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- 1. 10/16/2010 Inventory 12 Management Global Company Profile: Outline Amazon.com The Importance of Inventory PowerPoint presentation to accompany Functions of Inventory Heizer and Render Operations Management, 10e Types of Inventory Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 1 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 2 Outline – Continued Outline – Continued Managing Inventory Inventory Models for Independent ABC Analysis Demand Record Accuracy The Basic Economic Order Quantity Cycle Counting (EOQ) Model Control of Service Inventories Minimizing Costs Inventory Models Reorder Points Production Order Quantity Model Independent vs. Dependent Demand Quantity Discount Models Holding, Ordering, and Setup Costs© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 3 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 4 Outline – Continued Learning Objectives When you complete this chapter you Probabilistic Models and Safety should be able to: Stock Other Probabilistic Models 1. Conduct an ABC analysis Single-Period Model 2. Explain and use cycle counting 3. Explain and use the EOQ model for Fixed-Period (P) Systems independent inventory demand 4. Compute a reorder point and safety stock© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 5 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 6 1
- 2. 10/16/2010 Learning Objectives Amazon.com When you complete this chapter you should be able to: Amazon.com started as a “virtual” retailer – no inventory, no 5. Apply the production order quantity warehouses, no overhead; just model computers taking orders to be filled by others 6. Explain and use the quantity discount model Growth has forced Amazon.com to 7. Understand service levels and become a world leader in probabilistic inventory models warehousing and inventory management© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 7 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 8 Amazon.com Amazon.com 1. Each order is assigned by computer to the closest distribution center that has 5. Crates arrive at central point where items the product(s) are boxed and labeled with new bar code 2. A “flow meister” at each distribution 6. Gift wrapping is done by hand at 30 center assigns work crews packages per hour 3. Lights indicate products that are to be 7. Completed boxes are packed, taped, picked and the light is reset weighed and labeled before leaving 4. Items are placed in crates on a conveyor, warehouse in a truck bar code scanners scan each item 15 8. Order arrives at customer within 2 - 3 times to virtually eliminate errors days© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 9 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 10 Inventory Management Importance of Inventory One of the most expensive assets The objective of inventory of many companies representing as management is to strike a balance much as 50% of total invested between inventory investment and capital it l customer service Operations managers must balance inventory investment and customer service© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 11 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 12 2
- 3. 10/16/2010 Functions of Inventory Types of Inventory Raw material 1. To decouple or separate various parts of the production process Purchased but not processed Work-in-process 2. To decouple the firm from Undergone some change but not completed fluctuations in demand and provide a stock of goods that will A function of cycle time for a product provide a selection for customers Maintenance/repair/operating (MRO) Necessary to keep machinery and 3. To take advantage of quantity processes productive discounts Finished goods 4. To hedge against inflation Completed product awaiting shipment© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 13 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 14 The Material Flow Cycle Managing Inventory Cycle time 1. How inventory items can be 95% 5% classified Input Wait for Wait to Move Wait in queue Setup Run Output 2. 2 How accurate inventory records inspection be moved time for operator time time can be maintained Figure 12.1© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 15 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 16 ABC Analysis ABC Analysis Divides inventory into three classes based on annual dollar volume Item Percent of Number of Annual Annual Percent of Annual Stock Items Volume Unit Dollar Dollar Class A - high annual dollar volume Number Stocked (units) x Cost = Volume Volume Class #10286 20% 1,000 $ 90.00 $ 90,000 38.8% A Class B - medium annual dollar #11526 500 154.00 77,000 33.2% 72% A volume #12760 1,550 17.00 26,350 11.3% B Class C - low annual dollar volume #10867 30% 350 42.86 15,001 6.4% 23% B Used to establish policies that focus #10500 1,000 12.50 12,500 5.4% B on the few critical parts and not the many trivial ones© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 17 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 18 3
- 4. 10/16/2010 ABC Analysis ABC Analysis Percent of annua dollar usage Percent of Percent of A Items Item Number of Annual Annual Annual 80 – Stock Items Volume Unit Dollar Dollar Number Stocked (units) x Cost = Volume Volume Class 70 – #12572 600 $ 14.17 $ 8,502 3.7% C 60 – 50 – al #14075 2,000 .60 1,200 .5% C 40 – #01036 50% 100 8.50 850 .4% 5% C 30 – #01307 1,200 .42 504 .2% C 20 – B Items #10572 250 .60 150 .1% C 10 – C Items 8,550 $232,057 100.0% 0 – | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percent of inventory items Figure 12.2© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 19 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 20 ABC Analysis ABC Analysis Other criteria than annual dollar Policies employed may include volume may be used More emphasis on supplier Anticipated engineering changes development for A items Delivery problems Tighter physical inventory control for A items Quality problems More care in forecasting A items High unit cost© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 21 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 22 Record Accuracy Cycle Counting Accurate records are a critical Items are counted and records updated ingredient in production and inventory on a periodic basis systems Often used with ABC analysis Allows organization to focus on what to determine cycle is needed Has several advantages Necessary to make precise decisions 1. Eliminates shutdowns and interruptions about ordering, scheduling, and 2. Eliminates annual inventory adjustment shipping 3. Trained personnel audit inventory accuracy Incoming and outgoing record 4. Allows causes of errors to be identified and keeping must be accurate corrected Stockrooms should be secure 5. Maintains accurate inventory records© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 23 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 24 4
- 5. 10/16/2010 Cycle Counting Example Control of Service Inventories 5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Can be a critical component Policy is to count A items every month (20 working days), B of profitability items every quarter (60 days), and C items every six months (120 days) Losses may come from shrinkage or pilferage Item Number of Items Class Quantity Cycle Counting Policy Counted per Day Applicable techniques include A 500 Each month 500/20 = 25/day 1. Good personnel selection, training, and B 1,750 Each quarter 1,750/60 = 29/day discipline C 2,750 Every 6 months 2,750/120 = 23/day 2. Tight control on incoming shipments 77/day 3. Effective control on all goods leaving facility© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 25 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 26 Independent Versus Holding, Ordering, and Dependent Demand Setup Costs Independent demand - the Holding costs - the costs of holding demand for item is independent or “carrying” inventory over time o t e de a d o a y other of the demand for any ot e Ordering costs - the costs of item in inventory placing an order and receiving Dependent demand - the goods demand for item is dependent Setup costs - cost to prepare a upon the demand for some machine or process for other item in the inventory manufacturing an order© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 27 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 28 Holding Costs Holding Costs Cost (and range) Cost (and range) as a Percent of as a Percent of Category Inventory Value Category Inventory Value Housing costs (building rent or 6% (3 - 10%) Housing costs (building rent or 6% (3 - 10%) depreciation, operating costs, taxes, depreciation, operating costs, taxes, insurance) insurance) Material handling costs (equipment lease or 3% (1 - 3.5%) Material handling costs (equipment lease or 3% (1 - 3.5%) depreciation, power, operating cost) depreciation, power, operating cost) Labor cost 3% (3 - 5%) Labor cost 3% (3 - 5%) Investment costs (borrowing costs, taxes, 11% (6 - 24%) Investment costs (borrowing costs, taxes, 11% (6 - 24%) and insurance on inventory) and insurance on inventory) Pilferage, space, and obsolescence 3% (2 - 5%) Pilferage, space, and obsolescence 3% (2 - 5%) Overall carrying cost 26% Overall carrying cost 26% Table 12.1 Table 12.1© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 29 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 30 5
- 6. 10/16/2010 Inventory Models for Basic EOQ Model Independent Demand Important assumptions 1. Demand is known, constant, and Need to determine when and how independent much to order 2. Lead time is known and constant 3. Receipt of inventory is instantaneous and 1. Basic economic order quantity complete 2. Production order quantity 4. Quantity discounts are not possible 3. Quantity discount model 5. Only variable costs are setup and holding 6. Stockouts can be completely avoided© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 31 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 32 Inventory Usage Over Time Minimizing Costs Objective is to minimize total costs Usage rate Average Total cost of Order inventory holding and quantity = Q setup (order) Inventor level on hand (maximum inventory Q Minimum ry level) 2 total t t l cost t Annual cost Holding cost Minimum inventory Setup (or order) 0 cost Time Optimal order Order quantity quantity (Q*) Figure 12.3 Table 12.4(c)© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 33 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 34 The EOQ Model setup cost = Q S Annual D The EOQ Model setup cost = Q S Annual D Q Q = Number of pieces per order Q = Number of pieces per order Annual holding cost = H 2 Q* = Optimal number of pieces per order (EOQ) Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item D = Annual demand in units for the inventory item S = Setup or ordering cost for each order S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year H = Holding or carrying cost per unit per year Annual setup cost = (Number of orders placed per year) Annual holding cost = (Average inventory level) x (Setup or order cost per order) x (Holding cost per unit per year) Annual demand Setup or order Order quantity = = (Holding cost per unit per year) Number of units in each order cost per order 2 D (S) Q (H) = = Q 2© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 35 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 36 6
- 7. 10/16/2010 The EOQ Model setup cost = Q S Annual D An EOQ Example Q Q = Number of pieces per order Annual holding cost = H 2 Q* = Optimal number of pieces per order (EOQ) Determine optimal number of needles to order D = Annual demand in units for the inventory item D = 1,000 units S = Setup or ordering cost for each order S = $10 per order H = Holding or carrying cost per unit per year H = $.50 per unit per year Optimal d O ti l order quantity is found when annual setup cost tit i f d h l t t equals annual holding cost 2DS Q* = D S = Q H H Q 2 Solving for Q* 2(1,000)(10) 2DS = Q2H Q* = = 40,000 = 200 units Q2 = 2DS/H 0.50 Q* = 2DS/H© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 37 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 38 An EOQ Example An EOQ Example Determine optimal number of needles to order Determine optimal number of needles to order D = 1,000 units Q* = 200 units D = 1,000 units Q* = 200 units S = $10 per order S = $10 per order N = 5 orders per year H = $.50 per unit per year H = $.50 per unit per year Expected Number of working Demand D Expected days per year number of = N = = time between = T = orders Order quantity Q* orders N 1,000 250 N= = 5 orders per year 200 T= = 50 days between orders 5© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 39 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 40 An EOQ Example Robust Model Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year The EOQ model is robust H = $.50 per unit per year T = 50 days It works even if all parameters Total annual cost = Setup cost + Holding cost and assumptions are not met TC = D S + Q H The total cost curve is relatively Q 2 flat in the area of the EOQ 1,000 200 TC = ($10) + ($.50) 200 2 TC = (5)($10) + (100)($.50) = $50 + $50 = $100© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 41 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 42 7
- 8. 10/16/2010 An EOQ Example An EOQ Example Management underestimated demand by 50% Actual EOQ for new demand is 244.9 units D = 1,000 units 1,500 units Q* = 200 units D = 1,000 units 1,500 units Q* = 244.9 units S = $10 per order N = 5 orders per year S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days H = $.50 per unit per year T = 50 days D Q D Q TC = S + H TC = S + H Q 2 Q 2 Only 2% less 1,500 200 1,500 244.9 than the total TC = ($10) + ($.50) = $75 + $50 = $125 TC = ($10) + ($.50) cost of $125 200 2 244.9 2 when the TC = $61.24 + $61.24 = $122.48 order quantity Total annual cost increases by only 25% was 200© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 43 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 44 Reorder Points Reorder Point Curve EOQ answers the “how much” question Q* Inventory level (units) Resupply takes place as order arrives The reorder point (ROP) tells “when” to order Slope = units/day = d Demand Lead time for a ROP = per day new order in days ROP (units) =dxL D d = Number of working days in a year Time (days) Lead time = L Figure 12.5© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 45 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 46 Reorder Point Example Production Order Quantity Model Demand = 8,000 iPods per year 250 working day year Used when inventory builds up Lead time for orders is 3 working days over a period of time after an d= D order is placed Number of working days in a year Used when units are produced = 8,000/250 = 32 units and sold simultaneously ROP = d x L = 32 units per day x 3 days = 96 units© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 47 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 48 8
- 9. 10/16/2010 Production Order Quantity Production Order Quantity Model Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate Part of inventory cycle during which production (and usage) t = Length of the production run in days is taking place Inventory level Annual inventory Holding cost holding cost = (Average inventory level) x per unit per year l Demand part of cycle with no production Maximum inventory Annual inventory = (Maximum inventory level)/2 level Maximum Total produced during Total used during = – t inventory level the production run the production run Time = pt – dt Figure 12.6© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 49 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 50 Production Order Quantity Production Order Quantity Model Model Q = Number of pieces per order p = Daily production rate Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days D = Annual demand Maximum = Total produced during – Total used during Setup cost = (D/Q)S inventory level i t l l the th production run d ti the th production run d ti Holding cost = 1 HQ[1 - (d/p)] = pt – dt 2 However, Q = total produced = pt ; thus t = Q/p 1 (D/Q)S = 2 HQ[1 - (d/p)] Maximum Q Q d 2DS inventory level = p p –d p =Q 1– p Q2 = H[1 - (d/p)] Maximum inventory level Q d 2DS Holding cost = (H) = 1– H 2 2 p Q* = p H[1 - (d/p)]© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 51 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 52 Production Order Quantity Production Order Quantity Example Model D = 1,000 units p = 8 units per day Note: S = $10 d = 4 units per day D 1,000 H = $0.50 per unit per year d = 4 = Number of days the plant is in operation = 250 2DS Q* = H[1 - (d/p)] When annual data are used the equation becomes 2(1,000)(10) 2DS Q* = = 80,000 Q* = 0.50[1 - (4/8)] annual demand rate H 1– annual production rate = 282.8 or 283 hubcaps© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 53 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 54 9
- 10. 10/16/2010 Quantity Discount Models Quantity Discount Models Reduced prices are often available when A typical quantity discount schedule larger quantities are purchased Trade-off is between reduced product cost Discount Discount and increased holding cost Number Discount Quantity Discount (%) Price (P) 1 0 to 999 no discount $5.00 Total cost = Setup cost + Holding cost + Product cost 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75 D Q TC = S+ H + PD Q 2 Table 12.2© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 55 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 56 Quantity Discount Models Quantity Discount Models Steps in analyzing a quantity discount Total cost curve for discount 2 Total cost curve for 1. For each discount, calculate Q* discount 1 2. If Q* for a discount doesn’t qualify, y Total cost $ t choose the smallest possible order size to get the discount Total cost curve for discount 3 b 3. Compute the total cost for each Q* or a Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b adjusted value from Step 2 1st price 2nd price 4. Select the Q* that gives the lowest total break break cost 0 1,000 2,000 Figure 12.7 Order quantity© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 57 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 58 Quantity Discount Example Quantity Discount Example Calculate Q* for every discount 2DS Calculate Q* for every discount 2DS Q* = Q* = IP IP 2(5,000)(49) 2(5,000)(49) Q1* = = 700 cars/order Q1* = = 700 cars/order (.2)(5.00) ( 2)(5 00) (.2)(5.00) ( 2)(5 00) 2(5,000)(49) 2(5,000)(49) Q2* = = 714 cars/order Q2* = = 714 cars/order (.2)(4.80) (.2)(4.80) 1,000 — adjusted 2(5,000)(49) 2(5,000)(49) Q3* = = 718 cars/order Q3* = = 718 cars/order (.2)(4.75) (.2)(4.75) 2,000 — adjusted© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 59 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 60 10
- 11. 10/16/2010 Quantity Discount Example Probabilistic Models and Safety Stock Discount Unit Order Annual Product Annual Ordering Annual Holding Used when demand is not constant Number Price Quantity Cost Cost Cost Total or certain 1 $5.00 700 $25,000 $350 $350 $25,700 Use safety stock to achieve a desired 2 $4.80 1,000 $24,000 $245 $480 $24,725 service level and avoid stockouts 3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50 ROP = d x L + ss Table 12.3 Choose the price and quantity that gives Annual stockout costs = the sum of the units short the lowest total cost x the probability x the stockout cost/unit Buy 1,000 units at $4.80 per unit x the number of orders per year© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 61 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 62 Safety Stock Example Safety Stock Example ROP = 50 units Stockout cost = $40 per frame ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Orders per year = 6 Carrying cost = $5 per frame per year Safety Additional Total Number of Units Probability Stock Holding Cost Stockout Cost Cost 30 .2 20 (20)($5) = $100 $0 $100 40 .2 10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290 ROP 50 .3 0 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960 60 .2 70 .1 A safety stock of 20 frames gives the lowest total cost 1.0 ROP = 50 + 20 = 70 frames© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 63 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 64 Probabilistic Demand Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be Minimum demand during lead time determined Inventory level Maximum demand during lead time y Mean demand during lead time ROP = 350 + safety stock of 16.5 = 366.5 ROP = demand during lead time + ZσdLT ROP Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) where Z = number of standard deviations Safety stock 16.5 units σdLT = standard deviation of demand 0 Lead during lead time time Time Figure 12.8 Place Receive order order© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 65 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 66 11
- 12. 10/16/2010 Probabilistic Demand Probabilistic Example Average demand = μ = 350 kits Standard deviation of demand during lead time = σdLT = 10 kits 5% stockout policy (service level = 95%) Probability of Risk of a stockout no stockout (5% of area of 95% of the time normal curve)) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = ZσdLT = 1.65(10) = 16.5 kits Mean ROP = ? kits Quantity demand Reorder point = expected demand during lead time 350 Safety + safety stock stock = 350 kits + 16.5 kits of safety stock 0 z Number of = 366.5 or 367 kits standard deviations© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 67 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 68 Other Probabilistic Models Other Probabilistic Models When data on demand during lead time is Demand is variable and lead time is constant not available, there are other models available ROP = (average daily demand 1. 1 When demand is variable and lead x lead time in days) + ZσdLT time is constant where σd = standard deviation of demand per day 2. When lead time is variable and σdLT = σd lead time demand is constant 3. When both demand and lead time are variable© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 69 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 70 Probabilistic Example Other Probabilistic Models Average daily demand (normally distributed) = 15 Lead time is variable and demand is constant Standard deviation = 5 Lead time is constant at 2 days Z for 90% = 1.28 90% service level desired From Appendix I ROP = (daily demand x average lead time in days) ROP = (15 units x 2 days) + ZσdLT = Z x (daily demand) x σLT = 30 + 1.28(5)( 2) where σLT = standard deviation of lead time in days = 30 + 9.02 = 39.02 ≈ 39 Safety stock is about 9 iPods© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 71 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 72 12
- 13. 10/16/2010 Probabilistic Example Other Probabilistic Models Z for 98% = 2.055 Both demand and lead time are variable Daily demand (constant) = 10 From Appendix I Average lead time = 6 days Standard deviation of lead time = σLT = 3 ROP = (average daily demand 98% service level desired x average lead time) + ZσdLT ROP = (10 units x 6 days) + 2.055(10 units)(3) where σd = standard deviation of demand per day = 60 + 61.65 = 121.65 σLT = standard deviation of lead time in days σdLT = (average lead time x σd2) Reorder point is about 122 cameras + (average daily demand)2 x σLT2© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 73 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 74 Probabilistic Example Single Period Model Average daily demand (normally distributed) = 150 Only one order is placed for a product Standard deviation = σd = 16 Average lead time 5 days (normally distributed) Units have little or no value at the end of Standard deviation = σLT = 1 day the sales period 95% service level desired Z for 95% = 1.65 1 65 From Appendix I Cs = Cost of shortage = Sales price/unit – Cost/unit Co = Cost of overage = Cost/unit – Salvage value ROP = (150 packs x 5 days) + 1.65σdLT = (150 x 5) + 1.65 (5 days x + 162) (1502 x 1 2) Cs = 750 + 1.65(154) = 1,004 packs Service level = Cs + Co© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 75 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 76 Single Period Example Single Period Example Average demand = μ = 120 papers/day Standard deviation = σ = 15 papers From Appendix I, for the area .578, Z ≅ .20 Cs = cost of shortage = $1.25 - $.70 = $.55 The optimal stocking level Co = cost of overage = $.70 - $.30 = $.40 = 120 copies + (.20)(σ) Cs Service level = = 120 + (.20)(15) = 120 + 3 = 123 papers Cs + Co Service .55 level = 57.8% The stockout risk = 1 – service level .55 + .40 .55 = 1 – .578 = .422 = 42.2% = = .578 μ = 120 .95 Optimal stocking level© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 77 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 78 13
- 14. 10/16/2010 Fixed- Fixed-Period (P) Systems Fixed- Fixed-Period (P) Systems Target quantity (T) Orders placed at the end of a fixed period Inventory counted only at end of period Q2 Q4 On-hand inventory Order brings inventory up to target level g y p g Q1 P Q3 Only relevant costs are ordering and holding P Lead times are known and constant Items are independent from one another P Time Figure 12.9© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 79 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 80 Fixed- Fixed-Period (P) Example Fixed- Fixed-Period Systems 3 jackets are back ordered No jackets are in stock It is time to place an order Target value = 50 Inventory is only counted at each review period Order amount (Q) = Target (T) - On On- May be scheduled at convenient times y hand inventory - Earlier orders not yet Appropriate in routine situations received + Back orders May result in stockouts between Q = 50 - 0 - 0 + 3 = 53 jackets periods May require increased safety stock© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 81 © 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 82 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.© 2011 Pearson Education, Inc. publishing as Prentice Hall 12 - 83 14

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