1. Product Mix & Master Production Scheduling

2. Product Mix Problem Quantity of Each of Multiple Products to Produce
- Example: How Much of Various Flavors of Ice Cream to Produce?
Solution Methods
- Hueristics
- Linear Programming

3. Linear Programming (L.P.)
Continuous Decision Variables
Decision Variable Subject to Constraints
Objective Function that is Maximized or Minimized
Equations or Inequalities are Linear

4. Consider the Following:
The businessperson, Cindy Light, publishes two magazines, Paygirl (for men) and Payboy (for women). Monthly sales average about 6,000 and 4,500 issues respectively for the publications. Paygirls contribute $.60 per issue to net profits; Payboys add about $.50 per issue. No left over magazines are desirable.
Each Paygirl requires two minutes of actual machine and labor time to produce. Payboys only require one minute. There are 10,000 total minutes per month of time available. Inventory storage space imposes another limitation. 48,000 cubic inches are available and each magazine uses up about 8.
Determine monthly production for each magazine.

5. E.g. L.P. Formulation X1: Issues of Paygirl X2: Issues of Payboy
Objective Function: Max. Z = .6 X X2
Subject to (s.t.): 2 X1 + X2  10,000 (Labor)
8 X1 + 8X2  48,000 (Inventory)
X  6,000 (Demand)
X2  4,500 (Demand)
X1, X2,  0

6. Linear Programming (L.P.)
We Can Use the Computer (Simplex Method Using POM for Windows) to Find the Answer.
The Answer Would Be Incorporated in the Master Production Schedule

7. Master Production Scheduling (MPS)
Link between Production Planning and What is Built or What Service is Performed
Used for Calculating Resource and Capacity Needs
Drives Material Requirements Plan (MRP)
Keeps Priorities Valid – Is Negotiated Agreement

8. MPS Differs from Production Plan
Shorter Time Buckets
Used for Each End Item Not Families of Items as in Production Plan
Generally More Detailed

9. Items in MPS Must Add Up to What’s in Production Plan
WEEK 1 2 3 4 5 6
UNICYCLES
100 50 40
BICYCLES
TRICYCLES 20
TOTAL - Production Plan

10. What “End Items” Go into MPS

11. MPS Can Show Running Inventory
Made to Stock Only
WEEK 1 2 3 4
TOTAL
FORECAST
200
300
100
700
AVAILABLE
250
MPS

12. Optimizing MPS Develop Preliminary Plan
Maintain Desired Customer Service by Optimizing Available Goods
Make Best Use of Resources (Materials, Labor, Equipment)
Check Preliminary Plan Against Capacity
Resolve Differences Between MPS and Capacity

13. MPS with Minimum Available of 100
WEEK 1 2 3 4
TOTAL
FORECAST
200
300
100
700
AVAILABLE
250
MPS

14. (Two Hours per Bike; Three Hours per Trike)
MPS and Capacity
Made to Stock
(Two Hours per Bike; Three Hours per Trike)
WEEK 1 2 3 4 5 6
BIKES 10 20 30 40
TRIKES
TOTAL HOURS 80 70
120 90
CAPACITY
100

15. ATP (Available to Promise)
Portion of Inventory Not Committed – Available to Customer
ATP = Scheduled Receipts + Beginning Inventory - Actual Orders Scheduled

16. ATP Calculation On Hand:100 ATP (1) = 100 – 80 = 20
WEEK 1 2 3 4 5 6
CUSTOMER ORDERS 80 10 30
MPS
100
ATP 20 70