Transcript .Ch12AssignSolc

Assignment Ch12(c)
The Dine Corporation is both a producer and a user of brass couplings.
The firm operates 220 days a year and uses the couplings at a steady rate
of 50 per day. u = 50. Coupling can be produced at rate of 200 per day.
p=200. Annual storage cost is $1 per coupling, H=1, and machine setup
cost is $35 per run, S=35. Since there are 220 days per year and u is
equal to 50, therefore yearly demand is 50(220), D= 11000
Determine the economic run size.
Approximately how many runs per year will there be?
Compute the maximum inventory level.
Determine the cycle time, run time and pure consumption time.
Compute the total cost
Production, Consumption, Inventory
EPQ: One period and One year
p-u
u
One Period
One Year
Imax, Ordering Cost and Carrying Cost
I max
I max
D
I max
S 
TC 
H
Q
2
I max
I max
EPQ : Optimal Q
EPQ 
2 SDp
H ( p  u)
2 SD
EPQ 
H
p
p u
The Problem
The Dine Corporation is both a producer and a user of brass couplings.
The firm operates 220 days a year and uses the couplings at a steady
rate of 50 per day. u = 50. Coupling can be produced at rate of 200 per
day. p=200. Annual storage cost is $1 per coupling, H=1, and machine
setup cost is $35 per run, S=35. Since there are 220 days per year and u
is equal to 50, therefore yearly demand is 50(220), D= 11000
Determine the economic run size.
Approximately how many runs per year will there be?
Compute the maximum inventory level.
Determine the cycle time, run time and pure consumption time.
Compute the total cost
EPQ and # of Runs
u =50, p=200, H=1, S=35, D= 11000
Determine the economic run size.
EPQ 
2 SD
H
p
p u
2(35)(11000)
200
EPQ 
1
200  50
EPQ  1013
Approximately how many runs per year will there be?
D/Q = 11000/1013 = 10.85
Run Time
How much do we produce each time? Q
How long does it take to produce Q? d1
What is our production rate per day? p
Q  pd1
Run Time?
Q = pd1  1013 = 200d1
d1= 1013/200 = 5.06
p-u
d1
I max
d2
u
Maximum Inventory
Maximum Inventory ?
At what rate inventory is accumulated?
p-u
For how long?
d1
What is the maximum inventory?
IMax
IMax = (p-u)d1
IMax = (200-50)(5.06) = 759
I max
p-u
d1
d2
u
Pure Consumption Time
What is the Maximum inventory?
IMax
How long does it take to consume IMax ?
d2
At which rate Imax is consumed for d2 days
u
Imax = ud2
759 = 50d2
d2 = 15.18
I max
p-u
d1
d2
u
Cycle Time, Total Cost
Cycle Time ?
d1 + d2 = 5.06 + 15.18 = 20.24
Total Cost ?
TC = H(IMax/2) + S(D/Q)
TC = 1(759/2) + 35 (11000/1013)
TC = 379.5 + 379.5 = 759