Inventory McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Overview of inventory • Inventory functionality and definitions • Inventory carrying cost • Planning inventory • Managing uncertainty • Inventory management policies • Inventory management practices 7-2 Why do we have inventories? Because the customer usually isn’t sitting at the plant exit! Queen Elizabeth research station in Antarctica 7-3 Risks associated with holding inventory • Typical measures of exposure to investments in inventory – Time duration – Depth of commitment – Width of commitment • Supply chain exposure based on location – Manufacturer’s exposure is typically narrow, but deep and of long duration – Wholesaler’s exposure is wider than manufacturers and somewhat deep • Duration is medium – Retailer’s exposure is wide, but not very deep • Duration is usually short except for specialty retailers 7-4 Functions of Inventory • Geographical specialization allows us to specialize production across different locations • Decoupling allows us to run processes for maximum economic lot sizes within a single facility • Supply/Demand balancing accommodates the elapsed time between inventory availability and consumption • Buffering uncertainty accommodates uncertainty related to – Demand in excess of forecast or – Unexpected delays in delivery (aka safety stock) 7-5 Inventory policy • Inventory policy is a firm’s guidelines concerning – What to purchase or manufacture – When to take action – In what quantity should action be taken – Where products should be located geographically • Firm’s policy also includes decisions about which inventory management practices to adopt 7-6 Service level • Service level is a performance target specified by management and defines inventory performance objectives • Common measures of service level include – Performance cycle is the elapsed time between release of a purchase order by the buyer to the receipt of shipment – Case fill rate is the percent of cases ordered that are shipped as requested – Line fill rate is the percent of order lines (items) that were filled completely – Order fill is the percent of customer orders filled completely 7-7 Inventory definitions • Inventory includes materials, components, work-inprocess, and finished goods that are stocked in the company’s logistical system – The cycle inventory (base stock) is the portion of average inventory that results from replenishment – Order quantity is the amount ordered for replenishment – Transit inventory represents the amount typically in transit between facilities or on order but not received – Obsolete inventory is stock that is out-of-date or is not in recent demand – Speculative inventory is bought to hedge a currency exchange or to take advantage of a discount – Safety stock is the remainder of inventory in the logistics system 7-8 Average inventory is the typical amount stocked over time • Average inventory equals the maximum inventory plus the minimum inventory divided by two – Typically equal to ½ order quantity + safety stock + in-transit stock Figure 7.1 Inventory Cycle for Typical Product 7-9 Example #1 Average Inventory 1000 400 0 7-10 Example #1 Average Inventory 1000 (1000+400/ 2)=700 400 0 7-11 Example #2 Order Quantity 2000 1000 0 7-12 Example #2 Order Quantity 2000 1000 1000 0 7-13 Example #3 Average Inventory and Order Quantity 22000 14000 0 7-14 Example #4 Reorder Point Performance cycle = 4 days 2000 1000 0 0 10 20 7-15 When to order • Basic reorder formula if demand and performance are certain R= D × T – R = Reorder point in units – D = Average daily demand in units – T = Average performance cycle length in days • If safety stock is needed to accommodate uncertainty the formula is R = D × T + SS – – – – R = Reorder point in units D = Average daily demand in units T = Average performance cycle length in days SS = Safety stock in units 7-16 Example #4 Reorder Point Performance cycle = 4 days 2000 1000 Reorder = 4 x 100 + 1000 Reorder point = 1400 0 0 10 20 7-17 Smaller replenishment order quantities results in lower average inventory • Policy must decide how much inventory to order at a specified time – Reorder point defines when a replenishment order is initiated • However, other factors are important like performance cycle uncertainty, purchasing discounts, and transportation economies Figure 7.3 Alternative Order Quantity and Average Inventory 7-18 Inventory ordering cost components • • • • • Order preparation costs Order transportation costs Order receipt processing costs Material handling costs Total cost is driven by inventory planning decisions which establish when and how much to order 7-19 Inventory carrying cost is the expense associated with maintaining inventory • Inventory expense is – Annual inventory carrying cost percent times average inventory value • Cost components – Cost of capital is specified by senior management – Taxes on inventory held in warehouses – Insurance is based on estimated risk or loss over time and facility characteristics – Obsolescence results from deterioration of product during storage • E.g. food and pharmaceutical sell-by dates – Storage is facility expense related to product holding rather than product handling 7-20 Final carrying cost percent used by a firm is a managerial policy Table 7.2 Inventory Carrying Cost Components 7-21 How much to order • Economic order quantity is the amount that balances the cost of ordering with the cost of maintaining average inventory – Assumes demand and costs are relatively stable for the year – Does not consider impact of joint ordering of multiple products Figure 7.4 Economic Order Quantity 7-22 Standard mathematical solution for EOQ 7-23 Example #5- EOQ • • • • Annual demand = Unit value= Carrying cost %= Ordering costs = 2400 units $5.00 20% $19.00 7-24 Example#5 EOQ solution using Table 7.3 • Total ordering cost is $152 = (2400/300 x $19.00) • Inventory carrying cost is $150 = [300/2 x (5 x 0.20)] 7-25 Example #5 - EOQ Total Ordering cost = (Demand/ EOQ amount) x $ per order Total ordering cost is $152 = (2400/300 x $19.00) --------------------------------------------------------------------Inventory carrying cost = (EOQ amount/2) x (Unit price x Carrying cost %) Inventory carrying cost is $150 = [300/2 x (5 x 0.20)] 7-26 Example #6- EOQ • • • • Annual demand = Unit value= Carrying cost %= Ordering costs = 500 units $90.00 15% $35.00 Total Ordering cost = (Demand/ EOQ amount) x $ per order Inventory carrying cost = (EOQ amount/2) x (Unit price x Carrying cost %) 7-27 Example #6- EOQ • • • • EOQ = √(2x35x500)/(0.15x90) EOQ = √(35000)/(13.5) EOQ = √(2592.593) EOQ = 50.91 ≈ 50 7-28 Example #6 - EOQ Total Ordering cost = (Demand/ EOQ amount) x $ per order Total ordering cost is $350 = (500/50 x $35.00) --------------------------------------------------------------------Inventory carrying cost = (EOQ amount/2) x (Unit price x Carrying cost %) Inventory carrying cost is $337.5 = [50/2 x (90 x 0.15)] 7-29 Simple EOQ model assumptions • All demand is satisfied • Rate of demand is continuous, constant and know • Replenishment performance cycle time is constant and known • Constant price of product that is independent of order quantity or time • An infinite planning horizon exists • No interaction between multiple items of inventory • No inventory is in transit • No limit is placed on capital availability 7-30 Relationships useful for guiding inventory planning • EOQ is found at the point where annualized order placement cost and inventory carrying cost are equal • Average base inventory equal one-half order quantity • Value of the inventory unit, all other things being equal, will have a direct relationship with replenishment order frequency – Higher value products will be ordered more frequently 7-31 Typical adjustments to EOQ • Volume transportation rates offer a freight-rate discount for larger shipments – Compare total cost with each transportation rate option • Quantity discounts offer a lower per unit cost when larger quantities are purchased – If discount is sufficient to offset added inventory carrying cost less the reduced cost of ordering then it is viable choice • Other EOQ adjustments – – – – – Production lot size Multiple-item purchase Limited capital Dedicated trucking Unitization 7-32 Uncertainty in inventory management • Inventory policy must deal with uncertainty – Demand uncertainty — when and how much product will our customers order? – Performance cycle uncertainty — how long will it take to replenish inventory with our customers? • Variations must be considered in both areas to make effective inventory planning decisions 7-33 Demand uncertainty can be managed using safety stock • To protect against stockout when uncertain demand exceeds forecast we add safety stock to base inventory • Planning safety stock requires three steps – Determine the likelihood of stockout using a probability distribution – Estimate demand during a stockout period – Decide on a policy concerning the desired level of stockout protection 7-34 Probability theory enables calculation of safety stock for a target service level • Service level is equal to 100% minus probability % of stockout – E.g. a service level of 99% results in a stockout probability of 1% • The most common probability distribution for demand is the normal distribution – From analysis of historical demand data the safety stock required to ensure a stock out only 1% of the time is possible – A one-tailed normal distribution is used because only demand that is greater than the forecast can create a stockout 7-35 Example of historical demand analysis using a normal distribution Figure 7.6 Historical Analysis of Demand History Figure 7.7 Normal Distribution 7-36 Performance cycle uncertainty means operations cannot assume consistent delivery Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration 7-37 Example #7 (Standard Deviation) Days 6 7 8 9 10 11 12 13 14 (F) 2 4 6 8 10 8 6 4 2 7-38 Example #7 (Standard Deviation) Days 6 7 8 9 10 11 12 13 14 x (F) 2 4 6 8 10 8 6 4 2 50 12 28 48 72 100 88 72 52 28 500 500/50 = 10 7-39 Performance cycle uncertainty means operations cannot assume consistent delivery Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration 7-40 Example #7 (Standard Deviation) Days 6 7 8 9 10 11 12 13 14 -- Mean 10 10 10 10 10 10 10 10 10 (D) -4 -3 -2 -1 0 1 2 3 4 7-41 Example #7 (Standard Deviation) Days 6 7 8 9 10 11 12 13 14 Mean 10 10 10 10 10 10 10 10 10 (D) -4 -3 -2 -1 0 1 2 3 4 (D*D) 16 9 4 1 0 1 4 9 16 7-42 Example #7 (Standard Deviation) Days 6 7 8 9 10 11 12 13 14 (F) 2 4 6 8 10 8 6 4 2 50 Mean 10 10 10 10 10 10 10 10 10 (D) -4 -3 -2 -1 0 1 2 3 4 (D*D) 16 9 4 1 0 1 4 9 16 FD2 32 36 24 8 0 8 24 36 32 200 7-43 Performance cycle uncertainty means operations cannot assume consistent delivery Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration 7-44 Example #8 (Standard Deviation) Units 3 4 5 6 7 (F) 1 2 4 2 1 7-45 Example #8 (Standard Deviation) Units 3 4 5 6 7 (F) 1 2 4 2 1 10 Unit* F Mean (D) 3 5 -2 8 5 -1 20 5 0 12 5 1 7 5 2 50 D2 4 1 0 1 4 FD2 4 2 0 2 4 12 7-46 Example #8 (Standard Deviation) σ = √12/10 1.09 units 7-47 Safety stock with combined uncertainty • Planning for both demand and performance cycle uncertainty requires combining two independent variables • The joint impact of the probability of both demand and performance cycle variation must be determined – Direct method is to combine standard deviations using a convolution formula 7-48 Typical situation where both demand and performance cycle variation exists Figure 7.8 Combined Demand and Performance Cycle Uncertainty 7-49 Example #9 (Convolution) Using our previous answers: • Performance cycle mean (T) = • Performance cycle standard deviation (St) = • Demand mean (D)= • Demand standard deviation (Sd)= 10 2 5 1.09 σ = √((TSd2) + (D2St2))=√ ((10*1.092) + (5222))= 10.58 7-50 The fill rate is the magnitude rather than the probability of a stockout • Increasing the replenishment order quantity decreases the relative magnitude of potential stockouts • The formula for this relationship is 7-51 Number of stockouts is reduced from two to one when order quantity is increased Figure 7.9 Impact of Order Quantity on Stockout Magnitude 7-52 Reorder point formulas for reactive methods Perpetual Review Periodic Review 7-53 Planning approaches coordinate requirements across multiple locations in the supply chain • Two planning approaches – Fair share allocation provides each distribution facility with an equitable distribution of available inventory • Limited ability to manage multistage inventories – Requirements planning integrates across the supply chain taking into consideration unique requirements • Materials requirements planning (MRP) is driven by a production schedule • Distribution requirements planning (DRP) is driven by supply chain demand 7-54 Example of fair share allocation method +500 Figure 7.11 Fair Share Allocation Example Days Supply = (New inventory + sum inventory)/ sum demand DS = (500 +50 + 100 + 75)/ (10+50+15) DS = (725/75) = 9.67 days 7-55 Example of fair share allocation method Figure 7.11 Fair Share Allocation Example Allocate = (DS – (inventory/demand)) x demand Allocate = (9.67 – (50/10)) x 10 Allocate = 46.7 or 47. 7-56 Example of fair share allocation method Figure 7.11 Fair Share Allocation Example Allocate = (DS – (inventory/demand)) x demand 7-57 Example of fair share allocation method Figure 7.11 Fair Share Allocation Example • Allocation of 500 available units from plant – Warehouse 1 = 47 – Warehouse 2 = 383 – Warehouse 3 = 70 7-58 Overview of inventory • Inventory functionality and definitions • Inventory carrying cost • Planning inventory • Managing uncertainty • Inventory management policies • Inventory management practices 7-59