Search algorithms for efficient logistics chains

Logistics networks arise whenever there is a transfer of material substance or objects (such as checked baggage on international flights) as well as energy, information, or finance through links (channels). A general concept of logistics network is suggested and motivated for modeling a service of any kind supplied through links between the nodes of the network. The efficiency of a single link is defined to be the ratio of the volume of useful service at the output node to the volume of expended service at the input node of the link (for a specific period of time). Similarly, the efficiency of a chain is the ratio of the volume of service at the output to the volume of service at the input of the chain. The overall efficiency of the chain is calculated as the product of the efficiencies of its links; the more efficiency of the chain, the less are the losses in the chain. This paper introduces the notion of inadequacy of service in such a way that the overall inadequacy of a chain is equal to the sum of the inadequacies of its links. So the efficiencies are being multiplied, whereas the inadequacies are being added. Thus, the antagonistic pair (efficiency, inadequacy) appears to be analogous to the pair (reliability, entropy) in communication theory. Various possible interpretations of the proposed logistic model are presented: energy, material, information and financial networks. Four algorithms are provided for logistics chain search: two algorithms for finding the most effective chain from a specified origin to a specified destination, and two algorithms for finding the guaranteed minimum level of service between any pair of unspecified nodes in a given network. An example is shown as to how one of the algorithms finds the most efficient energy chain from the electrical substation to a specified user in a concrete energy network.