Inventory Models

1
Inventory Models

• Production Lot Size Models

2
PRODUCTION LOT SIZE MODELS

• In a production lot size model, we are a
  manufacturer, trying to determine how much to
  produce (the production lot size) during each
  production run.
• Like the EOQ model with Q the production lot
  size except
• We are producing at a rate P/yr. that is greater
  than the demand rate of D/yr.
• Otherwise run process continuously and sell items
  as fast as they are produced
• Inventory does not jump to Q but builds up to a
  value IMAX that is reached when production is
  ceased

3
What is the maximum inventory and the average
inventory per cycle?

• Length of a production run Q/P
• During a production run
• Amount Produced Q
• Amount Demanded D(Q/P)
• IMAX Q - D(Q/P) (1-D/P)Q
• Average inventory IMAX/2 ((1-D/P)/2)Q

4
PRODUCTION LOT SIZE -- TOTAL ANNUAL COST

• Q The production lot size
• CO Set-up cost rather than order cost /setup
• Number of Set-ups per year D/Q
• Average Inventory ((1-D/P)/2)Q
• Instantaneous set-up time/infinite time horizon
• TC(Q) CO(D/Q) Ch((1-D/P)/2)Q CD

5
OPTIMAL PRODUCTION LOT SIZE, Q

TC(Q) CO(D/Q) Ch((1-D/P)/2)Q CD
6
EXAMPLE-- Farah Cosmetics

• Production Capacity 1000 tubes/hr.
• Daily Demand 1680 tubes
• Production cost 0.50/tube (C 0.50)
• Set-up cost 150 per set-up (CO 150)
• Holding Cost rate 40 (Ch .4(.50) .20)
• Since demand is 1680 per day and the production
  rate is 1000 per hour
• D 1680(365) 613,200
• P 1000(24)(365) 8,760,000

7
OPTIMAL PRODUCTION LOT SIZE

8
TOTAL ANNUAL COST

• TOTAL ANNUAL COST TC(Q) TV(Q) CD
• TV(Q) CO(D/Q) Ch((1-D/P)/2)Q
• (150)(613,200/31,449) .2((1-(613,200/8,760,000)
  )(31,449)/2)
• 5,850
• TC(Q) TV(Q) CD
• 5,850 .50(613,200) 312,450

9
OTHER QUANTITES

• Length of a Production run Q/P
• 31,449/8,760,000 .00359yrs. .00359(365)
• 1.31 days
• Length of a Production cycle Q/D
• 31,449/613,200 .0512866yrs. .00512866(365)
  18.72 days
• of Production runs/yr. D/Q 19.5
• IMAX (1-(613,200/8,760,000))(31,449) 29,248

10
REORDER (SETUP) POINT ANALYSIS

• The reorder point (actually the setup point) and
  safety stock determination are not affected by
  the calculation of Q.
• It is found in the same way as before
• r LD SS if demand is constant
  over lead time
• r is found using service levels if demand
  varies during lead time

11
Using the Template
12
Review

• Production Lot Size Models find the amount to
  produce per production run
• P gt D, else optimal solution is to run machine
  continuously
• Same as EOQ except IMAX Q(1-D/P)
• Length of a production run Q/P
• Length of the production cycle Q/D
• Reorder (setup) point analysis is not affected.
• Use of template