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S. Okumura et al.
Q R (t; i R ) =
t
∫
t−i R
γ (t)dt.
(16.2)
Based on the above assumptions, the LCS software has been constructed using
the simulation modeling studio WITNESS Horizon.
16.2.3 Objective Function
Inventories for the finished products and the collected used products are managed
according to the production plan based on the time-series prediction data of demand
and collecting quantity. Also, new manufacture and remanufacturing are directed;
both of them incur the cost of ordering. Therefore, we consider the following total cost
as the objective function given by the sum of the ordering cost for new manufacture
and remanufacturing, and inventory for the collected products:
C O = C 1 + C 2 ,
(16.3)
where C 1 is the ordering cost, and C 2 is the inventory cost for collected products.
The ordering cost C 1 is the sum of ordering costs for new manufacture and
remanufacturing given by
C 1 (t; i M , i R ) = K M y M (Q M (t; i M )) + K R y R (Q R (t; i R )),
(16.4)
where K M and K R are an ordering cost for newly manufactured products, and an
ordering cost for remanufactured products, respectively. The number of new product
orders y M (·) and the number of remanufactured product orders y R (·) are influenced
by lot size Q M (t; i M ) and Q R (t; i R ), respectively. It is noted that ∂ y M /∂ Q M < 0 and
∂ y R /∂ Q R < 0.
Finally, the inventory cost incurred in [t 1 , t 2 ] (t 1 : start time of a stage, t 2 : end
time of a stage) is given by the sum of the costs for newly manufactured products
inventory and collected products inventory:
C 2 (t; i M , i R ) =h F
t 2
∫
t 1
I F (t; y M (Q M (t; i M )), y R (Q R (t; i R )))dt
+ h C
t 2
∫
t 1
I C (t; y M (Q M (t; i M )), y R (Q R (t; i R )))dt,
(16.5)
where h F is an inventory holding cost for the finished products which means the cost
when one remanufactured/manufactured product as a finished product is stocked
for a unit time in the finished product inventory, I F (·) is the number of remanufactured/manufactured products in the finished product inventory, h C is an inventory
S. Okumura et al.
Q R (t; i R ) =
t
∫
t−i R
γ (t)dt.
(16.2)
Based on the above assumptions, the LCS software has been constructed using
the simulation modeling studio WITNESS Horizon.
16.2.3 Objective Function
Inventories for the finished products and the collected used products are managed
according to the production plan based on the time-series prediction data of demand
and collecting quantity. Also, new manufacture and remanufacturing are directed;
both of them incur the cost of ordering. Therefore, we consider the following total cost
as the objective function given by the sum of the ordering cost for new manufacture
and remanufacturing, and inventory for the collected products:
C O = C 1 + C 2 ,
(16.3)
where C 1 is the ordering cost, and C 2 is the inventory cost for collected products.
The ordering cost C 1 is the sum of ordering costs for new manufacture and
remanufacturing given by
C 1 (t; i M , i R ) = K M y M (Q M (t; i M )) + K R y R (Q R (t; i R )),
(16.4)
where K M and K R are an ordering cost for newly manufactured products, and an
ordering cost for remanufactured products, respectively. The number of new product
orders y M (·) and the number of remanufactured product orders y R (·) are influenced
by lot size Q M (t; i M ) and Q R (t; i R ), respectively. It is noted that ∂ y M /∂ Q M < 0 and
∂ y R /∂ Q R < 0.
Finally, the inventory cost incurred in [t 1 , t 2 ] (t 1 : start time of a stage, t 2 : end
time of a stage) is given by the sum of the costs for newly manufactured products
inventory and collected products inventory:
C 2 (t; i M , i R ) =h F
t 2
∫
t 1
I F (t; y M (Q M (t; i M )), y R (Q R (t; i R )))dt
+ h C
t 2
∫
t 1
I C (t; y M (Q M (t; i M )), y R (Q R (t; i R )))dt,
(16.5)
where h F is an inventory holding cost for the finished products which means the cost
when one remanufactured/manufactured product as a finished product is stocked
for a unit time in the finished product inventory, I F (·) is the number of remanufactured/manufactured products in the finished product inventory, h C is an inventory