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## CHAPTER 4 INVENTORY MODELS (DETERMINISTIC)

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### LESSON 15 INVENTORY MODELS (DETERMINISTIC) EOQ MODEL FOR PRODUCTION PLANNING Outline EOQ Model for Production Planning The multi-product inventory control model with ... – PowerPoint PPT presentation

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Title: CHAPTER 4 INVENTORY MODELS (DETERMINISTIC)

1
LESSON 15INVENTORY MODELS (DETERMINISTIC)EOQ
MODEL FOR PRODUCTION PLANNING
• Outline
• EOQ Model for Production Planning
• The multi-product inventory control model with a
finite production rate
• An example showing the problem with separate EPQ
computation
• The procedure
• An example

2
EOQ Model for Production Planning
• This model is an extension of the EPQ model
• Consider the problem of producing many products
in a single facility. The facility may produce
only one product at a time.
• In each production cycle there is only one setup
for each product, and the products are produced
in the same sequence in each production cycle.
This assumption is called the rotation cycle
policy.
• For example, if there are three products A, B and
C, then a production sequence under the rotation
cycle policy is A, B, C, A, B, C, .

3
EOQ Model for Production Planning
• The goal is to determine the optimal production
quantities of various products produced in each
cycle and the optimal length of the cycle.
• Finding optimal production quantity of each
product separately using the EPQ formula
• may not give a good solution because a
production quantity may not be large enough to
meet the demand between two production runs of
the product.

4
EOQ Model for Production Planning
• For example, suppose that there are three
products A, B and C, then a production sequence
under the rotation cycle policy is A, B, C, A, B,
C, .
• The production quantity of product A obtained
from the EPQ formula may not be large enough to
meet the demand during the production run of
products B and C.
• The next example elaborates on the problem of
using EPQ formula separately for each product.

5
Optional
ExampleProblem with Separate EPQ Computation
• Example 6 Tomlinson Furniture has a single lathe
for turning the wood for various furniture pieces
including bedposts, rounded table legs, and other
items. Two products and some relevant information
appear below
• Annual Setup Time
Unit Annual
• Piece Demand (hours) Cost
Production
• J-55R 18,000 1.2
20 33,600
• H-223 24,000 0.8
35 52,800
• Worker time for setup is valued at 85 per
hour, and holding costs are based on a 20 percent
annual interest charge. Assume 8 hours per day
and 240 days per year.

6
Optional
ExampleProblem with Separate EPQ Computation
Find the optimal production quantities
separately for each product and show that
production quantity of H-223 is not large enough
to meet the demand between two production runs of
H-223.
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EOQ Model for Production Planning
• The previous example shows that if production
quantities of different products are computed
separately, then demand of every product may not
be met.
• Therefore, all the products must be considered at
the same time.
• To solve the integrated problem, first, the cycle
time is computed. For each product , the
production quantity is the demand of the
product during the cycle time. If is the
annual demand of product

13
EOQ Model for Production Planning
• Let T be the cycle time and Tj be the production
time of product j
• Let sj be the setup time of product j and n be
the number of products

14
EOQ Model for Production Planning
15
EOQ Model for Production Planning
• Two rules for T
• T is the maximum of the two. T max (Cycle1,
Cycle2)

16
Example EOQ Model for Production Planning
Example 7 Tomlinson Furniture has a single lathe
for turning the wood for various furniture pieces
including bedposts, rounded table legs, and other
items. Two products and some relevant information
appear below Annual
Setup Time Unit Annual Piece
Demand (hours) Cost
Production J-55R 18,000 1.2
20 33,600 H-223
24,000 0.8 35
52,800 Worker time for setup is valued at 85
per hour, and holding costs are based on a 20
percent annual interest charge. Assume 8 hours
per day and 240 days per year. Find the optimal
production quantities.
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