LSM733-PRODUCTION OPERATIONS MANAGEMENT By: OSMAN BIN SAIF LECTURE 18 1

Summary of last Session  Global Company Profile: Amazon.com  Functions of Inventory  Types of Inventory  Inventory Management  ABC Analysis  Record Accuracy  Cycle Counting  Control of Service Inventories 2

Summary of last Session (Contd.)  Inventory Models  Independent vs. Dependent Demand  Holding, Ordering, and Setup Costs 3

Agenda for this Session  Inventory Models for Independent Demand  The Basic Economic Order Quantity (EOQ) Model  Minimizing Costs  Reorder Points  Production Order Quantity Model  Quantity Discount Models 4

Agenda for this Session (Contd.)  Probabilistic Models and Safety Stock  Other Probabilistic Models  Fixed-Period (P) Systems 5

Inventory Models for Independent Demand  Basic economic order quantity  Production order quantity  Quantity discount model Need to determine when and how much to order 6

The EOQ Model Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the inventory item S= Setup or ordering cost for each order H= 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 Setup or order cost per order = Annual setup cost = S DQDQ = (S) DQ 7

The EOQ Model Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the inventory item S= Setup or ordering cost for each order H= Holding or carrying cost per unit per year Annual holding cost =(Average inventory level) x (Holding cost per unit per year) Order quantity 2 = (Holding cost per unit per year) = (H) Q2 Annual setup cost = S DQDQ Annual holding cost = H Q2Q2 8

The EOQ Model Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the inventory item S= Setup or ordering cost for each order H= Holding or carrying cost per unit per year Optimal order quantity is found when annual setup cost equals annual holding cost Annual setup cost = S DQDQ Annual holding cost = H Q2Q2 DQ S = H Q2 Solving for Q* 2DS = Q 2 H Q 2 = 2DS/H Q* = 2DS/H 9

An EOQ Example Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year Q* = 2DS H Q* = 2(1,000)(10)0.50 = 40,000 = 200 units 10

An EOQ Example Determine optimal number of needles to order D = 1,000 units Q*= 200 units S = $10 per order H = $.50 per unit per year = N = = Expected number of orders Demand Order quantity DQ* N = = 5 orders per year 1,

An EOQ Example Determine optimal number of needles to order D = 1,000 unitsQ*= 200 units S = $10 per orderN= 5 orders per year H = $.50 per unit per year = T = Expected time between orders Number of working days per year N T = = 50 days between orders

An EOQ Example Determine optimal number of needles to order D = 1,000 unitsQ*= 200 units S = $10 per orderN= 5 orders per year H = $.50 per unit per yearT= 50 days Total annual cost = Setup cost + Holding cost TC = S + H DQQ2 TC = ($10) + ($.50) 1, TC = (5)($10) + (100)($.50) = $50 + $50 = $100 13

Robust Model  The EOQ model is robust  It works even if all parameters and assumptions are not met  The total cost curve is relatively flat in the area of the EOQ 14

An EOQ Example Management underestimated demand by 50% D = 1,000 units Q*= 200 units S = $10 per orderN= 5 orders per year H = $.50 per unit per yearT= 50 days TC = S + H DQQ2 TC = ($10) + ($.50) = $75 + $50 = $125 1, ,500 units Total annual cost increases by only 25% 15

An EOQ Example Actual EOQ for new demand is units D = 1,000 units Q*= units S = $10 per orderN= 5 orders per year H = $.50 per unit per yearT= 50 days TC = S + H DQQ2 TC = ($10) + ($.50) 1, ,500 units TC = $ $61.24 = $ Only 2% less than the total cost of $125 when the order quantity was

Reorder Points  EOQ answers the “how much” question  The reorder point (ROP) tells when to order ROP = Lead time for a new order in days Demand per day = d x L d = D Number of working days in a year 17

Reorder Point Curve Q* ROP (units) Inventory level (units) Time (days) Figure 12.5 Lead time = L Slope = units/day = d 18

Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days ROP = d x L d = D Number of working days in a year = 8,000/250 = 32 units = 32 units per day x 3 days = 96 units 19

Production Order Quantity Model  Used when inventory builds up over a period of time after an order is placed  Used when units are produced and sold simultaneously 20

Production Order Quantity Model Inventory level Time Demand part of cycle with no production Part of inventory cycle during which production (and usage) is taking place t Maximum inventory Figure

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 = (Average inventory level) x Annual inventory holding cost Holding cost per unit per year = (Maximum inventory level)/2 Annual inventory level = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt 22

Production Order Quantity Example D =1,000 units p =8 units per day S =$10 d =4 units per day H =$0.50 per unit per year Q* = 2DS H[1 - (d/p)] = or 283 hubcaps Q* = = 80,000 2(1,000)(10) 0.50[1 - (4/8)] 23

Quantity Discount Models  Reduced prices are often available when larger quantities are purchased  Trade-off is between reduced product cost and increased holding cost Total cost = Setup cost + Holding cost + Product cost TC = S + H + PD DQQ2 24

Quantity Discount Models Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 no discount $ ,000 to 1,999 4$ ,000 and over 5$4.75 Table 12.2 A typical quantity discount schedule 25

Quantity Discount Models 1.For each discount, calculate Q* 2.If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount 3.Compute the total cost for each Q* or adjusted value from Step 2 4.Select the Q* that gives the lowest total cost Steps in analyzing a quantity discount 26

Quantity Discount Example Calculate Q* for every discount Q* = 2DS IP Q 1 * = = 700 cars/order 2(5,000)(49)(.2)(5.00) Q 2 * = = 714 cars/order 2(5,000)(49)(.2)(4.80) Q 3 * = = 718 cars/order 2(5,000)(49)(.2)(4.75) 27

Quantity Discount Example Calculate Q* for every discount Q* = 2DS IP Q 1 * = = 700 cars/order 2(5,000)(49)(.2)(5.00) Q 2 * = = 714 cars/order 2(5,000)(49)(.2)(4.80) Q 3 * = = 718 cars/order 2(5,000)(49)(.2)(4.75) 1,000 — adjusted 2,000 — adjusted 28

Quantity Discount Example Discount Number Unit Price Order Quantity Annual Product Cost Annual Ordering Cost Annual Holding Cost Total 1$ $25,000$350$350$25,700 2$4.801,000$24,000$245$480$24,725 3$4.752,000$23.750$122.50$950$24, Table 12.3 Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit 29

Probabilistic Models and Safety Stock  Used when demand is not constant or certain  Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the number of orders per year 30

Safety Stock Example Number of Units Probability ROP  ROP = 50 unitsStockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year 31

Safety Stock Example ROP = 50 unitsStockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Safety Stock Additional Holding Cost Stockout Cost Total Cost 20 (20)($5) = $100 $0$ (10)($5) = $ 50 (10)(.1)($40)(6)=$240 $290 0 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6)=$960 $960 A safety stock of 20 frames gives the lowest total cost ROP = = 70 frames 32

Safety stock16.5 units ROP  Place order Probabilistic Demand Inventory level Time 0 Minimum demand during lead time Maximum demand during lead time Mean demand during lead time Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) ROP = safety stock of 16.5 = Receive order Lead time Figure

Probabilistic Demand Safety stock Probability of no stockout 95% of the time Mean demand 350 ROP = ? kits Quantity Number of standard deviations 0 z Risk of a stockout (5% of area of normal curve) 34

Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + Z  dLT whereZ =number of standard deviations  dLT =standard deviation of demand during lead time 35

Summary of this Session  Inventory Models for Independent Demand  The Basic Economic Order Quantity (EOQ) Model  Minimizing Costs  Reorder Points  Production Order Quantity Model  Quantity Discount Models 36

Summary of this Session (Contd.)  Probabilistic Models and Safety Stock 37

THANK YOU 38