Lecture 10: Managing Uncertainty in the Supply Chain (Safety Inventory) INSE 6300/4-UU. Overview

Transcription

1 ecture 10: Managing Uncertainty in the Supply Chain (Safety Inventory) INSE 6300/4-UU Quality Assurance In Supply Chain Management Quality Assurance in Supply Chain Management (INSE 6300/4-UU) Winter 011 Supply Chain Coordination Supply Chain Engineering Information Technology in a Supply Chain Performance, Quality Attributes, and Metrics E-technology (E-business, ) Designing the Supply Chain Network Quality Assurance System Inventory Management Managing Uncertainty Overview The role of cycle and safety inventories in a supply chain Determining the appropriate level of safety Impact of supply uncertainty on safety Impact of aggregation on safety Inventory: Role in the Supply Chain Inventory exists because of a mismatch between supply and demand Source of cost and influence on responsiveness Impact on Material flow time: time elapsed between the point at which material enters the supply chain to the point at which it leaves the supply chain Throughput: Rate at which sales to end consumers occur I RT (ittle s aw) I ; R throughput; T flow time Example: Flow time of an auto assembly process is 10 hours and the throughput is 60 units an hour, ittle s law: I 60 * units 3 4

2 Inventory Cycle Inventory Process several flow units collectively at a given moment in time New New shipment shipment arrives arrives Days Role of Cycle Inventory in a Supply Chain ot, or batch size: quantity that a supply chain stage either produces or orders at a given time Cycle : average that builds up in the supply chain because a supply chain stage either produces or purchases in lots that are larger than those demanded by the customer Q lot or batch size of an order D demand per unit time Cycle Q/ (depends directly on lot size) Average flow time Avg. / Avg. flow rate Average flow time from cycle Q/(D) 5 6 Role of Cycle Inventory in a Supply Chain Q 1000 units D 100 units/day Cycle Q/ 1000/ 500 Avg. level from cycle Avg. flow time Q/D 1000/()(100) 5 days Cycle adds 5 days to the time a unit spends in the supply chain ower cycle is better because: Average flow time is lower ower holding costs Cumulative 100 Inflow and outflow Safety Inventory Stochastic demand: distinguishing predicted demand from the actual demand Safety Cumulative inflow Days of the month Cumulative outflow 7 8

3 The Role of Safety Inventory in a Supply Chain Role of Safety Inventory Forecasts are rarely completely accurate If average demand is 1000 units per week, then half the time actual demand will be greater than 1000, and half the time actual demand will be less than 1000; what happens when actual demand is greater than 1000? If you kept only enough in stock to satisfy average demand, half the time you would run out Safety : Inventory carried for the purpose of satisfying demand that exceeds the amount forecasted in a given period Average is therefore cycle plus safety There is a fundamental tradeoff: Raising the level of safety provides higher levels of product availability and customer service Raising the level of safety also raises the level of average and therefore increases holding costs Very important in high-tech industries where obsolescence is a significant risk (where the value of, such as PCs, can drop in value) 9 10 Two Questions to Answer in Planning Safety Inventory Overview What is the appropriate level of safety to carry? What actions can be taken to improve product availability while reducing safety? The role of cycle and safety inventories in a supply chain Determining the appropriate level of safety Impact of supply uncertainty on safety Impact of aggregation on safety 11 1

4 Determining the Appropriate evel of Safety Inventory Measuring demand uncertainty Measuring product availability Replenishment policies Evaluating cycle service level and fill rate Evaluating safety level given desired cycle service level or fill rate Impact of required product availability and uncertainty on safety Determining the Appropriate evel of Demand Uncertainty Appropriate level of safety determined by: Supply or demand uncertainty Desired level of product availability Higher levels of uncertainty require higher levels of safety given a particular desired level of product availability Higher levels of desired product availability require higher levels of safety given a particular level of uncertainty Measuring Demand Uncertainty Demand has a systematic component and a random component The estimate of the random component is the measure of demand uncertainty Random component is usually estimated by the standard deviation of forecast error Notation: D Average demand per period σ D standard deviation of demand per period (forecast error) lead time: time between when an order is placed and when it is received Uncertainty of demand during lead time is what is important 15 Measuring Demand Uncertainty Normal distribution with mean D K and std. dev. σ K D K : avrg. demand during k periods kd σ K : std. dev. of demand during k periods σ D Sqrt(k) Coefficient of variation: cv σ/µ (std. dev.)/mean: size of uncertainty relative to demand 16

5 Measuring Product Availability Replenishment Policies Product availability: a firm s ability to fill a customer s order out of available Stockout: a customer order arrives when product is not available Product fill rate (fr): fraction of demand that is satisfied from product in Order fill rate: fraction of orders that are filled from available Cycle Service evel (CS): fraction of replenishment cycles that end with all customer demand met Replenishment policy: decisions regarding when to reorder and how much to reorder Continuous review: is continuously monitored and an order of size Q is placed when the level reaches the reorder point ROP Periodic review: is checked at regular (periodic) intervals and an order is placed to raise the to a specified threshold (the orderup-to level) Continuous Review Policy: Safety Inventory and Cycle Service evel : ead time for replenishment D: Average demand per unit time σ D : Standard deviation of demand per period D : Mean demand during lead time : Standard deviation of demand during lead time CS: Cycle Service evel ss:safety ROP: Reorder Point D ss ROP D σ D 1 FS D + ( CS) ss CS F( ROP, D Average Inventory Q/ + ss, ) CS: Cycle Service evel CS Prob(demand during lead time of weeks ROP) We need to obtain the distribution of demand during the lead time For normal distribution: CS F(ROP, D, ) F is the cumulative normal distribution function (F(x, µ, σ)) 19 0

6 Example: Estimating Safety Inventory (Continuous Review Policy) Example: Estimating Safety Inventory (Continuous Review Policy) Assume that weekly demand for palms at B&M Computer World is normally distributed, with a mean of,500 and a standard deviation of 500 The manufacturer takes two weeks to fill an order placed by B&M manager The store manager currently orders 10,000 palms when the on hand drops to 6,000 Evaluate the safety carried by B&M and the average carried by B&M Evaluate the average time spend by a Palm at B&M D,500/week; σ D 500 weeks; Q 10,000; ROP 6,000 D D (500)() 5000 ss ROP - D Cycle Q/ 10000/ 5000 Average Inventory cycle + ss Average Flow Time Avg / throughput 6000/500.4 weeks Each Palm spends an average of.4 weeks at B&M 1 Example: Estimating Cycle Service evel (Continuous Review Policy) Assume that weekly demand for palms at B&M Computer World is normally distributed, with a mean of,500 and a standard deviation of 500 The replenishment lead time is two weeks The demand is independent from one week to the next Evaluate the SC resulting from a policy of ordering 10,000 Palms when there are 6,000 Palms in Example: Estimating Cycle Service evel (Continuous Review Policy) D,500/week; σ D 500 weeks; Q 10,000; ROP 6,000 σ σ (500) 707 D CS F(D + ss, D, ) NORMDIST (D + ss, D, ) NORMDIST(6000,5000,707,1) 0.9 (This value can also be determined from a Normal probability distribution table) In 9 percent of the replenishment cycles, B&M supplies all demand from available 3 4

7 Example: Estimating Cycle Service evel Fill Rate Proportion of customer demand satisfied from stock Stockout occurs when the demand during lead time exceeds the reorder point ESC is the expected shortage per cycle (average demand in excess of reorder point in each replenishment cycle) ss is the safety Q is the order quantity ESC fr 1 Q ESC ( x ROP) f ( x) dx x ROP ss ESC ss[1 F ] S σ ss + f σ S ESC -ss{1-normdist(ss/, 0, 1, 1)} + NORMDIST(ss/, 0, 1, 0) 5 6 Example: Evaluating Fill Rate Example: Evaluating Fill Rate Assume that weekly demand for palms at B&M Computer World is normally distributed, with a mean of,500 and a standard deviation of 500 The replenishment lead time is two weeks The demand is independent from one week to the next Evaluate the fill rate resulting from a policy of ordering 10,000 Palms when there are 6,000 Palms in ss 1,000, Q 10,000, 707, Fill Rate (fr)? ESC -ss{1-normdist(ss/, 0, 1, 1)} + NORMDIST(ss/, 0, 1, 0) -1,000{1-NORMDIST(1,000/707, 0, 1, 1)} NORMDIST(1,000/707, 0, 1, 0) fr (Q - ESC)/Q (10, )/10,

8 Example: Evaluating Fill Rate Factors Affecting Fill Rate Safety : Fill rate increases if safety is increased. This also increases the cycle service level ot size: Fill rate increases on increasing the lot size even though cycle service level does not change 9 30 Example: Evaluating Safety Inventory Given CS Weekly demand for ego at a Wal-Mart store is normally distributed, with a mean of,500 boxes and a standard deviation of 500 The replenishment lead time is two weeks Continuous review replenishment policy Evaluate the safety that the store should carry to achieve a CS of 90 percent Example: Evaluating Safety Inventory Given CS D,500/week; σ D 500 weeks; Q 10,000; CS 0.90 D 5000, 707 (from earlier example) ss F S -1 (CS) [NORMSINV(0.90)](707) 906 (this value can also be determined from a Normal probability distribution table) ROP D + ss

9 Evaluating Safety Inventory Given Desired Fill Rate D 500, σ D 500, Q If desired fill rate is fr 0.975, how much safety should be held? ESC (1 - fr)q 50 Solve (Goal Seek: Excel) ESC 50 ss 1 F S ss σ + σ f S ss σ ss ss 50 ss 1 NORMSDIST + σnormdist σ σ Evaluating Safety Inventory Given Fill Rate (try different values of ss) Fill R ate Safety In ventory 97.5% % % % % Impact of Required Product Availability and Uncertainty on Safety Inventory Overview Desired product availability (cycle service level or fill rate) increases, required safety increases Demand uncertainty ( ) increases, required safety increases Managerial levers to reduce safety without reducing product availability reduce supplier lead time, (better relationships with suppliers) reduce uncertainty in demand, (better forecasts, better information collection and use) The role of cycle and safety inventories in a supply chain Determining the appropriate level of safety Impact of supply uncertainty on safety Impact of aggregation on safety 35 36

10 Impact of Supply Uncertainty Impact of Supply Uncertainty D: Average demand per period σ D: Standard deviation of demand per period : Average lead time s : Standard deviation of lead time D D σ D + D s D,500/day; σ D days; Q 10,000; CS 0.90; s 7 days D D (500)(7) s σ D (7) 500 D + (500) (7) ss F -1 s (CS) NORMSINV(0.90) x 17550, Impact of Supply Uncertainty Overview Safety when s 0 is 1,695 Safety when s 1 is 3,65 Safety when s is 6,68 Safety when s 3 is 9,760 Safety when s 4 is 1,97 Safety when s 5 is 16,109 Safety when s 6 is 19,98 The role of cycle and safety inventories in a supply chain Determining the appropriate level of safety Impact of supply uncertainty on safety Impact of aggregation on safety 39 40

11 Impact of Aggregation on Safety Inventory Models of aggregation Information centralization Specialization Product substitution Component commonality Postponement Impact of Aggregation D C C σ D C ss F n D i 1 σ i s n i 1 1 i C σ D ( CS) C 41 4 Example: Impact of Aggregation Example: Impact of Aggregation A BMW dealership has 4 retail outlets serving the entire Chicago area Weekly demand at each outlet is normally distributed, with a mean od D5 cars and a std. dev. Of 5 The lead time for replenishment from the manufacturer is weeks The correlation of demand across any pair of areas is ρ The dealership is considering the possibility of replacing the 4 outlets with a single outlet (aggregate option) Car Dealer : 4 dealership locations (disaggregated) D 5 cars; σ D 5 cars; weeks; desired CS0.90 What would the effect be on safety stock if the 4 outlets are consolidated into 1 large outlet (aggregated)? At each disaggregated outlet: For weeks, 7.07 cars ss F s -1 (CS) x F s -1 (0.9) x Each outlet must carry 9 cars as safety stock, so safety for the 4 outlets in total is (4)(9) 36 cars 43 44

12 Example: Impact of Aggregation Impact of Aggregation One outlet (aggregated option): If number of independent stocking locations decreases by n, the expected level of safety will be reduced by square root of n (square root law) RC D 1 + D + D 3 + D cars/wk σ DC Sqrt( ) 10 C σ DC Sqrt() (10)Sqrt() (10)(1.414) Many e-commerce retailers attempt to take advantage of aggregation (Amazon) compared to bricks and mortar retailers (Borders) ss F s -1 (CS) x C F s -1 (0.9) x or about 18 cars If ρ does not equal 0 (demand is not completely independent), the impact of aggregation is not as great (Table 11.3) Aggregation has two major disadvantages: Increase in response time to customer order Increase in transportation cost to customer Some e-commerce firms (such as Amazon) have reduced aggregation to mitigate these disadvantages 45 46