7 Managing Flow Variability Safety Inventory Chapter 7

7. Managing Flow Variability: Safety Inventory Chapter 7 1 Managing Flow Variability: Safety Inventory 7. 1 Demand Forecasts and Forecast Errors 7. 2 Safety Inventory and Service Level 7. 3 Optimal Service Level – The Newsvendor Problem 7. 4 Lead Time Demand Variability 7. 5 Pooling Efficiency through Aggregation 7. 6 Shortening the Forecast Horizon 7. 7 Levers for Reducing Safety Inventory

7. Managing Flow Variability: Safety Inventory 7. 1 Demand Forecast Errors 2 In review, we have 3 stages of a process: 1. Input (e. g. raw materials) 2. Process 3. Output (finished goods) This is important to forecasting because it will allow us to more closely match outputs to inputs and vice versa.

7. Managing Flow Variability: Safety Inventory 7. 1 Demand Forecasts and Forecast Errors 3 We have previously assumed demand is known and is constant. § Demand varies in predictable and unpredictable ways. § Unpredictable, random factors affecting demand is referred to as “noise”. “As a process of predicting future demand, forecasting is, among other things, an effort to deal with NOISE. ”

7. Managing Flow Variability: Safety Inventory 7. 1 Demand Forecast Errors 4 Why do we forecast? We forecast so that we can make decisions about the future. We need to make rational decisions about process inventory. * How to spend money and how not to spend money. * When to buys more widgets. * When to hire more workers. * How to avoid stockouts (upset customers = business losses) * How to avoid holding excess inventory (= $ lost)

7. Managing Flow Variability: Safety Inventory 7. 1 Demand Forecasts and Forecast Errors 5 Forecasting methods § Subjective – Based on judgement and experience • Surveys and expert judgements § Objective – Based on data analysis • Causal models - Forecast methods that assume that in addition to data, there are other factors that influence demand (eg. Consumer prices. ) • Time series analyses - Methods that rely solely on past data.

7. Managing Flow Variability: Safety Inventory 7. 1 Demand Forecasts and Forecast Errors 6 4 Characteristics of Forecasts § Forecasts are usually wrong. Because of random noise – forecasts are inaccurate. § Forecasts should be accompanied by a measure of forecast error. A measure of forecast error quantifies the manager’s degree of confidence in the forecast. § Aggregate forecasts are more accurate than individual forecasts. Aggregate forecasts reduce the amount of variability – relative to the aggregate mean demand. § Long-range forecasts are less accurate than short-range forecasts. Precise forecasting of events far out in the future are much more difficult to predict than something that will occur in a matter of moments from now.

7. Managing Flow Variability: Safety Inventory 7. 1 Demand Forecasts and Forecast Errors 7 Forecasts should incorporate hard quantitaive data as well as qualitative factors such as managerial judgement, intuition, and market savvy. Forecasting is as much art as science.

7. Managing Flow Variability: Safety Inventory 7. 1 Demand Forecast Errors 8 Safety Inventory cushions the process against supply disruptions or surges in demand. Having adequate Safety Inventory reduces the uncertainty in supply and demand. Ensuring reliable suppliers and stable demand eliminates the need for Safety Inventory.

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 9 Objective: Review of common terms and a discussion of Service Level Where: SL = f (Safety Inventory, I safety) And some math using Excel…

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 10 SL: Service Level I safety: Safety Inventory (or Safety Stock) I cycle: Cycle Inventory LTD: Lead Time Demand ROP: Re-order Point L: Replenishment Lead Time Q: Order Size NORMDIST: Standard Normal Tables NORMSINV: Standard Normal Tables NORMINV: Standard Normal Tables

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 11 Inventory, I (t) ROP ORDER LTD, # of Units used during lead time Safety Inventory (I safety) 0 L L Time, t

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 12 I safety = ROP – LTD Inventory, I (t) ROP LTD, # of Units used during lead time Safety Inventory 0 (I safety)

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 13 An Inventory with an Order Size = Q Average Inventory = Q/2 I cycle = Q/2 I = I cycle + I safety = Q/2 + I safety Average Flow Rate = R Average Flow Time as expressed by Little’s Law T = I /R = (Q/2 + I safety ) R

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 14 The Service Level for a given ROP is given by: SL = Prob (LTD < ROP) To calculate SL, recall first that if LTD is normally distributed with mean LTD and standard deviation s. LTD then I safety = z x s. LTD , where z is a multiple of s. LTD Or the number of standard deviations

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 15 Example: At GE Lighting’s Paris warehouse, LTD (average Lead Time Demand) = 20, 000 lamps Actual Demand varies daily and s. LTD = 5, 000 The warehouse re-orders whenever ROP = 24, 000 Therefore, I safety = ROP – LTD = 24, 000 – 20, 000 = 4, 000 And: z = I safety / s. LTD = 4, 000 / 5, 000 = 0. 8 And: SL= Prob (Z< 0. 8) from Appendix II SL= 0. 7881

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 16 EXCEL Service Level

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 17 EXCEL Safety Inventory

7. Managing Flow Variability: Safety Inventory 7. 2 Safety Inventory and Service Level 18 EXCEL Reorder Point

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 19 So Far… Safety inventory has been defined for a desired level of customer service. But… How do we choose what level of service a firm should offer? Examples: • Newspapers / Magazines • Perishables (fish, produce, bread, milk, etc. ) • Seasonal Items (Summer & Winter Apparel)

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 20 Cost of Holding Extra Inventory Improved Service Optimal Service Level? ? The Newsvendor Problem Decision making under uncertainty whereby the decision maker balances the expected costs of ordering too much with the expected costs of ordering too little to determine the optimal order quantity.

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 21 Predicted Demand for HDTV’s Cost: $1, 800 Demand Probability Cumulative Probability Complementary Cumulative Probability r Prob(R = r) Prob(R ≤ r) Prob(R > r) 100 0. 02 0. 98 110 0. 05 0. 07 0. 93 120 0. 08 0. 15 0. 85 130 0. 09 0. 24 0. 76 140 0. 11 0. 35 0. 65 150 0. 16 0. 51 0. 49 160 0. 2 0. 71 0. 29 170 0. 15 0. 86 0. 14 180 0. 08 0. 94 0. 06 190 0. 05 0. 99 0. 01 200 0. 01 1 0 Price: $2, 500 Salvage: $1, 700 Profit: Loss: $700 $100 Mean: 151. 6 Std. Dev: 22. 44

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 22 Quantity Ordered Demand 100 110 120 130 140 150 160 170 180 190 200 100 $70, 000 $70, 000 $70, 000 110 $69, 000 $77, 000 $77, 000 $77, 000 120 $68, 000 $76, 000 $84, 000 $84, 000 $84, 000 130 $67, 000 $75, 000 $83, 000 $91, 000 $91, 000 140 $66, 000 $74, 000 $82, 000 $90, 000 $98, 000 $98, 000 150 $65, 000 $73, 000 $81, 000 $89, 000 $97, 000 $105, 000 $105, 000 160 $64, 000 $72, 000 $80, 000 $88, 000 $96, 000 $104, 000 $112, 000 $112, 000 170 $63, 000 $71, 000 $79, 000 $87, 000 $95, 000 $103, 000 $111, 000 $119, 000 180 $62, 000 $70, 000 $78, 000 $86, 000 $94, 000 $102, 000 $110, 000 $118, 000 $126, 000 190 $61, 000 $69, 000 $77, 000 $85, 000 $93, 000 $101, 000 $109, 000 $117, 000 $125, 000 $133, 000 200 $60, 000 $68, 000 $76, 000 $84, 000 $92, 000 $100, 000 $108, 000 $116, 000 $124, 000 $132, 000 $140, 000 =IF($A 3>B$1, B$1*700 -($A 3 -B$1)*100, $A 3*700) 100 x $700 – (110 -100) x $100 = $69, 000

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 23 Quantity Ordered Demand 100 110 120 130 140 150 160 170 180 190 200 100 $70, 000 $70, 000 $70, 000 110 $69, 000 $77, 000 $77, 000 $77, 000 120 $68, 000 $76, 000 $84, 000 $84, 000 $84, 000 130 $67, 000 $75, 000 $83, 000 $91, 000 $91, 000 140 $66, 000 $74, 000 $82, 000 $90, 000 $98, 000 $98, 000 150 $65, 000 $73, 000 $81, 000 $89, 000 $97, 000 $105, 000 $105, 000 160 $64, 000 $72, 000 $80, 000 $88, 000 $96, 000 $104, 000 $112, 000 $112, 000 170 $63, 000 $71, 000 $79, 000 $87, 000 $95, 000 $103, 000 $111, 000 $119, 000 180 $62, 000 $70, 000 $78, 000 $86, 000 $94, 000 $102, 000 $110, 000 $118, 000 $126, 000 190 $61, 000 $69, 000 $77, 000 $85, 000 $93, 000 $101, 000 $109, 000 $117, 000 $125, 000 $133, 000 200 $60, 000 $68, 000 $76, 000 $84, 000 $92, 000 $100, 000 $108, 000 $116, 000 $124, 000 $132, 000 $140, 000 $69, 000(0. 02) + $77, 000(0. 05) + …+ $77, 000(0. 01) = $76, 840

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 24 Order Quantit y (Q) Expected Profit 100 $70, 000 110 $76, 840 120 $83, 280 130 $89, 080 140 $94, 160 150 $98, 360 160 $101, 280 170 $102, 600 180 $102, 720 190 $102, 200 $101, 280

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 25 Net Marginal Benefit: MB = p – c MB = $2, 500 - $1, 800 = $700 Net Marginal Cost: MC = c - v MC = $1, 800 - $1, 700 = $100 We receive Marginal Benefit when R > Q, therefore at any order quantity Q, Expected MB = MB x Prob(R > Q) We receive Marginal Cost when R ≤ Q, therefore at any order quantity Q, Expected MC = MC x Prob(R ≤ Q) MC x Prob(R ≤ Q*) ≥ MB x Prob(R > Q*)

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 26 Time for Algebra… MC x Prob(R ≤ Q*) ≥ MB x Prob(R > Q*) Since, Prob(R > Q) = 1 – Prob(R ≤ Q) We can write, MC x Prob(R ≤ Q*) ≥ MB x [1 – Prob(R ≤ Q*)] After rearranging, Prob(R ≤ Q*) ≥ Newsvendor formula: SL* = Prob(R ≤ Q*) =

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 27 Going back to the example… So what quantity corresponds to this service level ? If we assume demand is normally distributed then,

7. Managing Flow Variability: Safety Inventory 7. 3 Optimal Service Level: The Newsvendor Problem 28

7. Managing Flow Variability: Safety Inventory 7. 4 Lead Time Demand Variability 29 Average Lead Time Demand: Variability in Periodic Demand: Variability in Lead Time: Variability in Demand Lead Time:

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 30 Third characteristic of forecasts Aggregation: pooling demand for several similar products Aggregate sales Safety Inventory: Uncertain demand Assume Decentralized: Warehouses operates independently Imbalance of inventory - Customer demand not satisfied

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 31 Physical Centralization: that the firm can consolidate all its stock in one location from which is can serve all its customers. ELIMINATES stock imbalance BETTER customer service SAME total inventory LESS inventory Location 1 Lead times demands: LTD 1 Mean of LTD Standard Deviation Location 2 LTD 2

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 32 LTD 1 and LTD 2: statistically identically distributed To provide desired level of service, SL each location must carry Safety Inventory: Z determined by the desired service level Each facility: Identical demand service levels Total safety inventory decentralized system:

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 33 Independent Demands Centralizing the two locations in one location when lead time demands at the two locations are independent. LTD = LTD 1 + LTD 2 Centralized Pool The mean of total lead time demand is: LTD + LTD = 2 LTD Variance is: Standard Deviation is:

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 34 Comparing safety inventories of decentralized and centralized systems. Safety Inventory in Centralized system is in a 2 location decentralized system by a factor of

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 35 Centralization of N locations: Safety Inventory needed is Centralization will reduce inventory by factor of

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 36 Example GE lighting operating 7 warehouses Consolidated in to one centralized warehouse Replenishment lead time remain at 10 days What will be the impact of accepting the task force recommendations?

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 37 A warehouse with average lead time demand of 20, 000 units with a standard deviation of 5, 000 units needs to carry a safety inventory to provide a 95% service level. Total safety inventory across 7 warehouses: Task force accepted, single central warehouse will face total lead time demand with mean and standard deviation of:

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 38 95% service level, the central warehouse must carry a safety inventory: Safety inventory with the single central warehouses is 35, 894 less than that required under the current decentralized network of 7 warehouses. Decrease in safety inventory by a factor of

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 39 Square Root Law States that the total safety inventory required to provide a specific level of service increases by the square root of the number of locations in which it is held. Previous example Correlated Demands Does centralization offer similar benefits when demands in multiple locations are correlated?

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 40 LTD 1 and LTD 2 are statistically identically distributed but correlated. Correlation between two locations with coefficient Mean of total lead time: LTD + LTD = 2 LTD Variance is: Total safety in centralized system is:

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 41 The total safety inventory in the decentralized system: The safety inventory in the two-location decentralized system is larger than in the centralized system by a factor of If demand is positively correlated centralization offers no benefits in the reduction of safety inventory

7. Managing Flow Variability: Safety Inventory 7. 5: Pooling Efficiency through Aggregation 42 Advantages 1. Centralized systems as the demand on the two locations become negatively correlated. 2. Centralized systems diminishes as the demand in the two locations become positively correlated Disadvantages of Centralization 1. Response time to Customers 2. Shipping Cost

7. Managing Flow Variability: Safety Inventory 7. 5. 2: Principle of Aggregation and Pooling Inventory 43 Statistical Principle Aggregation: the standard deviation of the sum of random variables is less than the sum of the individual standard deviations. Pooling inventory: available inventory is shared among various sources of demand Pooling inventory applied in other ways other than physical centralization

7. Managing Flow Variability: Safety Inventory 7. 5. 2: Principle of Aggregation and Pooling Inventory 44 Virtual Centralization Specialization Component Commonality Product Substitute

7. Managing Flow Variability: Safety Inventory 7. 5. 2: Principle of Aggregation and Pooling Inventory 45 Virtual Centralization Distribution System Location A Location B Exceeds Available stock Available 1. Information about product demand availability must be available at both locations 2. Shipping the product from one location to a customer at another location must be fast and cost effective

7. Managing Flow Variability: Safety Inventory 7. 5. 2: Principle of Aggregation and Pooling Inventory 46 Correlation is less than one – Pooling is Effective Inventory Decentralized instead of physically consolidated Virtual Centralization: is a system in which inventory pooling in a network of locations is facilitated using information regarding availability of goods and subsequent transshipment of goods between locations to satisfy demand.

7. Managing Flow Variability: Safety Inventory 7. 5. 2: Principle of Aggregation and Pooling Inventory 47 Specialization Each product only one specialized warehouse EXAMPLE Location A Location B P 1 P 2 Safety Inventory is reduced because each inventory is now centralized at one location

7. Managing Flow Variability: Safety Inventory 7. 5. 2: Principle of Aggregation and Pooling Inventory 48 Component Commonality Aggregating demand across various products. Computer companies with models that vary. Make-to-stock: produce in anticipation of product demand Make-to-Order: Produce in response to customer orders Reduce inventory investment maintaining the same level of service and product variety

7. Managing Flow Variability: Safety Inventory 7. 5. 2: Principle of Aggregation and Pooling Inventory 49 Disadvantage Make-to-Order Strategy Customer must wait for firm to produce product Advantage Make-to-Stock Strategy Available for immediate consumption

7. Managing Flow Variability: Safety Inventory 7. 6: Shortening the Forecast Horizon through Postponement 50 Postponement (or Delayed Differentiation): More Effective Short-Range forecast more accurate Two Alternative processes (both two weeks) Process A: Coloring the fabric, assembling Process B: Assembling T-shirts, coloring Does one have the advantage over the other?

7. Managing Flow Variability: Safety Inventory 7. 6: Shortening the Forecast Horizon through Postponement 51 By Reversing: assembling and dyeing process Process B postponed the color difference until one week closer to the time of sale Postponement: the practice of delaying part of a process in order to reduce the need for safety inventory

7. Managing Flow Variability: Safety Inventory 7. 6: Shortening the Forecast Horizon through Postponement 52 Process B has the advantage Aggregation Reduces Variability 1. Aggregates demands by color in the first phase 2. Requires shorter-range forecasts of individual T-shirts needed by color in the second phase. 3. Less Demand Variability 4. Less Total Safety Inventory

7. Managing Flow Variability: Safety Inventory 7. 7: Levers for Reducing Safety Inventory 53 Levers for Reducing Flow Variability and the Required Safety Inventory 1. Reduce demand variability through improved forecasting 2. Reduce replenishment lead time 3. Reduce variability in replenishment lead time 4. Pool safety inventory for multiple locations or products

7. Managing Flow Variability: Safety Inventory 7. 7: Levers for Reducing Safety Inventory 54 5. Exploit product substitution 6. Use common components 7. Postpone product-differentiation processing until closer to the point of actual demand