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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 a finite production rate An example showing the problem with separate EPQ computation The procedure An example. - PowerPoint PPT Presentation
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1
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
LESSON 15INVENTORY MODELS (DETERMINISTIC)
EOQ MODEL FOR PRODUCTION PLANNING
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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, ….
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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.
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j
jjj h
KQ
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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.
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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.
ExampleProblem with Separate EPQ Computation
Optional
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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.
/unit/year
/unit/yeartime workertime up-set
:55R-J Product
8571.1$5357.0141'
5357.0600,33000,18
4$2020.0102$852.1
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Optional
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met) demand (downtime days days
(days) for lastsinventory Maximum
days day per hr hr/ slide) next the (see days
223-H of time setup223-H for Uptime required (days), downtime Minimum
days Uptime,
units Inventory,Max
units EPQ
:slide) previous the from (continued 55R-J Product
3027.47047.8
2400001,188509.652
3027488020274
0439.10240600,331404.406,1
85.6525357.0114.406,11
1404.406,18571.1
000,181022'
2
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PQT
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hKQ
Optional
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days Uptime,
units Inventory,Max
units EPQ
/unit/year
/unit/yeartime workertime up-set
:223-H Product
2027.4240800,525848.924
32.5044545.0158.9241
5848.9248182.3
000,24682'
2
8182.3$4545.0171'
4545.0800,52000,24
7$3520.068$858.0
*
1
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PQT
PQH
hKQ
Phh
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Optional
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produced. is 55R-J product whenmet be cannot 223-H Product
for demand produced, are quantities EPQ If :Conclusion
met) be cannot demand (downtime days days
(days) for lastsinventory Maximumdays day per hr hr/ days
55R-J of time setup55R-J for Uptime required (days), downtime Minimum
:slide) previous the from (continued 223-H Product
1939.100432.5
240000,243190.504
1939.1082.10439.10
H
Optional
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J-55R H-223Annual production rate (units/year) 33600 52800Annual Demand rate (units/year) 18000 24000Setup time (hour) 1.2 0.8K, Setup cost, $Unit cost, $ 20 35h, Holding cost/unit/yeardemand/productionh'
Separate EPQ solutionQ*Maximum inventoryUptime (days)Minimum downtime (days)Maximum inventory lasts for (days)
Optional
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J-55R H-223Annual production rate (units/year) 33600 52800Annual Demand rate (units/year) 18000 24000Setup time (hour) 1.2 0.8K, Setup cost, $ 102 68Unit cost, $ 20 35h, Holding cost/unit/year 4 7demand/production 0.5357 0.4545h' 1.8571 3.8182
Separate EPQ solutionQ* 1406.1404 924.5848Maximum inventory 652.8509 504.3190Uptime (days) 10.0439 4.2027Minimum downtime (days) 4.3027 10.1939Maximum inventory lasts for (days) 8.7047 5.0432
Optional
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• 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
EOQ Model for Production Planning
T
TQ jj
jjQ
j j
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• 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
EOQ Model for Production Planning
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time Idle nn TsTsTsT 2211
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time Idle
EOQ Model for Production Planning
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• Two rules for T*
• T* is the maximum of the two. T* = max (Cycle1, Cycle2)
EOQ Model for Production Planning
n
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j
n
jj
P
sT
1
1*
1Cycle1
n
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2Cycle2
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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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2211
2
11
2
2
1
12
11
21
2
11
21
2
11
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Cycle2Cycle1,
Cycle2
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max
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(check) 223-H of time) setup uptime55R-J of downtime
(days) for lastsinventory Maximum
Uptime Downtime
Uptime,
Inventory,Max
:55R-J Product
(
*
*
*
**
HTPQT
PQH
TQ
1
1
20
(check) 55R-J of time) setup uptime223-H of downtime
(days) for lastsinventory Maximum
Uptime Downtime
Uptime,
Inventory,Max
:223-H Product
(
*
*
*
**
HTPQT
PQH
TQ
1
1
21
J-55R H-223 TotalK, Setup cost, $ 102 68 170h, Holding cost/unit/year 4 7demand/production 0.5357 0.4545 0.9903h' 1.8571 3.8182h'(demand)
EOQ Model for Production PlanningCycle1 in days Cycle2 in daysCycle time=max(cycle1, cycle2) in daysQ* = cycle time demandMaximum inventoryUptime (days)Downtime (days)Maximum inventory lasts for (days)
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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.)