Consider a chain as leader that wants to open p new facilities in a linear market, like metro. In this market, there is a competitor, called follower. The leader and the follower have established some facilities in advance. When the leader opens p new facilities, its competitor, follower, reacts the leader’s action and opens r new facilities. The optimal locations for leader and follower are chosen among predefined potential locations. Demand is considered as demand points and is assumed inelastic. Considering huff model, demand points are probabilistically absorbed by all facilities. The leader’s objective is maximization of its market share after opening follower’s new facilities. For solving leader problem, first the follower’s problem is solved for all leader’s potential locations and the best location for leader is obtained and then, a heuristic model is proposed for leader problem when the leader and the follower want to open one new facility. Computational results show that the proposed method is efficient for large scale problems.

During the past two decades, there have been increasing interests on permutation flow shop with different types of objective functions such as minimizing the makespan, the weighted mean flow-time etc. The permutation flow shop is formulated as a mixed integer programming and it is classified as NP-Hard problem. Therefore, a direct solution is not available and meta-heuristic approaches need to be used to find the near-optimal solutions. In this paper, we present a new discrete firefly meta-heuristic to minimize the makespan for the permutation flow shop scheduling problem. The results of implementation of the proposed method are compared with other existing ant colony optimization technique. The preliminary results indicate that the new proposed method performs better than the ant colony for some well known benchmark problems.

The blood supply chain (BSC) is a crucial and intricate system in the healthcare sector, which is marked by perishable products, fluctuating supply and demand, and a major impact of inefficiency. This paper showcases a detailed scientific review of BSC literature from 2010 to 2025 through scientometric methods, thereby mapping out its intellectual structure and development. By scrutinizing both foundational and recent publications, the authors are able to point out the research streams, methodological trends and main scholars. The scrutiny brings forward three leading research paradigms: (1) robust and resilient network design for disaster response, with Jawad as the leading scholar; (2) green and sustainable BSC modeling under uncertainty, where Pishvaee and his team are the main contributors; and (3) integrated inventory-routing problems for perishables, with Ramezanian as the pivotal author. This discipline is moving away from deterministic, single-objective models to the development of intricate multi-objective frameworks under hybrid uncertainties (robust, fuzzy, stochastic) which are being solved increasingly with metaheuristics and supported by case studies from real applications. The new trends include the combination of AI/ML for forecasting and decision-making, blockchain for transparency, and drones for the delivery part. The present review collects all these advancements and gives a succinct direction for both researchers and practitioners.