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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.
7
Optional
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Optional
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Optional
12
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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READING AND EXERCISES
Lesson 15 Reading Section 4.9 , pp. 226-229
(4th Ed.), pp. 215-220 (5th Ed.) Exercise 29,
30 pp. 230-231(4th Ed.), pp. 219-220 (5th Ed.)
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