Uploaded byAxelBlaze62
PPTX, PDF167 views

Inventory.pptx

This document outlines key concepts related to inventory management. It begins with an overview of inventory management at Amazon, noting how Amazon has transitioned from a virtual retailer to a leader in warehousing and inventory management. It then discusses the economic order quantity (EOQ) model, which aims to minimize total inventory costs by balancing ordering and holding costs. The optimal order quantity is derived using the formula that sets ordering and holding costs equal. An example demonstrates how to apply the EOQ model to determine the optimal order quantity, expected number of orders per year, and time between orders.

Embed presentation

Download to read offline
12 - 1 © 2014 Pearson Education, Inc. Inventory Management PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh Edition Principles of Operations Management, Ninth Edition PowerPoint slides by Jeff Heyl 12 © 2014 Pearson Education, Inc.
12 - 2 © 2014 Pearson Education, Inc. Outline ► Global Company Profile: Amazon.com ► The Importance of Inventory ► Managing Inventory ► Inventory Models ► Inventory Models for Independent Demand
12 - 3 © 2014 Pearson Education, Inc. Outline - Continued ► Probabilistic Models and Safety Stock ► Single-Period Model ► Fixed-Period (P) Systems
12 - 4 © 2014 Pearson Education, Inc. Learning Objectives When you complete this chapter you should be able to: 1. Conduct an ABC analysis 2. Explain and use cycle counting 3. Explain and use the EOQ model for independent inventory demand 4. Compute a reorder point and safety stock
12 - 5 © 2014 Pearson Education, Inc. Learning Objectives When you complete this chapter you should be able to: 5. Apply the production order quantity model 6. Explain and use the quantity discount model 7. Understand service levels and probabilistic inventory models
12 - 6 © 2014 Pearson Education, Inc. Inventory Management at Amazon.com ► Amazon.com started as a “virtual” retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled by others ► Growth has forced Amazon.com to become a world leader in warehousing and inventory management © 2014 Pearson Education, Inc.
12 - 7 © 2014 Pearson Education, Inc. Inventory Management at Amazon.com 1.Each order is assigned by computer to the closest distribution center that has the product(s) 2.A “flow meister” at each distribution center assigns work crews 3.Lights indicate products that are to be picked and the light is reset 4.Items are placed in crates on a conveyor, bar code scanners scan each item 15 times to virtually eliminate errors © 2014 Pearson Education, Inc.
12 - 8 © 2014 Pearson Education, Inc. Inventory Management at Amazon.com 5. Crates arrive at central point where items are boxed and labeled with new bar code 6. Gift wrapping is done by hand at 30 packages per hour 7. Completed boxes are packed, taped, weighed and labeled before leaving warehouse in a truck 8. Order arrives at customer within 1 - 2 days © 2014 Pearson Education, Inc.
12 - 9 © 2014 Pearson Education, Inc. Inventory Management The objective of inventory management is to strike a balance between inventory investment and customer service
12 - 10 © 2014 Pearson Education, Inc. Importance of Inventory ▶One of the most expensive assets of many companies representing as much as 50% of total invested capital ▶Operations managers must balance inventory investment and customer service
12 - 11 © 2014 Pearson Education, Inc. Functions of Inventory 1. To provide a selection of goods for anticipated demand and to separate the firm from fluctuations in demand 2. To decouple or separate various parts of the production process 3. To take advantage of quantity discounts 4. To hedge against inflation
12 - 12 © 2014 Pearson Education, Inc. Types of Inventory ▶Raw material ▶Purchased but not processed ▶Work-in-process (WIP) ▶Undergone some change but not completed ▶A function of cycle time for a product ▶Maintenance/repair/operating (MRO) ▶Necessary to keep machinery and processes productive ▶Finished goods ▶Completed product awaiting shipment
12 - 13 © 2014 Pearson Education, Inc. The Material Flow Cycle Figure 12.1 Input Wait for Wait to Move Wait in queue Setup Run Output inspection be moved time for operator time time Cycle time 95% 5%
12 - 14 © 2014 Pearson Education, Inc. Managing Inventory 1. How inventory items can be classified (ABC analysis) 2. How accurate inventory records can be maintained
12 - 15 © 2014 Pearson Education, Inc. ABC Analysis ▶Divides inventory into three classes based on annual dollar volume ▶Class A - high annual dollar volume ▶Class B - medium annual dollar volume ▶Class C - low annual dollar volume ▶Used to establish policies that focus on the few critical parts and not the many trivial ones
12 - 16 © 2014 Pearson Education, Inc. ABC Analysis ABC Calculation (1) (2) (3) (4) (5) (6) (7) ITEM STOCK NUMBER PERCENT OF NUMBER OF ITEMS STOCKED ANNUAL VOLUME (UNITS) x UNIT COST = ANNUAL DOLLAR VOLUME PERCENT OF ANNUAL DOLLAR VOLUME CLASS #10286 20% 1,000 $ 90.00 $ 90,000 38.8% A #11526 500 154.00 77,000 33.2% A #12760 1,550 17.00 26,350 11.3% B #10867 30% 350 42.86 15,001 6.4% B #10500 1,000 12.50 12,500 5.4% B #12572 600 $ 14.17 $ 8,502 3.7% C #14075 2,000 .60 1,200 .5% C #01036 50% 100 8.50 850 .4% C #01307 1,200 .42 504 .2% C #10572 250 .60 150 .1% C 8,550 $232,057 100.0% 72% 23% 5%
12 - 17 © 2014 Pearson Education, Inc. ABC Analysis A Items B Items | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percentage of annual dollar usage 80 – 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Percentage of inventory items Figure 12.2 C Items
12 - 18 © 2014 Pearson Education, Inc. ABC Analysis ▶ Other criteria than annual dollar volume may be used ▶ High shortage or holding cost ▶ Anticipated engineering changes ▶ Delivery problems ▶ Quality problems
12 - 19 © 2014 Pearson Education, Inc. ABC Analysis ▶Policies employed may include 1. More emphasis on supplier development for A items 2. Tighter physical inventory control for A items 3. More care in forecasting A items
12 - 20 © 2014 Pearson Education, Inc. Record Accuracy ► Accurate records are a critical ingredient in production and inventory systems ► Periodic systems require regular checks of inventory ► Two-bin system ► Perpetual inventory tracks receipts and subtractions on a continuing basis ► May be semi-automated
12 - 21 © 2014 Pearson Education, Inc. Record Accuracy ► Incoming and outgoing record keeping must be accurate ► Stockrooms should be secure ► Necessary to make precise decisions about ordering, scheduling, and shipping
12 - 22 © 2014 Pearson Education, Inc. Cycle Counting ▶Items are counted and records updated on a periodic basis ▶Often used with ABC analysis ▶Has several advantages 1. Eliminates shutdowns and interruptions 2. Eliminates annual inventory adjustment 3. Trained personnel audit inventory accuracy 4. Allows causes of errors to be identified and corrected 5. Maintains accurate inventory records
12 - 23 © 2014 Pearson Education, Inc. Cycle Counting Example 5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) ITEM CLASS QUANTITY CYCLE COUNTING POLICY NUMBER OF ITEMS COUNTED PER DAY A 500 Each month 500/20 = 25/day B 1,750 Each quarter 1,750/60 = 29/day C 2,750 Every 6 months 2,750/120 = 23/day 77/day
12 - 24 © 2014 Pearson Education, Inc. Control of Service Inventories ▶Can be a critical component of profitability ▶Losses may come from shrinkage or pilferage ▶Applicable techniques include 1. Good personnel selection, training, and discipline 2. Tight control of incoming shipments 3. Effective control of all goods leaving facility
12 - 25 © 2014 Pearson Education, Inc. Inventory Models ▶Independent demand - the demand for item is independent of the demand for any other item in inventory ▶Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory
12 - 26 © 2014 Pearson Education, Inc. Inventory Models ▶Holding costs - the costs of holding or “carrying” inventory over time ▶Ordering costs - the costs of placing an order and receiving goods ▶Setup costs - cost to prepare a machine or process for manufacturing an order ▶May be highly correlated with setup time
12 - 27 © 2014 Pearson Education, Inc. Holding Costs TABLE 12.1 Determining Inventory Holding Costs CATEGORY COST (AND RANGE) AS A PERCENT OF INVENTORY VALUE Housing costs (building rent or depreciation, operating costs, taxes, insurance) 6% (3 - 10%) Material handling costs (equipment lease or depreciation, power, operating cost) 3% (1 - 3.5%) Labor cost (receiving, warehousing, security) 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) 11% (6 - 24%) Pilferage, space, and obsolescence (much higher in industries undergoing rapid change like PCs and cell phones) 3% (2 - 5%) Overall carrying cost 26%
12 - 28 © 2014 Pearson Education, Inc. Holding Costs TABLE 12.1 Determining Inventory Holding Costs CATEGORY COST (AND RANGE) AS A PERCENT OF INVENTORY VALUE Housing costs (building rent or depreciation, operating costs, taxes, insurance) 6% (3 - 10%) Material handling costs (equipment lease or depreciation, power, operating cost) 3% (1 - 3.5%) Labor cost (receiving, warehousing, security) 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) 11% (6 - 24%) Pilferage, space, and obsolescence (much higher in industries undergoing rapid change like PCs and cell phones) 3% (2 - 5%) Overall carrying cost 26%
12 - 29 © 2014 Pearson Education, Inc. Inventory Models for Independent Demand Need to determine when and how much to order 1. Basic economic order quantity (EOQ) model 2. Production order quantity model 3. Quantity discount model
12 - 30 © 2014 Pearson Education, Inc. Basic EOQ Model 1. Demand is known, constant, and independent 2. Lead time is known and constant 3. Receipt of inventory is instantaneous and complete 4. Quantity discounts are not possible 5. Only variable costs are setup (or ordering) and holding 6. Stockouts can be completely avoided Important assumptions
12 - 31 © 2014 Pearson Education, Inc. Inventory Usage Over Time Figure 12.3 Order quantity = Q (maximum inventory level) Usage rate Average inventory on hand Q 2 Minimum inventory Inventory level Time 0 Total order received
12 - 32 © 2014 Pearson Education, Inc. Minimizing Costs Objective is to minimize total costs Table 12.4(c) Annual cost Order quantity Total cost of holding and setup (order) Holding cost Setup (order) cost Minimum total cost Optimal order quantity (Q*)
12 - 33 © 2014 Pearson Education, Inc. Minimizing Costs ▶By minimizing the sum of setup (or ordering) and holding costs, total costs are minimized ▶Optimal order size Q* will minimize total cost ▶A reduction in either cost reduces the total cost ▶Optimal order quantity occurs when holding cost and setup cost are equal
12 - 34 © 2014 Pearson Education, Inc. Minimizing Costs 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 = = D Q æ è ç ö ø ÷S Annual setup cost = D Q S
12 - 35 © 2014 Pearson Education, Inc. 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 Minimizing Costs Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity 2 (Holding cost per unit per year) = = Q 2 æ è ç ö ø ÷H Annual setup cost = D Q S Annual holding cost = Q 2 H
12 - 36 © 2014 Pearson Education, Inc. Minimizing Costs D Q S = Q 2 æ è ç ö ø ÷H Optimal order quantity is found when annual setup cost equals annual holding cost Solving for Q* 2DS = Q2 H Q2 = 2DS H Q* = 2DS H 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 = D Q S Annual holding cost = Q 2 H
12 - 37 © 2014 Pearson Education, Inc. 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
12 - 38 © 2014 Pearson Education, Inc. An EOQ Example Determine expected number of orders D = 1,000 units Q* = 200 units S = $10 per order H = $.50 per unit per year N = = 5 orders per year 1,000 200 = N = = Expected number of orders Demand Order quantity D Q*
12 - 39 © 2014 Pearson Education, Inc. An EOQ Example Determine optimal time between orders D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders/year H = $.50 per unit per year T = = 50 days between orders 250 5 = T = Expected time between orders Number of working days per year Expected number of orders
12 - 40 © 2014 Pearson Education, Inc. An EOQ Example Determine the total annual cost D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders/year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC = D Q S + Q 2 H = 1,000 200 ($10)+ 200 2 ($.50) = (5)($10)+(100)($.50) = $50+$50 = $100
12 - 41 © 2014 Pearson Education, Inc. The EOQ Model When including actual cost of material P Total annual cost = Setup cost + Holding cost + Product cost TC = D Q S + Q 2 H + PD
12 - 42 © 2014 Pearson Education, Inc. 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
12 - 43 © 2014 Pearson Education, Inc. An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders/year H = $.50 per unit per year T = 50 days TC = D Q S + Q 2 H = 1,500 200 ($10)+ 200 2 ($.50) = $75+$50 = $125 1,500 units = 1,500 244.9 ($10)+ 244.9 2 ($.50) = 6.125($10)+122.45($.50) = $61.25+$61.22 = $122.47 Only 2% less than the total cost of $125 when the order quantity was 200
12 - 44 © 2014 Pearson Education, Inc. Reorder Points ▶ EOQ answers the “how much” question ▶ The reorder point (ROP) tells “when” to order ▶ Lead time (L) is the time between placing and receiving an 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
12 - 45 © 2014 Pearson Education, Inc. Reorder Point Curve Q* ROP (units) Inventory level (units) Time (days) Figure 12.5 Lead time = L Slope = units/day = d Resupply takes place as order arrives
12 - 46 © 2014 Pearson Education, Inc. Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days, may take 4 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 = 32 units per day x 4 days = 128 units
12 - 47 © 2014 Pearson Education, Inc. Production Order Quantity Model 1. Used when inventory builds up over a period of time after an order is placed 2. Used when units are produced and sold simultaneously Inventory level Time Demand part of cycle with no production (only usage) Part of inventory cycle during which production (and usage) is taking place t Maximum inventory Figure 12.6
12 - 48 © 2014 Pearson Education, Inc. 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
12 - 49 © 2014 Pearson Education, Inc. 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 inventory level Total produced during the production run Total used during the production run = pt – dt However, Q = total produced = pt ; thus t = Q/p Maximum inventory level = p – d = Q 1 – Q p Q p d p Holding cost = (H) = 1 – H d p Q 2 Maximum inventory level 2
12 - 50 © 2014 Pearson Education, Inc. 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 Setup cost = (D / Q)S Holding cost = 1 2 HQ 1- d p ( ) é ë ù û D Q S = 1 2 HQ 1- d p ( ) é ë ù û Q2 = 2DS H 1- d p ( ) é ë ù û Qp * = 2DS H 1- d p ( ) é ë ù û
12 - 51 © 2014 Pearson Education, Inc. 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 Qp * = 2DS H 1- d p ( ) é ë ù û Qp * = 2(1,000)(10) 0.50 1-(4 8) é ë ù û = 20,000 0.50(1 2) = 80,000 = 282.8 hubcaps, or 283 hubcaps
12 - 52 © 2014 Pearson Education, Inc. Production Order Quantity Model When annual data are used the equation becomes Note: d = 4 = = D Number of days the plant is in operation 1,000 250 Qp * = 2DS H 1- Annual demand rate Annual production rate æ è ç ö ø ÷
12 - 53 © 2014 Pearson Education, Inc. Quantity Discount Models ▶Reduced prices are often available when larger quantities are purchased ▶Trade-off is between reduced product cost and increased holding cost TABLE 12.2 A Quantity Discount Schedule DISCOUNT NUMBER DISCOUNT QUANTITY DISCOUNT (%) DISCOUNT PRICE (P) 1 0 to 999 no discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75
12 - 54 © 2014 Pearson Education, Inc. Quantity Discount Models Q* = 2DS IP Total annual cost = Setup cost + Holding cost + Product cost TC = D Q S + Q 2 H + PD where Q = Quantity ordered P = Price per unit D = Annual demand in units H = Holding cost per unit per year S = Ordering or setup cost per order Because unit price varies, holding cost (H) is expressed as a percent (I) of unit price (P)
12 - 55 © 2014 Pearson Education, Inc. Quantity Discount Models Steps in analyzing a quantity discount 1. For each discount, calculate Q* 2. If Q* for a discount doesn’t qualify, choose the lowest possible quantity 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
12 - 56 © 2014 Pearson Education, Inc. Quantity Discount Models 1,000 2,000 Total cost $ 0 Order quantity Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b a b 1st price break 2nd price break Total cost curve for discount 1 Total cost curve for discount 2 Total cost curve for discount 3 Figure 12.7
12 - 57 © 2014 Pearson Education, Inc. Quantity Discount Example Calculate Q* for every discount Q1* = = 700 cars/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 cars/order 2(5,000)(49) (.2)(4.80) Q3* = = 718 cars/order 2(5,000)(49) (.2)(4.75) Q* = 2DS IP
12 - 58 © 2014 Pearson Education, Inc. Quantity Discount Example Calculate Q* for every discount Q1* = = 700 cars/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 cars/order 2(5,000)(49) (.2)(4.80) Q3* = = 718 cars/order 2(5,000)(49) (.2)(4.75) Q* = 2DS IP 1,000 — adjusted 2,000 — adjusted
12 - 59 © 2014 Pearson Education, Inc. Quantity Discount Example TABLE 12.3 Total Cost Computations for Wohl’s Discount Store DISCOUNT NUMBER UNIT PRICE ORDER QUANTITY ANNUAL PRODUCT COST ANNUAL ORDERING COST ANNUAL HOLDING COST TOTAL 1 $5.00 700 $25,000 $350 $350 $25,700 2 $4.80 1,000 $24,000 $245 $480 $24,725 3 $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
12 - 60 © 2014 Pearson Education, Inc. 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
12 - 61 © 2014 Pearson Education, Inc. Safety Stock Example NUMBER OF UNITS PROBABILITY 30 .2 40 .2 ROP  50 .3 60 .2 70 .1 1.0 ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year
12 - 62 © 2014 Pearson Education, Inc. Safety Stock Example ROP = 50 units Stockout 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 $100 10 (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 = 50 + 20 = 70 frames
12 - 63 © 2014 Pearson Education, Inc. Safety stock 16.5 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 = 350 + safety stock of 16.5 = 366.5 Receive order Lead time Figure 12.8
12 - 64 © 2014 Pearson Education, Inc. Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + ZsdLT where Z = Number of standard deviations sdLT = Standard deviation of demand during lead time
12 - 65 © 2014 Pearson Education, Inc. 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)
12 - 66 © 2014 Pearson Education, Inc. Probabilistic Example m = Average demand = 350 kits sdLT = Standard deviation of demand during lead time = 10 kits Z = 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = ZsdLT = 1.65(10) = 16.5 kits Reorder point = Expected demand during lead time + Safety stock = 350 kits + 16.5 kits of safety stock = 366.5 or 367 kits
12 - 67 © 2014 Pearson Education, Inc. Other Probabilistic Models ▶When data on demand during lead time is not available, there are other models available 1. When demand is variable and lead time is constant 2. When lead time is variable and demand is constant 3. When both demand and lead time are variable
12 - 68 © 2014 Pearson Education, Inc. Other Probabilistic Models Demand is variable and lead time is constant ROP = (Average daily demand x Lead time in days) + ZsdLT where sdLT = sd Lead time sd = standard deviation of demand per day
12 - 69 © 2014 Pearson Education, Inc. Probabilistic Example Average daily demand (normally distributed) = 15 Lead time in days (constant) = 2 Standard deviation of daily demand = 5 Service level = 90% Z for 90% = 1.28 From Appendix I ROP = (15 units x 2 days) + ZsdLT = 30 + 1.28(5)( 2) = 30 + 9.02 = 39.02 ≈ 39 Safety stock is about 9 computers
12 - 70 © 2014 Pearson Education, Inc. Other Probabilistic Models Lead time is variable and demand is constant ROP = (Daily demand x Average lead time in days) + Z x (Daily demand) x sLT where sLT = Standard deviation of lead time in days
12 - 71 © 2014 Pearson Education, Inc. Probabilistic Example Daily demand (constant) = 10 Average lead time = 6 days Standard deviation of lead time = sLT = 1 Service level = 98%, so Z (from Appendix I) = 2.055 ROP = (10 units x 6 days) + 2.055(10 units)(1) = 60 + 20.55 = 80.55 Reorder point is about 81 cameras
12 - 72 © 2014 Pearson Education, Inc. Other Probabilistic Models Both demand and lead time are variable ROP = (Average daily demand x Average lead time) + ZsdLT where sd = Standard deviation of demand per day sLT = Standard deviation of lead time in days sdLT = (Average lead time x sd 2) + (Average daily demand)2s2 LT
12 - 73 © 2014 Pearson Education, Inc. Probabilistic Example Average daily demand (normally distributed) = 150 Standard deviation = sd = 16 Average lead time 5 days (normally distributed) Standard deviation = sLT = 1 day Service level = 95%, so Z = 1.65 (from Appendix I) ROP = (150 packs´5 days)+1.65sdLT sdLT = 5 days´162 ( )+ 1502 ´12 ( ) = 5´256 ( )+ 22,500´1 ( ) = 1,280 ( )+ 22,500 ( ) = 23,780 @154 ROP = (150´5)+1.65(154) @ 750+254 =1,004 packs
12 - 74 © 2014 Pearson Education, Inc. Single-Period Model ▶Only one order is placed for a product ▶Units have little or no value at the end of the sales period Cs = Cost of shortage = Sales price/unit – Cost/unit Co = Cost of overage = Cost/unit – Salvage value Service level = Cs Cs + Co
12 - 75 © 2014 Pearson Education, Inc. Single-Period Example Average demand = m = 120 papers/day Standard deviation = s = 15 papers Cs = cost of shortage = $1.25 – $.70 = $.55 Co = cost of overage = $.70 – $.30 = $.40 Service level = Cs Cs + Co = = = .579 .55 .55 + .40 .55 .95 Service level 57.9% Optimal stocking level m = 120
12 - 76 © 2014 Pearson Education, Inc. Single-Period Example From Appendix I, for the area .579, Z  .20 The optimal stocking level = 120 copies + (.20)(s) = 120 + (.20)(15) = 120 + 3 = 123 papers The stockout risk = 1 – Service level = 1 – .579 = .422 = 42.2%
12 - 77 © 2014 Pearson Education, Inc. Fixed-Period (P) Systems ▶Orders placed at the end of a fixed period ▶Inventory counted only at end of period ▶Order brings inventory up to target level ▶Only relevant costs are ordering and holding ▶Lead times are known and constant ▶Items are independent of one another
12 - 78 © 2014 Pearson Education, Inc. Fixed-Period (P) Systems On-hand inventory Time Q1 Q2 Target quantity (T) P Q3 Q4 P P Figure 12.9
12 - 79 © 2014 Pearson Education, Inc. Fixed-Period Systems ▶Inventory is only counted at each review period ▶May be scheduled at convenient times ▶Appropriate in routine situations ▶May result in stockouts between periods ▶May require increased safety stock
12 - 80 © 2014 Pearson Education, Inc. 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.

More Related Content

PPTX
Chopra Meindl Chapter 8
byRupam Jash l CSCA
 
PPTX
Supply Chain Management chap 12
byUmair Arain
 
PPTX
Supply Chain Management chap 17
byUmair Arain
 
PPTX
Chopra scm5 ch03_ge
byEmransiddique
 
PPTX
Chopra Meindl Chapter 7
byRupam Jash l CSCA
 
PPTX
Supply Chain Management chap 14
byUmair Arain
 
PPT
aggregate planning in the supply chain
byManish Kaushik
 
PPTX
Supply Chain Management chap 18
byUmair Arain
 
Chopra Meindl Chapter 8
byRupam Jash l CSCA
 
Supply Chain Management chap 12
byUmair Arain
 
Supply Chain Management chap 17
byUmair Arain
 
Chopra scm5 ch03_ge
byEmransiddique
 
Chopra Meindl Chapter 7
byRupam Jash l CSCA
 
Supply Chain Management chap 14
byUmair Arain
 
aggregate planning in the supply chain
byManish Kaushik
 
Supply Chain Management chap 18
byUmair Arain
 

What's hot

PPTX
Supply Chain Management chap 11
byUmair Arain
 
PDF
Supply chain slides
byPresident Career Development Academy
 
PPTX
Capacity planning
byAfendi Hassan
 
PPTX
Chopra Meindl Chapter 9
byRupam Jash l CSCA
 
PPTX
Supply Chain Management chap 13
byUmair Arain
 
PPTX
Chopra scm5 ch01_ge
byEmransiddique
 
PPT
Supply chain management ch05 chopra
byJamil Ahmed AKASH
 
PPTX
Supply Chain Management chap 15
byUmair Arain
 
PPT
Location Strategy
byJoanmaines
 
PPT
NETWORK DESIGN AND FACILITY LOCATION
byAshish Hande
 
PPTX
Issues and Trends in Supply Chain Management
byMiles Weaver
 
PPT
Scor
bydashinhotguy143
 
PPT
Chapter 9 layout strategies
byRAFIZA MOHD RADZI
 
PPTX
Supply Chain Management chap 17
byUmair Arain
 
PPTX
Supply Chain Management chap 1
byUmair Arain
 
PPTX
Supply Chain Management chap 6
byUmair Arain
 
PPTX
Chopra Meindl Chapter 5
byRupam Jash l CSCA
 
PPTX
Chopra Meindl Chapter 10
byRupam Jash l CSCA
 
PPTX
Supply chain management
byMohamed Effat
 
PPTX
Reorder point
byDon Paul
 
Supply Chain Management chap 11
byUmair Arain
 
Supply chain slides
byPresident Career Development Academy
 
Capacity planning
byAfendi Hassan
 
Chopra Meindl Chapter 9
byRupam Jash l CSCA
 
Supply Chain Management chap 13
byUmair Arain
 
Chopra scm5 ch01_ge
byEmransiddique
 
Supply chain management ch05 chopra
byJamil Ahmed AKASH
 
Supply Chain Management chap 15
byUmair Arain
 
Location Strategy
byJoanmaines
 
NETWORK DESIGN AND FACILITY LOCATION
byAshish Hande
 
Issues and Trends in Supply Chain Management
byMiles Weaver
 
Scor
bydashinhotguy143
 
Chapter 9 layout strategies
byRAFIZA MOHD RADZI
 
Supply Chain Management chap 17
byUmair Arain
 
Supply Chain Management chap 1
byUmair Arain
 
Supply Chain Management chap 6
byUmair Arain
 
Chopra Meindl Chapter 5
byRupam Jash l CSCA
 
Chopra Meindl Chapter 10
byRupam Jash l CSCA
 
Supply chain management
byMohamed Effat
 
Reorder point
byDon Paul
 

Similar to Inventory.pptx

PPT
Inventory Management.ppt
bySRIDEVIVVMSG
 
PPTX
Inventory Management didalam perusahaan indusrty
byNofrizalDewanto
 
PPTX
heizer_om12_ch012 final.pptx Inventory Inventory
bymohamedzakar1
 
PPTX
Ch12-Inventory.pptx
byDinesh Saini
 
PDF
Heizer om10 ch12
byryaekle
 
DOCX
12 - © 2014 Pearson Education, Inc.Inventory Mana.docx
byjesusamckone
 
PPT
Lecture 10_Inventory Management.ppt
byMaiLinh301193
 
PPT
hr_om11_ch12_Inventory hello management.ppt
byMaulikSidana
 
PPTX
INVENTORY MANAGEMENT.pptx
byJesilin James
 
PPT
Inventory control (management)
byManthan Chavda
 
PPTX
Inventory. management and cost control information
bymahmoudadel553505
 
PPTX
Chapter 6-Inventory Management ..........
byabubakarshakeel774
 
PPT
inventory management.ppt
bySandipanMaji3
 
PPTX
5 Inventory Models for teaching copy.pptx
bylindaduku4
 
PPT
4. inventory management
bySudipta Saha
 
DOCX
12 - © 2014 Pearson Education, Inc.Inventory Mana.docx
byaulasnilda
 
PPTX
Lesson 10 Inventory Management-Operationspptx
bykagorabasoma
 
PPTX
Inventory Management-53 slides.pptx
byTithiDas30
 
PDF
Ch_4.pdf
bykidusmesfin
 
PPTX
Inventory Management under OPERATIONS and SCM.pptx
byraddddzzzzzz
 
Inventory Management.ppt
bySRIDEVIVVMSG
 
Inventory Management didalam perusahaan indusrty
byNofrizalDewanto
 
heizer_om12_ch012 final.pptx Inventory Inventory
bymohamedzakar1
 
Ch12-Inventory.pptx
byDinesh Saini
 
Heizer om10 ch12
byryaekle
 
12 - © 2014 Pearson Education, Inc.Inventory Mana.docx
byjesusamckone
 
Lecture 10_Inventory Management.ppt
byMaiLinh301193
 
hr_om11_ch12_Inventory hello management.ppt
byMaulikSidana
 
INVENTORY MANAGEMENT.pptx
byJesilin James
 
Inventory control (management)
byManthan Chavda
 
Inventory. management and cost control information
bymahmoudadel553505
 
Chapter 6-Inventory Management ..........
byabubakarshakeel774
 
inventory management.ppt
bySandipanMaji3
 
5 Inventory Models for teaching copy.pptx
bylindaduku4
 
4. inventory management
bySudipta Saha
 
12 - © 2014 Pearson Education, Inc.Inventory Mana.docx
byaulasnilda
 
Lesson 10 Inventory Management-Operationspptx
bykagorabasoma
 
Inventory Management-53 slides.pptx
byTithiDas30
 
Ch_4.pdf
bykidusmesfin
 
Inventory Management under OPERATIONS and SCM.pptx
byraddddzzzzzz
 

Recently uploaded

PDF
Account Audit of a Sport Supplement Brand
byAlethLanuza
 
PDF
Dimi Design Intelligence Addendum, All Parts.pdf
byBrij Consulting, LLC
 
PDF
Andrew C. Belton, MBA Experience Portfolio January 2026
byAndrew C. Belton
 
PDF
Adam and Daniel Kaplan - A Head For Entrepreneurship
byAdam and Daniel Kaplan
 
PDF
Global Tokenization Landscape Updates 2025
byGarima Singh
 
PDF
Stuart Frost - The Chief Executive Officer
byStuart Frost
 
PDF
Comments on Dimi Design Intelligence Addendum, All Parts.pdf
byBrij Consulting, LLC
 
PDF
Adieu 2025 - Cyber Security way forward in 2026
byPrime Infoserv
 
PDF
One Of The Best Website To Buy Verified Venmo Accounts.pdf
by7zpjneju23g4b3ph3whf
 
PDF
Top 7 Place to Buy Verified MoonPay Accounts.pdf
by2h6w4ottve01a8x2u23v
 
PDF
“Previous-version” (ITIL v3/2011) view
byJS
 
PDF
Tips for Successfully Buying Old Gmail Accounts in Bulk.pdf
byBuy Verified Cash App Accounts
 
PDF
Where Can I Buy a Cash App Account Verified 4k.pdf
bypropvaservice is a Developer business
 
PDF
Comments on Dimi Design Intelligence Addendum2, All Parts.pdf
byBrij Consulting, LLC
 
PDF
Your Guide to Buying Verified Chime Bank Accounts Effectively.pdf
bybuyverifiedpaypalaccounts
 
DOCX
The Ultimate Guide to Bulk Purchasing Old Gmail Accounts.docx
byBuy Verified Cash App Accounts
 
PDF
Pension Schemes Bill.pdf Have you forgotten me
byHenry Tapper
 
PDF
How Do iPads Enhance Student Engagement in 2025?
byVRS Technologies LLC
 
DOCX
How to buy Yahoo accounts and Outlook accounts in 2026..docx
bygetsmmpro getsmmpro
 
DOCX
Tips for Successfully Buying Old Gmail Accounts in Bulk.docx
byBuy Verified Cash App Accounts
 
Account Audit of a Sport Supplement Brand
byAlethLanuza
 
Dimi Design Intelligence Addendum, All Parts.pdf
byBrij Consulting, LLC
 
Andrew C. Belton, MBA Experience Portfolio January 2026
byAndrew C. Belton
 
Adam and Daniel Kaplan - A Head For Entrepreneurship
byAdam and Daniel Kaplan
 
Global Tokenization Landscape Updates 2025
byGarima Singh
 
Stuart Frost - The Chief Executive Officer
byStuart Frost
 
Comments on Dimi Design Intelligence Addendum, All Parts.pdf
byBrij Consulting, LLC
 
Adieu 2025 - Cyber Security way forward in 2026
byPrime Infoserv
 
One Of The Best Website To Buy Verified Venmo Accounts.pdf
by7zpjneju23g4b3ph3whf
 
Top 7 Place to Buy Verified MoonPay Accounts.pdf
by2h6w4ottve01a8x2u23v
 
“Previous-version” (ITIL v3/2011) view
byJS
 
Tips for Successfully Buying Old Gmail Accounts in Bulk.pdf
byBuy Verified Cash App Accounts
 
Where Can I Buy a Cash App Account Verified 4k.pdf
bypropvaservice is a Developer business
 
Comments on Dimi Design Intelligence Addendum2, All Parts.pdf
byBrij Consulting, LLC
 
Your Guide to Buying Verified Chime Bank Accounts Effectively.pdf
bybuyverifiedpaypalaccounts
 
The Ultimate Guide to Bulk Purchasing Old Gmail Accounts.docx
byBuy Verified Cash App Accounts
 
Pension Schemes Bill.pdf Have you forgotten me
byHenry Tapper
 
How Do iPads Enhance Student Engagement in 2025?
byVRS Technologies LLC
 
How to buy Yahoo accounts and Outlook accounts in 2026..docx
bygetsmmpro getsmmpro
 
Tips for Successfully Buying Old Gmail Accounts in Bulk.docx
byBuy Verified Cash App Accounts
 

Inventory.pptx

  • 1.
    12 - 1 ©2014 Pearson Education, Inc. Inventory Management PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh Edition Principles of Operations Management, Ninth Edition PowerPoint slides by Jeff Heyl 12 © 2014 Pearson Education, Inc.
  • 2.
    12 - 2 ©2014 Pearson Education, Inc. Outline ► Global Company Profile: Amazon.com ► The Importance of Inventory ► Managing Inventory ► Inventory Models ► Inventory Models for Independent Demand
  • 3.
    12 - 3 ©2014 Pearson Education, Inc. Outline - Continued ► Probabilistic Models and Safety Stock ► Single-Period Model ► Fixed-Period (P) Systems
  • 4.
    12 - 4 ©2014 Pearson Education, Inc. Learning Objectives When you complete this chapter you should be able to: 1. Conduct an ABC analysis 2. Explain and use cycle counting 3. Explain and use the EOQ model for independent inventory demand 4. Compute a reorder point and safety stock
  • 5.
    12 - 5 ©2014 Pearson Education, Inc. Learning Objectives When you complete this chapter you should be able to: 5. Apply the production order quantity model 6. Explain and use the quantity discount model 7. Understand service levels and probabilistic inventory models
  • 6.
    12 - 6 ©2014 Pearson Education, Inc. Inventory Management at Amazon.com ► Amazon.com started as a “virtual” retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled by others ► Growth has forced Amazon.com to become a world leader in warehousing and inventory management © 2014 Pearson Education, Inc.
  • 7.
    12 - 7 ©2014 Pearson Education, Inc. Inventory Management at Amazon.com 1.Each order is assigned by computer to the closest distribution center that has the product(s) 2.A “flow meister” at each distribution center assigns work crews 3.Lights indicate products that are to be picked and the light is reset 4.Items are placed in crates on a conveyor, bar code scanners scan each item 15 times to virtually eliminate errors © 2014 Pearson Education, Inc.
  • 8.
    12 - 8 ©2014 Pearson Education, Inc. Inventory Management at Amazon.com 5. Crates arrive at central point where items are boxed and labeled with new bar code 6. Gift wrapping is done by hand at 30 packages per hour 7. Completed boxes are packed, taped, weighed and labeled before leaving warehouse in a truck 8. Order arrives at customer within 1 - 2 days © 2014 Pearson Education, Inc.
  • 9.
    12 - 9 ©2014 Pearson Education, Inc. Inventory Management The objective of inventory management is to strike a balance between inventory investment and customer service
  • 10.
    12 - 10 ©2014 Pearson Education, Inc. Importance of Inventory ▶One of the most expensive assets of many companies representing as much as 50% of total invested capital ▶Operations managers must balance inventory investment and customer service
  • 11.
    12 - 11 ©2014 Pearson Education, Inc. Functions of Inventory 1. To provide a selection of goods for anticipated demand and to separate the firm from fluctuations in demand 2. To decouple or separate various parts of the production process 3. To take advantage of quantity discounts 4. To hedge against inflation
  • 12.
    12 - 12 ©2014 Pearson Education, Inc. Types of Inventory ▶Raw material ▶Purchased but not processed ▶Work-in-process (WIP) ▶Undergone some change but not completed ▶A function of cycle time for a product ▶Maintenance/repair/operating (MRO) ▶Necessary to keep machinery and processes productive ▶Finished goods ▶Completed product awaiting shipment
  • 13.
    12 - 13 ©2014 Pearson Education, Inc. The Material Flow Cycle Figure 12.1 Input Wait for Wait to Move Wait in queue Setup Run Output inspection be moved time for operator time time Cycle time 95% 5%
  • 14.
    12 - 14 ©2014 Pearson Education, Inc. Managing Inventory 1. How inventory items can be classified (ABC analysis) 2. How accurate inventory records can be maintained
  • 15.
    12 - 15 ©2014 Pearson Education, Inc. ABC Analysis ▶Divides inventory into three classes based on annual dollar volume ▶Class A - high annual dollar volume ▶Class B - medium annual dollar volume ▶Class C - low annual dollar volume ▶Used to establish policies that focus on the few critical parts and not the many trivial ones
  • 16.
    12 - 16 ©2014 Pearson Education, Inc. ABC Analysis ABC Calculation (1) (2) (3) (4) (5) (6) (7) ITEM STOCK NUMBER PERCENT OF NUMBER OF ITEMS STOCKED ANNUAL VOLUME (UNITS) x UNIT COST = ANNUAL DOLLAR VOLUME PERCENT OF ANNUAL DOLLAR VOLUME CLASS #10286 20% 1,000 $ 90.00 $ 90,000 38.8% A #11526 500 154.00 77,000 33.2% A #12760 1,550 17.00 26,350 11.3% B #10867 30% 350 42.86 15,001 6.4% B #10500 1,000 12.50 12,500 5.4% B #12572 600 $ 14.17 $ 8,502 3.7% C #14075 2,000 .60 1,200 .5% C #01036 50% 100 8.50 850 .4% C #01307 1,200 .42 504 .2% C #10572 250 .60 150 .1% C 8,550 $232,057 100.0% 72% 23% 5%
  • 17.
    12 - 17 ©2014 Pearson Education, Inc. ABC Analysis A Items B Items | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percentage of annual dollar usage 80 – 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Percentage of inventory items Figure 12.2 C Items
  • 18.
    12 - 18 ©2014 Pearson Education, Inc. ABC Analysis ▶ Other criteria than annual dollar volume may be used ▶ High shortage or holding cost ▶ Anticipated engineering changes ▶ Delivery problems ▶ Quality problems
  • 19.
    12 - 19 ©2014 Pearson Education, Inc. ABC Analysis ▶Policies employed may include 1. More emphasis on supplier development for A items 2. Tighter physical inventory control for A items 3. More care in forecasting A items
  • 20.
    12 - 20 ©2014 Pearson Education, Inc. Record Accuracy ► Accurate records are a critical ingredient in production and inventory systems ► Periodic systems require regular checks of inventory ► Two-bin system ► Perpetual inventory tracks receipts and subtractions on a continuing basis ► May be semi-automated
  • 21.
    12 - 21 ©2014 Pearson Education, Inc. Record Accuracy ► Incoming and outgoing record keeping must be accurate ► Stockrooms should be secure ► Necessary to make precise decisions about ordering, scheduling, and shipping
  • 22.
    12 - 22 ©2014 Pearson Education, Inc. Cycle Counting ▶Items are counted and records updated on a periodic basis ▶Often used with ABC analysis ▶Has several advantages 1. Eliminates shutdowns and interruptions 2. Eliminates annual inventory adjustment 3. Trained personnel audit inventory accuracy 4. Allows causes of errors to be identified and corrected 5. Maintains accurate inventory records
  • 23.
    12 - 23 ©2014 Pearson Education, Inc. Cycle Counting Example 5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) ITEM CLASS QUANTITY CYCLE COUNTING POLICY NUMBER OF ITEMS COUNTED PER DAY A 500 Each month 500/20 = 25/day B 1,750 Each quarter 1,750/60 = 29/day C 2,750 Every 6 months 2,750/120 = 23/day 77/day
  • 24.
    12 - 24 ©2014 Pearson Education, Inc. Control of Service Inventories ▶Can be a critical component of profitability ▶Losses may come from shrinkage or pilferage ▶Applicable techniques include 1. Good personnel selection, training, and discipline 2. Tight control of incoming shipments 3. Effective control of all goods leaving facility
  • 25.
    12 - 25 ©2014 Pearson Education, Inc. Inventory Models ▶Independent demand - the demand for item is independent of the demand for any other item in inventory ▶Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory
  • 26.
    12 - 26 ©2014 Pearson Education, Inc. Inventory Models ▶Holding costs - the costs of holding or “carrying” inventory over time ▶Ordering costs - the costs of placing an order and receiving goods ▶Setup costs - cost to prepare a machine or process for manufacturing an order ▶May be highly correlated with setup time
  • 27.
    12 - 27 ©2014 Pearson Education, Inc. Holding Costs TABLE 12.1 Determining Inventory Holding Costs CATEGORY COST (AND RANGE) AS A PERCENT OF INVENTORY VALUE Housing costs (building rent or depreciation, operating costs, taxes, insurance) 6% (3 - 10%) Material handling costs (equipment lease or depreciation, power, operating cost) 3% (1 - 3.5%) Labor cost (receiving, warehousing, security) 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) 11% (6 - 24%) Pilferage, space, and obsolescence (much higher in industries undergoing rapid change like PCs and cell phones) 3% (2 - 5%) Overall carrying cost 26%
  • 28.
    12 - 28 ©2014 Pearson Education, Inc. Holding Costs TABLE 12.1 Determining Inventory Holding Costs CATEGORY COST (AND RANGE) AS A PERCENT OF INVENTORY VALUE Housing costs (building rent or depreciation, operating costs, taxes, insurance) 6% (3 - 10%) Material handling costs (equipment lease or depreciation, power, operating cost) 3% (1 - 3.5%) Labor cost (receiving, warehousing, security) 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) 11% (6 - 24%) Pilferage, space, and obsolescence (much higher in industries undergoing rapid change like PCs and cell phones) 3% (2 - 5%) Overall carrying cost 26%
  • 29.
    12 - 29 ©2014 Pearson Education, Inc. Inventory Models for Independent Demand Need to determine when and how much to order 1. Basic economic order quantity (EOQ) model 2. Production order quantity model 3. Quantity discount model
  • 30.
    12 - 30 ©2014 Pearson Education, Inc. Basic EOQ Model 1. Demand is known, constant, and independent 2. Lead time is known and constant 3. Receipt of inventory is instantaneous and complete 4. Quantity discounts are not possible 5. Only variable costs are setup (or ordering) and holding 6. Stockouts can be completely avoided Important assumptions
  • 31.
    12 - 31 ©2014 Pearson Education, Inc. Inventory Usage Over Time Figure 12.3 Order quantity = Q (maximum inventory level) Usage rate Average inventory on hand Q 2 Minimum inventory Inventory level Time 0 Total order received
  • 32.
    12 - 32 ©2014 Pearson Education, Inc. Minimizing Costs Objective is to minimize total costs Table 12.4(c) Annual cost Order quantity Total cost of holding and setup (order) Holding cost Setup (order) cost Minimum total cost Optimal order quantity (Q*)
  • 33.
    12 - 33 ©2014 Pearson Education, Inc. Minimizing Costs ▶By minimizing the sum of setup (or ordering) and holding costs, total costs are minimized ▶Optimal order size Q* will minimize total cost ▶A reduction in either cost reduces the total cost ▶Optimal order quantity occurs when holding cost and setup cost are equal
  • 34.
    12 - 34 ©2014 Pearson Education, Inc. Minimizing Costs 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 = = D Q æ è ç ö ø ÷S Annual setup cost = D Q S
  • 35.
    12 - 35 ©2014 Pearson Education, Inc. 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 Minimizing Costs Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity 2 (Holding cost per unit per year) = = Q 2 æ è ç ö ø ÷H Annual setup cost = D Q S Annual holding cost = Q 2 H
  • 36.
    12 - 36 ©2014 Pearson Education, Inc. Minimizing Costs D Q S = Q 2 æ è ç ö ø ÷H Optimal order quantity is found when annual setup cost equals annual holding cost Solving for Q* 2DS = Q2 H Q2 = 2DS H Q* = 2DS H 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 = D Q S Annual holding cost = Q 2 H
  • 37.
    12 - 37 ©2014 Pearson Education, Inc. 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
  • 38.
    12 - 38 ©2014 Pearson Education, Inc. An EOQ Example Determine expected number of orders D = 1,000 units Q* = 200 units S = $10 per order H = $.50 per unit per year N = = 5 orders per year 1,000 200 = N = = Expected number of orders Demand Order quantity D Q*
  • 39.
    12 - 39 ©2014 Pearson Education, Inc. An EOQ Example Determine optimal time between orders D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders/year H = $.50 per unit per year T = = 50 days between orders 250 5 = T = Expected time between orders Number of working days per year Expected number of orders
  • 40.
    12 - 40 ©2014 Pearson Education, Inc. An EOQ Example Determine the total annual cost D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders/year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC = D Q S + Q 2 H = 1,000 200 ($10)+ 200 2 ($.50) = (5)($10)+(100)($.50) = $50+$50 = $100
  • 41.
    12 - 41 ©2014 Pearson Education, Inc. The EOQ Model When including actual cost of material P Total annual cost = Setup cost + Holding cost + Product cost TC = D Q S + Q 2 H + PD
  • 42.
    12 - 42 ©2014 Pearson Education, Inc. 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
  • 43.
    12 - 43 ©2014 Pearson Education, Inc. An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders/year H = $.50 per unit per year T = 50 days TC = D Q S + Q 2 H = 1,500 200 ($10)+ 200 2 ($.50) = $75+$50 = $125 1,500 units = 1,500 244.9 ($10)+ 244.9 2 ($.50) = 6.125($10)+122.45($.50) = $61.25+$61.22 = $122.47 Only 2% less than the total cost of $125 when the order quantity was 200
  • 44.
    12 - 44 ©2014 Pearson Education, Inc. Reorder Points ▶ EOQ answers the “how much” question ▶ The reorder point (ROP) tells “when” to order ▶ Lead time (L) is the time between placing and receiving an 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
  • 45.
    12 - 45 ©2014 Pearson Education, Inc. Reorder Point Curve Q* ROP (units) Inventory level (units) Time (days) Figure 12.5 Lead time = L Slope = units/day = d Resupply takes place as order arrives
  • 46.
    12 - 46 ©2014 Pearson Education, Inc. Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days, may take 4 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 = 32 units per day x 4 days = 128 units
  • 47.
    12 - 47 ©2014 Pearson Education, Inc. Production Order Quantity Model 1. Used when inventory builds up over a period of time after an order is placed 2. Used when units are produced and sold simultaneously Inventory level Time Demand part of cycle with no production (only usage) Part of inventory cycle during which production (and usage) is taking place t Maximum inventory Figure 12.6
  • 48.
    12 - 48 ©2014 Pearson Education, Inc. 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
  • 49.
    12 - 49 ©2014 Pearson Education, Inc. 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 inventory level Total produced during the production run Total used during the production run = pt – dt However, Q = total produced = pt ; thus t = Q/p Maximum inventory level = p – d = Q 1 – Q p Q p d p Holding cost = (H) = 1 – H d p Q 2 Maximum inventory level 2
  • 50.
    12 - 50 ©2014 Pearson Education, Inc. 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 Setup cost = (D / Q)S Holding cost = 1 2 HQ 1- d p ( ) é ë ù û D Q S = 1 2 HQ 1- d p ( ) é ë ù û Q2 = 2DS H 1- d p ( ) é ë ù û Qp * = 2DS H 1- d p ( ) é ë ù û
  • 51.
    12 - 51 ©2014 Pearson Education, Inc. 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 Qp * = 2DS H 1- d p ( ) é ë ù û Qp * = 2(1,000)(10) 0.50 1-(4 8) é ë ù û = 20,000 0.50(1 2) = 80,000 = 282.8 hubcaps, or 283 hubcaps
  • 52.
    12 - 52 ©2014 Pearson Education, Inc. Production Order Quantity Model When annual data are used the equation becomes Note: d = 4 = = D Number of days the plant is in operation 1,000 250 Qp * = 2DS H 1- Annual demand rate Annual production rate æ è ç ö ø ÷
  • 53.
    12 - 53 ©2014 Pearson Education, Inc. Quantity Discount Models ▶Reduced prices are often available when larger quantities are purchased ▶Trade-off is between reduced product cost and increased holding cost TABLE 12.2 A Quantity Discount Schedule DISCOUNT NUMBER DISCOUNT QUANTITY DISCOUNT (%) DISCOUNT PRICE (P) 1 0 to 999 no discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75
  • 54.
    12 - 54 ©2014 Pearson Education, Inc. Quantity Discount Models Q* = 2DS IP Total annual cost = Setup cost + Holding cost + Product cost TC = D Q S + Q 2 H + PD where Q = Quantity ordered P = Price per unit D = Annual demand in units H = Holding cost per unit per year S = Ordering or setup cost per order Because unit price varies, holding cost (H) is expressed as a percent (I) of unit price (P)
  • 55.
    12 - 55 ©2014 Pearson Education, Inc. Quantity Discount Models Steps in analyzing a quantity discount 1. For each discount, calculate Q* 2. If Q* for a discount doesn’t qualify, choose the lowest possible quantity 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
  • 56.
    12 - 56 ©2014 Pearson Education, Inc. Quantity Discount Models 1,000 2,000 Total cost $ 0 Order quantity Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b a b 1st price break 2nd price break Total cost curve for discount 1 Total cost curve for discount 2 Total cost curve for discount 3 Figure 12.7
  • 57.
    12 - 57 ©2014 Pearson Education, Inc. Quantity Discount Example Calculate Q* for every discount Q1* = = 700 cars/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 cars/order 2(5,000)(49) (.2)(4.80) Q3* = = 718 cars/order 2(5,000)(49) (.2)(4.75) Q* = 2DS IP
  • 58.
    12 - 58 ©2014 Pearson Education, Inc. Quantity Discount Example Calculate Q* for every discount Q1* = = 700 cars/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 cars/order 2(5,000)(49) (.2)(4.80) Q3* = = 718 cars/order 2(5,000)(49) (.2)(4.75) Q* = 2DS IP 1,000 — adjusted 2,000 — adjusted
  • 59.
    12 - 59 ©2014 Pearson Education, Inc. Quantity Discount Example TABLE 12.3 Total Cost Computations for Wohl’s Discount Store DISCOUNT NUMBER UNIT PRICE ORDER QUANTITY ANNUAL PRODUCT COST ANNUAL ORDERING COST ANNUAL HOLDING COST TOTAL 1 $5.00 700 $25,000 $350 $350 $25,700 2 $4.80 1,000 $24,000 $245 $480 $24,725 3 $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
  • 60.
    12 - 60 ©2014 Pearson Education, Inc. 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
  • 61.
    12 - 61 ©2014 Pearson Education, Inc. Safety Stock Example NUMBER OF UNITS PROBABILITY 30 .2 40 .2 ROP  50 .3 60 .2 70 .1 1.0 ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year
  • 62.
    12 - 62 ©2014 Pearson Education, Inc. Safety Stock Example ROP = 50 units Stockout 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 $100 10 (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 = 50 + 20 = 70 frames
  • 63.
    12 - 63 ©2014 Pearson Education, Inc. Safety stock 16.5 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 = 350 + safety stock of 16.5 = 366.5 Receive order Lead time Figure 12.8
  • 64.
    12 - 64 ©2014 Pearson Education, Inc. Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + ZsdLT where Z = Number of standard deviations sdLT = Standard deviation of demand during lead time
  • 65.
    12 - 65 ©2014 Pearson Education, Inc. 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)
  • 66.
    12 - 66 ©2014 Pearson Education, Inc. Probabilistic Example m = Average demand = 350 kits sdLT = Standard deviation of demand during lead time = 10 kits Z = 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = ZsdLT = 1.65(10) = 16.5 kits Reorder point = Expected demand during lead time + Safety stock = 350 kits + 16.5 kits of safety stock = 366.5 or 367 kits
  • 67.
    12 - 67 ©2014 Pearson Education, Inc. Other Probabilistic Models ▶When data on demand during lead time is not available, there are other models available 1. When demand is variable and lead time is constant 2. When lead time is variable and demand is constant 3. When both demand and lead time are variable
  • 68.
    12 - 68 ©2014 Pearson Education, Inc. Other Probabilistic Models Demand is variable and lead time is constant ROP = (Average daily demand x Lead time in days) + ZsdLT where sdLT = sd Lead time sd = standard deviation of demand per day
  • 69.
    12 - 69 ©2014 Pearson Education, Inc. Probabilistic Example Average daily demand (normally distributed) = 15 Lead time in days (constant) = 2 Standard deviation of daily demand = 5 Service level = 90% Z for 90% = 1.28 From Appendix I ROP = (15 units x 2 days) + ZsdLT = 30 + 1.28(5)( 2) = 30 + 9.02 = 39.02 ≈ 39 Safety stock is about 9 computers
  • 70.
    12 - 70 ©2014 Pearson Education, Inc. Other Probabilistic Models Lead time is variable and demand is constant ROP = (Daily demand x Average lead time in days) + Z x (Daily demand) x sLT where sLT = Standard deviation of lead time in days
  • 71.
    12 - 71 ©2014 Pearson Education, Inc. Probabilistic Example Daily demand (constant) = 10 Average lead time = 6 days Standard deviation of lead time = sLT = 1 Service level = 98%, so Z (from Appendix I) = 2.055 ROP = (10 units x 6 days) + 2.055(10 units)(1) = 60 + 20.55 = 80.55 Reorder point is about 81 cameras
  • 72.
    12 - 72 ©2014 Pearson Education, Inc. Other Probabilistic Models Both demand and lead time are variable ROP = (Average daily demand x Average lead time) + ZsdLT where sd = Standard deviation of demand per day sLT = Standard deviation of lead time in days sdLT = (Average lead time x sd 2) + (Average daily demand)2s2 LT
  • 73.
    12 - 73 ©2014 Pearson Education, Inc. Probabilistic Example Average daily demand (normally distributed) = 150 Standard deviation = sd = 16 Average lead time 5 days (normally distributed) Standard deviation = sLT = 1 day Service level = 95%, so Z = 1.65 (from Appendix I) ROP = (150 packs´5 days)+1.65sdLT sdLT = 5 days´162 ( )+ 1502 ´12 ( ) = 5´256 ( )+ 22,500´1 ( ) = 1,280 ( )+ 22,500 ( ) = 23,780 @154 ROP = (150´5)+1.65(154) @ 750+254 =1,004 packs
  • 74.
    12 - 74 ©2014 Pearson Education, Inc. Single-Period Model ▶Only one order is placed for a product ▶Units have little or no value at the end of the sales period Cs = Cost of shortage = Sales price/unit – Cost/unit Co = Cost of overage = Cost/unit – Salvage value Service level = Cs Cs + Co
  • 75.
    12 - 75 ©2014 Pearson Education, Inc. Single-Period Example Average demand = m = 120 papers/day Standard deviation = s = 15 papers Cs = cost of shortage = $1.25 – $.70 = $.55 Co = cost of overage = $.70 – $.30 = $.40 Service level = Cs Cs + Co = = = .579 .55 .55 + .40 .55 .95 Service level 57.9% Optimal stocking level m = 120
  • 76.
    12 - 76 ©2014 Pearson Education, Inc. Single-Period Example From Appendix I, for the area .579, Z  .20 The optimal stocking level = 120 copies + (.20)(s) = 120 + (.20)(15) = 120 + 3 = 123 papers The stockout risk = 1 – Service level = 1 – .579 = .422 = 42.2%
  • 77.
    12 - 77 ©2014 Pearson Education, Inc. Fixed-Period (P) Systems ▶Orders placed at the end of a fixed period ▶Inventory counted only at end of period ▶Order brings inventory up to target level ▶Only relevant costs are ordering and holding ▶Lead times are known and constant ▶Items are independent of one another
  • 78.
    12 - 78 ©2014 Pearson Education, Inc. Fixed-Period (P) Systems On-hand inventory Time Q1 Q2 Target quantity (T) P Q3 Q4 P P Figure 12.9
  • 79.
    12 - 79 ©2014 Pearson Education, Inc. Fixed-Period Systems ▶Inventory is only counted at each review period ▶May be scheduled at convenient times ▶Appropriate in routine situations ▶May result in stockouts between periods ▶May require increased safety stock
  • 80.
    12 - 80 ©2014 Pearson Education, Inc. 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.