Developing approximation algorithm for elastic competitive facility location model

Organizations continuously endeavour to enhance their decision-making processes. With the advancement in information system, customers are becoming more attentive towards the market condition, competition and, the availability of substitute products. Therefore, instead of placing fixed demand, customers vary demand in response to market dynamics. To capture these factors, the model takes into account the dynamic nature of customer behaviour and incorporates the "law of demand" theory into the price-demand relationship, assuming demand to be a concave function of the price of goods. The study examines a location-price game to identify equilibrium location for firm operating in a foresight competitive market where firms first choose their respective locations and then establish delivered prices to maximize profits. To maximize profit while meeting customers demand satisfactorily, firms compete for providing the goods at a minimum price in minimum time. Due to the NP-hardness of the problem, even the small data set requires excessive computational time by the conventional method. Therefore, to addresses computational challenges associated with this complex CFL model the study employed a two-phase exploration and exploitation based heuristic. Comparative analysis against established algorithms across 33 datasets reveals that the proposed heuristic perform extremely well within negligible computational time across all cases. The study aims to provides insights for managers involved in foresight planning of facility location and pricing, offering a competitive advantage in today's rapidly evolving marketplace.