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

Assignment Ch12(c)

Production, Consumption, Inventory

EPQ: One period and One year

One Period

p-u u

One Year

Imax, Ordering Cost and Carrying Cost

I max I max I max I max

SQ

DH

I

2maxTC

EPQ : Optimal Q

)(

2

upH

SDpEPQ

up

p

H

SDEPQ

2

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

The Problem

u =50, p=200, H=1, S=35, D= 11000Determine the economic run size.

EPQ and # of Runs

up

p

H

SDEPQ

2

50200

200

1

)11000)(35(2

EPQ

1013EPQ

Approximately how many runs per year will there be? D/Q = 11000/1013 = 10.85

Run Time?Q = pd1 1013 = 200d1 d1= 1013/200 = 5.06

Run Time

p-u u

I max

d1d2

How much do we produce each time? QHow long does it take to produce Q? d1

What is our production rate per day? p

1pdQ

Maximum Inventory

Maximum Inventory ?At what rate inventory is accumulated?p-uFor how long?d1

What is the maximum inventory?IMax IMax = (p-u)d1

p-u u

I max

d1d2

IMax = (200-50)(5.06) = 759

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

uImax = ud2 759 = 50d2

d2 = 15.18

p-u u

I max

d1d2

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