a...

In this paper, we deal with competitive facility location problems in which the demand of each customer depends on the facilities. In our models two competitive companies intend to locate their facilities on the market in order to maximize the total demand acquired from the market. The distances between the facilities and the demand points are measured by rectangular distance. At first we consi...

Two players sequentially locate a fixed number of facilities, competing to capture market share. Facilities face disruption risks, and each customer patronizes the nearest operational facility, regardless of who operates it. The problem therefore combines competitive location and location with disruptions. This combination has been absent from the literature. We model the problem as a Stackelbe...

In this paper, there are two competitors in a planar market. The first competitor, called, the leader, opens p new facilities. After that, the second competitor, the follower, reacts to the leader’s action and opens r new facilities. The leader and the follower have got some facilities in advance in this market. The optimal locations for leader and follower are chosen among predefined candidate...

The facility location problem is a strategic decision-making for a supply chain, which determines the profitability and sustainability of its components. This paper deals with a scenario where two supply chains, consisting of a producer, a number of distribution centers and several retailers provided with similar products, compete to maintain their market shares by opening new distribution cent...