Operations Research · Mathematical Inventory Models · Introduction

Introduction

What this guide covers

The mathematical theory of inventories constitutes one of the most sophisticated pillars of Operations Research. Its fundamental purpose is the optimal determination of replenishment policies (when and how much to order) to balance the economic forces in tension: acquisition costs, order costs, stock maintenance costs, and stock outage costs.

Overview

Topics covered

Introduction
Inventory Models
Introduction and Fundamentals of Inventory Theory
General Cost Structure
The Economic Order Quantity Model (Classic EOQ)
Mathematical Derivation of the Cost Function

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

\bar{I} = \frac{1}{T} \int_0^T (Q - Dt) \dd t = \frac{1}{T} \left[ Qt - \frac{Dt^2}{2} \right]_0^T = \frac{Q}{T} \cdot T - \frac{D}{2T} T^2 = Q - \frac{DQ}{2D} = \frac{Q}{2}

View LaTeX source

\bar{I} = \frac{1}{T} \int_0^T (Q - Dt) \dd t = \frac{1}{T} \left[ Qt - \frac{Dt^2}{2} \right]_0^T = \frac{Q}{T} \cdot T - \frac{D}{2T} T^2 = Q - \frac{DQ}{2D} = \frac{Q}{2}