1. OUTLINE Questions? Midterm Results Go over Midterm Go over Homework
New homework
Production planning
Quiz on 10/04

2. Midterm Results

3. Midterm Results

4. Aggregate Planning
Demand enters as units of products
We convert these to common units such as machine hours, labor hours, earned hours, pounds of material, etc. to create an aggregate schedule
The master schedule details how many of each product are to be built in each period
The major variables are the costs of changing the level of resources such as:
labor
machinery
inventory
impact of lot sizes

5. Example
Note that definitions of variables are different in each book.
Our objective is to minimize the total cost by:
Varying labor levels
Varying Inventory
Varying lot sizes
t periods (length of the horizon)
n products
m resources
Inventory carrying cost
Hiring and layoff costs
Off loading (subcontracting) costs
Overtime costs

6. Example (continued)
We are usually subject to a number of constraints:
Hours or shifts per day (a shift is usually 8 hours)
Workdays per month (range from 19 to 31, usually use 20)
Machine capacities (units made per hour)
Overtime limits (how long can a person work per day?)
Hours required per product (x.xxxx hrs/unit)
Whether or not shortages are allowed
Non-negativity constraints (all variables >=0)

7. Example (continued)
Things that need to be balanced in each period
Inventory
Work
Work Force
Balance total demand with total production

8. Methods for solving Aggregate Planning Problems
Spreadsheet trial end error
Linear Programming (Simplex method, Dantzig 1947 – see the link on the links page)
Excel Solver
Other LP programs
Non linear optimization methods (ISE520)

9. LP example

10. LP Example (see spreadsheet)

11. Using the Solver in Excel
The solver is located under the “Tools” menu. The dialog box looks like this:

12. Using the Solver in Excel (continued)
The dialog box for the constraints look like this: