On the location of new facilities for chain expansion under delivered pricing

• Published in: Omega (Oxford) Vol. 40; no. 2; pp. 149 - 158
• Main Authors: PELEGRIN, Blas, FERNANDEZ, Pascual, GARCIA PEREZ, Maria Dolores, CANO HERNANDEZ, Saúl
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.04.2012; Elsevier; Pergamon Press Inc
• Series: Omega
• Subjects: Applied sciences; Exact sciences and technology; Linear programming; Location; Location analysis; Location Optimization Sensitivity analysis; Logistics; Mathematical programming; Operational research and scientific management; Operational research. Management science; Optimization; Pricing policies; Sensitivity analysis; Studies; Murcia Spain; Spain; Optimization; Sensitivity analysis; Location; ISO; Linear programming; Mixed integer programming; Location problem; Integer programming; Facility location; Pricing; Cost function; Discrete programming; Profit; Objective function; ISO standard; Marginal cost
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2011.04.005

We study the problem of locating new facilities for one expanding chain which competes for demand in spatially separated markets where all competing chains use delivered pricing. A new network location model is formulated for profit maximization of the expanding chain assuming that equilibrium prices are set in each market. The cannibalization effect caused by the entrance of the new facilities is integrated in the objective function as a cost to be paid by the expanding chain to the cannibalized facilities. It is shown that the profit of the chain is maximized by locating the new facilities in a set of points which are nodes or iso-marginal delivered cost points (points on the network from which the marginal delivered cost equals the minimum marginal delivered cost from the existing facilities owned by the expanding chain). Then the location problem is reduced to a discrete optimization problem which is formulated as a mixed integer linear program. A sensitivity analysis respect to both the number of new facilities and the cannibalization cost is shown by using an illustrative example with data of the region of Murcia (Spain). Some conclusions are presented. ► A new facility location model for chain expansion where cannibalization is compensated by side payments is presented. ►Optimal facility locations on a network are found in the nodes and the iso-marginal delivered cost points. ► The location model is solved by a mixed integer linear programming formulation. ► A sensitivity analysis with respect to the number of new facilities and the cost of side payment is carried out. ► The cannibalization effect is reduced by increasing side payments with a very small decrease in profit.