Some math background for supply-chain

Abstract

Table of Contents

1. Notations and Conventions

2. Base statistics

2.1. Quantity in stock

2.1.1. Definition
2.1.2. Rationale
2.1.3. Example

2.2. Total sales

2.2.1. Definition
2.2.2. Rationale
2.2.3. Example

2.3. Average stock quantity

2.3.1. Definition
2.3.2. Rationale
2.3.3. Example
2.3.4. Algorithm
2.3.5. An alternate way to calculate it.
2.3.6. Example

2.4. Average supply time

2.4.1. Definition
2.4.2. Rationale
2.4.3. Example

2.5. Average daily sale

2.5.1. Definition
2.5.2. Rationale
2.5.3. Example

2.6. Rotation Index

2.6.1. Definition
2.6.2. Rationale
2.6.3. Example

3. Reorder Point and Safety Stock

3.1. Theoretical order point

3.1.1. Definition
3.1.2. Rationale
3.1.3. Example

3.2. Safety Stock

3.2.1. Definition
3.2.2. Rationale
3.2.3. Example

3.3. Order point

3.3.1. Definition
3.3.2. Rationale
3.3.3. Example

3.4. Economic Order Quantity (EOQ)

3.4.1. Definition
3.4.2. Assumptions
3.4.3. Rationale
3.4.4. Example
3.4.5. Dealing with the assumptions

4. Evaluation of the inventory

4.1. Effective cost method
4.2. Average cost method
4.3. LIFO method
4.4. FIFO method

5. Cost analysis

5.1. Direct costing
5.2. Full costing
5.3. ABC Analysis

6. PUBLIC LICENSE

1. Notations and Conventions

Trough all the paper we assume that we have two series of pairs: O=(o_{\textrm{i}},d_{i})_{i=0}^{n} (orders) and S=(q{i},d{i})_{i=0}^{n} (stock movements) each pair up to n-1 is composed of a quantity and a date and represents a log in our inventory archive. the last pair has 0 for quantity by convention and the date is the last day for the time interval under consideration. For simplicity we assume that we have only one article in stock, so if we have the following logs for the period 1-10 January:

32 items in stock.	1 Jan
Ordered 100 items.	3 Jan
20 items sold.	4 Jan
100 items arrived.	6 Jan
15 items sold.	6 Jan

then we have the following series: O=\{(0,1-\textrm{jan}),(100,3-\textrm{jan}),(-100,6-\textrm{jan}),(0,10-jan)\} and S=\{(32,1-\textrm{jan}),(-20,4-\textrm{jan}),(100,6-\textrm{jan}),(-15,6-\textrm{jan}),(0,10-jan)\} we also denote with t the time interval.

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		Base statistics