Browsing by Subject "Discrete optimization"

Now showing 1 - 3 of 3
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    A discrete competitive facility location model with proportional and binary rules sequentially applied
    (SPRINGER, 2023) Fernández Hernández, Pascual; Lancinskas, Algirdas; Pelegrín Pelegrín, Blas; Zilinskas, Julius; Estadística e Investigación Operativa
    The paper is focused on discrete competitive facility location problem for an entering firm considering different customer behavior models: for essential goods, customers generally spread their buying power among all facilities within an attraction area, but if there are no facilities nearby, then customers choose a single highly attractive facility outside the attraction area to satisfy their demand. The new facility location model has been proposed considering the proportional customer choice rule for customers with facilities within the attraction area and the binary rule—for customers which facilities are located outside the attraction area. The model has been formulated as a non-linear binary programming problem and a heuristic optimization algorithm has been applied to find the optimal solutions for different instances of the problem using real geographical coordinates and population data of thousands of municipalities in Spain.
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    On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand
    (SPRINGER, 2023) Pelegrín Pelegrín, Blas; Fernández Hernández, Pascual; García Pérez, María Dolores; Estadística e Investigación Operativa
    We address the location-price decision problem for firms that offer the same type of product and compete on delivered pricing. If firms set equilibrium prices at demand points, the problem can be seen as a location game for which the Nash equilibrium (NE) is used as solution concept. For spatially separated markets, with inelastic demand, there exists a NE and it can be found by social cost minimization, as happens in network and planar location. However, with price sensitive demand, the existence of a NE has not been proven yet and socially optimal locations may not be a NE. In this paper we show that a NE can be found in discrete and network location when demand is price sensitive. A Mixed Integer Linear Programming formulation is implemented in the best response procedure which allow to find a NE for a variety of demand functions. An empirical study with data of Spanish municipalities is performed in which the procedure is applied to 200 large size test problems with linear, quadratic, exponential and hyperbolic demand functions.
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    Threshold distance versus side payment to reduce the cannibalization effect in retail chain expansion
    (OXFORD UNIVERSITY PRESS. ENGLAND, 2019) Pelegrín Pelegrín, Blas; Fernández Hernández, Pascual; Pelegrín García, Juan Diego; García Pérez, María Dolores; Estadística e Investigación Operativa
    We deal with the store location problem for an expanding retail chain in competition with other retail chains that offer the same type of product. The aim of the expanding retail chain is profit maximization, but counteracting the possible loss in profit of the existing stores in the chain caused by the appearance of the new ones. In this article, we compare two approaches, one based on a threshold distance and another based on a side payment, to reduce the effect of cannibalization of existing stores under a delivered pricing policy in a transportation network. It is proved that optimal store locations can be found at the nodes of the network and an integer linear programming model is shown to solve the store location problem for each approach. A study with data of Spanish municipalities is presented where the percentage of profit increase after the expansion and the percentage of cannibalized profit corresponding to the optimal solutions of the two models are compared for different combinations of the threshold distance, the side payment, and the number of new stores.