Lecture 23 - Order Quantities. The contents of this chapter include all of the following: Objectives of inventory management, lot size decision, inventory models, EOQ, robust model, reorder point, production order quantity model, quantity discount model.
Lecture 23 Order Quantities Books • Introduction to Materials Management, Sixth Edition, J. R. Tony Arnold, P.E., CFPIM, CIRM, Fleming College, Emeritus, Stephen N. Chapman, Ph.D., CFPIM, North Carolina State University, Lloyd M. Clive, P.E., CFPIM, Fleming College • Operations Management for Competitive Advantage, 11th Edition, by Chase, Jacobs, and Aquilano, 2005, N.Y.: McGrawHill/Irwin • Operations Management, 11/E, Jay Heizer, Texas Lutheran University, Barry Render, Graduate School of Business, Rollins College, Prentice Hall Objectives • • • • • • • • Objectives of inventory management Lot size decision Inventory models EOQ Robust model Reorder point Production order quantity model Quantity discount model Objectives of Inventory Management Determine: • How much should be ordered at one time? • When should an order be placed? LotSize Decision Rules Lotforlot. Order exactly what is needed Fixedorder quantity. Arbitrary Order “n” periods supply. Satisfy demand for a given periodofdemand InventoryModelsforIndependentDemand Needtodeterminewhenandhowmuch toorder Basic economic order quantity ỵ Production order quantity ỵ Quantity discount model ỵ BasicEOQModel Importantassumptions Demand is known, constant, and independent Lead time is known and constant Receipt of inventory is instantaneous and complete Quantity discounts are not possible Only variable costs are setup and holding Stockouts can be completely avoided Inventory Usage Over Time Usage rate Inventory level Order quantity = Q (maximum inventory level) Minimum inventory Time Average inventory on hand Q Minimizing Costs Objective is to minimize total costs Curve for total cost of holding and setup Annual cost Minimum total cost Holding cost curve Setup (or order) cost curve Optimal order quantity (Q*) Order quantity The EOQ ModelAnnual setup cost = Q Q* D S H = Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Annual setup cost = = = (Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order D (S) Q Setup or order cost per order D S Q The EOQ ModelAnnual setup cost = Q Q* D S H D S Q Q Annual holding cost = H = Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity = = Q (H) (Holding cost per unit per year) Production Order Quantity Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days Maximum = Total produced during – Total used during inventory level the production run the production run = pt – dt However, Q = total produced = pt ; thus t = Q/p Maximum inventory level = p Holding cost = Q Q –d p p =Q 1– d p Q Maximum inventory level (H) = 2 d 1– p H Production Order Quantity Model Q = Number of pieces per order H = Holding cost per unit per year D = Annual demand p = Daily production rate d = Daily demand/usage rate Setup cost = (D/Q)S Holding cost = HQ[1 - (d/p)] (D/Q)S = HQ[1 - (d/p)] Q2 = Q* = p 2DS H[1 - (d/p)] 2DS H[1 - (d/p)] Production Order Quantity Example D = 1,000 units S = $10 H = $0.50 per unit per year Q* = Q* = p = units per day d = units per day 2DS H[1 - (d/p)] 2(1,000)(10) 0.50[1 - (4/8)] = = 282.8 or 283 hubcaps 80,000 Production Order Quantity Model Note: D = Number of days the plant is in operation d=4= 1,000 250 When annual data are used the equation becomes 2DS Q* = H 1– annual demand rate annual production rate EPQ Proble m: HP Ltd. Pr oduces pre 100,000 lbs mium plan /week. The t food in 50 y operate 5 Setup cost i # bags. Dem w ks/year; H s $200 and and is P t p h e roduces 25 annual ho EPQ. Dete lding cost r rmine the m ate is $.55/b ,000 lbs/week. aximum in ag. Calcula ventory lev te the e l C a lculate the t using the E PQ policy otal cost of EPQ 2DS d H p I MAX Q TC EPQ D S Q d p I MAX H EPQ Problem Solution 2DS d H p EPQ I MAX TC EPQ Q D S Q EPQ IMAX d p I MAX H TC 2(50)(100,000)( 200) 100,000 55 250000 7, 5,000,000 200 77,850 0, 0 0, 0 77,850 Bags 6, 0b a g s 46,710 55 $25,690 Quantity Discount Models Reduced prices are often available when larger quantities are purchased þ Trade-off is between reduced product cost and increased holding cost ỵ Totalcost=Setupcost+Holdingcost+Productcost TC = D Q S+ H + PD Q Quantity Discount Models A typical quantity discount schedule Discount Number Discount Quantity Discount (%) Discount Price (P) to 999 no discount $5.00 1,000 to 1,999 $4.80 2,000 and over $4.75 Quantity Discount Models Steps in analyzing a quantity discount For each discount, calculate Q* If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount Compute the total cost for each Q* or adjusted value from Step Select the Q* that gives the lowest total cost Quantity Discount Models Total cost curve for discount Total cost $ Total cost curve for discount Total cost curve for discount b a 1st price break Q* for discount is below the allowable range at point a and must be adjusted upward to 1,000 units at point b 2nd price break 1,000 2,000 Order quantity Quantity Discount Example Calculate Q* for every discount Q* = Q1* = 2(5,000)(49) = 700 cars/order (.2)(5.00) Q2* = 2(5,000)(49) = 714 cars/order (.2)(4.80) Q3* = 2(5,000)(49) = 718 cars/order (.2)(4.75) 2DS IP Quantity Discount Example Calculate Q* for every discount Q* = 2DS IP Q1* = 2(5,000)(49) = 700 cars/order (.2)(5.00) Q2* = 2(5,000)(49) = 714 cars/order (.2)(4.80) 1,000 — adjusted Q3* = 2(5,000)(49) = 718 cars/order (.2)(4.75) 2,000 — adjusted Quantity Discount Example Order Quantity Annual Product Cost Annual Ordering Cost Annual Holding Cost Discount Number Unit Price $5.00 700 $25,000 $350 $350 $25,700 $4.80 1,000 $24,000 $245 $480 $24,725 $4.75 2,000 $23.750 $122.50 $950 $24,822.50 Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit Total Quantity Discount Ex ample: Collin’s S port store is consid hat supplier. The pre ering going to a dif sent supplier charg ferent es $10/hat and requ quantities of 490 hat ir es minimum s. The annual dema nd is 12,000 hats, t and the inventory c he ordering cost is arrying cost is 20% $20, of the hat cost, a n ew supplier is offeri hats at $9 in lots of ng 4000. Who should h e buy from? • EOQ at lowest price $9. Is it feasible? 2(12,000)( 20) 516 hats $1.80 Since the EOQ of 516 is not feasible, calculate the total cost (C) for each price to make the decision 12,000 490 C$10 $20 $2 $10 12,000 $120,980 490 12,000 4000 C$9 $20 $1.80 $9 12,000 $101,660 4000 EOQ$9 • • 4000 hats at $9 each saves $19,320 annually. Space? End of Lecture 23 ... Objectives? ?of? ?inventory? ?management Lot size decision Inventory? ?models EOQ Robust model Reorder point Production order quantity model Quantity discount model Objectives? ?of? ?Inventory? ?Management. .. Demand is known, constant, and independent Lead time is known and constant Receipt of inventory is instantaneous and complete Quantity discounts are not possible Only variable costs are setup and. .. units are produced and sold simultaneously ỵ Inventory level ProductionOrderQuantityModel Part of inventory cycle during which production (and usage) is taking place Demand part of cycle with no