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

Midterm Results

Midterm Results

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

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

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)

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

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)

LP example

LP Example (see spreadsheet)

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

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