Product Mix

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Product Mix Master Production Scheduling
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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

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Linear Programming (L.P.)

• Continuous Decision Variables
• Decision Variable Subject to Constraints
• Objective Function that is Maximized or Minimized
• Equations or Inequalities are Linear

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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.

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E.g. L.P. Formulation

• X1 Issues of Paygirl
  X2 Issues of Payboy
• Objective Function Max. Z .6 X1 .5 X2
• Subject to (s.t.) 2 X1 X2 ? 10,000
  (Labor)
• 8 X1 8X2 ? 48,000 (Inventory)
• X1 ? 6,000 (Demand)
• X2 ? 4,500 (Demand)
• X1, X2, ? 0

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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

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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

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MPS Differs from Production Plan

• Shorter Time Buckets
• Used for Each End Item Not Families of Items as
  in Production Plan
• Generally More Detailed

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Items in MPS Must Add Upto Whats in Production
Plan
WEEK 1 2 3 4 5 6
UNICYCLES   100 50   50 40
BICYCLES 100     100   40
TRICYCLES     50   50 20
TOTAL - Production Plan 100 100 100 100 100 100
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What End Items Go into MPS
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MPS Can Show Running Inventory

• Made to Stock Only

WEEK 0 1 2 3 4 TOTAL
FORECAST   200 300 100 100 700
AVAILABLE 200 250 200 100 100  
MPS   250 250   100  
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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

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MPS with Minimum Available of 100
WEEK 0 1 2 3 4 TOTAL
FORECAST   200 300 100 100 700
AVAILABLE 200 250 200 100 100  
MPS   250 250   100  
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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 20 40 0
TRIKES 20 10 20 10 0 30
TOTAL HOURS 80 70 120 70 80 90
CAPACITY 100 100 100 100 100 100
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ATP (Available to Promise)

• Portion of Inventory Not Committed Available to
  Customer
• ATP Scheduled Receipts Beginning
  Inventory - Actual Orders Scheduled

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ATP Calculation

• On Hand100
• ATP (1) 100 80 20
• ATP (2) 100 (1010) 80
• ATP (4) 100 30 70

WEEK 1 2 3 4 5 6
CUSTOMER ORDERS 80 10 10   30  
MPS   100   100    
ATP 20 80   70    
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