[Paper Review] Search algorithms for efficient logistics chains

Serge Lawrencenko, Irina Albertovna Duborkina|arXiv (Cornell University)|Apr 9, 2015

Process Optimization and Integration1 references3 citations

TL;DR

This paper proposes a novel model for logistics networks using efficiency and inadequacy as complementary metrics, where chain efficiency is the product of link efficiencies and inadequacy is the sum of link inadequacies. It introduces four search algorithms—two for finding the most efficient path between specified nodes and two for ensuring a guaranteed minimum service level across any node pair—demonstrated in an energy network case study with quantitative results on loss minimization.

ABSTRACT

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.

Motivation & Objective

• To model logistics networks as chains of links with measurable service efficiency and inadequacy.
• To define overall chain efficiency as the product of individual link efficiencies and overall inadequacy as the sum of individual inadequacies.
• To develop algorithms that identify the most efficient logistics chain from a given origin to destination.
• To design algorithms ensuring a guaranteed minimum service level between any pair of nodes in a network.
• To demonstrate the applicability of the model and algorithms in real-world contexts such as energy distribution networks.

Proposed method

• Define link efficiency as the ratio of useful output service to input service over a time period.
• Define link inadequacy as the complement of efficiency, ensuring additive properties across chains.
• Model the overall chain efficiency as the product of individual link efficiencies, minimizing losses.
• Model the overall chain inadequacy as the sum of individual link inadequacies, enabling additive optimization.
• Develop two algorithms for finding the most effective chain between a specified origin and destination using efficiency maximization.
• Develop two algorithms for identifying guaranteed minimum service levels across all node pairs, based on inadequacy thresholds and network-wide constraints.

Experimental results

Research questions

• RQ1 How can logistics networks be modeled using a dual metric of efficiency and inadequacy to reflect service loss and reliability?
• RQ2 What algorithmic approaches enable the identification of the most efficient logistics chain between two specified nodes in a network?
• RQ3 How can a guaranteed minimum level of service be ensured across all possible node pairs in a logistics network?
• RQ4 What is the mathematical relationship between efficiency (product-based) and inadequacy (sum-based) in chain-level performance evaluation?
• RQ5 How do the proposed algorithms perform in real-world logistics scenarios such as energy distribution?

Key findings

• The model successfully frames logistics networks using a duality analogous to reliability and entropy in communication theory, enabling systematic analysis.
• The most efficient chain from a specified origin to destination was identified in a concrete energy network, demonstrating practical applicability.
• The algorithm for guaranteed minimum service level ensures that no pair of nodes in the network experiences service below a predefined threshold.
• The use of additive inadequacy and multiplicative efficiency allows for scalable and mathematically consistent optimization across complex chains.
• The case study on an electrical substation network confirmed that the algorithm effectively minimizes losses and maximizes service delivery efficiency.