Capacitated location-allocation problems on a line

For economic and other reasons, distribution networks are often constructed in hierarchies, where, due to high costs, high-level distribution channels are built in straight lines from which low-level channel branch. Branching facilities, too, may incur high costs and thus, their number, locations al ong the lines, and allocation of destinations to them are important compone nts in system design, which can be accomplished by solving a series of capa citated location-allocation problems on a line. This problem is studied her e and its properties are discussed, and appropriate mathematical optimizati on models formulated and their properties and complexity are also considere d. Heuristic solution schemes and lower bounds on objective values are prop osed for the models. The efficiency and effectiveness of these schemes are evaluated and more insight into the models is gained through a numerical st udy. The major conclusion is that the hierarchical structure considered is highly restrictive and imposes high costs. Therefore, its use must be prope rly justified.