The associate cycle length is T ) (/ ) 0 days ecause the lead time 1 ) 2 days e4ceeds the cycle length t )0 days!. e must compute 1e. The no. of integer cycles included in 1 is n ) largest integer ≤ 2(0 ! Thus, Le = L − nt = 2 days The reorder point thus occurs when the inventory level drops to Le D = 2 × 00 = 200 neon lights The inventory policy for ordering the neon lights is order 00 units whenever the inventory order drops to 200 units. The daily inventory cost associated with the proposal inventory policy is C Q = ' 2 + C 3 ÷ Q (D 2
= 20 ( day Question
ind the optimal order 7uantity for a product for which the price8reaks are as follows9 Items 0 ≤ 7 : 00 00 ≤ 7 : 200 200 ≤ 7
*ri+e,-nit ;s. 20 ;s. < ;s. 6
The monthly demand for the product is 600 units. The storage cost is 5= of unit cost and the cost of ordering is ;s. 30 per order. Solution:
>? at ;s. 20 ) >? at ;s. < ) >? at ;s. < )
2 × 600 × 30 20 × 0.5 2 × 600 × 30 < × 0.5 2 × 600 × 30 6 × 0.5
=
[email protected]+ = 5.+A = 22.+A
The >? at ;s. 20 per item )
[email protected]+. ut the price per item is ;s. 20 only if the items are ordered in the range of 0 to less then00. This is therefore an infeasile solution. *imilarly the >? at ;s. 6 per item is 22.+A. This price is valid only for items ordered in the range 200 or more. This is also an infeasile solution.
Question 4 " company stocks an item that is demanded 000 units per month and the shortages are allowed. %f the unit cost is ;s 20 per unit, the cost of making one purchase is ;s 000, the holding cost for one unit is ;s +0 per year and the cost of one shortage is ;s 50 per year, determine9
a! The economic purchase 7uantity. ! The time etween orders. c! The numer of orders per year. d! The optimum shortages. e! The ma4imum inventory. f! The time of items eing held. g! The optimum annual cost. Solution: 1et D = 000 units ( month = 2000 units ( year C. C3
= 20 ( unit = +0 units ( year
, C2 = 000 , C+
= 50 ( year
T.e e+onomi+ /ur+.ase uantit"
Q=
2C2 D C3 + C + C3
C +
)
ASSIGNMENT 2 (Operation Research) Maximum Marks: 40 Due Date:
Question 1
The demand for a product is 600 units per week, and the items items are withdrawn at a constant rate. The setup cost for placing an order to replenish inventory is $25. The unit cost of each item is $3, and the inventory holding cost is $0.05 per item per week. a! "ssuming "ssuming shortages shortages are not allowed, allowed, determine determine how often to make a production production run and what si#e it should e. ! %f shortage shortage are allowed allowed ut cost $2 per item per month, determine determine how often often to order and what si#e the order should e. Solution: (a) &ere si#e of order Q
'
2C2 D
=
C 3
!!4"#$%!
' &ow often to order for time etween order t
(&) *i#e of order
Q' =
' Time etween order t
2C2 D C3
=Q
'
C3 +C+ C +
=Q
'
( D ) 1"2$1
'12"40$
( D ) 1"#40
Question 2
eon lights on the - of " campus are replaced at the rate of 00 units per day. The physical plant orders the eon eo n lights periodically. %t cost $00 to initiate a purchase order. " neon light kept in storage is estimated to cost aout $0.02 per day. The load time etween placing and receiving an order is 2 days. /etermine the optimal %nventory policy for ordering the neon lights.
Solution:
/ ) 00 units per day 2 ) $00 per day 3 ) $0.02 per day 1 ) 2 days Q'
= =
2C2 D C 3
2 × 0 0 × 0 0 0.02
= 000
neonlights
