A firefly algorithm for solving competitive location-design problem: a case study

Abstract

This paper aims at determining the optimal number of new facilities besides specifying both the optimal location and design level of them under the budget constraint in a competitive environment by a novel hybrid continuous and discrete firefly algorithm. A real-world application of locating new chain stores in the city of Tehran, Iran, is used and the results are analyzed. In addition, several examples have been solved to evaluate the efficiency of the proposed model and algorithm. The results demonstrate that the performed method provides good-quality results for the test problems.

A Mathematical Model for Competitive Location Problem with Product Selection

“…The notation used in the proposed model is as follows: Based on Hu rule, the attraction of customer j to product t at facility i can be as follows [67]:…”

“…Therefore, the greater the attraction of a given customer to a facility, the greater the share of the facility from the demand of the customer. If this share is considered by dividing the attraction of the customer to the facility by the overall attraction of the facilities, then the share of the chain from the demand of a particular customer equals the total attraction of the facilities of the chain (existing and new) divided by the attraction of all facilities [12,13,26,44,67]. Therefore, market share of the chain from the demand of customer j for product t can be as follows:…”

“…Sayadi et al [74] suggested a discrete re y algorithm for ow shop scheduling problem. Sadjadi et al [67] presented a hybrid continuous and discrete re y algorithm for the competitive locationdesign model.…”

A hybrid DEA-based K-means and invasive weed optimization for facility location problem

“…The research results were compared with exacts those of multi-objective methods (Khalili-Damghani et al 2015). Sadjadi et al (2016) proposed a mathematical model to solve the location design problem with respect to budget constraints on inelastic demands and customer patronizing behavior. This model was developed by the firefly algorithm (Sadjadi et al 2016).…”

“…Sadjadi et al (2016) proposed a mathematical model to solve the location design problem with respect to budget constraints on inelastic demands and customer patronizing behavior. This model was developed by the firefly algorithm (Sadjadi et al 2016). Rabbani et al (2016) employed a mathematical modeling approach to study social and economic objectives in a location problem and a routing problem simultaneously.…”