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Inventory Models. Production Lot Size Models. 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:

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inventory models

Inventory Models

Production Lot Size Models

production lot size models
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
what is the maximum inventory and the average inventory per cycle
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
production lot size total annual cost
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

optimal production lot size q
OPTIMAL PRODUCTION LOT SIZE, Q*

TC(Q) = CO(D/Q) + Ch((1-D/P)/2)Q + CD

example farah cosmetics
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
total annual cost
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

other quantites
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
reorder setup point analysis
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
using the template
Using the Template

Optimal Values

Enter Parameters

Production Lot Size

Worksheet

review
Review
  • Production Lot Size Models find the amount to produce per production run
  • P > D, else optimal solution is to run machine continuously
  • Same as EOQ exceptIMAX= 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