文档介绍：Prof. Y. Peter Chiu
3 / 2003
Material Management
Class note # 3b
~ Multiple product EPQ analysis ~
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§ . Inventory Management for Finite Production Rate
• Inventory Levels for Finite Production
Rate Model
Slope=P- λ
Slope= - λ
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P : production rate (per unit time)
λ: demand rate (per unit time)
P >λ
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§. Finite Production Rate Model
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~ EPQ (Finite Production Rate ) Models
for Production Planning ~
◆ Producing n products on a single machine (or line)
◆ Goals:(1) To determine the optimal procedure for producing
n products on the machine to minimize the cost
of holding & setups.
(2) To guarantee that no stock-outs occur during
the production cycle.
Demand rate for product j
Production rate for product j
Holding cost per unit per unit time for product j
Cost of setting up the production facility to produce product j
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◆ Assumption (required)
◇ To ensure that the facility has sufficient capacity to
satisfy the demand for all products.
~ Multiple items production planning ~
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◆ Rotation cycle policy assumption :
means that in each cycle there is exactly one setup for each product, and products are produced in the same sequence in each production cycle .
◇ Recall “the finite production rate “ solution
where
H
T
~ Multiple items production planning ~
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◆ Let T be the cycle time ( new , for the rotation cycle policy)
During time T , we assume that exactly one lot of each
product is produced.
◇ In order that the lot for product j be large enough to
meet the demand occurring during time T , it follows
that the lot size should be
◇ The average annual cost
(. if T= year , =12,000
then =6,000)
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◇ The average annual cost for all products
◇ The avg. annual cost for n products in terms of the cycle time T
◇ To find T, minimize G(T) ;
(check G”(T)>0
for minimal)
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where
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