An inventory manager for a furniture manufacturing company has collected the nec

Question

An inventory manager for a furniture manufacturing company has collected the necessary information to determine the optimal production policy for a Louis V bed model. The marketing department has ensured him/her that the demand for this model over the next year will be constant at a rate of 20 units per month. The production manager is maintaining a constant production rate of 45 units per month. He/She has also estimated a setup cost of $1000 per production run and a unit manufacturing cost of $300. The finance department advised the inventory manager to use a monthly interest rate of 10%.

1- Find the optimal production policy.

2- The inventory manager decided to allow shortages at a monthly cost of $1/3 per unit. What is the new production lot size, maximum shortages level, and monthly total system cost?

Explanation / Answer

1)EPQ = 2SD / H * p/ p-u

=2* $1,000 * 240 * 45 / 45- 20

=693 * 1.34

=928.62 Units

___________________________________________________________________

2)Annual Demand =240 units(20 per month *12=240)

Setup cost = $1000 per production

Ch=Carrying cost = $300

d=20 per month

p=45 units per month

new production lot size

=   2DC / Ch(1-d/p)

= 2 * 240 * $1000 / $300(1-20 / 45 )

=480,000 / 168

=53 Units

__________________________________________________________________________

Total System cost = Set up cost +   Carrying cost + Shortage cost

=$1000 per production + $300 + $435

=$1,735

Shortage cost:

$1000 + $300=$1,300 /45 units=$29 per unit * $1/3=$9.6 per unit *45=435

Maximum shortages level

=Ch / Ch +Cs( 1- d / p) q

= $300 / $300 +$1000 (1- 20/ 45)53 units

=0.231 * 0.56*53 units

=7 units

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