Inventory Models

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# Inventory Models - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Inventory Models' - hanna-riggs

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Presentation Transcript

### 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:
• 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
• 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
• 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*

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

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 = 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
• 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
• 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

Optimal Values

Enter Parameters

Production Lot Size

Worksheet

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