Inventory ModelsProduction Lot Size Models

PRODUCTION LOT SIZE MODELSIn 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 producedInventory 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?Length of a production run = Q/PDuring a production run Amount Produced = QAmount Demanded = D(Q/P)IMAX = Q - D(Q/P) = (1-D/P)QAverage inventory = IMAX/2 = ((1-D/P)/2)Q

PRODUCTION LOT SIZE -- TOTAL ANNUAL COST Q = The production lot sizeCO = Set-up cost rather than order cost =$/setupNumber of Set-ups per year = D/QAverage Inventory = ((1-D/P)/2)QInstantaneous 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 CosmeticsProduction Capacity 1000 tubes/hr.Daily Demand 1680 tubesProduction 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

OPTIMAL PRODUCTION LOT SIZE

TOTAL ANNUAL COSTTOTAL 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 QUANTITESLength 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 ANALYSISThe 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

ReviewProduction Lot Size Models find the amount to produce per production runP > D, else optimal solution is to run machine continuouslySame as EOQ except IMAX = Q(1-D/P)Length of a production run = Q*/PLength of the production cycle = Q*/DReorder (setup) point analysis is not affected.Use of template