# A study of problems with multiple interdependent components - Part I

## TL;DR

This paper explores formal models for problems with multiple interdependent components, focusing on how to define and classify dependencies by modeling components and their connections, with examples from logistics.

## Contribution

It introduces a reverse perspective to model interdependent problems, formalizes dependency notions, and classifies multi-component problem dependencies.

## Key findings

- Proposes a formal framework for modeling component dependencies.
- Provides classification of dependency types in multi-component problems.
- Uses real-world logistics examples to illustrate concepts.

## Abstract

Recognising that real-world optimisation problems have multiple interdependent components can be quite easy. However, providing a generic and formal model for dependencies between components can be a tricky task. In fact, a PMIC can be considered simply as a single optimisation problem and the dependencies between components could be investigated by studying the decomposability of the problem and the correlations between the sub-problems. In this work, we attempt to define PMICs by reasoning from a reverse perspective. Instead of considering a decomposable problem, we model multiple problems (the components) and define how these components could be connected. In this document, we introduce notions related to problems with mutliple interndependent components. We start by introducing realistic examples from logistics and supply chain management to illustrate the composite nature and dependencies in these problems. Afterwards, we provide our attempt to formalise and classify dependency in multi-component problems.