2.1. Notation
A ordering cost per order
c purchasing price per item
D demand rate per year
h OW stock-holding cost per item per year
I
interest earned per $ per year
I
e
interest charged per $ in stocks per year by the supplier
k RW stock-holding cost per item per year
M the retailers trade credit period offered by supplier in years
N the customers trade credit period offered by retailer in years
p
s selling price per item
t
w
the rented warehouse time in years, t
>
>
:
T the cycle time in years
w
8
¼
DT W
>
>
<
D
if DT > WT>
0ifDT 6 WT6
W
W retailers OW storage capacity
TRC(T) the annual total relevant cost, which is a function of T
T* the optimal cycle time of TRC(T)
2.2. Assumptions
(1) Demand rate is known and constant.
(2) Shortages are not allowed.
(3) Time horizon is infinite.
(4) Replenishments are instantaneous.
(5) s P c, k Ph, I
p
P I
e
W
D
D
and M P N.
(6) If the order quantity is larger than retailers OW storage capacity W, the retailer will rent the
warehouse to storage these exceeding items. And the RW storage capacity is unlimited. When
the demand occurs, it first is replenished from the RW which storages those exceeding items.
(7) During the time the account is not settled, generated sales revenue is deposited in an interestbearing
account. When T PM, the account is settled at T = M, the retailer pays off all units
sold and keeps his/her profits, and starts paying for the higher interest charges on the items
in stock with rate I
. When T 6 M, the account is settled at T = M and the retailer does not
need to pay any interest charge.
p
(8) The retailer can accumulate revenue and earn interest after his/her customer pays for the
amount of purchasing cost to the retailer until the end of the trade credit period offered
by the supplier. That is, the retailer can accumulate revenue and earn interest during the period
N to M with rate I
2.3. The model
Y.-F. Huang / Applied Mathematical Modelling 30 (2006) 418–436 421
e
under the condition of trade credit.
The total annual relevant cost consists of the following elements. Three situations may arise. (I)
M P N PW/D, (II) M P W/D P N and (III) W/D PM PN.
2.1. NotationA ordering cost per orderc purchasing price per itemD demand rate per yearh OW stock-holding cost per item per yearIinterest earned per $ per yearIeinterest charged per $ in stocks per year by the supplierk RW stock-holding cost per item per yearM the retailers trade credit period offered by supplier in yearsN the customers trade credit period offered by retailer in yearsps selling price per itemtwthe rented warehouse time in years, t>>:T the cycle time in yearsw8¼DT W>><Dif DT > WT>0ifDT 6 WT6WW retailers OW storage capacityTRC(T) the annual total relevant cost, which is a function of TT* the optimal cycle time of TRC(T)2.2. Assumptions(1) Demand rate is known and constant.(2) Shortages are not allowed.(3) Time horizon is infinite.(4) Replenishments are instantaneous.(5) s P c, k Ph, IpP IeWDDand M P N.(6) If the order quantity is larger than retailers OW storage capacity W, the retailer will rent thewarehouse to storage these exceeding items. And the RW storage capacity is unlimited. Whenthe demand occurs, it first is replenished from the RW which storages those exceeding items.(7) During the time the account is not settled, generated sales revenue is deposited in an interestbearingaccount. When T PM, the account is settled at T = M, the retailer pays off all unitssold and keeps his/her profits, and starts paying for the higher interest charges on the itemsin stock with rate I. When T 6 M, the account is settled at T = M and the retailer does notneed to pay any interest charge.p(8) The retailer can accumulate revenue and earn interest after his/her customer pays for theamount of purchasing cost to the retailer until the end of the trade credit period offeredby the supplier. That is, the retailer can accumulate revenue and earn interest during the periodN to M with rate I2.3. The modelY.-F. Huang / Applied Mathematical Modelling 30 (2006) 418–436 421eunder the condition of trade credit.The total annual relevant cost consists of the following elements. Three situations may arise. (I)M P N PW/D, (II) M P W/D P N and (III) W/D PM PN.
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English translation English online translation translate text article translation translation translation sentence, English to Thai whole sentences. Translation of English both sentences translate sentences from English to Thai translation English translation for free [] English Translate to Thai.English translation English online translation translate text article translation translation translation sentence, English to Thai whole sentences. Translation of English both sentences translate sentences from English to Thai translation English translation for free [] English Translate to Thai.English translation English online translation translate text article translation translation translation sentence, English to Thai whole sentences. Translation of English both sentences translate sentences from English to Thai translation English translation for free [] English Translate to Thai.English translation English online translation translate text article translation translation translation sentence, English to Thai whole sentences. Translation of English both sentences translate sentences from English to Thai translation English translation for free [] English Translate to Thai.English translation English online translation translate text article translation translation translation sentence, English to Thai whole sentences. Translation of English both sentences translate sentences from English to Thai translation English translation for free [] English Translate to Thai.English translation English online translation translate text article translation translation translation sentence, English to Thai whole sentences. Translation of English both sentences translate sentences from English to Thai translation English translation for free [] English Translate to Thai.
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