---
date: '2025-09-18'
description: chapter 7
id: supply chain analytics and capacity growth
modified: 2026-06-05 15:08:38 GMT-04:00
tags:
  - commerce4qa3
title: supply chain analytics and capacity growth
created: '2025-09-18'
published: '2025-09-18'
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slug: thoughts/university/twenty-five-twenty-six/commerce-4qa3/supply-chain-analytics-and-capacity-growth
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---
see also [[thoughts/university/twenty-five-twenty-six/commerce-4qa3/financial analysis]]

## break-even analysis

ex. Restaurant expansion

$$
\begin{aligned}
Rx &= F + Vx \\
\overline{x} &= \operatorname{BEP}(x) = \frac{F}{R-V} \\
\operatorname{BEP}(\$) &= \operatorname{BEP}(x) \times R
\end{aligned}
$$

## dynamic capacity expansion policy

see also [[thoughts/economies of scales]]

| variable | description                                                              |
| -------- | ------------------------------------------------------------------------ |
| $D$      | annual increase in demand                                                |
| $x$      | time interval between introduction of successive plants (i.e: decision)  |
| $r$      | annual discount rate                                                     |
| $f(y)$   | cost of building and operationg a plant of capacity $y$                  |
| $c(x)$   | discounted cost infinite orizon given a plant opening at $0,x,2x,\ldots$ |